Long Range Interactions In Nanoscale Science Roger H. French,a,b,* V. Adrian Parsegian,c Rudolf Podgornik,c,d Rick F. Rajter,e Anand Jagota,f Jian Luo,g Dilip Asthagiri,h Manoj K. Chaudhury,i Yet-ming Chiang,j Steve Granick,k Sergei Kalinin,l Mehran Kardar,m Roland Kjellander,n David C. Langreth,o Jennifer Lewis,p Steve Lustig,q David Wesolowski,r John Wettlaufer,s Wai-Yim Ching,t Mike Finnis,u Frank Houlihan,v O. Anatole von Lilienfeld,w Carel Jan van Oss,x Thomas Zemby a. DuPont Co. Central Research, E400-5207 Experimental Station, Wilmington, DE 19880, USA b. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA19104 c. Laboratory of Physical and Structural Biology, NICHD, National Institutes of Health, Bethesda, Maryland 20892-0924, USA d. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia and Department of Theoretical Physics, J. Stefan Institute, Ljubljana 1000, Slovenia e. Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139-4307, USA f. Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania, USA g. School of Materials Science and Engineering, Clemson University, 201 Olin Hall, Clemson, SC 29634 h. Department Of Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218 i. Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania, USA j. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (USA) k. Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA l. Materials Science and Technology Division and The Center for Nanophase Materials Science, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA m. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA n. Department of Chemistry, Göteborg University, SE-412 96 Göteborg, Sweden o. Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019 p. Frederick Seitz Materials Research Laboratory, Materials Science and Engineering, Department, University of Illinois, Urbana, Illinois 61801 q. DuPont Co. Central Research, E400-5472 Experimental Station, Wilmington, DE 19880, USA r. Oak Ridge National Laboratory, Chemical Sciences Division, P.O. Box 2008, Oak Ridge, TN 37831-6110, USA s. Department Of Geophysics and Physics, Yale University, New Haven, CT 06520-8109 t. Department of Physics, University of Missouri–Kansas City, Kansas City, Missouri 64110, USA u. Department of Materials and Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom v. AZ Electronic Materials Corp USA, 70 Meister Avenue, Somerville, NJ 08876 w. Multiscale Dynamic Material Modeling Department, Sandia National Laboratories, Albuquerque, NM 87185, USA x. Department of Microbiology, 2Department of Chemical Engineering, and Department of Geology, University at Buffalo, Buffalo, New York, USA y. CEA/SACLAY, LIONS at Service de Chimie Moléculaire, 91191-Gif-sur-Yvette Cedex, France * corresponding author: [email protected]

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Abstract Focusing on the electrodynamic, electrostatic and acid-base interactions that dominate the organization of small objects at separations of a few nanometers, we first review the strengths and weaknesses in our understanding of these interactions. With this perspective, we describe a large number of potentially instructive systems from which we can learn about organizing forces and the means to modulate them. We then survey the many practical systems whose design is guided by intuition and by systematic manipulation made to harness these nanoscale forces. Our survey of these ingenious systems reveals not only the promise of new devices and materials but also the need to be able to design them using better knowledge of the operative forces. Having identified areas where basic research is now needed, we can discern how this research can contribute to nascent and ongoing applications of nano-devices.

Table Of Contents Long Range Interactions In Nanoscale Science.................................................................. 2.1.1—1 Abstract ............................................................................................................................... 2.1.1—2 Table Of Contents ............................................................................................................... 2.1.1—2 1 Introduction................................................................................................................. 2.1.1—4 2 Fundamental Interactions............................................................................................ 2.1.1—6 2.1 Electrodynamic interactions................................................................................ 2.1.1—6 2.1.1 Introduction................................................................................................. 2.1.1—6 2.1.2 Lifshitz Theory From Optical Properties.................................................... 2.1.2—8 2.1.3 ab initio optical properties of complex materials ..................................... 2.1.3—14 2.1.4 Electrodynamic Interactions For Arbitrary Shapes................................... 2.1.4—16 2.1.5 Non-covalent Interactions From Electronic Structure Calculations ......... 2.1.5—20 2.1.6 Challenges and Opportunities ................................................................... 2.1.6—28 2.2 Electrostatics ..................................................................................................... 2.1.6—31 2.2.1 Electrostatics in Density Functional Theory............................................. 2.2.1—33 2.2.2 Electrostatics in Equilibrium Statistical Mechanics ................................. 2.2.2—36 2.2.3 Challenges and Opportunities ................................................................... 2.2.3—41 2.3 Polar and Acid-Base Interactions...................................................................... 2.2.3—45 2.3.1 Motivation and Recent Advances ............................................................. 2.3.1—45 2.3.2 Challenges and Opportunities ................................................................... 2.3.2—50 3 Instructive Systems ................................................................................................... 2.3.2—52 3.1 Atoms and Molecules ....................................................................................... 2.3.2—53

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3.1.1

Optical Spectra and the Lifshitz Theory for Complex Biomolecular Systems 3.1.1—53 3.1.2 DFT Results on DNA Base Pair vdW Interactions................................... 3.1.2—57 3.1.3 Macromolecules and Polyelectrolytes ...................................................... 3.1.3—60 3.2 Interfaces, Surfaces and Defects in Solids........................................................ 3.1.3—70 3.2.1 Impurity-Based Quasi-Liquid Surficial and Interfacial Films .................. 3.2.1—70 3.2.2 Charged Defects in Solids......................................................................... 3.2.2—72 3.3 Solid/Liquid Interfaces and Suspensions .......................................................... 3.2.2—74 3.3.1 Water and Ice ............................................................................................ 3.3.1—74 3.3.2 Hydration .................................................................................................. 3.3.2—80 3.3.3 Structure and Dynamics at Oxide/Electrolyte Interfaces.......................... 3.3.3—84 3.3.4 Colloidal Suspensions............................................................................... 3.3.4—91 3.3.5 Solution Based Manipulation of SWCNT ................................................ 3.3.5—93 4 Harnessing LRIs...................................................................................................... 3.3.5—101 4.1 Surfaces and Interfaces ................................................................................... 3.3.5—101 4.1.1 Proton Exchange Membranes for Hydrogen Fuel Cells ......................... 4.1.1—103 4.1.2 Intergranular and Surficial Films ............................................................ 4.1.2—105 4.1.3 Premelting Dynamics.............................................................................. 4.1.3—110 4.2 Colloids and Self-Assembly ........................................................................... 4.1.3—116 4.2.1 Tailored Building Blocks: From Hard Spheres to Patchy Colloids....... 4.2.1—116 4.2.2 Synthesis and Assembly of Designer Colloidal Building Blocks........... 4.2.2—117 4.2.3 Challenges and Opportunities ................................................................. 4.2.3—118 4.3 Devices: Electronic, Optical, Sensing............................................................. 4.2.3—119 4.3.1 Frontiers in Lithography: What is the Importance of LRIs in Materials? . 4.3.1— 119 4.3.2 193 nm Lithography Immersion and Double Exposure.......................... 4.3.2—120 4.3.3 EUV (Extreme Ultraviolet)..................................................................... 4.3.3—123 4.3.4 Nano Imprinting...................................................................................... 4.3.4—124 4.3.5 Self Assembly ......................................................................................... 4.3.5—126 4.3.6 Frontiers in Lithography 10 Years on ..................................................... 4.3.6—127 4.3.7 Emerging Electronic Applications: Active electronic devices made from SingleWalled Carbon Nanotubes ...................................................................................... 4.3.7—128 4.4 Materials Design and Chemical Construction ................................................ 4.3.7—130 4.4.1 Molecular Design.................................................................................... 4.4.1—130 4.4.2 Materials Design ..................................................................................... 4.4.2—137 4.5 Local Studies of Long-Range Interactions by Scanning Probe Microscopy .. 4.4.2—141 4.5.1 The SPM approach.................................................................................. 4.5.1—142 4.5.2 Types of SPM measurements.................................................................. 4.5.2—144 4.5.3 Future developments............................................................................... 4.5.2—151 4.6 Scattering Probes of LRIs ............................................................................... 4.5.2—155 4.6.1 Probing LRI’s at interfaces using X-ray scattering................................. 4.5.2—155 4.6.2 Probing LRI’s at interfaces using neutron scattering.............................. 4.5.2—158 4.7 Self-Assembling Electrochemical Devices: Li-Ion Batteries from Heterogeneous Colloids....................................................................................................................... 4.5.2—160 5 Findings and Recommendations: LRI in NS Workshop......................................... 4.5.2—162 5.1 Recent Scientific Advances In LRI in NS ...................................................... 4.5.2—163

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6 7 8 9

5.2 Challenges and Needs in LRI in NS ............................................................... 4.5.2—164 5.3 Transformative Opportunities from LRI in NS .............................................. 4.5.2—166 Conclusions............................................................................................................. 4.5.2—168 Acknowledgements................................................................................................. 4.5.2—170 Figures..................................................................................................................... 4.5.2—170 References............................................................................................................... 4.5.2—191

1 Introduction R.P. Feynman in his by now famous musings on the possibility of nanotechnology (Feynman, 1959) noted that “...as we go down in size, there are a number of interesting problems that arise. All things do not simply scale down in proportion. There is the problem that materials stick together by the molecular (Van der Waals) attractions. It would be like this: After you have made a part and you unscrew the nut from a bolt, it isn't going to fall down because the gravity isn't appreciable; it would even be hard to get it off the bolt. It would be like those old movies of a man with his hands full of molasses, trying to get rid of a glass of water. There will be several problems of this nature that we will have to be ready to design for”. The importance of long-range interactions (LRIs) - which according to the background and preferences are also referred to as van der Waals,

Casimir, Lifshitz, electrodynamic fluctuation or dispersion

interactions - in the synthesis, design and manipulation of materials at a nanometer scale was thus recognized from the very beginning of nanosciences. Nevertheless it was only quite recently that all the intricacies of not just van der Waals, as alluded to by Feynman, but all LRIs on the nanoscale came to the front of scientific endeavors, in research areas as varied as quantum field theory, quantum and classical density functional theories, various mean-field and strong coupling statistical mechanical formulations, liquid state integral equation – closure approximations, computer simulations as well as novel experimental designs and methods, not to say anything about the exciting new developments and prospects in technological applications. The

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role

of

LRIs in self-assembling active devices from heterogeneous components appears to be fundamental, since they govern the stability of component clusters on the nanoscale and for better or for worse can not be ignored in the design of nanodevices and nanoactuators. The new technological paradigms that might be developed as a consequences of these fundamental studies and ensuing technological breakthroughs on the nanoscale will no doubt contribute to solving some pressing societal problems on the macroscale and introduce new ways of thinking and paradigm shifts necessary in order to make some old problems closer to a solution. The present review is the outcome of a workshop panel entitled Long Range Interactions In Nanoscale Science, convened under the auspices of the United States Department Of Energy, Council for the Division of Materials Sciences and Engineering, Basic Energy Sciences, set to survey, identify, report and assess basic research challenges, needs and opportunities in the area of LRIs at the nanoscale. It assessed recent advances in the theory, computation, and measurement of the primary LRIs: electrodynamic, electrostatic, and polar, as well as secondary LRIs, closely based upon but distinct from the primary variety: hydrogen bonding, hydrophobic/hydrophilic/hydration, steric, structural and entropic interactions.

It set out to

create a comprehensive framework and language of LRIs in nano-sciences as well as to identify strategies to harness these forces for the design of new materials and devices. This endeavor requires spanning a vast range of scientific landscapes from field theory all the way to colloid science, from physical sciences to chemistry and biology, from theory to experiment and computation, coupling the tenets of basic science fundamentals of LRIs to tractable experimentally accessible systems that are manipulable on the nanoscale and can in the not too distant future launch sophisticated technological applications. The review focuses on the fundamental aspects of electrodynamic, electrostatic and polar acid/base foundations of LRIs, by

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invoking various instructive systems that accentuate different aspects of LRIs, such as atoms, molecules, nano-, meso- and macro-scopic interfaces, surfaces and defects, as well as chemical equilibria in liquids, suspensions and colloidal aggregates. The aim being all the time to understand and harness the properties of LRIs in nanoscale systems such as e.g. surfaces and interfaces that are enabled by the LRIs, colloidal macro and nanoscale self-assembly, and the design and chemical construction of electronic, optical and sensing properties of devices constructed from nanomaterials. This review sets out to map and assess this vast space of scientific endevor in as comprehensive and simple terms as possible, but not simpler. Hopefully it meets at least a part of these goals and requirements.

2 Fundamental Interactions 2.1 Electrodynamic interactions 2.1.1 Introduction Everyday matter is largely held together by electromagnetic (EM) forces between (on the average) neutral objects, mediated by the ‘coordinated dance of fluctuating charges’ (Parsegian 2005). Between atoms in gasses, this attractive interaction appears in the guises of Keesom, Debye, and London dispersion forces. The collective behavior of atoms in condensed matter is better formulated in terms of its macroscopic dielectric properties. In 1948, Casimir computed the force between two parallel ideally metallic plates in vacuum by focusing on the quantum fluctuations of the EM field between the two plates (Casimir 1948). This approach was later extended by Lifshitz to realistic dielectric materials by taking into account the fluctuating charge sources in the media (Lifshitz, 1956).

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While the following decades were marked mainly by theoretical advances, this trend has been reversed by recent high precision measurements (Lamoreaux, 1997; Mohideen, 1998; Roy et al, 1999).

As the most relevant interaction between neutral bodies at short distance,

electrodynamic LRIs play an important role in micro-electromechanical systems (MEMS), causing metals to attract and to stick at short distances, a phenomenon known as “stiction” (Serry 1998). Why do we witness such a burst of activity in electrodynamic – “London”, “dispersion”, “van der Waals”, “Casimir” or “Lifshitz” – forces, given that the theoretical foundation and early experiments were developed in the mid 1940’s and 1950’s? Was it the advent of high precision measurements, the ability to manipulate materials, the technical ability to measure spectra for computation, or something else? Whatever the reason, it is clear that the different languages and training of those working on different facets of the same problem continues to impede progress and inhibit collaborations to this very day. The

diverse

nomenclature

of

interactions

that

collectively

fall

under

the

“electrodynamic” label can generally be separated into two distinct categories: continuum methods using bulk/macroscopic material properties (Lifshitz, Casimir, etc) and atomistic (classical force field, DFT, etc). Presently these vastly different end points can happily coexist as separate entities and can comfortably give meaningful results and insights within their particular regimes. However the nanotech, biotech, and other popular fields are placing ever-increasing demands upon these formulations to be applicable for systems of all sizes and seperation distances, essentially requiring a way to blend them together in a straightford and fundamentally sound manner. This is no easy task, but it also provides an abundance of great opportunities for what is typically seen by outsiders as a “mature” field. What follows is both a brief overview of

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the foundational components of electrodynamic LRIs as well as specific examples of where these challenging areas remain.

2.1.2 Lifshitz Theory From Optical Properties Van der Waals - London dispersion (vdW-Ld) interactions as a paradigm of the LRIs are of considerable importance to scientists and engineers across many disciplines. They influence properties ranging from colloidal forces in solution to fracture of bulk materials. They can significantly impact a given system even when so-called "stronger" forces, such as electrostatic or polar interactions, are present. An example of this is the single wall carbon nanotubes (SWCNT) separation experiments by Zheng (2003). Although the single stranded DNA coatings essentially wrap the different chiralities with an equivalent surface charge density, one is able to robustly and repeatably separate them during a salt elution experiment. How could this be if only electrostatics were involved? One of the theories as to why this occurs revolves around the chiraity-dependent optical properties of the SWCNT core. And in fact, later calculations of the vdW-Ld interactions via the Lifshitz formulation have shown that these exploitable differences do indeed exist and can be potentially exploited via other experimental designs (Rajter, 2007a). Thus the study of vdW-Ld spectra and forces can enrich our understanding of particular phenomena, related to the self-assembly processes that create nanoscale structures and devices. At least in principle, proper understanding and a consistent theoretical formulation of the vdW-Ld interaction has been fully achieved within the Lifshitz theory of dispersion interactions (Parsegian 2005). It provides the link between optical properties or “London dispersion spectra” and the magnitude of these interactions for geometries that are either analytically tractable or easily approximated with simpler geometries. Here we provide the fundamental overview of the vdW-Ld energy calculation from the bulk material properties perspective.

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2.1.2.1 Hamaker Coefficients In the framework of the Lifshitz theory (Parsegian, 2005) the non-retarded dispersion interaction free energy per unit area between two semi-infinite halfspaces is conveniently written as

A123 12πl 2 where ‘l’ is the thickness of the intervening medium and A123 is the effective Hamaker Equation 1.

G(l) = −

coefficient, which is defined in this case as

A123 = −

Equation 2.

∞ ∞

3 2

∞

kB T ∑ ∫ QdQln(1− ∆ 32 (iξ n )∆12 (iξ n )e ) ≈ kT ∑ ∆ 32 (iξ n )∆12 (iξ n ) −u

3 2

n= 0 0

n= 0

Here 1 and 3 (of 123) represent the left and right infinite half space materials separated by medium 2 of thickness l. Q is the magnitude of the wave-vector in the plane of the two opposed interfaces. The summation in the expression above is not continuous but rather over a discrete set of Matsubara, or boson, frequencies ξn = 2π (kBT) n /ħ , where kB is the Boltzmann constant and ħ is the Planck constant divided by 2π. At room temperature, this interval per n is approximately 0.16 eV. The prime in the summation signifies that the first, n = 0 term, is taken with weight 1/2. The Hamaker coefficient is largely determined by material properties. Its magnitude and sign depends on the values of ∆’s that describe the relative optical spectra mis-matches between neighboring materials at the frequency ξ involved in the interaction,

εi (iξ n ) − ε j (iξ n ) εi (iξ n ) + ε j (iξ n )

Equation 3. ∆ ij (iξ n ) =

The dielectric function at imaginary values of the frequency argument, ε(iξ ) , the fundamental ingredient of the Lifshitz theory of vdW-Ld interactions, can be obtained via the Kramers Kronig (KK) transform in the form

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Equation 4.

ε(iξ ) = 1+

2

π

∞

∫ 0

ε′′(ω )dω ω2 + ξ2

where ε′′(ω) is the imaginary part of the dielectric response function in real frequency space, i.e.

ε(ω) = ε′(ω) + iε′′(ω). ε(iξ) is referred to as the van der Waals-London dispersion spectrum (or vdW-Ld spectrum). The magnitude of ε(iξ) essentially describes how well the material responds and is polarized by fluctuations up to a given frequency. Note that the integration in Eq. 4 requires frequencies out to infinity. In practice this is impossible, but also unnecessary, as long as all the inter-band transition energies are either known or properly approximated. For simple systems, it may be acceptable to use this simple formulation for planar geometries to get a general feel for the magnitude and sign of the Hamaker coefficient. However, there are situations where the geometry can also influence the Hamaker coefficent by altering the form of the ∆ terms (Rajter and French 2007a).

2.1.2.2 Full Spectral Optical Properties Equation 2 clearly shows how the Hamaker coefficient calculation involves a summation over all frequencies, theoretically reaching out to infinity. One cannot stress enough how important it is to have accurate, full spectral optical properties when determing vdW-Ld interactions via the Lifshitz formulations. Without them, one is usually left to just simply “guess” a Hamaker coefficient. While this might be acceptable for ballpark figures, it prevents the discovery and exploiting some of the more exicting phenomenon that will be described later in section 1.1.2.4. Traditionally these optical spectra were either obtained experimentally or approximated with damped oscillators, but recently it has been extended to include ab initio calculations. Although some methods tend to be more preferred than others, the exact method used is only relevant if there are singular caveats to consider, such as a particular frequency/energy range

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where the data tend to not be trustworthy. Beyond that, the various experimental or ab initio optical properties are interchangeable and can be directly transformed into the required vdW-Ld spectra using the appropriate KK transforms. For example: VEELS (valence electron energy loss spectrum) measurement might give the frequency dependent results in Jcv (eV) (interband transition strength form in eV frequency units) while the ab initio codes give the imaginary part of the dielectric spectrum over real frequencies, ε′′(ω). One can convert between the two via the following identity: m o2ω 2 (ε′′(ω ) + iε′(ω )) e 2 h 2 8π 2 And then one can straightforwardly convert to the vdW-Ld spectra that need ε′′(ω) as an input

Equation 5.

J cv (ω ) =

function for the calculation of the Hamaker coefficients.

2.1.2.3 Model System: Plane-Plane interactions of (PS-water-PS) and (SiO2water-SiO2) The many layers of abstraction within the Lifshitz formulation are generally straightforward from a calculation standpoint, but can hide the linkage of the optical properties to the underlying material properties for those merely plugging and chugging to obtain a number. But knowing how those optical properties depend on the underlying material composition and crystal structure can be very beneficial from a material design / engineering standpoint. For example — the interband optical properties of polystyrene in the vacuum ultraviolet (VUV) region can be investigated using combined spectroscopic ellipsometry and VUV spectroscopy (French et al 2007). Over the range 1.5–32eV, the optical properties exhibit electronic transitions that can be assigned to three groupings, corresponding to a hierarchy of interband transitions of aromatic (π →π*), non-bonding (n→π*, n→σ*), and saturated (σ→σ*) orbitals. In polystyrene there are strong features in the interband transitions arising from the side-

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chain π bonding of the aromatic ring consisting of a shoulder at 5.8 eV and a peak at 6.3 eV, and from the σ bonding of the C–C backbone at 12eV and17.1eV. These transitions have characteristic critical point line shapes associated with one-dimensionally delocalized electron states in the polymer backbone. A small shoulder at 9.9eV is associated with excitations possibly from residual monomer or impurities. Having obtained polystyrene’s optical spectra from the above experiments, it is then trivial to calculate Hamaker coefficients and vdW-Ld interaction energies in the plane-parallel geometry (Figure 1) at all seperation distance. One can also vary the intervening medium (by changing its full spectral optical properties) in order to get the Hamaker coefficients and the vdW-Ld component of the surface free energy for polystyrene immersed in these other materials. The values of the Hamaker coefficient for planar geometry are shown in Table 1.

Table 1. Full spectral Hamaker coefficients

for vdW-Ld interaction of different physical

configurations with polystyrene, amorphous SiO2 , or water as one component, determined from interband transition strength spectra. A similar and related type of calculations and analysis can be done also for two semiinfinite slabs of SiO2 interacting across various media (Tan et al, 2005). The interband optical properties of crystalline quartz and amorphous SiO2 in the vacuum ultraviolet VUV region have been investigated using combined spectroscopic ellipsometry and VUV

Page 2.1.2—12 of 213

spectroscopy. Over the range of 1.5–42 eV the optical properties exhibit similar exciton and interband transitions, with crystalline SiO2 exhibiting larger transition strengths and index of refraction. Crystalline SiO2 has more sharp features in the interband transition strength spectrum than amorphous SiO2, the energy of the absorption edge for crystalline SiO2 is about 1 eV higher than that for amorphous SiO2, and the direct band-gap energies for X-cut and Z-cut quartz are 8.30 and 8.29 eV within the absorption coefficient range 2–20 cm−1. By calculating and analyzing the Hamaker coefficients, we can determine the degree by which changes in crystal structure influence the overall vdW-Ld interaction. Comparing c-SiO2 or a-SiO2 in the plane-plane geometry, there is clearly an appreciably increase in the overall vdW-Ld strength for the c-SiO2, which is a result of its increased physical density, index of refraction, transition strengths, and oscillator strengths in comparison to the a-SiO2. The corresponding Hamaker coefficients are again shown in Table. 1.

2.1.2.4 Advanced Effects and Phenomenology Although we have quickly illustrated the simplest of cases, there are many other effects that arise as we make the system more complex. The first is that the Lifshitz formulation allows for attractive as well as repulsive Hamaker coefficients based on the spectral contrast between the objects and the medium. An example would be liquid helium films of Anderson and Sabisky (1970) where the substrate material would rather be surrounded by as much of the medium as possible rather than air and thus there is a “wetting” that occurs as the system prefers to make the medium as large as possible. The next effect is that of retardation and/or sign reversal. Because of the finite speed of light, the high-energy frequency contributions to the Equation 2 summation dampen out quickly as the separation distance increases.

Page 2.1.2—13 of 213

Thus the Hamaker coefficient itself has a non-linear

dependence on separation. For example, suppose we were to design system such that the higher energy part of the spectra gives rise to primarily repulsive terms and the low energy terms contributed attractive terms. At far separations where retardation eliminates all but the low energy terms contributions, the overall interaction would be positive. However as the particles attract and get closer, the Hamaker coefficient would continue to add repulsive terms to the overall summation until it hit zero and actually starts to reverse. This combination of attractive and repulsive contributions can lead to interesting effects, such as an equilibrium 1-2 nm vdWLd separation energy well and the existance of pre-melting in surface layers of ice (see section 2.3.1). There are other effects that are covered elsewhere extensively but mentioned here for completeness. Multi-layer effects (such as coatings) creates a whole new set of competing interactions because the effective optical properties of the entire object can change drastically as a function of seperation distance (Podgornik et al, 2006). Next there is the effect of optical anisotropy. Here the overall interaction will have a configurational/direction component, which will cause alignment forces and torques as first derived by Parsegian and Weiss (1972). Similar to optical anisotropy is the effect of geometry upon the Hamaker coefficient and total energy. Many of these advanced effects are only beginning to be exploited simply because the necessary optical properties and extensions to the Lifshitz formulations are still becoming available. But it is likely that both the simple and more advanced behaviors will be of great importance, particularly for those working on the nano and molecular scale.

2.1.3 ab initio optical properties of complex materials The previous two sections outlined the important effects that result from even small changes in the full spectral optical properties. One might naively assume, due to the overall

Page 2.1.3—14 of 213

importance of vdW-Ld interactions in condensed matter physics, that there would be a very large catalogue of these spectra available. This information could then be datamined and used in all sorts of ways, particularly in experimental design. Unfortunately, obtaining full optical spectra is a more difficult endeavor than most realize.

While vacuum ultraviolet (VUV) spectroscopy and valence electron energy loss

spectroscopy (V-EELS) are well established, robust methods that have proven to be critical in bringing us to where we are today (French, 2000; French et al, 1995), they have stringent sample preperation specifications (among other factors) that make a generalized cataloguing process of hundreds of materials very cost/time prohibitive. Some materials, most notably liquids, are particularly difficult to characterize because of the need of being under vacuum and thus require containers and/or other strategies. To experimentally characterize spatially varying, deep UV optical properties of a complex material in a liquid medium would be difficult or impossible. More recently, ab initio codes have proven to be a viable alternative and even opening the door to analyze these materials that cannot be cleanly obtained experimentally (e.g. biological molecules immersed in a liquid solution). These OLCAO-DFT codes use very large basis sets in order to capture all possible electron transitions between the valence and conduction bands of the total electronic structure. Test calculations on several ceramic crystals showed that the calculated Hamaker coefficients using theoretical spectra do not differ much from those obtained using experimental spectra (French and Ching, unpublished). More recently, this approach has been applied to obtain Hamaker constants for both metallic and semiconducting single wall carbon nanotubes (SWCNT) and multi-wall carbon nanotubes (MWCNT) of different chiralities with considerable success (Rajter et al, 2007c; Rajter et al, 2008).

Page 2.1.3—15 of 213

In Figure 2 and 3, we show ε”(ω) and the corresponding vdW-Ld spectra properties of [6,5,s] and [9,3,m] SWCNTs. It is important to capture all of these transition states out to at least 30 eV in this case because even the seemingly “boring” areas that lack any large spikes are still adding to the overall summation and can shift the magnitude of the resulting spectra considerably. This illustrates the clear need to have accurate information for electronic transition well beyond just the band gap, which is where attention is focused for those interested in device performance. But beyond a 30-40 eV cutoff, the transitions become less important because they are considerably dampened by the KK transform and therefore need to be much larger in order to still be significant. While the ascertaining and usage of ab initio optical properties for vdW-Ld interactions is still a very new and small field, its speed, low cost, and broad utility makes it a very appealing solution to the long standing problem of a dearth of optical property catalogues. Additionally, it even provides exciting new possibilities, such as spatially resolving the optical properties for e.g. biological materials, which will be described in more detail in section 2.1.1

2.1.4 Electrodynamic Interactions For Arbitrary Shapes The impact of shape/geometry is a more complex but equally important component in determing the multi-bodied behavior of electrodynamic LRIs. Recall that the sources of these LRIs arise from the quantum fluctuations of the electromagnetic (EM) field as they are modified by the presence, positions, and shapes of metallic ("Casimir") or dielectric ("Lifshitz") objects (Casimir and Ned, 1948; Lifshitz, 1956). The advent of high precision measurements (Lamoreaux, 1997; Mohideen, 1998; Roy et al, 1999), and the possibility that they can be applied to nanoscale electromechanical devices (Chan et al, 2001; Decca et al, 2003; Serry et al,

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1998), has stimulated interest in developing a practical way to calculate the dependence of electrodynamic energies on the shapes of the objects. The simplest and most commonly used methods for dealing with complex shapes rely on pair-wise summations: In the proximity force approximation (PFA), also referred to as the Deryaguin approximation, the energy is obtained as an integral over infinitesimal parallel surface elements at their local separation measured perpendicular to a surface (Rempel et al 2001) and works well when two objects are very close together as e.g. in the case of SWCNTs at small separations (Rajter et al, 2007c). A second method described by Sedmik et al (2007) is based upon addition of Casimir-Polder ‘atomic’ interactions (CPI). Unfortunately both methods are heuristic and not easily amenable to systematic improvements. A rather general method, based on a multiple scattering expansion, was put forward by Balian and Duplantier (1978), for calculating Casimir energies for arbitrary shape. However, this method has not proved practical. An approach based on path integral methods has also been used to compute corrections to the parallel plate result perturbatively for small deformations (Emig et al, 2003). The limitations of perturbation theory weaken the usefulness of this approach, but in special cases it can be overcome by specialized numerical methods (Büscher and Emig, 2005). There is also a numerical implementation of the path integral method (Gies and Klingmuller, 2006) which has so far been applied only to scalar fields. The most recent numerical approaches have been based either on an explicit discretization of the EM fields in space, and computation of the mean stress tensor (Rodriguez et al, 2007), or on the boundary element method by rewriting the van der Waals interaction energy exclusively in terms of surface integrals of surface operators (Veble and Podgornik, 2007). In principle, both schemes can deal with arbitrary geometries and a spatially varying dielectric constant.

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2.1.4.1 Cylinders and Plates The geometry of the cylinder, as intermediate between sphere and plate, is ideally suited to testing the limitations of PFA and CPI approximations. It is also relevant to important experimental systems such as carbon nanotubes and stiff polymers such as DNA. The translational symmetry along the cylinder axis considerably simplifies the problem, as the electromagnetic (EM) field (with metallic objects) can be decomposed into transverse magnetic (TM) and transverse electric (TE) components, with Dirichlet and Neumann boundary conditions, respectively. Emig et al (2006) exploited this to find the exact Casimir force between a plate and a cylinder, and there have been further elaborations (Bordag, 2006; Brown-Hayes et al, 2005). The force (F) has an unexpectedly weak decay

L H 3 ln( HR ) at large plate–cylinder separations H (L and R are the cylinder length and radius), due to Equation 6.

F(H) ∝

transverse magnetic modes. Path integral quantization with a partial wave expansion additionally provides the density of states, and corrections at finite temperatures. A remarkable example of the failure of pair-wise additivity was obtained by Rodriguez et al, (2007), in which the Casimir force between two squares exhibits a non-monotonic dependence on the distance from enclosing side-walls. Figure 4, left panel, shows the same effect for two cylinders, with one or two nearby side-walls (all metals), as depicted in the following figure (left panel – Rahl et al, unpublished). The right panel of Figure 4, shows preliminary results for the force between two cylinders, normalized by the PFA result. The solid and dashed lines correspond to one or two side-walls respectively; in each case the contributions of TM and TE modes to the total force are also depicted. For the plotted separation of a/R = 2, PFA overestimates the force by roughly a factor of 2. More significantly, in pair wise approximations (PFA or CPI) the side-wall(s) have

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no effect on the force between the cylinders. The non-monotonic variation with the separation H to the plates is thus a direct illustration of the importance of three body effects.

2.1.4.2 Spheres and Compact Shapes A potentially quite powerful approach for computing electrodynamic forces for materials of arbitrary shape and composition was developed recently (Emig et al, 2007). There are dual, and equivalent perspectives on the Casimir interaction: in terms of the fluctuating EM field, or the fluctuating sources (charges and currents) in the material bodies (Schwinger, 2004); we shall employ the latter. The fluctuating sources on the different objects (labeled by Greek letters) are indicated by {Qα }. Each Qα carries multiple indices, designating the source (charge or current), partial wave (l, m) in a multi-pole representation, and frequency (after Fourier transformation in time), which will be suppressed for brevity. In path integral quantization, each configuration is weighted using an action S[{Qα}], which is quadratic and comprised of several parts. The offdiagonal elements of the action,

Equation 7. S[{Qα }] = Qα Vαβ Qβ , represent the interaction between charges. As is familiar from electrostatics, we expect that the lowest multipoles dominate the interaction at large separations. The matrix elements Vαβ are thus a function of the separation Dαβ and the implicit multipoles. The “diagonal” components,

Equation 8. S[{Qα }] = 12 Qα Tα−1 Qα , are more interesting and represent the self-energy (action) of the source. The crucial observation is that the matrices Tα , which encode all relevant shape and material properties of the objects, are simply related to scattering from the object (Newton, 1996). This connection was also noted by Kenneth and Klitch (2006), and provides a link to the mature and well-developed field of scattering of EM waves from different objects.

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The T-matrix can be obtained for dielectric objects of arbitrary shape by integrating the standard vector solutions of the Helmholtz equation in dielectric media over the object’s surface (Waterman, 1971), and both analytical and numerical results are available for many shapes (Mishchenko et al, 1971). For the specific case of two dielectric spheres, for which explicit formulas for the T-matrix are available, the Casimir force can be obtained at all separations. Focusing on low-order multipoles, gives an expansion in powers of the ratio of sphere radius to separation (R/D). Due to alternating signs, the convergence of this series is problematic, but a convergent approach can be obtained by including all terms coming from a given order in the multipole order l (irrespective the power in R/D), and extrapolating to l → ∞. This procedure yields a curve for the force that interpolates all the way from the Casimir-Polder limit to the PFA result at short separations. This concludes our basic overview of the foundational aspects of continuum model, electrodynamic LRIs. We now turn our attention to the atomistic methods, specifically the wide variety available using ab initio quantum codes.

2.1.5 Non-covalent Interactions From Electronic Structure Calculations Approximate numerical solutions to the electronic Schrödinger equation have become a standard tool for ab initio predicting materials’ properties in the fields of computational physics, chemistry, and biology. Quantum Monte Carlo and post Hartree-Fock methods, such as Coupled Cluster or Configuration Interaction, are able to reach an accuracy which is more than sufficient for comparison to spectroscopic experiments. They suffer, however, from a prohibitive computational cost with an increasing number of electrons. Alternatively, the solution of the Schrödinger equation within the Kohn-Sham Density Functional Theory (KS-DFT) frame work (Hohenberg and Khon, 1964; Kohn and Sham, 1965; Parr and Yang, 1989) frequently proves to

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represent not only a reasonable trade-off between accuracy and computational cost (Koch and Holthausen 2002) but also a conceptually more appealing view on the electronic many-body problem in terms of a single particle electron density, n(r). Furthermore, the modest computational cost of DFT led to the development of ab initio molecular dynamics methods, such as Born-Oppenheimer or Car-Parrinello molecular dynamics (Iftimie et al, 2005). In principle, KS-DFT is an exact theory that yields the exact electronic ground state and interatomic potential. In practice, however, the exchange-correlation energy, Exc [n(r)] – the unknown term in the KS-Hamiltonian, must be approximated, thereby rendering the accuracy less than perfect. DFT has been widely successfully for describing the properties in dense materials and isolated molecules, where local and semi local approximations and their generalizations typically give satisfactory results (Staroverov et al, 2004; Staroverov et al, 2003), with hybrid functionals (Sousa et al, 2007), playing a special role in the molecular case. However, sparse systems, soft matter, molecular van der Waals (vdW) complexes, biomolecules, and the like cannot be adequately described by the previously standard DFT approximations. These “weak” LRIs are among the phenomena for which the first generations of approximations to vxc , the local density and generalized gradient approximations, LDA and GGA, yielded qualitatively erroneous predictions. Kristyan and Pulay and Pérez-Jordá (1994) and Becke (1995) showed this already more than a decade ago for rare gas, Meijer and Sprik (1996) for the benzene dimer and benzene crystal. See Zhao and Truhlar (2005) for a recent assessment of the performance of 44 approximations to vxc for describing non-bonded dimers. These difficulties have now become widely recognized, and a number of different techniques are being developed and exploited to deal with the situation, where the LRIs are important. We start by reviewing these new techniques. These represent only a beginning to the solution of a critical problem.

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2.1.5.1 Recently evolving DFT methods We can approximately characterize the emerging methods as (i) Many-body methods using KS orbitals; (ii) Empirical and non-empirical explicit density functional methods; (iii) Perturbative methods which leave the electronic structure uncorrected and aim solely at predicting the correct interatomic potentials, usually requiring the input of C6 coefficients, polarizabilities, or damping functions which are consistent with the employed vxc . This characterization scheme is to some extent arbitrary. Another scheme might be according to whether or not it would be necessary to identify distinct fragments of matter in order to define and apply the method; this would split the methods in each of the categories above.

2.1.5.1.1 Many-body methods using KS orbitals Random-phase approximation based methods. We begin by discussing an important type of method whose use has recently expanded and is based on the random phase approximation (RPA), often enhanced in various ways, such as using corrections in the style of time dependent density functional theory to the RPA density-density correlation function. The RPA approximates long-range correlations including van der Waals, but when applied to uniform systems, is less accurate than the modern form of LDA based on fitting of exact limits and quantum Monte Carlo simulations, so it was abandoned decades ago as a DFT technique. A suggestion by Kurth and Perdew (1999) to simply apply the full RPA and to correct the above error with an extra local or semi local correction seems to have resurrected its use. RPA methods have recently been applied not only to model systems (Dobson and Wang, 1999; Pitarke and Perdew, 2003; Jung et al, 2004), but also to molecules (Furche and Voorhis, 2005; Fuchs and Gonze, 2002; Aryasetiawan et al, 2002) and solids (Miyake et al, 2002); many of these are not obviously vdW systems, but of recent interest is the application by Marini et al. (2006) to a vdW Page 2.1.5—22 of 213

bonded layered solid (BN). By separating the layers, the system can be brought into the region where vdW-Ld is predominant, where both the strength and weakness of the method is shown. It’s strength is that there is no empirical input, distinct fragments do not need to be defined, and it can be applied to both finite and extended systems. It’s weakness is shown by the error bars: it is computationally intensive; one must calculate excited KS states accurately, which implies either a fine grid or a large basis set, depending on the method used. Symmetry adapted perturbation theory based methods. Symmetry adapted perturbation theory (SAPT) is a quantum chemical method which treats the interaction between monomers via perturbation theory. A half dozen years ago a method was introduced that mimics the SAPT procedure using KS orbitals (Williams and Chabalowski, 2001), which we will term SAPTDFT. The initial version was rather inaccurate, but various improvements, some of which are semi empirical, have yielded a method capable of giving good results (Misquitta et al, 2003; Heßelmann and Janzen, 2003). However, there are also weaknesses. First, the method has not been developed for application to extended systems. For finite systems, although the scaling with system size is superior to the state of the art coupled cluster wave function methods, it is nevertheless significantly worse than for either standard DFT methods, or the recent DFT methods that include vdW-Ld, as discussed below. Its application necessitates the identification of individual fragments, so it cannot be seamless as fragments merge together to become single entities.

2.1.5.1.2 Explicit density functional methods By this we mean that the exchange and correlation energies are given as explicit functionals; this means specifically that once the occupied KS orbitals and hence the density is obtained, the exchange and correlation energy components are simply evaluated, without the

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need to calculate unoccupied KS orbitals. This requirement virtually guarantees that the scaling of the computational requirements with system size will not destroy the cubic scaling enjoyed by ordinary DFT. Non-empirical vdW-DF. The modern version of this functional was introduced several years ago (Dion et al, 2004), with the fully self-consistent version (Thonhauser et al, 2007) coming more recently. This version supplants the obsolete functional for planar systems (Rydberg et al, 2000). Like the RPA methods, the correlation functional of vdW-DF is nonempirical. Unlike them, however, it does not automatically provide its own exchange functional. For this the revPBE (Zhang, 1998) flavor of the generalized gradient approximation (GGA) was used, because it appeared to give the best agreement with Hartree-Fock calculations when the correlation functional was omitted. The vdW-DF method has shown promise for a variety of system-types where vdW-Ld interactions are important (Thonhauser et al, 2007; Chakarova et al, 2006; Kleis et al, 2007; Cooper et al, 2008). The method appears to be most accurate for larger systems, where the multiplicity of probable particle-hole excitations more closely matches the assumptions under which it was derived. Even for small systems like rare gas dimers, it qualitatively captures the vdW-Ld interaction, which is missed by standard density functionals. It can handle extended systems with large unit cells, as well as large finite systems, as its scaling with system size is the same as ordinary DFT. It is fully self-consistent, which means that it can produce Hellmann-Feynman internuclear forces, that are crucial for relaxation and molecular dynamics. It does not require the identification of fragments, and if they physically exist, the theory is seamless as they merge together. Prototypical results for large systems include physisorption of benzene and naphthalene on graphite, the structure and binding of a

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polyethylene crystal, and a DNA base pair dimer, whose sequence dependent twist matched trends from high resolution data (Olson et al, 1998). Empirical explicit functionals. One can aim to improve the electron-electron interaction such that the corrected electron density yields correct atomic forces. This is tantamount to improving vxc empirically, as it has already been done for functionals which yield reasonable atomic and intramolecular energie. Usually, a small set of parameters is fitted to many reliable reference results, in this case non-bonded complexes. The recently introduced X3LYP functional (Xu and Goddard, 2004), was quickly shown to fail completely for stacked nucleic acid bases and amino acid pairs (Cerny and Hobza, 2005) although hydrogen bonding was found to be well described. It thereby follows the typical pattern of conventional density functionals that fail to properly describe the dispersion interaction. Zhao and Truhlar likewise presented various empirical functionals for weak interactions (Zhao and Truhlar, 2005). Alternatively, and also quite recently, and inspired by the idea that molecular properties can be influenced through the parameterization of effective core potentials (Hellmann, 1935), an electron-nucleus correction, named London dispersion corrected atom centered potentials (DCACP), has been introduced (Lilienfeld et al, 2004). In that approach, a set of parameters, {σi }, in an atom-centered potential is calibrated for every atom I in the periodic table and added to a GGA exchange- correlation potential,

Equation 9. Conventionally, the DCACP has the functional form of the analytical pseudopotentials proposed by Goedecker and Hutter (1996). Current flavors of this correction use two σ-parameters per atom which are calibrated to experimental or highly accurate theoretical results for prototypical van- der-Waals complexes. Thereafter, the same atomic potential is employed for all the

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different chemical environments. The latest generation of calibrated potentials can be found by Lin et al (2007). This scheme has already successfully been applied to a range of systems and situations, such as small rare-gas clusters, the hydrogen bromide dimer, and conformational changes in cyclooctane (Lilienfeld et al, 2005), to the adsorption of Ar on graphite (Tkatchenko and Lilienfeld, 2006), to the coarse-graining of intermolecular potentials of discotic aromatic materials (Lilienfeld and Andrienko, 2006), to the dimers of small organic molecules, and to cohesive energies and the lattice constant of the benzene crystal (Tapavicza et al, 2007), to the intermolecular binding of DNA base- pairs and base-pair/intercalator drug candidate (Lin et al, 2008), and liquid water. However, for all of these empirical approaches to the exact vxc the fundamental problem remains that a priori not only parameters in vxc are unknown but also its functional form.

2.1.5.2 Methods requiring the input of consistent C6 coefficients of polarizabilities, and damping functions DFT-dampedC6. We will use the term DFT-dampedC6 to describe any of the methods that treat short-range interactions by DFT, but vdW-Ld via a damped interaction directly between atomic nuclei. This is based on London’s original perturbational work yielding the C6/R6 asymptotic dissociative scaling between two atoms at distance R (Heitler and London, 1927). The total energy is then extended by

Equation 10. , and must be damped to avoid any spurious effects on the repulsive potential which originates in the nuclear and electronic Coulomb, and the Pauli repulsion. The vdW-Ld interaction is thus not treated by DFT at all, but rather by a force-field method with a dissociative Lennard-Jonespotential. There exists a multiplicity of such methods (Elstner et al, 2001; Wu et al, 2001; Wu

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and Yang, 2002) that generally require a substantial amount of empirical input. Recently, Grimme and coworkers systematically tabulated C6 coefficients for usage in various GGA functionals. They employed them for studies of supra molecular host guest systems (Parac et al, 2005), for organic reactions involving anthracene, for supramolecular aggregates of bio-organic compounds (Grimme et al, 2007), and even fullerenes and graphene sheets. Ortmann, Schmidt, and Bechstedt used the same C6 /r6 -approach to study the adsorption of a DNA base on graphite (2005), as well as solid state properties (2006). While they do find significant improvement for isolated dimers or surface adsorption, condensed phase properties, such as the lattice constants and bulk moduli of the Ne and Ar crystal show no improvement at all. This is discouraging because it indicates an intrinsic limit of the applicability of the C6 correction as such when dealing with all condensed phase systems. In particular, a probable reason for the failure to improve upon crystal properties is that many-body contributions to the vdW-Ld forces in the condensed phase that can only be accounted for effectively. Nevertheless, because of their low computational requirements, methods of this type are used by many groups. Determination of C6 coefficients. The C6 coefficients can be determined from atomic static polarizabilities (Israelachvili, 1985), from electronic excitations (Marques et al, 2007), or from the exchange-correlation hole as proposed by Becke and Johnson (2005). The latter method has been applied as the dispersion energy part of a density functional (Becke and Johnson, 2005; Johnson and Becke, 2006). It has some similarities to DFT-dampedC6, but with less semiempirical input, and more importantly with a carefully reasoned, although heuristic argument for its validity. This method requires the monomer static polarizabilities as input, very much like very early asymptotic functionals which either required these polarizabilities (Hult, 1998) or a cutoff which determined them (Anderson et al, 1996), and determined the C6 coefficient and

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eventually higher order C’s. However, instead of the multi parameter damping functions used in DFT-dampedC6 type theories, it was found that a single universal parameter could be used, when combined computed atomic correlation energies, though using a more complex algorithm when higher order C’s were considered. The method makes use of the exchange-correlation holes of the constituent monomers. These are linearly related to the equal-time density-density correlation functions of the respective monomers. In contrast, an exact treatment of the vdW-Ld energy would require knowledge of the non-equal-time density-density correlation functions of the monomers. The method has been applied with reasonable promise to large numbers of smaller van der Waals complexes.

2.1.6 Challenges and Opportunities There are several challenges to understanding and controlling the electrodyamic LRIs, such as the role of geometry (the easy calculations are for simple shapes and topologies) and material properties (external factors such as temperature and pressure, and internal aspects such as defects and impurities). These questions can be broadly grouped in terms of length scales: At the longest scales, the material can be approximated by a continuum formulation, and the problem is to calculate the dependence of the force on shape and orientation. At the shortest scales, the atomic/molecular nature of the material is paramount, and there is need for accurate ab initio approaches and density functional methods. At the intermediate scales, it would be valuable to have effective potentials that capture the crossover between different regimes, which can be used for efficient and accurate numerical simulations. But these scientific challenges may actually pale in comparison to some of the more pressing sociological issues that continue to plauge this field.

For example: although the

foundations of the modern day continuum models were laid over fifty years ago, a segment of

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the community still prefers to employ and speak in terms of the even earlier (1930’s) picture by Hamaker (1937) that made little conceptual distinction between gasses and condensed materials. Much of this resistence to embrace the Lifshitz/Casimir formulations revolves around the perception of being too unwieldy or difficult to use. This is not too unfair a charge, because much of the details were scattered across many papers of varying notation and scope, failing to fill in many gaps and illuminate various insights.

However, this drawback has now been

hopefully eliminated (Parsegian, 2005). Another perception issue revolves around the optical properties. When many biologist and chemists think of optical properties, they tend to focus primiarly around the visible and infrared regimes because those are the areas of interest for many useful characterization methods. Unfortunately, the vdW-Ld properties are dominated in many materials by the properties arising out to deep UV frequencies. When this difficulty of obtaining the full spectral optical proerties via experimental means is conveyed, the tendancy is to give up and instead just approximate or ignore these “weak” interactions and focus back on the electrostatics or orther forces only. Luckily this is where ab initio codes may prove to be most useful due to the speed, ease, and low cost by which this information can be obtained. Eliminating this barrier and bridging the gap between the electrodynamic community and other fields (biology, chemisty, MEMs, etc) would be tremendously advantageous to each. From the atomistic standpoint, the needs and challenges are quite different. Although large progress has been made, we can now only do ab initio calculations on relatively small systems. The long range of the vdW-Ld interaction gives a radius surrounding many atoms that must be solved with ordinary algorithms before reaching the unit size that makes linear scaling

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possible. We would like to do large biological systems such as DNA and proteins interacting, and problems of like size in many subfields of physics and chemistry. We need ways to handle metals and semi-metals, graphene, and nanotubes. This issue here is that the non-retarded asymptotic forms differ from the integral inverse power laws in certain geometries of reduced dimensionality. This has been discussed by a number of authors (Barash and Notysh, 1988; Bostrom and Sernelius, 2000; Dobson et al, 2006). The long-range limit of the vdW interaction between infinite metallic fragments of reduced dimensionality have long range tails that falls off more slowly than would be implied by the integration of |r − r|−6 over their respective volumes. This occurs because the polarizability of the fragments may become singular for a small frequency and wave vector. There is certainly the possibility that this effect will affect calculations on graphene layers, which can be weak metals in some of their manifestations. One of the downfalls of a report that is charged with finding “challenges and opportunities” is that it can sometimes paint too pessimistic a picture and gloss over the major successes and foundational work that exists in any particular field. However it is clear that substantial progress has been made towards the inclusion of LRIs into DFT, thereby opening the door towards the predictive simulation of various phenomena involving weak intermolecular interactions. Ultimately, for example, ab initio, i.e., electronic structure based, rational compound design approaches (Franceschetti and Zunger, 1999; Johanneson et al, 2002; Lilienfeld et al, 2005; Lilienfeld et al, 2006; Wang et al, 2006;) will profit from the enhanced accuracy and probably prosper. More on this will be addressed and illustrated in section 3.4. And finally, there is a clear need to get these two overarching communities (continuum/atomistic) to begin to talk to and communicate with one another. This may involve

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many things, starting with the development of a common language and means by which the understanding of how optical properties and EM waves from the bulk perspective can translate to a discussion of functionals and/or pair potentials on the atom by atom level. This has just but started as both groups are beginning to turn towards each other for ideas in solving their respective shortcomings. In order to summarize section 1.1, a list of present needs and opportunities for the electrodynamic LRIs include (but is certainly not limited to) the following items: •

Efficient and reliable analytical and numerical methods for computing Casimir forces (and torques) between objects of arbitrary shape and material.

•

Accounting for anisotropy in material properties, for nanotubes and other objects.

•

Alternative methods for electronic structure calculations incorporating dispersion forces.

•

Interaction potentials for complex biomolecules such as DNA

•

Interactions of biopolymers with substrates (e.g. proteins on ice)

•

Temperature/pressure dependence of force and associated Hamaker coefficients

•

Wetting on patterned substrates and more complex geometries.

•

Thermodynamic buoyancy

•

Dynamic Casimir phenomena- dissipation from moving plates.

•

A common language between the continuum and atomistic communities.

•

A mechanism to interpolate between the continuum and atomistic regimes, or at least an idenfication of the distance limits when each formulation and its assumptions break down.

•

Multi-body and/or repulsive vdW-Ld effects for ab initio codes.

•

vdW-Ld functionals for DFT codes that can coexist with methods for solving cavitation and solvation energies.

2.2 Electrostatics The only forces of nature that directly control most of the mechanical and thermodynamic properties of materials are the electrostatic forces between electrons and nuclei,

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between nuclei and nuclei, and (indirectly) also the electrostatic forces between electrons. We refer here to all the properties of matter for which the electrons may be treated as in their ground state, following the Born-Oppenheimer approximation, and the nuclei or ions may be treated as classical particles in whose potential the electrons move. In this approximation the ions are in no sense in their ground state and can redistribute in response to gradients in temperature, stress, electric fields, chemical potential, etc. The range of validity of the Born-Oppenheimer approximation includes most of the chemistry as well as equilibrium and non-equilibrium thermodynamics of materials and much of biology. It includes all interatomic forces between ions, thermally activated atoms, in electrolytes, metals, insulators and semiconductors, Van der Waals solids, liquids and gases, while excluding fast-moving ions in radiation damage events, radiative processes, such as luminescence, and electron transport in which quantum electrodynamics or electromagnetism start to play a role. It matches the range of validity for density functional theory (Kohn and Sham, 1965; Hohenberg and Kohn, 1964), which is a unifying principle, the basis of many practical schemes of calculation, and a source of insights into the long-range electrostatic interactions detailed in this section. Various approximate theories exist for the specific treatment of electrolyte systems in classical statistical mechanics, e.g. the Poisson-Boltzmann (PB) approximation, classical density functional and integral equation theories. Computer simulations give in principle precise results for a given model (for sufficiently large system and simulation time). Simulations have together with the more refined approximate theories made a great impact on our understanding of electrolyte systems.

It has become increasingly more apparent during the last decades that

effects of many-body ionic correlations and discrete solvent must be understood in more detail.

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Both of these effects are entirely neglected in the PB approximation (Vlachy, 1999; Hansen and Lowen, 2000; Bhuiyan et al, 20002; Linse, 2005; Henderson et al, 2001).

2.2.1 Electrostatics in Density Functional Theory

2.2.1.1 Formulation Good accounts of DFT are now plentiful in textbooks (Parr and Yang, 1989; Koch and Holthauser, 2001), the notation in this summary follows that of Finnis (2003). Although mentioned earlier in section 1.1.5, the details of DFT are summarised here in a way that brings out the role of long-range electrostatic forces. For simplicity of notation, Hartree atomic units are used throughout. According to DFT, the total internal potential energy of a system of electrons in their ground state, interacting with a system of ions, is the sum of five terms:

Equation 11. E HKS [ρ ] = Ts[ ρ] + E H [ ρ ] + E xc [ ρ] + E eZ [ ρ ] + E ZZ . The first three terms on the right hand side are functionals of the electron density ρ alone, independently of the potential supplied by the ions or nuclii. Ts[ ρ] is the kinetic energy of the electrons regarded as non-interacting particles. E H[ ρ] is the Hartree or electrostatic self-energy of the electron density, regarded as a classical continuum of charge:

∫

ρ(r ) ρ(r ′)

dr dr ′ . r - r′ E xc [ ρ] is usually described as the exchange and correlation energy functional, but it also

Equation 12.

EH =

1 2

includes the difference between the true kinetic energy of electrons at a density ρ(r) and the kinetic energy given by the functional Ts[ ρ] . E eZ [ρ ] is the interaction between the electrons and the positive charges (ions or nuclei) in the system, which supply what is usually called an ‘external’ potential Vext (r ) , hence Equation 13.

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E eZ [ρ ] =

∫ ρ(r)V

ext

(r)dr .

The final term E ZZ is the long-ranged electrostatic interaction between the ions, which we suppose carry charges {ZI } located at {RI } :

ZI Z J . − R I J I≠ J carries no information about the electrons, but its presence is necessary to complete the Equation 14.

E ZZ

E ZZ =

1 2

∑R

total internal potential energy of the system, and thereby to cancel the electrostatic divergencies which occur in the limit of large systems. Because the Coulomb sum diverges, the electrostatic terms E H and EeZ scale with increasing system size as N 5 3 , where N is the total number of atoms. The leading-order terms in E ZZ and E H are equal and positive, and together, in a system that is overall neutral, they cancel the leading term in the negative quantity E eZ . The resulting total energy then scales correctly as N . In practical calculations, the range over which this cancellation takes effect, and how to exploit it, are matters of great importance, and still controversial, as we shall see. Furthermore, when the electrons are in their ground state DFT tells us that the energy functional E HKS [ρ ] is at a minimum with respect to variations in ρ : Equation 15. δE HKS = 0 = δ (Ts[ ρ] + E H[ ρ] + E xc [ρ ]) + ∫ δρ(r)Vext (r)dr . From these principles, the practical implementation (Martin, 2004) in standard DFT codes, guided by the classic paper of Kohn and Sham, exploits the variational calculus to recast the problem into one of solving, self-consistently, an effective Schrödinger equation for noninteracting electrons, known as the Kohn-Sham equation.

2.2.1.2 Strengths and weaknesses of the standard DFT approaches In a DFT code, the only approximation made, besides the Born-Oppenheimer approximation, is made in the form of the functional E xc [ ρ ] . It is normally assumed to be ‘local’,

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meaning that simultaneous changes in the density at two separate positions r and r ′ have a purely additive effect on the functional; the changes do not interfere with each other at a distance. Symbolically: Equation 16. E xc [ ρ + δρ (r ) + δρ(r ′)] − E xc [ ρ] = E xc [ρ + δρ (r )] − E xc [ ρ] + E xc [ ρ + δρ(r ′)] − E xc [ ρ] . There are several variants of the functional that make this approximation, which is known as the LDA (local density approximation). A related class of functionals is sometimes favoured, in which the gradient (and perhaps also the Laplacian) of the density is included in the functional; this is the GGA (generalized gradient approximation). The GGA does not always make for more accurate results, because it still omits the long-range correlation that should ideally be incorporated in E xc [ ρ ] , and it may negate some of the cancellation of errors that is a virtue of the LDA (see the previous section). The LDA or GGA paradigms have led to codes that are very fast compared to any tractable quantum chemical techniques that might be more accurate, such as those involving multiconfiguration wavefunctions, or quantum Monte Carlo. In terms of the number of atoms N , computation time with the LDA/GGA has been reduced to scale linearly for insulators and at worst as N 3 for metals. The method is ab initio in the sense of not requiring any parameters to be fitted to experiment. It is generally good for predicting structures, and has many advantages over empirical methods. For instance, as electronic components are reduced in size, the effect of point defects and interfaces on the properties of semiconductors and capacitors is of increasing interest. In these systems, the defects may carry a charge, the magnitude and sign of which depends on the Fermi energy. Such a situation is difficult or impossible to describe with classical interatomic potentials, or other non-self-consistent models of the energy. On the other hand standard DFT, i.e. using conventional functionals, can readily describe charged defects and their

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long-ranged electrostatic interactions. Nevertheless, it should be recognised that the inherent absolute errors in standard DFT/LDA may be of order 0.1eV (~1200K) per bond or more in some cases, which is too large for many questions of chemistry and particularly biology.

2.2.2 Electrostatics in Equilibrium Statistical Mechanics

2.2.2.1 Formulation Despite important advances, much of the current understanding of electrostatics in many applications is based on mean field PB (Poisson-Boltzmann) thinking. When the PB approximation does not agree with experiments it is still common to patch up the PB theory by introducing various devices rather than questioning the basis of it. Surely, there are several important cases where the PB approximation work sufficiently well (many cases with low electrostatic coupling, like monovalent electrolyte in water at low concentrations), but we have reached a point where patched up PB approaches in many cases cause more hindrances to advances than gains in understanding. The elimination of the too common unreflective meanfield thinking about electrostatic interactions is thus important.

2.2.2.2 PB and beyond Since the PB approximation still forms the basis of much of the general thinking of electrolytes, many effects of many-body correlations were surprising when they were initially found, for example like-charge attractions (Oosawa, 1971; Guldbrand et al, 1984; Kjellander and Marcelja, 1984) and effective charge reversals (Valleau and Torrie, 1982; Lozada-Cassou et al, 1982; Outhwaite and Bhuiyan, 1983; Ennis et al, 1996) caused by ion-ion correlations in aqueous divalent and multivalent electrolytes (in absence of specific ion adsorption), and it has taken decades for the knowledge to spread. The appearance of nonzero effective charges for Page 2.2.2—36 of 213

electroneutral particles, e.g. a hard sphere or surface, in asymmetric electrolytes is another example. These are all examples of cases where the solution composition determines the qualitative features of the interactions, not only the quantitative ones. To assess such effects correctly requires a deep and fundamental understanding of the interactions involved. The importance of ion-ion correlation effects between multivalent counterions for the appearance of attractions between equally charged particles has been recognized in many kinds of systems, although it is still taking a long time for this knowledge to spread. Early examples include DNA (Guldbrand 1986), lamellar surfactant phases (Wennerström 1991), clay minerals (Kjellander 1988) and mica surfaces (Kékicheff 1993). A particularly clear example of great practical value is the cohesion of cement paste (Jönsson 2005, Labbez 2007). To illustrate we shall focus on the properties of DNA in electroyte solution as a model system.

2.2.2.3 Model System: DNA-DNA Interactions in Charged Electrolytes The predictions of the PB theory for interactions between charged macroions in electrolyte solutions of univalent salts conform well with osmotic stress experiments on ordered DNA arrays, to the extent of a near quantitative agreement between theory and experiment (Strey et al, 1998). Conversely, when the PB analysis is furthermore applied to salts containing at least one higher valency counterion, such as Mn2+, Co(NH3)63+ or various polyamines , the theoretical predictions tend to lose agreement with experiment. Not only does the PB theory give the wrong numerical values for the strength of the electrostatic interactions, but also and more importantly misses their sign, since experiments point to the existence of electrostatic attractions (Rau and Parsegian, 1992). This attraction is deduced from the shape of the osmotic pressure as a function of density of DNA, viz. there are regions of DNA density where the corresponding

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osmotic pressure in a DNA array remains constant (Vlachy 1999; Hansen 2000; Belloni 2000; Bhuiyan 2002; Linse 2005; Henderson 2001). This is quite similar to the pressure vs. volume isotherms in the case of a liquid-gas transition. In that case due to attractive van der Waals interactions between gas molecules. In the DNA case the role of inverse temperature is played (roughly) by the concentration of the polyvalent counterion. For sufficiently large concentration of e.g. Co(NH3)63+ the DNA array spontaneously precipitates or condenses into an ordered high density phase. One thus concludes that the polyvalent counterion should confer some kind of attractive interactions between nominally equally charged DNA molecules. In order to understand this observation, we should first relinquish a seemingly obvious explanation, namely, that we are dealing with the effects of DNA-DNA van der Waals interactions as is the case in condensation of gases, see above. These forces are much too small to account for the strong attractions seen with polyvalent counterions (Parsegian, 2005). When dealing with small univalent counterions in the PB framework, we actually assume that they can be described collectively, on a mean-field level used in a plethora of contexts (Andelman, 1995). However, when we go to polyvalent counterions of valency Z, Z >> 1, this demands that one goes beyond the PB approximation and includes the effects of ion-ion correlations. Such approaches include simulations (Guldbrand 1984), integral equation theory (Kjellander 1984) and strong coupling and strong correlation approximations (Boroudjerdi H et al. 2005, Naji 2005; Grosberg 2002).

2.2.2.4 Electrostatics with surfaces and interfaces New chapters are being written as regards colloidal dispersion stability. Stabilization of dispersions has been observed due to the appearance of substantial effective charges for weakly

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charged macroparticles from correlation effects among smaller charged particles (Martinez et al, 2005; Liu and Luijten, 2005). On the other hand, clustering and phase separation in systems with highly and equally charged colloidal particles can be invoked by effects of ion-ion correlations among counterions (Linse, 2001; Hribar and Vlachy, 2000; Rescic and Linse, 2001; Hynninen and Panagiotopoulos, 2007). In some cases, various forms of depletion interactions can play a decisive role; they can for instance be caused by electrostatic ion-ion correlation or excluded volume effects. The study of polar liquids and electric double layers near one surface and interactions between two surfaces (e.g. double layer interactions) are closely related to the study of properties of electrolytes and polar liquids in pores and other confined geometries. All are special cases of inhomogeneous fluids. In the presence of surfaces electrostatic correlations and thereby the electric screening are changed in profound manners compared to bulk electrolytes (power-law screening along a surface (Jancovici, 1982), exponential screening perpendicular to it). The treatment of non-local dielectric response, dielectric saturation and other effects on solvent due to electrostatic fields from surfaces, molecules and other particles is a long-standing issue of great relevance (Bopp et al, 2007; Ballenegger et al, 2006; Ballenegger and Hansen, 2005; Yeh and Berkowitz, 1999). In all these areas one can expect important advances. The complexity of electrostatic interactions and their coupling to other modes of interactions is illustrated by the recent advances on the interdependence of dispersion and electrostatic interactions (Ninham and Yaminsky, 1997; Tavares et al, 2004; Wernersson and Kjellander, 2007; Kunz et al, 2004). Ion-macromolecule dispersion interactions can explain a substantial part of the ion specificity in effects of electrolytes on macromolecular interactions. vdW-Ld interactions between the constituent molecules of electrolytes affect the screening of

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electrostatic interactions in non-trivial ways, for instance by changing the exponential screeening in bulk to a power-law screeening in both quantum (Brydges and Martin, 1999) and classical (Kjellander and Forsberg, 2006) statistical mechanics theory. These matters require a lot more attention in order to elucidate under what conditions these effects are important and when they are not. We have just seen the beginning of this story. More attention should be spent on the correct treatment of the screening by electrolytes of the static part of the van der Waals interaction (Mahanty and Ninham, 1976), which is important in some systems like water-hydrocarbon of some relevance to biology. This is intimately linked to the correct treatment of electrostatic image charge interactions in ion-ion correlations (Attard et al, 1987). Dielectric polarization of interfaces by charged and polar solutes is a subject that, in general, should be properly treated in more cases than what is customary today. This is, however, less important at high electrolyte concentrations due to screening of the polarization charges by the electrolyte. It was recently realized that in electrolytes the anisotropy of the electrostatic potential from a molecule extends to the far field region (Rowan et al, 2000; Hoffmann et al, 2004). The full directional dependence of the electrostatic potential from a charged or uncharged molecule in electrolytes remain in the longest range tail (i.e. from all multipole moments) (Ramirez and Kjellander, 2007). In particular, the range of the potential from an ion and that from an electroneutral polar particle is exactly the same in general. This is contrary to the case in vacuum or pure polar liquids, where the potential from a single charge is more long ranged than that from a dipole, which in turn is more long ranged than from a quadrupole etc. The orientational dependence of the electrostatic interaction between two molecules in electrolytes is therefore

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rather complex even at large distances and the consequences of this must be further explored, see (Trizac et al, 2002; Agra et al, 2004).

2.2.3 Challenges and Opportunities Much like the well-established vdW-Ld formulations, there is a perception that there is little else to discover in electrostatics or that we can already solve every system of interest. Although this field does rest on some very solid and long-standing foundations, both the quantum mechanical and classical statistical mechical aspects still have some areas that can be enhanced greatly, as well as bridged to end-users more effectively. We will outline some of these opportunities below. DFT already provides a rigourous framework for the treatment of all LRIs in materials, when the Born-Oppenheimer approximation is valid and the electrons are close to their ground state. The recent introduction of non-local functionals by Langreth and coworkers (see section 1.2.1.1) has extended the practical scope of DFT to situations in which dispersion forces are important, by including the non-local vdW contributions to correlation energy. There are grounds for optimism that at least in some systems this will give a useful approximation to the dispersion interaction and supercede the unphysical linear addition of pairwise attractive potentials. However there are still some remaining challenges:

•

In metals, long-ranged electrostatic forces manifest themselves as anomalies in phonon spectra, and even in elastic moduli. Short-range empirical potentials of the embedded atom type fold such effects into their parameter fitting, but they may be a source of error in transferability of the models, and their ability to describe the energetics of phase transitions.

Page 2.2.3—41 of 213

•

Charged point defects in insulators are a challenge to describe theoretically, not because of the inaccuracy of DFT but because of the large length and time scales needed to simulate the equilibrium distribution of charged carriers, together with the detailed electronic structure calculations needed to obtain their formation and segregation energies. With respect to the classic electrostatic methods, one of the major barriers is trying to

strike a balance. Specifically: approximate analytical theories for soft matter systems are useful, partly since they provide formulas that can be analyzed mathematically and thereby give insight into the behavior of physical quantities when, for example, the state of the system is changed. The disadvantage is that these formulations are approximate and therefore not reliable in general. Simulations give accurate and reliable results (if correctly performed), but only provide numbers. Therefore one usually has to do a series of simulations to observe the changes in physical quantities and obtain a qualitative picture of the behavior of the system. In short: analytical approximations are physically transparent but unreliable, while simulations are reliable but not so transparent. This tends to result in end-users choosing in an either/or fashion, and is probably the reason that mean-field models, like the PB equation, continue to be used for systems that are well beyond its capabilities. One can obtain exact statistical mechanical results in certain limits (e.g. low densities, high or low temperatures or large distances). Such results are very useful since they provide firm handles on which the understanding of several important aspects of the systems can be secured. There is much more work to be done in exploring and mapping out the large parameter space beyond these limits, which will provide fundamental insights into the pertinent mechanisms.

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Another issue is the strong shift in focus from formal theory to numerical calculations that has been occurring for a long time now, which is primarily a result of the great increase in efficiency of computers. Despite the versatility and usefulness of simulation methods, there will always be limits on what can be accomplished and it is simply not enough to just add more and more computational power. The combination of insights from formal theory and numerical evaluations is necessary for attaining deep understanding of electrostatic interactions in, for example, polar liquids and electrolyte systems. Therefore a great challenge for the future is to integrate simulations with results from formal theory in clever ways that will enhance the efficiency and applicability of simulations. One example: There exist formal results for the long-range tails of various distribution functions that relies on the behavior at short range (González-Mozuelos and Bagatella-Flores, 2000; Kjellander and Ramirez, 2005). By formulating this in terms of suitable response functions and extend the distributions in the formally correct manner during the simulations one may in the future correct truncation errors on-the-fly. Since the response functions depend on the distribution functions, this has to be done in a self-consistent manner. Another example of the use of clever combination of formal theory and numerical evaluations is the construction of effective interaction potentials where some molecular degrees of freedom are included implicitly (Lyubartsev and Laaksonen, 2004; Lyubartsev and Laaksonen, 1995; Ayton et al, 2007; Tóth, 2007). This is important in many systems where one faces the problem of how to treat several length scales accurately at the same time (e.g. colloid or surfactant dispersions, solutions of polyelectrolytes or other macromolecules like proteins). The different length scales one has to consider is, for example, the small size of the solvent molecules and dissolved salt ions, the appreciably larger size of the macroparticles or aggregates and the

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average separation between the particles (Lobaskin et al, 2001). The range of the electrostatic interactions in the system may span either length scale depending on the salt concentration of the solution. Thus, even when the main interest concerns phenomena on the large scale, the effects of the molecular details somehow have to be taken into account without loosing their important features. This is where correctly designed effective interactions have a particularly important future. Another challenge is finding ways to increase accuracy by including or using “first principles simulations,” e.g. Born-Oppenheimer simulations (classical simulations where the interaction potentials for each configuration of molecules is calculated quantum chemically) and Car-Parrinello molecular dynamics. Currently this is far too expensive computationally for many interesting problems in soft matter science, but see a review by Schwegler (2007) for brief review on simple aqueous systems. Therefore at the present time, it is common in soft matter systems to instead model the molecular interaction potentials in terms of site-site interactions, often with Lennard-Jones and electrostatic interactions between the sites. Finally, there is also a need to convince others in the community to move forward with these more sophisticated formulations and tools. Too often in the past one has invoked various effects as explanations for deviations between experiments and predictions of approximate theory. Ideally, one should first eliminate the possibility that the deviations occur because the theory used is too approximate. It is important to be sure that one compares the experimental results with the true properties of model of the system at hand. If there are deviations, then the model has to be changed (i.e. the model Hamiltonian of the system). An example of this is the PB treatment of primitive model electrolyte systems. When the true properties of the primitive model were evaluated with accurate statistical mechanical methods, many new features were

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found that the PB approximation does not give. Several of the observed deviations between experiments and the PB prediction were due to the mathematical approximations implicit in the PB approach and not due to the underlying model. There still remain many such instances in the common understanding of electrostatic and other interactions in several applications.

2.3 Polar and Acid-Base Interactions 2.3.1 Motivation and Recent Advances Although polar or acid-base (AB) interactions are not as long ranged as electrostatic interactions, like vdW-Ld interactions they play important roles in chemical reaction, adhesion, triboelectrification and colloidal interactions to name a few. There are several approaches to quantify the AB interaction. Among these, Gutmann’s idea of donor-acceptor interactions (Gutmann, 1978), hard-soft AB principle of Parr and Pearson (1983) and the s.c. C and E equations of Drago and Wayland (1965) are most popular. What can be learned from these various theories is that an AB interaction is composed of electrostatic, covalent and a charge transfer interactions. The first two interactions (electrostatic and covalent components) can be understood in terms of an equation proposed by Hudson and Klopman (1967)

Equation 17.

 (c1m )2 (c 2n )2 β 2  q1 q2 + 2∑ ∑  ∆E = −  R12ε E m* − E n*  m n   occ unocc

where the first term is the Coulombic interaction and the second term is due to frontier orbital interactions. In Equation 17, m and n denote the donor and acceptor orbitals, c1m and c 2n are the coefficients of atomic orbitals participating in interaction and β is a resonance integral. E m* and

E n* are the energy of the donor and acceptor orbitals, which are equivalent to the energies of

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their highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Drago used an empirican version of Equation 17 to account for the heat of formation (-

∆H ) of AB complex as follows: Equation 18. − ∆H = E A E B + C A C B where, E and C are the electrostatic and covalent interaction constants respectively. Fowkes (1953), in turn, used Drago’s equation (with appropriate conversion to interfacial units) to study the effects of AB interactions to such problems as wetting, adsorption and adhesion. Equation 17 and Equation 18 do not however describe a very important component of AB interaction, namely the charge transfer interaction. This is where Parr and Pearsons’s HSAB (hard soft AB) principle has been rather successful. There are two important parameters needed to describe the HSAB principle: absolute electonegativity ( χ ) and absolute hardness ( η ). Using the density functional theory, Parr and Pearson showed that the absolute electronegativity is basically the same as the chemical potential of electrons, whereas hardness is the derivative of the chemical potential with respect to the numbers of electrons. These treatments yield the following definitions of χ and η : Equation 19.

 ∂E 

χ = −   = ( I + A)  ∂N  Z 2 1

and,

1  ∂2E  1 Equation 20. η =  2  = ( I − A) 2  ∂N  Z 2 where, I is the ionization potential and A is the electron affinity of a species. Pearson et al also estimated the change of the electronic energy asscociated with the charge transfer from a donor to an acceptor as follows: Equation 21.

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(χ ∆E = −

− χ Bo ) 4 (η A + η B ) o A

2

As the softness of a species is basically a chemical potential of electrons, χ o corresponds to that of the standard chemical state. According to the principle of HSAB, strong AB interaction will result when the gap between the HOMO of the donor and the LUMO of the acceptor is very low. This kind of interaction is called the soft AB interaction. On the other hand, if the above gap is rather large, there will be very little AB interaction via charge transfer complexation. In this case, the primary AB interaction is due to electrostatics. Deryaguin et al (1963) considered the donor acceptor interactions across two condensed phases to describe their adhesion. According to these authors, as electrons are transferred across an interface from the donor to the acceptor sites, an electrical potential difference ( ∆V (n ) ) would develop depending upon the numbers of electrons transferred, or the AB pairs (n) formed, across the interface, which can be obtained by minimizing the total free energy of the system with respect to n. The following expression is thus obtained:

∂V (n )   − ∆E − e∆V (n ) − en  n ∂n  Equation 22. = exp   N −n kT     In this treatment ∆E was left as an experimentally determined parameter and should be exactly the same as that given in Equation 21. Another equation relating ∆V (n ) and n is however necessary to obtain the optimum number of AB pair and the resulting electrical potential across an interface. Equation 21 in conjunction with Equation 22 form the basis for a well-known phenomenon -- triboelectrification – on the basis of AB interaction across an interface. Fowkes5 first proposed that the interfacial interaction can be decomposed into two terms, one arising from the dispersion forces and the other arising from the AB interaction. The treatment of Van Oss et al (1988; 1987) expressed as γ TOT = γ LW + γ

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AB

8,9

is similar to Fowkes in that the interfacial energy is

. While the vdW-Ld component of the adhesive interaction

follows the geometic combining rule (i.e. W12LW = 2 γ 1LW γ 2LW ), the AB component does not. The AB component of the adhesive interaction is expressed as:

W12AB = 2 γ 1+ γ 2− + 2 γ 1−γ 2+

Equation 23.

Thus, the AB component of interfacial energy γ

AB

comprises two non-additive parameters, an

electron-acceptor surface tension parameter ( γ + ) and an electron-donor surface tension parameter ( γ − ). The total AB contribution to the surface tension is given by γ

AB

= 2 γ +γ − .

The total interfacial tension between condensed phases i and j is described by

(

γ ijAB = 2 γ i+γ i− + γ +j γ −j − γ i+ γ −j − γ i−γ +j

Equation 24.

)

which is not a geometric combining rule, but rather expresses the doubly asymmetric interaction between two different materials resulting from the fact that a material can be a good electron donor, electron acceptor, neither (apolar), or both (bipolar). This theory predicts that monopolar (predominantly acidic or basic) materials will interact strongly with bipolar materials or with monopolar materials of the opposite type, and if this adhesive interaction is strong enough, the interfacial interaction between two condensed phases can become negative. Based on the Dupré equation, which can be applied for both polar and nonpolar materials, the polar interactions between two solid materials, 1 and 2, in a liquid medium, 3, using the interfacial energy given by Equation (4), is:

[( γ

=2

+ 1

− γ 2+

)( γ

Equation 25. − 1

) (γ

− γ 2− −

+ 1

− γ 3+

)( γ

AB ∆G132 = γ 12 − γ 13 − γ 23 − 1

) (γ

− γ 3− −

+ 2

− γ 3+

)( γ

− 2

− γ 3−

)]

(5) For two identical or different polar materials separated by a solvent, it is then possible for the

interaction to be repulsive or attractive. The validity of these concepts have been tested in a variety of phenomena in condensed phases. In numerous liquids and polymers, the quantitative interpretation of surface tensions is incomplete without inclusion of AB interaction energies as shown in Figure 5. The same is true Page 2.3.1—48 of 213

of the solubility of various polymers in solvents. AB interactions can also generate osmotic pressure more than a hundredfold greater than that due to van’t Hoff. The AB approach can give clear indications about the nature of complex surfaces, for example the preferential segregation of certain groups on the surface of solid copolymers (Adão et al, 1999). Parameters have also been determined for biological surfaces such as skin (Mavon et al, 1998) and bacterial cells (Ong et al, 1999). Empirical methods for estimating the strength of AB interactions are summarized in a review by Chaudhury (1997). There nonetheless remains a lack of consensus, expressed in recent literature, regarding the most appropriate approach to quantification of the strength of the AB interaction (Correia et al, 1997; Douillard, 1997; Lee, 1998). Polar interactions are therefore important as part of the LRIs “tool kit” for understanding physical behavior, and in the future, for the manipulation and design of new materials and devices. One recent example concerns the use of AB interactions to produce self-organized devices such as lithium-ion batteries (Figure 6). Cho et al. (2007) proposed a general approach to the direct formation of bipolar devices from heterogeneous colloids in which attractive and repulsive interactions could be combined to produce a network of one material (e.g., an anode) that is everywhere separated from a network of a second (e.g., a cathode). An ensuing search for suitable combinations of conductive device materials and solvents using AFM measurements showed first that inclusion of AB interactions was essential to understanding experimental data for the inorganic compounds studied, and second led to the successful identification of several electronically conductive materials (carbon, ITO, LiCoO2) between which repulsive AB interactions are obtained in an appropriately chosen liquid medium and in the absence of electrostatics. As a result, a colloidal-scale self-organized lithium rechargeable battery based on graphite-LiCoO2 was demonstrated (Figure 6).

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2.3.2 Challenges and Opportunities There have also been a few studies attempting to generalize the methods for estimating AB interactions based on molecular concepts of hardness and softness in acids and bases to other classes of materials such as metals and semiconductors (Cain et al, 1969; Ho et al, 1991). While the currents theories of AB interactions can reasonably predict whether or not a specific AB interaction would prevail, the ability to predict quatitatively the strength of AB interaction, the AB coefficients of an arbitrarily chosen material from first principals or from basic physical properties must be presently regarded as poor. Even though on a fundamental level one may not make a clear distinction between these and other consequences of highly directional interactions and/or excluded volume effects, they remain conceptually important. Experimentally, few data exist for classes of materials outside of simple liquids and polymers. This situation is similar to that of the study of Hamaker coefficients for vdW-Ld interactions, which are well understood and established for only a very small number of systems and materials. The major difference is that a systematic cataloguing of more Hamaker coefficients is straightforward process in comparison to doing a similar systematic catalouging of AB interactions. This is clearly an area ripe for scientific advance. AB interactions have the potential to be a key new tool for the self-organization of materials and devices. Improved fundamental understanding would lead to the ability to use AB interactions to controllably synthesize novel heterogeneous materials, and to produce selforganizing junctions, sub-assemblies, and devices, amongst other applications. Inorganic and crystalline materials, including metals, semiconductors, and insulators, as well as biological materials, are likely components of such “engineered” materials and devices. In crystalline

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compounds, the AB coefficients are presumably anisotropic – even possibly amphoteric on the basis of orientation. Another area for systematic scientific studies is the effect of AB interaction on the distance dependent ineractions in self-associating liquids. There are numerous experimental and theoretical studies that show that a distance dependent attractive or repulsive interaction should prevail in correlated or self-associating liquids. The integration of this force, however, must reduce to the interfacial tension of the two condensed phases in question. The very objective of the AB theory is to predict this interfacial tension. One can thus imagine that the LRIs in correlated liquids and the interfacial AB interaction are coupled. Experimental method standards for characterizing AB interactions are also in need of development. Historically, indirect methods such as wetting and solubility have been used; now, scanning probe techniques can be used to measure interactions directly and at nanoscale spatial resolution. Model liquids and solids representing γ+ γ− surfaces could be probed using AFM (including chemically modified tips) to better understand how the structures identified by methods such as contact angles as having γ+ or γ− character differ structurally. Certain model material do exists in which careful experiments can connect acid/base behavior to fundamental properties, but many more are needed in order to isolate the various components of the complex AB interactions and improve our understanding. As one example, consider the observation (Lee and Sigmund, 2002) that there are few monopolar materials (i.e., predominantly a donor or acceptor) of the electron acceptor type. A class of such compounds may be fluoroalcohols and fluoroalcohol bearing polymers. (See Figure 7) These materials have been shown experimentally to only be hydrogen bond donors with no capability to act as

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hydrogen acceptors (based on infrared spectra). This is because of both the highly electron withdrawing properties of the fluorosubstituents and also their steric bulk. And finally, the work thus far for AB interactions appears to be primarily experiment based. However, all three of the major components (electrostatic, covalent and a charge transfer) of the total AB interaction are areas where ab initio codes excel at describing with great precision. It seems like an opportunity was overlooked here, or maybe this is a naïve claim. However, if a collection of first principles calculations was able to match favorably to the currently available experimental results, one could conceivably and cheaply begin to catalogue the AB properties of a wide array of materials. This would be therefore immensely useful for chemists, biologist, etc for material selection and experimental design purposes. It would also eliminate the resistance of end-users from considering AB interactions in their calculations as they would finally be able to use them for their systems of interest.

3 Instructive Systems After reviewing the fundamentals, this Section elaborates several classes of instructive systems to articulate various aspects of LRIs. In Section 3.1, we discuss computation of optical spectra and Hamaker coefficients of complex bimolecular systems using SWCNT and B-DNA as two illustrative examples, followed by a discussion of DFT results on DNA based pair vdW interactions. Then, several illustrative examples of macromolecules and polyelectrolytes are presented, including anionic-cationic polyelectrolyte complexes, LRIs in polyelectrolytes, hydration interaction and ionic specificity, extraction/separation and phase transfer reactions, and surfactant decorated interfaces. In Section 3.2, impurity-based quasi-liquid films and space charges at solid interfaces are discussed; these two phenomena often co-exist and intermingle at the grain boundaries and surfaces of many structural and functional ceramics. Five additional

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classes of instructive systems related to aqueous solutions and suspensions, namely: premelting and related phenomena in ice and water, ion hydration, oxide/electrolyte interfaces, colloidal suspensions, and SWCNT hybrids, are discussed in Section 3.3.

Parts of the Section

"Harnessing LRIs" furthermore elaborate certain aspects of practical implications and technological importance of the instructive systems discussed in Section 3.2.1, Section 3.3.1and Section 3.3.4, respectively.

3.1 Atoms and Molecules 3.1.1 Optical Spectra and the Lifshitz Theory for Complex Biomolecular Systems The Lifshitz theory for quantifying vdW-Ld forces is reviewed in Section 2.1.2. For systems of high complexity and delicacy such as biomolecular membranes or proteins, experimental measurement of optical spectra using UVU at high frequency is not possible. On the other hand, although theoretical calculations of the optical spectra for such complicated systems are equally daunting, recent development in the computational methodologies and theory finally make such calculations feasible. Calculation of optical properties via ab initio theories has been discussed in Section 2.1.4. Here, we present two illustrative examples of SWCNTs and B-DNA and discuss challenges and opportunities. Several general computation issues are discussed here before presenting specific results. Optical properties calculation at the level of local density approximation (LDA) of the density functional theory (DFT) in the random phase approximation (RPA) seems to be adequate for this purpose as demonstrated in the case of ceramic crystals (French and Ching, unpublished) and SWCNTs (Rajter, Ching et al., 2007). It appears that higher level theory such as time-dependent density functional theory (TDDFT) or theories that include some aspects of many body corrections or self-interaction correction (SIC) may not be necessary. Still, there are several

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issues. First, it is necessary to make further approximations for geometrical shapes of real objects. For example, one may approximate small-radius SWCNT as a cylinder, or a bucky ball as a sphere, graphene as an infinite planar sheet, or biomembranes as plane-parallel blocks to make valid use of the analytic formula that have been derived. Second, in real situations, there could be several media involved. Additional approximations for averaging or mixing the dielectric functions that will be sufficiently realistic for the input in the calculation must be developed. Third, the actual calculation of optical dielectric functions for large complex biological systems such as DNA models or proteins in fluids is still computationally prohibitive. Further development in the computational codes and adequate computational resources are necessary.

3.1.1.1 Optical Properties of SWCNTs Computed Hamaker coefficients for two types of CNTs with gold in a water medium are shown in Figure 8. First, we look at the changes in the Hamaker coefficient with distance in the SWCNT-water-Au substrate system (Rajter et al., 2007).

This demonstrates the relative

magnitude differences that exist because small changes in chirality of the SWCNTs lead to big changes in the optical spectra. It also highlights the importance of the full spectrum. Glancing at the vdW-Ld spectra curves in Section 2.1.4, one might fall into the trap that the large low energy wing in the [9,3,m] would necessarily make the interaction much larger than for a semiconducting [6,5,s]. However the [6,5,s] has stronger interactions in the remainder of the summation in both the near and far limit formulations, leading to a stronger vdW-Ld interaction overall, as shown in Figure 8. The next effect that falls out is the orientation dependence of the Hamaker coefficient when interacting with another anisotropic material. In the far limit of the anisotropic solid

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cylinder-cylinder, we see an increase of the Hamaker coefficient by a factor of nearly 30%. Similar results were reported for the Al2O3 substrate-substrate system by Knowles (Knowles 2005), although to a lesser extent because the degree of anisotropy was less. Regardless of which situation is being described, the potential implications for design and manipulation of pieces during construction of nano-devices are real. As we move forward and incorporate the effects of a changing internal medium of the SWCNT core, as well as adding the effects of surfactant layers, etc, we believe additional effects will arise beyond what is shown here. Nevertheless this is an important foundation by which to start upon in our understanding of SWCNT and other nanoscale vdW-Ld interactions.

3.1.1.2 Optical properties of B-DNA Only very recently, ab initio optical properties of different models of B-DNA and collagen have been obtained using the DFT based orthogonalized linear combination of atomic orbital (OLCAO) method (Ching 1990). In these calculations, Na ions were added to the bare DNA model to neutralize the negatively charged PO4 groups from the DNA backbone. Figure 10 shows a 17-base pair b-DNA model used in such calculation. Without the compensating

counter ions, the self-consistent potential in the electronic structure calculation will not converge. Another calculation with a 5 base pair model with 318 atoms in the model, 8 Na+ as counter ions and 696 water molecules has also been completed, showing the presence of the water molecules essentially mediate the presence of Na+ ions with considerable changes to the optical spectrum. Figure 11 and Figure 12 show the calculated total density of states (TDOS) and the imaginary

part of the frequency-dependent dielectric function ε”(ω) of the model (Rulis, Liang and Ching, to be published).

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The above heavy calculations depend on several advantages of the OLCAO method used. First, the local orbital basis expansion keeps the total dimension of the Kohn-Sham equation at a manageable level of more than thousands of atoms. Second, the effective Gaussian representation in both the basis function and atom-centered potential functions facilitates the evaluation of multi-center integrals. Third, the inclusion of the optical matrix elements in the calculation for transitions up to high unoccupied states provides the needed accuracy at both the low and high frequencies limits. Finally, the ability to explore the inter-atomic, inter-molecular and intra-molecular bonding using the concept of partial density of states (PDOS) from different groups of atoms facilitates the interpretation of the calculated results. It is envisioned that the same approach can be used for calculating the theoretical optical spectra in other systems such colloidal suspensions, intergranular films (IGFs) in polycrystalline ceramics (Sections 3.2.1 and 4.1.2), interfacial models of different materials, etc to be used for quantitative estimation of the long range dispersive forces. Theoretical experiments can be designed to look into particular aspects of the interaction or the structure of the system.

3.1.1.3

Challenges and Opportunities

The above practical approach for calculating the vdW-Ld force faces several challenges: •

The limitations of various approximations involved must be carefully assessed. Will it be necessary to use more accurate DFT for the optical properties calculation?

•

Technical difficulties in the electronic structure and optical properties calculations (gap states, counterions, H2O etc.) should be overcome.

•

There is a critical need for realistic atomic-scale structural models for large biological molecules or complex microstructures in ceramics that can be used for ab initio electronic and optical properties calculations.

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•

In biological systems, we still have no idea in what way should the fluids and counter ions be included in the calculations of optical properties, or they should be treated as from different media.

•

How to approximate the shapes of biological entities in order to use the analytical formula derived for simple objects?

•

There should be bench marks for validations of the calculations. We need to ask what experimental data, if exit, can be collaborated with the calculations.

The opportunities of using the full spectrum approach to obtain quantitative results for the long range interaction forces are considerable. First, it makes the subject matter more quantitative and can be applied to real systems of great importance such as carbon nanotubes, colloidal suspensions, surfactants, interface models, B-DNA, proteins, collagen, etc. Second, it couples the state-of-the-art computational methodology with potential experiments to be designed, therefore contributes to the understanding of fundamental questions facing biologists. For example, what role the H-bonding plays in determining the long-range interaction forces? What types of biological entities (proteins, enzymes, macromolecules, membranes, etc.) can best exemplify the role of vdW-Ld forces in their experiments and how they can be measured? What will be the most ideal system to test and validate the optical spectral approach for the LRI? Can we model solvation forces and hydrophobic attraction in biological systems where other approaches may not be practical? It is also possible to design suitable theoretical experiments for long-range interactions in some simple model systems where laboratory experiments may not be feasible or expedient. Finally, it is truly interdisciplinary approach addressing important problems facing many areas of science and technology.

3.1.2 DFT Results on DNA Base Pair vdW Interactions In Section 2.1.5, we reviewed a number of recently developed methods for including the vdW-Ld interaction in electronic DFT. Prior to these developments, DFT had been generally Page 3.1.2—57 of 213

very successful in the description of dense matter and isolated molecules. The newer methods are beginning to extend this success to sparse matter, biological matter, and vdW molecular complexes, and thereby to systems where DFT with conventional functionals generally have failed. Some of these methods are highly empirical, while others are not.

Here we give an

illustrative example of the use of the non-empirical vdW density functional (vdW-DF) (Dion et al, 2004; Thonhauser et al., 2007) as applied to nucleic acid base pair steps (Cooper et al., 2008). The latter work considers Watson-Crick base pairs (see Figure 13) in a stacking geometry as illustrated in Figure 14. The work uses vdW-DF to calculate the interaction energy between the two components of each of the ten possible DNA base pair duplexes as a function of the so-called twist angle (see Figure 14) with the separation (rise) between each component being optimized. In this way one could determine whether the twist and of each step of a DNA polymer has its precursor within the properties of the isolated duplex step. By comparing the results with analyses (Olson et al., 2001) of high resolution crystalline data from the Nucleic Acid Database, the authors imply that on a broad scale, the answer to this question is yes. They find a mean twist of 34° ± 10°, where the ± sign indicates the standard deviation here arising from sequence dependence. The Olson et al. (2001) experimental database indicates a corresponding twist of 36° ± 7°. More detailed results from Cooper et al. (2008) are shown in Figure 15 for three steps which show revealing behavior. Simply said, base pairs gain on the order of 10 or more kcal/mol by stacking in an untwisted configuration, and typically gain several more kcal/mol by twisting by an amount of the same order of magnitude as found in high resolution studies of crystalline DNA. As for the sequence dependence of the twist, Cooper et al. (2008) point out

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that their results generally follow the trend variations of the databases, but with larger fluctuations. Not all the results are as simple as those in Figure 15.

Consider the results for the

AT:AT step, shown in Figure 16. Here the curve is very flat, with just a shallow minimum. In this case it is clear that this base pair stacking interaction is not going to have a large effect on the ultimate twist, which is more likely to be influenced by flanking pairs and the encircling phosphodiester strands, which were not included in the calculation. However, what causes the kink in the AT:AT curve in the vicinity of 20°? This can be understood by referring to Figure 14.

When the twist approaches 20°, a hydrogen on each methyl group of the thymine bases comes to its closest approach to the unsaturated nitrogen on the adjacent adenine (as indicated by the thin blue lines), as if to form an incipient hydrogen bond. The authors proved that this kink was a methyl effect by redoing the calculation with thymine replaced by uracil. The latter has thymine's methyl group simply replaced by a hydrogen termination, and is the nucleobase found in RNA in place of thymine. These results are also shown in Figure 16. The implication is clear: not only is the kink at around 20° missing, but the AU:AU curve has no minimum at all at any reasonable twist angle. Not only has the methyl group of thymine made this DNA step more stable in absolute terms than the corresponding RNA step, but has eliminated the propensity for this step to undergo gross overtwisting. In order to evaluate the accuracy of vdW-DF in the context of the calculations reviewed here, it would be useful to have fully converged quantum chemical calculations on the full duplexes that Cooper at al. (2008) studied. The current gold standard for such computational methods is a coupled cluster technique known by the abbreviation CCSD(T). This method has

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been extensively applied to smaller nucleic acid systems by Hobza and collaborators (Hobza and Sponer, 2002; Sponer et al, 2006). Unfortunately, the computational resources required increase as a high power of system size, and so far a direct application of CCSD(T) to systems of the size studied by Cooper et al. (2008) has proved unfeasible. However, in a recent work, Sponer et al. (2006) devised a partitioning approximation, which replaced the full calculation by a number of calculations on systems half the original size. By this method they found it feasible to compute a stacking energy at a single hypothetical twist angle of 36° for each of the ten possible base pair steps. A comparison between the CCSD(T) points in the partitioning approximation and the vdW-DF predictions is shown in Figure 17. The error in the partitioning approximation was estimated (Sponer et al, 2006) by using a smaller basis set. To simplify the discussion here, we simply state that the root mean square error over the ten steps was found to be less than one kcal/mol. A more complete comparison is contained in the Supporting Information for Cooper et al. (2008). From the above comparison one can conclude that vdW-DF is sufficiently accurate to obtain meaningful results for this type of problem. Combining this information with the fact that the scaling with system size for vdW-DF is no worse than for standard DFT suggests that vdWDF can be applied to systems that are significantly larger than those considered above, with reasonable confidence of obtaining valid predictions.

3.1.3 Macromolecules and Polyelectrolytes

3.1.3.1 Anionic-Cationic Polyelectrolyte Complexes Complexes of anionic and cationic polyelectrolytes can be obtained by simple mixing of dilute solutions, slow diffusion, and subsequent osmotic stress or, better, layer-by-layer deposition that creates polyelectrolyte complexes that can be dialyzed or ripened by heating. The

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resulting gels have been the subject of intense research over the past thirty years. Because these complexes are stable in the absence of net charge, i.e. when positive and negative charge compensate, LRIs are deeply involved in their stability (Miller et al., 2005). One striking point is that even at equimolar anionic and cationic components, these gels are highly "swollen": they contain anywhere between 70% and 20% of "residual" water, even without electrostatic forces, because the gels are globally neutral.

This swelling is the

combination of two effects: perfect pairing of chains would have a large cost in entropy and polyelectrolyte chains repel per se due to hydration forces between adjacent cylinders. In the absence of electrostatics, in these systems, the fast decaying hydration force becomes the dominating "long range" force. Systematic osmotic pressure, which does NOT vanish at electroneutrality, can indicate binding of excess counter-ion. This binding relates to partial dehydration of the counter-ion, and therefore follows the Hofmeister series. "Catanionics," i.e. mixtures of anionic and cationic surfactants, were studied due to their strange stability and phase diagram including a lamellar phase swelling even in the absence of net structural charge (Zemb et al. 2003). In the absence of excess salt formed by combination of the counter-ions of the surfactant used, the situation similar to the lamellar phase of zwitterionic lipids. In the case of catanionics, mechanism responsible for swelling could only be hydration force, since the osmotic pressure is the same on both sides of the chain melting transition, as was already noticed for other charged bilayers (Parsegian et al., 1991). So any mechanism of longrange repulsion related to molecular protrusion can be disregarded in these bilayers, as it was for synthetic lipids. The hydration force responsible for stability in the absence of excess salt can be studied in the "gel" state, when rigid hollow or flat crystalline colloids are formed. Stability of these

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colloids is linked again to the existence of hydration force extending over several nanometers between uncharged “hydrophilic” bilayers, since no precipitation is observed at equimolarity (Jokela et al., 1988). Unfortunately, these types of giant crystalline colloids are very sensitive to added salt. A central question is if the hydration force dominating in the last nanometer is itself depending on the chaotropic/cosmotropic nature of salt as suggested by Marčelja (Marčelja, 2000). This hypothesis could not be experimentally verified up to now. It seems however that water structure contribution ('hydration force') and the ionic contribution are approximately additive. The ionic part depends of course on the specific ion. The accuracy of the first order expansion, starting from the McMillan-Meyer formulation, has never been tested. Quantitative evaluations require accurate simulations. The existence of a critical point in binary lipid-water mixtures (Dubois et al, 1998) as well as the presence at one given temperature of two critical point occurring in the phase diagrams of ternary systems made with mixed glycolipids (Ricoul et al., 1998) could only be explained when two repulsive mechanisms are present: a shorter range hydration and a longer range electrostatics (Harries et al., 2006). This situation occurs typically in the presence of moles of salt. The osmotic pressure at the plateau of coexistence as well as the variation of this plateau with temperature is one of the most sensitive determination of the value of the contact pressure and decay length of the hydration force. The evolution of the plateau of pressure versus temperature is the unique case of direct determination of entropy cost associated to a transition between a condensed and a dilute lamellar phase (Dubois et al., 1998).

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3.1.3.2

LRIs in Polyelectrolyte Systems

In solutions of polyelectrolytes the electrostatic interactions acquires properties that are specifically related to the connectivity between charged segments along the polymer chain . This connectivity can often lead to a very peculiar interaction, where long charged polymers can mediate interactions between macroions of opposite charge. The term bridging interactions (Podgornik, 2004) is usually applied to this situation where a single chain can adsorb to different, two or more, macroions and via its connectivity mediate attractive interactions between them. This interaction can be either short ranged or long ranged (Podgornik and Saslow, 2005), depending on how many macromolecular counterions the chain spans. Polyelectrolyte bridging interaction is closely connected with correlation attraction in strongly charged system and there are indications, based on detailed simulation work, that there exists a continuity of states between correlation attraction and bridging interaction (Turesson et al. 2006). Polyelectrolyte bridging interactions have been observed experimentally in the case of polyacrylic acid (PAA) between mica surfaces (Abraham et al., 2001). Long-range bridging attractions showed up indirectly as a jump into a primary minimum located at small interface separations ~10 nm, followed by a repulsive regime closer in Abraham et al. (2004). The range of polymer-mediated interactions can usually be correlated with the size of the chain but can sometimes appear to be a lot longer (Bele et al., 2000). Polyelectrolyte bridging interaction has been also used in irreversible self-assembly of magnetic nanowires that open up the way to "macrocolloidal chemistry”. A fundamental role of polyelectrolyte bridging has been recently invoked in the context of interactions between nucleosomal core particles (NCPs) that make up the fundamental units of chromatin (Boroudjerdi et al., 2005). The anomalous (non-monotonic) behavior of the second

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virial coefficient of reconstituted NCPs in aqueous solutions as a function of salt was taken as an indication of short-ranged salt-dependent attractions between NCPs (Boroudjerdi et al., 2005). The first attempt to calculate explicitly the bridging interaction potential between two NCPs with polyelectrolyte tails was made by Podgornik (2003). Simulation of macroions with grafted polyelectrolyte tails showed explicitly how bridging interaction can indeed lead to nonmonotonicity in the second virial coefficient as a function of added monovalent salt (Muhlbacher et al., 2006). Molecular dynamics simulations with explicit counterions and salt ions have been performed by Korolev et al. (2006). The size, charge and distribution of the N-tails relative to the histone core were built to mimick real NCPs. These authors have been able to study the effects of monovalent as well as multivalent counterions that are strongly coupled to all the other charges in the system. They were also able to study more detailed mechanisms of the histone N-tail-DNA interactions and dynamics by performing all-atom molecular dynamics simulations (including water), comprised of three DNA 22-mers and 14 short fragments of the H4 histone tail (amino acids 5-12) carrying three positive charges on lysine(+) interacting with DNA. Polyelectrolyte bridging might also play an important role in the case of polyplexes: the complexes between DNA and polycations that are generally seen as promising systems for gene delivery (Podgornik et al. 2004).

The polycation-DNA complex forms spontaneously upon

mixing positively charged polymers, such as poly-arginine or poly-lysine, with negatively charged nucleic acids. The exact nature of long range interactions in these systems is not completely understood. The data do set limits that show inconsistency with several proposed ionic fluctuating models such as direct ionic bridging, ionic fluctuation, and vdW attraction balanced against hydration or electrostatic repulsion (DeRouchey et al., 2005).

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Though different from electrodynamic or electrostatic forces that fall within the purview of this review, the nm-scale correlation lengths of polymers at high concentration are also relevant to events that occur at surfaces and in small spaces, entropic nanoscale events with consequence for microscopic transport and assembly. Polymers such as neutral PEO/PEG can penetrate and even cross regions that are much smaller than their nominal radius of gyration (Bezrukov and Vodyanoy, 1994, Bezrukov et al., 1996), driven by their osmotic pressure in the bulk that can be effectively described by either the van’t Hoff or the des Clozeaux scaling regime (Cohen et al. 2007). It remains an open question why PEO/PEG in aqueous solutions can be at all described by the same scaling language as PAMS (poly-alpha methyl styrene) in toluene, the standard reference for polymer osmotic pressure scaling regimes.

3.1.3.3 Hydration Interaction and Ionic Specificity We focus here on aspects of phase stability of surfactant solutions or colloidal microcrystals when stability, coexistence or swelling is due to a hydration force, and is not of immediate electrostatic origin. In such situations, the absence of an identified “electrostatic effect” such as link between Debye lengths and phase limits is either due to the absence of charge, or to an effect independent of the presence of added salt. It may seem paradoxical to attribute “long range” to the hydration force. This force is “long" versus hydrogen bonding, complexation and other nearest neighbor interactions considered in chemistry of colloids. For good model systems in the absence of salt, the hydration force can only be detected via osmotic pressure as low as few hundred Pa and typical distances between surfactant aggregates of up to ten nanometers. Compared to ultra-long range of electrostatics in the absence of screening, hydration force is short range. Combination of hydration force and electrostatics is the source of several interesting behaviors of surfactants systems, which can only be explained if hydration is

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considered as a fundamental repulsive mechanism which can be dominant in the absence of structural charge: experiments about mixing anionic and cationic components, producing colloidal aggregates of known charge, play here a crucial role. The distance dependence characterizing exclusion of small solutes from macromolecular surfaces follows the same exponential behavior as the hydration force between macromolecules at close spacings. Very similar repulsive forces are seen for the exclusion of nonpolar alcohols from highly charged DNA and of salts and small polar solutes from hydrophobically modified cellulose. Exclusion magnitudes for different salts follow the Hofmeister series that has long been thought connected to water structuring (Todd et al, 2008). One thing that one notes here is the intriguing connection with the distributions of salts in thin liquid films on ice. The connection between hydration effects in water and the Bjerrum defect distribution in ice has been noted before (Gruen and Marelja, 1983) and is due to the structuring of water molecules close to macroscopic surfaces. In ice this is described by a redistribution of orientational Bjerrum defects, whereas in water it is usually discussed within water solvation or hydration models. In both cases however, ion redistribution couples with hydration patterns. Solvation of interacting macromolecular surfaces and modulation of this solvation by cosolutes such as salts exquisitely regulates equilibria of specific association in chemistry and biology. Depending on whether the cosolute is preferentially excluded from, or attracted to, the surfaces of the macromolecules, a cosolute can either increase or decrease complex stability. However, the dynamic action of cosolute on complexation is yet not understood, and there is no way to predict which kinetic constant, the "on-rate" or the "off-rate" is impacted.

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A decade ago "molecular Coulter counting" demonstrated that a single protein nanopore could be used to detect polymer exchange between pore and bulk, a demonstration that stimulated modern development of nano-sensors (Bezrukov et al., 1994). This same method also allows one to address the dynamic side of preferential solvation. Using an alpha-hemolysin nanopore as a sensor, it is possible to follow the effect of solutes on a simple complexation reaction at the single-molecule level (Gu et al., 1999). Monitoring transient obstruction of current through a nanopore complex reveals the kinetics underlying the reaction equilibrium in the presence of various cosolute salts. Measurements with alpha-hemolysin progressively blocked by cyclodextrin and adamantane reveal changes in on-rates as well as off-rates, depending on the type of salt used. Chloride and bromide salts mainly impact the off-rates; sulfate changes on-rate -- qualitatively different dynamic action of different cosolutes (Harries et al., submitted, 2008).

3.1.3.4 Extraction, Separation and Phase Transfer Reactions Liquid-liquid phase transfer of metals in the form of ions is a crucial step in re-processing nuclear fuel, allowing to close the nuclear fuel cycle. Currently available technologies rely in vast majority on “hydro-metallurgy”, i.e. on liquid-liquid extraction: A concentrated ionic solution is contacted with a formulated “solvent phase” with selective properties and possibilities of controlling extraction/de-extraction via pH or oxidation state. The oldest process uses a triple chain weak surfactant, the tributyl phosphate in acidic form. It was suggested since a long time that this type of amphilipilic selective extractant molecule self-assembles (Osseo-Asare, 1991) in the form of reverse micelles, alias water in oil microemulsion at low water content. The small aggregates of less than ten molecules responsible for the selective extraction were detected directly for the first time using high sensitivity small angle scattering combining X-rays and neutrons. Neutrons evidence the whole without aggregate

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while X-rays are sensitive to the “polar core” of less than 1 nm radius of the aggregates used in the nuclear fuel cycle as well as in industrial purification/extraction of lathanides (Erlinger, 1999). So-called “third phase” instability known by chemical engineers in the field of extraction is similar in nature to the liquid-gas transition known in the field of microemulsion, when a concentrated W/O micellar solution is in equilibrium with a diluted one (Vollmer, 1994). The existence and localization of the position of the critical point in the phase diagram has demonstrated the predominance of vdW which is in this case – as compared to complexation of ion with the phosphate group – a “long range” interaction in phase separation of this dispersion of water nanodroplets covered by extracting molecules (Nave et al, 2004). Further, the extracting process involves the cations, associated anions as well as coextracted water. All these species are confined in a dehydrated form in the polar core of w/o micelles formed. Using series of homologue acids, it has been proven that the Hofmeister series (Collins K D, 2004) of the anion involved in the co-extraction process profoundly influences the efficiency and selectivity of the extraction as well as the overall stability of the dispersion of reverse micelles involved in the process (Testard et al., 2007). In such reactions reagents in two immiscible phases (either two liquids or a liquid and a solid) meet at an interphase between these two immiscible materials and react together. This meeting is allowed by the action of what are termed phase transfer catalysis. These materials either extract monovalent anions (eg hydroxide, bromide, alkylsulfide) to an interphase employing large cations (eg tetrabutylammonium) or extract these anions to an interphase by complexing alkali metals (e.g., 18-crown-6) to form a larger cation species whose charge density allows it to achieve a high concentration at the interphase.

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3.1.3.5 Liquid-Liquid Interfaces at Microscopic Scale Decorated by Surfactants Interfaces In the case of ionic micelles in water, long-range interactions influence the “depletion” of monomers in equilibrium with micelles. With a typical aggregation number of ~20-200, the approximation that monomer concentration is equal to the critical micellar concentration usually holds within experimental precision, classically a few percent using radioactive tracers or liquid state NMR relaxation or peak shifts. However, in the case of short ionic surfactants, such as sodium octanoate, the concentration of monomers in equilibrium with micelles has been shown to be lower than the critical micellar concentration (Lindman et al, 1984). After this unexpected result has been established for the first time, this effect could be consistently attributed using the pseudo-phase approach: charged dissociated monomers in solution are in dynamic equilibrium with surfactants inserted in micelles, typically on a nanosecond scale. Hence, chemical potential of surfactants in monomeric form and in micelles need to be equal. Since ionic micelles interact via unscreened long-range electrostatics in the absence of salt, the monomers, as co-ions of the micelles, are depleted from the “solvent” pseudo-phase and can be noticeably different from the “cmc”. This effect has to be taken into account when X-ray or neutron scattering experiments are interpreted using absolute values of the scattering cross-section in order to obtain independently the aggregation numbers and the osmotic compressibility of micelles , for example as a function of surface charge set by pH of surfactants bearing phosphate head-groups (Chevalier et al., 1985).

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3.2 Interfaces, Surfaces and Defects in Solids 3.2.1 Impurity-Based Quasi-Liquid Surficial and Interfacial Films Nanoscale, impurity-based, quasi-liquid interfacial films of similar character have been found in an increasing number of different material systems and configurations [Figure 21; see a recent review (Luo, 2007) and references therein], including: •

silicate-based intergranular films (IGFs) in Si3N4, SiC and several oxides (where SiO2 additive was once considered essential to stabilize such nanoscale IGFs),

•

IGFs in ZnO-Bi2O3 and (Sr, Ba)TiO3, where SiO2 is not involved,

•

IGFs at oxide-oxide hetero-interfaces,

•

SiO2-enriched IGFs at metal-oxide interfaces,

•

analogous IGFs in metal systems, e.g., Ni-doped W, and

•

surficial amorphous films (SAFs).

These intergranular or surficial films are often referred to as glassy or amorphous films despite the existence of partial structural order within them. Systematical data have been collected for several SAF systems, namely Bi2O3 on ZnO (Luo and Chiang 2000; Luo, Chiang and Cannon 2005), VOx on TiO2 (Qian and Luo, 2007) and SiOx on Si (Tang et al., 2008), where film stability and thickness have been measured as functions of temperature and composition (or dopant activities). Thus, they can be considered as "instructive systems" to illustrate the thermodynamic stability of the aforementioned broader class of interfacial films (Luo, 2007). The experimental observations and thermodynamic models for SAFs in two analogous binary oxide systems (Bi2O3 on ZnO and VOx on TiO2) have recently been reviewed (Luo and

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Chiang, 2008) and are briefly discussed here as illustrative examples. In both systems, the equilibrium film thickness was found to decrease monotonically with decreasing temperature in the subeutectic regimes. Furthermore, dewetting transitions (from a nanoscale SAF to Langmuir submonolayer adsorption) were observed at lower temperatures in both systems; a hysteresis loop in film thickness versus temperature curve was also observed for VOx on TiO2, which is an indication (but not a proof) for the existence of a first-order monolayer-to-multilayer adsorption transition.

Premelting like force-balance models (with the volumetric free energy penalty for

forming undercooled liquids being the dominating attractive force) predicted subeutectic SAF stability and thickness that agree with experiments for both systems (Luo, Tang, et al., 2006; Qian and Luo, 2007), suggesting an analogy between the stabilization of subeutectic quasi-liquid SAFs in these binary systems and premelting in unary systems (the latter is discussed in Section 3.3.1). For Bi2O3 on ZnO, SAFs of similar character were also observed in single-phase ZnO samples containing Bi2O3 concentrations below the bulk solid-solubility limits, where the films are thinner. For Bi2O3 on ZnO, nanometer-thick SAFs persist into solid-liquid coexistence regime, in equilibrium with partial-wetting drops (Luo and Chiang 2000; Luo, Chiang and Cannon 2005; Qian, Luo and Chiang, 2008Error! Reference source not found.), where an analogy to the phenomena of frustrated-complete wetting (Bertrand, Dobbs et al. 2000) and pseudo-partial wetting (Brochard-Wyart, di Meglio et al. 1991) can be made. The average SAF composition is markedly different from the associated bulk liquid phase (Luo and Chiang, 2000), even when these quasi-liquid SAFs are in thermodynamic equilibration with the bulk liquid phase (Luo and Chiang 2000).

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In a diffuse-interface theory (Luo, Tang et al., 2006), these SAFs are alternatively considered as multilayer adsorbates formed from coupled prewetting and premelting transitions. For Bi2O3 on the ZnO {11 2 0} surfaces where nanometer-thick SAFs are present in equilibrium with partial wetting drops, the measured contact angle decreases with increasing temperature in the solid-liquid co-existence regime (Qian, Luo et al. 2008).

In contrast, with increasing

temperatures, the contact angle is virtually a constant on the {1 1 00} surfaces where SAFs are not present. This observation suggests that wetting in the presence of nanoscale SAFs follows a generalized Cahn wetting model (Cahn, 1977).

However, an expected complete wetting

transition is inhibited by the presence of an attractive vdW-Ld force of significant strength (Qian, Luo and Chiang, 2008). The technological importance of the nanoscale intergranular and surficial films in ceramics and metals is further discussed in Section 4.1.2.

3.2.2 Charged Defects in Solids As a second illustrative example related to solid surfaces and interfaces, space charges related to interfacial segregation of charged defects are discussed here. This is an issue of practical importance for many technological ceramics, where the space charges can often coexist and interact with IGF or SAF formation (which is discussed in the previous section and further elaborated in Section 4.1.2). Analogous space charges effects are present at both internal interfaces (such as grain boundaries) and free surfaces. While their individual energies can be calculated by DFT and the LDA, charged defects present several technical challenges because of their long-range electrostatic interactions. One in particular is worth describing here. It is frequently observed by electron microscopy that interfaces in ceramics are charged, and these charges are compensated by space charges, in the Page 3.2.2—72 of 213

form of screening distributions of electrons or other mobile charged species. Such space charges are expected to have a profound effect on the electronic conductivity and capacitance of boundaries, but their occurrence and extent is unpredictable. The difficulty in understanding and therefore predicting the occurrence of such space charges lies in the length scales involved. The segregation of charged species to the boundary can only be understood at the atomic level, it depends on the details of the atomic structure of the boundary, and atomic scale calculations are necessary to predict the segregation energy. On the other hand, space charges may extend over a length scale up to microns. This is far too big for an atomistic description, and the appropriate physics in this regime is described by a continuum approach, embodied in the PoissonBoltzmann equation. An example of setting up and solving the Poisson-Bolzmann equation was given in a study of the energy of a system of mobile charges within an IGF (Johnston and Finnis, 2002). Consider a planar boundary in the y − z plane. We suppose it somehow lowers its energy by picking up a charge σ per unit area. By how much is the energy lowered? We can imagine this as a two stage process. In the absence of a space charge, and omitting electrostatic selfenergy of the segregated charge (which would be infinite in the absence of compensation) it would cost a chemical energy of segregation E seg to move the charge carriers to the boundary, which must be a negative energy. Then a space charge, consisting in general of positive and/or negative mobile carriers of density n + and n − develops to compensate the boundary charge. These carriers have charges q + and q− . The distribution of the carriers as a function of x in the continuum approximation can be obtained by solving the Poisson-Boltzmann equation. Within the simplest classical density functional theory, assuming the carrier densities are low and linearizing the Poisson-Boltzmann equation, the boundary energy would be lowered by

Page 3.2.2—73 of 213

Equation 26.

∆γ (equil) = Eseg + 12 VH (0)σ − 12

∫

∞ 0

(n + (x)q + + n − (x)q− )VH (x)dx .

This simple example illustrates how the chemical segregation term is modified by the entropy and separation energy of charged defects. The approach is readily generalized to include the classical correlation energy of the carriers. However, computational strategy for welding the continuum Poisson-Boltzmann equation onto the discrete atomic sites at a boundary that are available for segregation has yet to be established.

3.3 Solid/Liquid Interfaces and Suspensions 3.3.1 Water and Ice This section uses water and ice as an example to illustrate the effects of LRIs. Here, one phenomenon of crucial importance is premelting or surface melting, which can occur at ice surfaces, grain boundaries, and interfaces with inert walls, with significant geophysical and ecological implications. Furthermore, ice and water can also be used as an instructive system to understand analogous, but usually more complex, interfacial behaviors in multicomponent ceramics and metals, e.g., the impurity-based quasi-liquid surficial and interfacial films discussed in Sections 3.2.1 and 4.1.2. Premelting dynamics and its implications are further discussed in Section 4.1.3. Lifshitz theory has had remarkable success in predicting the nature of the surface melting or premelting of many materials (Dash et al. 2006). Of special interest here is ice because of the novel influence of the retardation effects responsible for the change from complete to incomplete surface melting. This is because as described before retardation effects attenuate the LRIs that are driving the film growth (Elbaum and Schick, 1991; Wilen et al, 1995). The basic idea is as follows. When the polarizability of the substrate is greater than that of the film, wetting occurs. Therefore, when dispersion forces dominate, the wetting of the ice by water at temperatures

Page 3.3.1—74 of 213

below Tm will be driven when the polarizability of the water lies between that of the ice and the other material (vapor phase or chemically inert solid). However, the net wetting forces depend on the entire frequency spectrum that underlies the polarizability of the system. The novelty of the ice/water system, first pointed out by Stranski (1942), is that the polarizability of ice is greater than that of water at frequencies higher than the ultraviolet whereas it is smaller at lower frequencies. Therefore, while the surface melted layer of water is thin, the polarizabilities at all frequencies contribute to drive surface melting. However, when the film thickens the finite speed of light attenuates the wetting forces by favoring those in which the polarizability of water dominates over that of the ice. Hence, the self attraction of the water begins to dominate and the film of water on ice stops growing. Details of these effects will be elaborated here. Here we also noted the more familiar mechanisms associated with the extension of the equilibrium domain of the liquid phase into the solid region of the bulk phase diagram; GibbsThomson and Colligative effects. Cumulatively we refer to these effects as premelting. Premelting phenomena characterize the equilibrium structure of the material. As noted above, a thorough review of all of the premelting phenomena observed in ice and other materials has been recently reviewed (Dash et al. 2006) and hence here we describe the basic tenets of this aqueous system as they may apply to materials of interest across a range of disciplines.

3.3.1.1 The Phase Architecture of Ice: Veins, Nodes, Trijunctions and Grain Boundaries Naturally occurring polycrystalline ice holds much in common with all polycrystalline materials but with some distinct advantages. It is transparent, optically birefringent, can be easily doped and can be held near its local melting point without sophisticated cryogenic systems. Like all materials held sufficiently close to their bulk melting points, ice is not entirely

Page 3.3.1—75 of 213

solid. Ice has a phase geometry that is characterized by a closely packed hexagonal crystal structure, interlaced with liquid films threading through its volume. Where three ice grains come together a thin liquid vein exists, and where four grains join a node of liquid water forms (Figure 22).

The mechanisms responsible for this liquid water are the Gibbs-Thomson and Colligative effects.

While seen here on the scale accessible with an optical microscope there is a finite

dihedral angle, but a probe that can penetrate into the grain boundary on a finer scale can assess the conditions under which a film between two grain boundaries, grain boundary premelting, may exist. Namely, moving away from the veins and nodes into the planar interface between two grains the interfacial curvature effects disappear and the existence of liquid, if present, depends on long-ranged intermolecular and electrostatic forces. Here, specific models of electrostatic interactions, modeled for example using Poisson-Boltzman theory, can compete admirably with than the vdW attraction; they are required for a complete study of grain boundary melting (Benatov and Wettlaufer, 2004). Therein it was shown that when the film contains an electroyte, the solid grains may be held apart by repulsive screened Coulomb interactions against the attractive interactions of dispersion forces, but the latter must be taken out to their full range using Lifshitz theory to insure that the longest range behavior is captured. In a gedanken experiment Benatov and Wettlaufer (2004) doped the grain boundary with a monovalent electrolyte; NaCl. Due to the fact that missing bonds at any ice surface give rise to an increase in the Bjerrum defect density they treated the surface as having a finite charge density screened in a manner that depends on the number density of impurity ions. Hence, the detailed consequences rely on a correct treatment of the frequency dependent dispersion forces and the peculiar functional dependence of the range and amplitude of the repulsive Coulomb

Page 3.3.1—76 of 213

interaction on the dopant concentration.

In such circumstances, researchers in colloid and

interface science typically treat the Debye length to be constant, and their systems this is well justified and it is experimentally realizable. Here, in the case of grain boundary premelting (and indeed surface melting) it is not necessarily realizable. Due to the nearly perfect rejection of salt from the ice lattice the electrolyte remains in the film and thus an increase (decrease) in film thickness is accommodated by melting (freezing) of the solid so that, up to the solubility limit, the dopant level is simply inversely proportional to the film volume. Hence, when the film thins at low temperatures the impurity concentration in the film increases and the Debye length decreases through the impurity effect. The novelty then is that the Debye length, and the amplitude and range of he Coulomb interaction, are themselves a function of temperature through the dilution/concentration of the film. This influences the abruptness of the transition from premelted to dry grain boundaries. In the surface melting of ice, this same confluence of effects is at play (Wettlaufer, 1999) and is the most likely explanation of the wide spread of experimental data across laboratories that use the same methodology (Dash et al. 2006).

3.3.1.2 Optical Properties of Ice and Water As has been described previously in this article, the finite travel time of the photon is manifested in the incomplete surface melting of ice against a pure vapor phase. The origin is in the frequency dependence of the polarizabilities of water and ice. Two enormously important tasks lay before the community. Firstly, we need to develop novel and quantitatively accurate methodologies to refine and expand our experimental understanding of these data. At present, we must use limited spectra from a variety of sources to fit the data to a damped oscillator model (Dash et al., 2006). Whereas, in UHV systems, full spectra are much more simply obtained, we need full spectra for these high vapor pressure materials using modern methods. This will be

Page 3.3.1—77 of 213

impeded by the possibility that the spectra themselves differ in an interfacial environment in which they are ultimately of interest whereas they may be more easily obtained in bulk samples. It is essential to overcome such impediments if we are to understand the phase behavior not only of ice and water but mixtures across all manner of colloidal and engineering materials.

3.3.1.3 Geophysical, Ecological and Astrobiological Implications Ice formed rapidly from solution, such as occurs in the polar seas during the formation of sea ice, experiences a range of instabilities involving, molecular diffusion, hydrodynamics (external and internal flows of brine) and crystallization, and these conspire to create a complex material with the liquid phase throughout (Figure 24). The interaction of competing instabilities results in the formation of liquid regions within the ice matrix that exist on many length scales. We understand that many of these processes are intrinsic to the dynamics of all solidifying allow systems and hence occur in a host of different materials (Feltham et al, 2006). Hence, there is a generality to their physical description. There are internal processes, such as buoyancy driven convection within the pore space (Wettlaufer, 1997) and there are external processes that couple to these, such as shear flows adjacent to the ice (Feltham et al, 2006; Neufeld, 2007). There are important geophysical, biological and ecological reasons to study these phenomena. Earth's climate is strongly influenced by the extent of the global ice cover, and these physical processes influence polar ocean ecology. Not only is the issue at the heart of the food web in Earth’s Oceans, but it also serves as a test bed for Astrobiology and Life in Extreme Environments. Because some 13% of the surface area of the ocean surface is seasonally ice covered the ice cover as a whole comprises a complex ecosystem, it is of a size that exceeds deserts, grasslands or tundra (Lizotte, 2001). Considered in its entirely, the sea ice ecosystem includes (i) bacteria, algae and protists (microbes), (ii) crustaceans, worms (small metazoans),

Page 3.3.1—78 of 213

(iii) fish and zooplankton (mobile grazers), (iii) birds, seals and polar bears (large vertebrates). Due to the fact that the liquid phase forms a spatial network that spans many orders of magnitude, depending on the thermodynamic conditions of growth between a few and twenty percent of the total sea ice volume consists of a connected network of brine. This translates into an interior surface area of up to 4 m2 kg-1 (Krembs et al, 2000). The importance of the liquid system is that it serves as habitat for sympagic communities which are cold adapted groups of organisms including viruses, bacteria, autotrophic and heterotrophic protists and metazoan (Meiners et al, 2002). These organisms are adapted to the extreme environmental conditions of sea ice brine and can use the brine channel walls as sites of locomotion, attachment and grazing. Finally, it is found that the blood of many cold-adapted living organisms contains anti-freeze proteins (AFPs). A range of AFPs are known to be produced by insects and fish, but have been most extensively studied in polar fish, where they extend the thermal habitability of the fishes into a low temperature regime. They have also been developed by a wide range of insect, plants, bacteri, fungi, as well as vertebrates. Thus, although there are few unifying principals for AFP structure itself, which is known because comparison of the DNA sequences that code for these proteins shows that they developed separately (Chen et al, 1997), their function is the same across all organisms. However, their function in keeping ice from embodying an organism intimately involves the effects of long range interactions in all of their manifestations as described in this article. Dispersion forces and solute effects in a dynamic environment are at the heart of how the protein interacts with a dynamic surface (Pertaya et al., 2007; 2007b) and we are just now at a point where these effects can be combined to build a predictive framework for their biological efficacy.

Page 3.3.1—79 of 213

3.3.2 Hydration The ability to predict the properties of solutes in liquid water is a pre-requisite for rationally guiding nanoscale processes in aqueous media, continues to challenge our imagination. Since the earliest realistic simulation of liquid water (Rahman and Stillinger, 1971), computer simulations have proven to be vital complements to experiments in understanding the phenomena of hydration. For simulation studies of hydration, the most common target is the ex

excess free energy of hydration, µ . The excess free energy is the reversible work done to transfer a solute from some phase (typically the vapor) into liquid water. This important quantity directly informs us about solubility of the solute and with minor extensions to interaction of the solute with other solutes and interfaces. Most simulation approaches to interrogate hydration derive from the coupling parameter approach introduced originally by Kirkwood (1935). In this approach, the work done in transferring from, say, vapor to liquid water is computed by the work done in slowly transforming a point solute (in liquid water) to the solute with all interactions involved. The Born model of hydration of ions and the Debye-Hückel and Poisson-Boltzmann approaches (cf. Section 2.2.2) provide transparent instances of this approach. An alternative route to computing excess free energies is founded on perturbative approaches (Zwanzig, 1954). For example, to describe the hydration of argon in water we assume that the aqueous phase properties of a hard-sphere reference solute the size of argon is known. The effects of the attraction between the argon solute and water is then included via perturbative corrections to the excess free energy of the hard-sphere in water. Of course, the predictions are only as good as the reference adopted. For simple solutes, such as those that interact with water weakly, this is usually not a problem.

Page 3.3.2—80 of 213

Though the original perturbative ideas were developed for weak coupling (beyond the reference state), this technique can be used to study hydration of solutes that interact strongly +

+

with water. For example, the difference in hydration free energy of Na (aq) and K (aq) is of much interest in the study of ion-channels (Asthagiri et al, 2006). In perturbative or coupling parameter approaches, this free energy change is calculated by introducing many artificial states +

+

X intermediate in properties between Na (aq) and K (aq). Thus i

Equation 27 Na + → X 1 → ... X i ... → K + +

+

Thus X (aq) is only slightly different from Na (aq), such that Na (aq) is a useful reference 1

system and so on. Then the free energy changes between X and X i

+

i±1

is estimated and the net

+

change between Na and K assessed. (Note that in the limit of a continuum of X, we recover the coupling parameter approach.) Such techniques have greatly advanced and these developments are summarized in recent book edited by Chipot and Pohorille (2007). Though the above techniques are by now standard lore in computer simulation studies of hydration, in an era of increasing sophistication of simulations including ab initio approaches (cf. Section 2.1.6), the above approaches are neither physically revealing nor readily applicable. For example, if intermolecular potentials from an ab initio calculation are desired, then no real chemical object corresponds to X . Quantum chemistry can provide us information only about i

+

+

how Na and K interact with water. In the past decade or so, a new theoretical approach has been advanced based on the insight that the distribution of potential a solute feels in a solvent can be parsed on the basis of local chemical structures (see, e.g., Ch. 9 in Chipot and Pohorille (2007). These quasi-chemical generalizations of the potential distribution provide a clear theoretical scaffold to interrogate

Page 3.3.2—81 of 213

problems such as the one discussed above. These techniques have revealed interesting insights about hydrophobic and hydrophilic hydration. Here, a quasi-chemical approach to hydration is briefly discussed: +

For concreteness, consider water molecules around Na (aq) as the ion-water system samples numerous configurations. Define a neighborhood around the ion. This definition achieves two things: (1) a separation of strong ion-water interaction within the inner shell (Asthagiri et al, 2003) from the less strong long-range interactions, and (2) a way to track the number n of water molecules coordinating the ion. The populations immediately give us the +

fraction x of cases where Na has n water molecules. x is the case with no inner shell water n

0

molecules. Let W be the reversible work done to vacate the inner shell of water molecules. But by standard results in statistical mechanics x =e 0

+

-W/k T B

. T is the temperature of the system. If the

ex

+

hydration free energy of Na[H O]0 is µouter, then the hydration free energy of Na is given by 2 ex

ex

µ =-W+µouter. All the fractions x are related, because at equilibrium we have n

Equation 28:

Na[H 2 O]0+ + nH 2 O ⇔ Na[H 2 O]+n

A mass balance immediately gives Equation 29:

x0 =

1 1 + ∑ Km ρ m

,

m ≥1

where K is the equilibrium constant for the above chemical reaction and ρ is the density of m

water. Thus we have

Page 3.3.2—82 of 213

Equation 30:

W = k BT (1 + ∑ K m ρ m ) m ≥1

The basis for W in reaction equilibrium constants gives the name ‘quasi-chemical’. Typically the equilibrium constants are computed using standard quantum chemical packages. Thus chemical detail is readily included in the model. (In the primitive quasi-chemical approach developed here, these equilibrium constants are obtained ignoring the effect of the medium outside the inner ex

shell.) µouter includes the effects of the longer-range interaction between the ion and the medium outside the inner shell and can be described by simpler models, such as those using either classical potentials or continuum dielectric approaches. With these two pieces, one can readily ex

compose µ . Several features of the above development are noteworthy. First, µ

ex

is transparently

linked to the hydration structures that the solute forms. In fact the theory allows prediction of the most optimal hydration structures. In the cases of hydration of ions with high charge-density, these predictions have been supported by results based on ab initio molecular dynamics simulations (Asthagiri et al, 2005). Second we avoid all considerations of intermediate states that are not physically realizable. Lastly it is possible to study directly configurations resulting from an ab initio simulation, i.e. avoiding the mixing of ab initio and classical types of treatment above. So far for reasons of computational cost this has been done only for a classical model of liquid water (Paliwal et al., 2006). The hydration structures predicted by the primitive quasichemical approach are in good accord with hydration structures observed in ab initio simulations. Further prospects are discussed as follows. A clear understanding of the hydration of various ions and their role in biological structures and long-range interactions in biological self-

Page 3.3.2—83 of 213

assembly is still elusive, despite the fact that over a century has transpired since the first identification of these effects (Kunz et al, 2004). Whereas ab initio simulations of ions in water can provide chemical insights, they are still much too expensive for large-scale simulations. An interesting development in the area of simulations has been the use of classical potentials that attempt to include polarization [see, e.g., Grossfield et al. (2003)]. Such polarization effects have been shown to be very important in how ions partition near an air-water interface (Jungwirth and Tobias, 2006). These simulation efforts can be complemented by the theoretical directions laid out above and these can begin to better illuminate specific ion effects and thus also hydration in nanoscale science.

3.3.3 Structure and Dynamics at Oxide/Electrolyte Interfaces The interface between oxides and aqueous solutions controls ionic and molecular adsorption (and thus contaminant transport), mineral dissolution/precipitation kinetics, corrosion rates, heterogeneous catalysis, nutrient and energy supply to bacterial communities, chargetransfer processes, and in deep subsurface settings, fracture propagation and hydrous melt formation. Crystalline phases with oxygen as the dominant anion (oxides, silicates, carbonates, phosphates, etc.) are ubiquitous in natural and industrial environments (Brown, 1999). In the Earth’s crust and in many industrial settings, such as nuclear and fossil power plants and an enormous range of chemical and materials industries, interactions between liquid aqueous electrolytes

and

oxide

surfaces,

over

wide

ranges

of

temperature,

pressure

and

chemical/mineralogical composition, are the dominant processes controlling mass transport, solution chemistry and mineral transformations. In many natural and industrial systems, nothing interesting happens before aqueous solutions come in contact with solid surfaces, and the rates of

Page 3.3.3—84 of 213

fluid-fluxed reactions are so much greater than anhydrous processes, that they completely dominate such subjects as geochemistry and corrosion science. There is no more fundamental process at oxide/water interfaces than the charging of the surface and the structuring of the adjacent fluid phase due to the undercoordination of atoms at the crystal termination. Typically, when oxide surfaces come in contact with water, monovalent cations are rapidly leached and multivalent cations immediately react with water to produce a surface that is completely covered with variably-protonated oxygens bonded to underlying metal ions of the bulk crystal. Commonly this process is modeled using hypothetical reactions such as the “two-pK” model (Stumm, 1992): Equation 31: >SO- + H+ ⇔ >SOH0 KH1 = {>SOH0}/({H+}{>SO-}] Equation 32: >SOH0 + H+ ⇔ >SOH2+ KH2 = {>SOH2+}/({H+}{>SOH0}] where >S is a generic surface site. Here the critical role of water dissociation to supply H+ is

apparent. The solution pH can often be considered the master variable in aqueous processes and the pH at which oxide surfaces have equal concentrations of negatively and positively charged surface sites, referred to as the pHpzc or just PZC - ‘point of zero charge” (Sposito, 1998), is a fundamental parameter, obtainable directly from pH titrations with careful mass and charge balance. For the generic two-pK surface protonation scheme, pHpzc ≡ PZC = ½(logKH1 + logKH2), which perhaps explains its popularity. Another fundamental variable is the ‘zeta potential’ (ZP) measured by electrokinetic methods such as electrophoresis or streaming potential. The pH at which ZP = 0 is referred to as the isoelectric point (pHiep or simply IEP). For (‘indifferent’) electrolytes whose cations and anions interact nearly equally with the surface, IEP ≈ PZC. The exact meaning of ZP is however, more ambiguous and highly model-dependent (Hunter, 1989, Knecht et al., 2008).

In recent years, new experimental approaches have been

developed to determine zeta potential, surface charge density and PZC’s for a number of oxides

Page 3.3.3—85 of 213

at temperatures above 100 °C (Wesolowski et al., 2000; Machesky et al., 2001, Zhou et al., 2003; Fedkin et al., 2003). The surface charge density at pH’s other than the PZC is governed by the site densities of the surface species and the screening of surface charge build-up by water dipoles and charged, polar and/or polarizable species in the solution. Electrostatic screening effects are taken into consideration by any of a number of parallel-plate capacitor-type models of the ‘electrical double layer’ or EDL (Israelachvili, 1992).However, very few real oxides (with the notable exception of quartz and other crystalline and amorphous forms of silica) exhibit surfaces characterized by the simple stoichiometry of reactions Equation 31 and Equation 32. Rather, most oxide and silicate surfaces are characterized by oxygens bonded to as many as 3 or 4 underlying metal cations and these can be dissimilar cations with formal valencies ranging from 1 to 5 or more (Koretsky et al., 1998). Furthermore, the activity coefficients of surface sites are typically assumed to be unity and equated to their volume or mass concentration or mole fraction, ignoring steric and electrostatic attractive or repulsive forces that might alter their thermodynamic concentrations (Sverjensky, 2003). A major advance in predicting the surface charging process has been the development of the ‘MUSIC’ or multi-site-complexation model (Hiemstra et al, 1996), which applies the Pauling bond-valence principle to calculate the unsatisfied valence of oxygens in specific bonding configurations on oxide surfaces, and incorporates hydrogen bonding with sorbed water molecules to provide a truly predictive capability for estimating surface site densities, PCZ’s and the protonation states of individual surface sites. The protonation constant for an individual surface oxygen in this approach depends on its local bonding environment and is defined as Equation 33:

Page 3.3.3—86 of 213

logKH = -A(V + ΣsMeO + m(sH) + n(1-sH))

where V is the formal valence of oxygen (-2), the summation totals the bond valence contribution to the oxygen from all metal ions of the substrate bonded to the surface oxygen (a function of bond length and charge of the cation), m is the number of donating H-bonds from adsorbed water molecules, n is the number of H-bonds contributed by any hydrogen directly bonded to the surface oxygen to adsorbed water molecules, and sH is the assumed bond valence contribution of H+. The ‘A’ parameter in Equation 33 is a regression constant derived from a large number of hydrolysis reactions of hydrated metal ions in aqueous solution. Machesky, et al. (2001, 2008) have extended this model to 300°C and demonstrated its validity for the very few oxides (magnetite, rutile, zirconia, nickel ferrite) for which PZC data are available at temperatures above 100°C.

This and other surface protonation models and temperature

extrapolation approaches are reviewed by Lützenkirchen (2006), who also provides a good review of current ‘surface-complexation-models’ describing ion adsorption and descriptions of the ion, charge density and electrical potential distributions in the EDL based on these simplified concepts. These generally involve Gouy-Chapman approximations for the effect of surface charge density on ion distributions in the diffuse layer, together with various ‘Stern’ or ‘Helmholtz’ planes of specific ion binding. Sverjensky and co-workers (Sverjensky, 2006; Fukushi and Sverhensky, 2007; Criscenti and Sverjensky, 1999) have analyzed a large database of ion adsorption studies on a large number of oxide and silicate surfaces, mainly conducted at room temperature, using the 2-pK surface protonation model and the ‘triple layer’ description of the EDL, providing a semi-empirical predictive capability for modeling electrolyte oxideinteractions based on Born solvation principles and taking into consideration the dielectric properties of the substrate as well as the solution.

Page 3.3.3—87 of 213

All such electrostatic and structural models of the EDL are characterized by numerous adjustable parameters (capacitance terms, specific ion binding constants, estimations of the solvent dielectric properties in the double layer, etc.). They generally lack a predictive capability for Stern layer capacitances and ion binding energies, and the defining parameters are highly covariant and difficult to render physically-meaningful, even at room temperature where abundant experimental data are available.

Most importantly, they are largely based on hypothetical

interfacial structures that ignore the discrete atomic nature of the interface at the angstromnanometer scale. In recent years, there has been a concerted effort to elucidate the actual structure and dynamics of the oxide/water interface using a variety of analytic and computational approaches. Surface forces have been directly measured to determine the dynamics of the electrolyte layer between mica sheets brought into nanometer-scale contact (Raviv and Klein, 2002; Zhu and Granick, 2003). Synchrotron-based EXAFS, X-ray standing wave and reflectivity measurements are being used to map out the 3-dimensional distributions of atoms of the crystal surface, the solvent and the ionic species in the EDL, with subangstrom resolution (Fenter et al., 2002; Fenter and Sturchio, 2004). Second Harmonic Generation (SHG) studies have been applied to determine the point of zero charge of individual crystal faces (Eisenthal, 2006; Stack et al., 2001). To illustrate these approaches, we briefly review recent, integrated studies of the interaction of water and aqueous electrolytes with the <110> crystal surface of rutile (α-TiO2), perhaps the most intensely-studied of all metal oxide surfaces (Diebold, 2003). Bandura et al. (2003) used ab initio density functional theory (DFT) to calculate the minimum energy configuration of the rutile <110> surface in contact with a significant number of water molecules. Fitts et al. (2005) used the DFT relaxed bond lengths and partial charges of surface oxygens as input into the MUSIC model (eq. 29) to calculate the protonation constants

Page 3.3.3—88 of 213

for the reactive surface oxygens, obtaining a calculated PZC (~5.0 at 25°C) in quantitative agreement with SHG measurements of real rutile <110> single-crystal surfaces in contact with dilute aqueous sodium nitrate solutions. Figure 25 shows the protonation scheme for the reactive oxygens on this surface, namely ‘bridging’ oxygens each bonded to two underlying Ti atoms, and ‘terminal’ oxygens, which result from the chemisorption of water molecules onto bare 5coordinated Ti atoms exposed on the <110> surface. The ab initio-optimized surface, and interaction potentials of water and ions with the surface oxgyens determined from the DFT calculations were also used by Předota et al. (2004, 2007) as input into large-scale classical molecular dynamics (MD) simulations of the interface between the rutile <110> surface and 40 Å layers of SPC/E model water (Berendsen, et al., 1987) at the density (1.0g/cc) of real liquid water. Figure 26 shows typical MD results for SPC/E containing about 2 mol⋅kg-1 dissolved

SrCl2 in contact with uncharged and negatively-charged surfaces at 1 atmosphere and 298 K. On the negatively-charged surface, the MD simulations predict sorption of solution cations at ‘inner sphere’ sites in direct contact with the surface oxygens. Using synchrotron X-ray standing wave (XSW) and crystal truncation rod (CTR) techniques, Zhang et al. (2004, 2007) were able to image the <110> surfaces of real rutile single crystals in contact with real bulk water containing a variety of dissolved ions, at sub-angstrom resolution. As shown in Figure 27, many ions were found to sorb at a ‘tetradentate’ site in contact with two bridging and two terminal oxygens, while smaller, transition metal cations sorb at ‘monodentate’ and ‘bidentate’ sites that are approximately the same as Ti lattice-equivalent sites in the bulk crystal structure. Figure 28 shows the remarkable agreement obtained from the synchrotron XSW, CTR and X-ray Absorption Fine Structure (EXAFS) measurements of real electrolyte solutions in contact with

Page 3.3.3—89 of 213

real rutile <110> surfaces, compared with results of the DFT calculations and classical MD simulations. The latter is rather surprising, given the simplicity of the non-dissociating, nonpolarizable SPC/E water model. These intergrated computational, chemical imaging and macroscopic experimental studies reveal features of the rutile/aqueous electrolyte interface that may be representative of other oxide/water interfaces. The true relaxed state of the crystal surface in contact with bulk water (both real water and SPC/E model water) is shown to be more similar to the undistorted bulk termination than previously indicated from studies of the dry surface under UHV conditions. The ordering of water molecules adjacent to neutral and charged surfaces is shown to extend only a few monolayers (∼ 1.5 nm) before bulk solvent properties are observed. The first few water layers are highly ordered, in registry with the bulk and surface crystal structures including strong dipole reorientations and H-bonding within these layers (with no resemblance to liquid water or ice). Cations that sorb as inner sphere complexes in direct contact with surface oxygens are absolutely ordered with respect to the crystal surface structure, and solventseparated ion pairs further out in the EDL show lateral and axial ordering related to both the crystal structure and the distribution of sorbed water dipoles. These studies provide the first direct evidence that cations of nominally ‘indifferent’ background electrolyte media (Na+, K+, Rb+) also bind at inner sphere sites, competing for sorption at such sites with multivalent trace cations that are much more strongly attracted (much higher binding constants in the thermodynamic sense). These studies also provide fairly direct confirmation of the general features of the MUSIC model and the Guoy-Chapman-Stern models of surface protonation and binding of counterions in discrete and well-defined layers that screen most of the surface charge within 1 nm of the surface.

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In order to advance the field of study of oxide/electrolyte interfaces for future applications the following focus areas are suggested: •

Much more intensive experimental studies of ion adsorption and surface charging at elevated temperatures and pressures, as well as in low-density supercritical water. • Development of ever more accurate water models and calibration of pairwise interactions of ions and surfaces with these model waters for input into very large scale classical molecular dynamics simulations • Development of parallel codes for making high level static and dynamic quantum mechanical calculations of interfaces involving meaningful numbers of solid and solution species, in order to capture the collective (non-pairwise) interactions of complex systems. • Intense focus on chemical imaging of interfacial structures and dynamics at the subangstrom to micron scales for ground-truthing and guidance of computational methods development • Application of EDL features and phenomena in predicting surface reaction rates and mechanisms with atomic-scale validity • Utilization of very-near-surface features of the interface to create new materials with novel and predictable properties. These same principles can be extended to metal/electrolyte interfaces, and integrated experimental and computational studies of such interfaces are beginning to appear in the literature (see for example Denzler et al., 2003; Ogaswara et al., 2002; Schiros et al., 2007).

3.3.4

Colloidal Suspensions What can we learn from traditional colloidal building blocks? Before increasing system

complexity, it is instructive to examine the behavior of model colloidal building blocks composed of either hard or attractive (i.e., sticky) spheres. The phase behavior, structure, and dynamics of colloidal suspensions composed of traditional building blocks depend both on the colloid volume fraction, φ, and on their interparticle interactions. In hard-sphere suspensions, the critical parameter for determining phase behavior is φ (see Figure 29) (Prasad, 2007). For φ just below 0.49, the suspension forms a dense liquid with particle positions that are disordered. The radial distribution function, g(r), is a measure of the probability of a particle center being located at a distance, r, from a given particle, relative to a uniform distribution. For a dense colloidal

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fluid, g(r) contains local maxima and minima at integer multiples of the interparticle spacing. As

φ is increased toward 0.49, the particle positions become increasingly correlated, as shown in the micrograph of a colloidal fluid suspension (Figure 29a). When φ is increased above 0.49 and the system is allowed to equilibrate, entropy drives the formation of crystalline domains. From φ = 0.49 – 0.54, the liquid and crystal phases coexist. Above φ = 0.54, the state of the suspension is a crystalline solid with a high degree of positional order, as shown in Figure 29b. The sharp maxima in the crystal g(r) correspond to spacing of particles within this ordered structure. By contrast, when φ is increased above 0.49 in systems that are not allowed to equilibrate, the suspension resides in a supercooled fluid state, which is a metastable solid that eventually relaxes. From φ = 0.58 – 0.63, the suspension retains its glassy nature and is unable to relax over the experimental time frame. The particle arrangements in colloidal glasses closely resemble those of liquids (Figure 29c). Similarly, g(r) for a glass is like that of a dense fluid, with correlations extending over multiple coordination shells. What distinguishes a glass from a liquid are the particle dynamics; local caging of particles leads to dynamic arrest in the solid glass, whereas in the liquid the particles freely rearrange. The repulsive potential in soft-sphere systems increases the particle’s effective size and therefore phase transitions occur at lower φ, while the liquid-crystal coexistence phase is relatively smaller than in hard spheres (Liu et al, 2002). In colloidal systems with uniform attractive interaction energy, U, between particles, phase behavior is influenced by both the magnitude and range of attraction as well as by φ. This is shown schematically in the U-φ phase diagram for colloidal suspensions with short-range potential, U (Figure 30) (Trappe and Sandkuhle, 2004) When φ is increased while U is small, local caging drives the transition from an equilibrium fluid to non-equilibrium solid glass at high

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φ. In the other limit, when U is increased while φ is small, the attraction drives the formation of clusters of particles, leading to a non-equilibrium fluid cluster phase (Poon and Haw, 1997). At high U, these clusters aggregate to form a space-spanning gel network that supports an elastic stress (Trappe and Sandkuhle, 2004; Poon and Haw, 1997). Between the two limits, increasing either φ or U can drive gelation. Additionally, in the gel phase, at constant U, increasing φ leads to changes in the gel structure. When φ is increased from φ = 0.26 – 0.50, the structure of the gel changes from a more open network to a dense network (Varadan and Solomon, 2003). Colloidal mixtures exhibit rich phase behavior. The simple act of mixing two particle populations together can lead to unexpectedly rich phase behavior. For example, van Blaaderen and co-workers (Leunissen et al, 2005) demonstrated that oppositely charged microspheres can self-assemble into ionic crystals under appropriate solution conditions. Figure 31 shows a CsCl lattice assembled from 1 µm spheres that are weakly positively (green) and negatively (red). In another important example, Lewis and co workers (Mohraz et al., 2008) recently developed biphasic mixtures of attractive and repulsive microspheres, in which both the structure of colloidal gels formed by the attractive species as well as the dynamics of the repulsive species can be tuned solely by varying the ratio of the two constituents. As the above examples illustrate, there is still much to learn even in colloidal systems based on simple mixtures. Nevertheless, there is a strong drive to introduce greater complexity by tailoring colloidal building blocks at the sub-particle level. Manipulating colloids and selfassembly via harnessing LRIs are further discussed in Section 4.2.

3.3.5 Solution Based Manipulation of SWCNT Here we direct our attention to SWCNT, in particular on how manipulation of LRIs has played a critical role in their solution based processing. SWCNT are single layers of carbon Page 3.3.5—93 of 213

atoms rolled into a seamless tube with diameter of about 1 nm. This can be accomplished in many ways, which are enumerated by indices that count the number of steps along the two basis vectors (m,n) that one must traverse to navigate the circumference of a given SWCNT (Saito, Dresselhaus, Dresselhaus 1999). To first order, if one regards their band structure as that of graphite with some k-vectors disallowed due to circumferential symmetry, one finds that twothirds of all allowed SWCNT have a bandgap and the remaining are metallic in nature (Saito, Dresselhaus, Dresselhaus 1999). This fact is at the same time the bane and the promise of these materials. While each form has highly desirable properties, all known syntheses result in some mixture of the two forms. The ability either to synthesize a known type, or to sort individual types in a mixture, is therefore a critical problem. For electronic applications, there are two broad approaches. One may either grow the SWCNT on a substrate (Javey et al. 2003), or process it in a liquid and attempt to place it on the substrate (Arnold et al. 2006, McLean et al. 2006). In the latter case, the process is almost invariably governed by long-range interactions such as interactions between the SWCNT and a substrate or another interface. Here we focus our attention on solution-based processing, which is applicable more generally. The first problem that must be addressed is the ability to disperse SWCNT individually in a solvent. Because of their large aspect ratio and small size, SWCNT adhere very strongly to each other and form bundles and are very difficult to suspend. While there has been much work on covalent modification to aid in dispersion (and to enhance coupling with a matrix for composite applications), this generally introduces side wall defects that are deleterious for its unique properties. We will restrict our attention to noncovalent modification using surfactants and biological molecules (Arnold et al. 2006, Bachilo et al. 2002; Zheng et al. 2003). Here longrange interactions play a critical role, and this approach has been very successful in solving the

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dispersion problem. Obtaining high quality dispersions then allows SWCNT to be subjected to a number of solution-based manipulation techniques.

Several solution-based techniques for

sorting by metallic versus semiconducting character, or by diameter, have also been demonstrated (Weisman 2003) based on selective adsorbtion (Chattopadhyay et al. 2003), dielectrophoresis (Krupke et al. 2003), density differentiation (Arnold et al. 2006), and using a DNA-CNT hybrid (Zheng et al. 2003; Zheng and Semke 2007). In the remainder of this section, we discuss further how control of long-range interactions in solution has contributed to solving problems associated with dispersion, sorting, and

placement of SWCNT. We consider approaches where dispersion is achieved by forming a hybrid of the SWCNT with small molecule or polymeric surfactants.

For the sake of

concreteness, we focus only on a few successful examples.

3.3.5.1 Dispersion and Structure Many amphiphilic molecules have been used successfully to disperse SWCNT’s in water, presumably by binding their hydrophobic domain non-covalently to the hydrophobic SWCNT surface, thus converting the resulting hybrid into a water-soluble object.

Specific examples

include surfactant molecules with charged head groups and flexible alkyl tails such as sodium dodecyl sulphate (SDS) (Bachilo et al. 2002, Krupke et al. 2003). More rigid and planar surfactants such as sodium cholate (SC), sodium deoxycholate and sodium taurodeoxycholate have also been used successfully (Arnold et al. 2006). Dispersions are typically obtained by a combination of intense sonication and centrifugation of mixtures of SWCNT and the surfactant molecule in aqueous medium.

As a side benefit, this procedure results in separation of

impurities such as catalyst particles, unseparated SWCNT bundles, and amorphous carbon. A signature of successful dispersion is the appearance of distinct bandgap absorbance peaks in the

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near infrared, and of corresponding band gap fluorescence (Bachilo et al. 2002). Resulting dispersions are very stable as long as sufficient excess of surfactant is maintained. The ability to extract the surfactant relatively cleanly can be an advantage if one eventually wishes to obtain the bare SWCNT; it can be a disadvantage if dispersions in otherwise clean solvent are desirable. Qualitatively, the nature of the hydrophobic-hydrophobic interaction that controls surfactant-SWCNT hybrid formation can be readily understood in analogy to micelle formation. Dispersion conditions such as surfactant concentration and sonication time and intensity are again a qualitative proxy for the binding strength. However, there are two basic issues about which there is at present little quantitative understanding. The first concerns the structure of the resulting hybrid and the second the binding strength. Knowledge of the structure determines the effective density of the hybrid material, and this is a delicate matter. Small differences in density have been invoked to explain the basic dispersion mechanism, i.e., why individual SWCNT hybrids remain suspended while small clusters are dispatched to the bottom of the centrifuge tube (Bachilo et al. 2002). More importantly, as discussed further in the next sub-section, modulation of the effective density of the SWCNT-surfactant hybrid both by the diameter of the SWCNT core and by its electronic properties (e.g., metallic vs semiconducting character) is understood in allowing their separation by centrifugation in a density gradient (Arnold et al. 2006). Some molecular simulations have been conducted (Bachilo et al. 2002) to further our understanding of structure. Direct observation of the structure is difficult and has rarely been reported (see Figure 33 below). Experimental and theoretical studies of the structure and binding thermodynamics & kinetics would be intimately linked, and are much needed. Experimental time, temperature, and concentration studies of desorbtion, or of competitive binding are likely to yield information on binding free energies. Theoretically, one would need

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to quantify the basic interactions between the surfactant molecules and between them and a SWCNT as a prelude to modeling the complete hybrid. That the structure seems to depend on the electronic character of the core SWCNT suggests that its electronic responsiveness to its environment, for example, charges on the surfactant, play an important role. This point recurs when one seeks to understand polymer-SWCNT hybrids and will be discussed again later. Dispersion of SWCNT has also been demonstrated by coating with water-soluble polymers (Zheng et al. 2003, O’Connell et al. 2001).

As for small-molecule surfactants,

pertinent issues relate to the binding free energy and the structure of the resulting hybrid. We will focus on DNA-dispersed SWCNT (DNA-CNT) as this hybrid is an excellent dispersant and allows for separation. Because the two constituents themselves have been studied extensively, it may prove to be a good model system. Much is known about the two constituents themselves. Carbon nanotubes have been studied intensively over the last fifteen years. Their physical and electronic structure is wellknown, as are many other properties including elasticity, strength, transport, and optical properties (Saito, Dresselhaus, Dresselhaus, 1999).

There are several optical techniques

including absorbance, Raman, Circular Dichroism, Fluorescence spectroscopy that have been developed to help study and identify CNT’s. Scanning probe techniques such as STM and AFM have been used widely to study their structure and properties. Single and double-stranded DNA have been studied very extensively as well (Saenger 1984). A few (inter-related) aspects are particularly relevant for the understanding of DNA-CNT structure and properties: (a) mechanics of the molecule, (b) electrostatics, and (c) its interactions with other molecules and materials. At the coarsest level, dsDNA and ssDNA can be represented as a worm-like or freely-jointed chain, respectively (Bustamante, Bryant, Smith 2003, Marko and Siggia 1995). These descriptions

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suffice to capture the gross behavior of these molecules. Many models of varying complexity are available both for dsDNA and ssDNA (Bustamante, Bryant, Smith 2003, Marko and Siggia 1995), ranging from these idealized chains to all-atom descriptions adjusted for full molecular dynamics simulations in water (Reddy, Leclerc, Karplus, 2003). It is believed that the interaction between the DNA and SWCNT’s is mediated by stacking of bases onto the CNT side-wall and that the entire hybrid is rendered water soluble because of the charged sugar phosphate backbone (Figure 34). By subjecting it to a combination of ion-exchange and size exclusion chromatography techniques, one can obtain excellent model systems, for instance, consisting primarily of one type of CNT with controlled length wrapped by ssDNA with known sequence and length (Zheng et al. 2003a; Zheng et al. 2003b; Zheng and Semke 2007) (Figure 34). Various contributions to the free energy of binding of DNA homopolymers to a SWCNT have been discussed in (Manohar, Tang, Jagota 2007). Dispersion efficiency appears to be optimal for sequences with about 30 bases although it has also been achieved with small dsDNA molecules (6-mers) (Vogel et al. 2007). Dispersion by individual nucleotides, which is not as effective as with longer strands, shows that purines are more effective than pyrimidines and that charge on the phosphate plays a very important role. Binding strength decreases in the sequence Guanine>Adenine>Cytosine/Thymine (Ikeda et al. 2006). Similar findings have been reported

for binding of bases onto graphite; the sequence is G>A>T>C (Sowerby et al. 2001a, Sowerby et al. 2001 b) with binding enthalpy of Adenine reported to be about 20 kJ/mol. Since the nominal Kuhn length of ssDNA (~ 1.6 nm (Bustamante, Bryant, Smith 2003)) includes several bases, this suggests that binding is strong enough to overcome entropic increase in free energy, and that all bases should be bound. However, experiments find that the binding strength of homopolymers

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follows a different sequence (T>A>C) (Zheng et al. 2003a) and simulations suggest that the difference is because steric hindrance between adjacent bases results in only partial base stacking with effective binding strength in the sequence T>G>A>C (Manohar, Tang, Jagota 2007). That the DNA binds in helical fashion has been suggested by molecular models (Zheng et al. 2003a, Manohar, Tang, Jagota 2007, Johnson, Johnson, Klein 2008) and confirmed by AFM (Zheng et al. 2003a). It has been suggested that certain structures are further stabilized by unconventional base-pairing (Zheng et al. 2003b, Saenger 1984). For example, Adenine is known to form hydrogen bonded monolayers on graphite (Sowerby et al. 2001a). There is currently a lack of experimental measurements on binding free energies and structure. Single-stranded DNA in water carries a charge on its backbone about every 0.6 nm. On wrapping around the CNT, it therefore renders the hybrid into a highly charged rod. Therefore, electrostatics is expected to play a very important role in determining the structure, in sorting, and during placement.

Handling electrostatic interactions for DNA-CNT, even within the

Poisson-Boltzmann approximation, raises new questions because of the high linear charge density and the variable electronic properties of the SWCNT core. This issue will be discussed further in the following subsection.

3.3.5.2 Sorting and Placement The ability to create hybrids of surfactant and polymeric molecules with individual SWCNT has made it possible to subject the resulting dispersions to sorting techniques (Weisman 2003). While techniques based on covalent modification of the SWCNT have been demonstrated, we will consider only those that rely on non-covalent (long-range) interactions. Separation by metallic and semiconducting character and by diameter has been demonstrated by differential adsorbtion (Chattopadhyay et al. 2003), by dielectrophoresis (Krupke et al. 2003)

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that differentiates based on difference in polarizability with respect to that of water, by density differentiation (Arnold et al. 2006), and by ion-exchange chromatrography (Zheng et al. 2003b). We will further restrict our attention to the last two examples. Figure 35 shows that hybrids of sodium cholate with SWCNT’s can be separated by

ultracentrifugation in a medium with a density gradient (Arnold et al. 2006). SC/SWCNT hybrids travel to the location in the medium that has the same effective density; separation is therefore an indication that hybrid effective density depends systematically on SWCNT diameter and electronic properties. As discussed in the previous subsection, little is known about how interactions between the SC molecules and SWCNT control structure. For DNA-CNT, ionexchange chromatography is understood to differentiate between SWCNT cores because the latter modulates the electrostatic interactions of the hybrid with external substrates or fields (Lustig et al. 2005). In both cases, it is likely that hydrophobic, van der Waals, and electrostatic interactions will all play an important role. The role of electrostatic interactions on separation has been modeled (Lustig et al. 2005) as being mediated by counterion release. The model does not include van der Waals interactions, nor can it account for the known ion-type dependence (chaotropic salts are preferred). Much more work is needed to understand how the charged SWCNT rod interacts with an external field, with other rods, and with a substrate (either for deposition or for sorting). In particular effects not captured by the PB theory (Lau et al. 2001, Gronbech-Jensen 1997) are likely very important but have not yet been handled. In summary, much progress has been made recently in solution-based processing of CNTs. The examples discussed in this section work by converting the SWCNT into a hybrid with an amphiphilic molecule (surfactants or polyelectrolytes). Systematic variations in the structure and effective electrostatics of the hybrid rely on delicate control of long-range

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interactions between the constituents of the hybrid, and between the hybrid and external fields or substrates. Both because of the interest in this application and because SWCNT hybrids provide model systems, there is scope for considerable further work on these materials both to understand how they work and to improve dispersion, sorting, and placement techniques.

4 Harnessing LRIs 4.1 Surfaces and Interfaces The nanoscale interface between solids and liquids or quasi-liquids is a complex regime in which electrostatic, vdW-Ld, acid-base, solvation, steric and other long-range interactions result in the formation of an interfacial region, the properties of which are uniquely dictated by the nature of the bounding bulk phases and the system temperature and pressure, but which are often poorly characterized at the atomic level. In this section, three examples are given of the potential to manipulate long-range interactions at such interfaces to achieve unique and desirable properties of the overall system.

First, the specific case of proton-conducting polymer

membranes is discussed as an archetypical example of a system whose function is entirely dictated by a complex interplay of long-range forces and interactions that can be easily manipulated and tailored to achieve major improvements in performance as a function of materials and environmental parameters. However, to this point, such ‘tailoring’ has been largely achieved by the Edisonian approach in which the many variables, such as polymer backbone, side chain and functional group properties and distributions and the type, size and distribution of inorganic additives and processing methods are simply altered by many hundreds of researchers, in search of ideal characteristics. A fundamental understanding of the molecularlevel driving forces of polymer self-assembly and molecular and ionic transport in such membranes could lead to revolutionary advances in functionality and economy. Page 3.3.5—101 of 213

Second, the formation of amorphous intergranular and surface films during ceramic and metals processing is discussed. The thickness, composition and structural/dynamic properties of such films are clearly driven by the bulk compositions and structures of the substrates on which they form, trace levels of contaminants which often migrate to these films, and environmental parameters such as temperature, pressure and gradients in these parameters. Intergranular films strongly influence the toughness, strength, permeability and many other physico-chemical properties of the processed material, and surface films can alter catalytic activity, resistance to corrosion or sequestration of contaminants. As is the case for ion-conducting membranes, an atomic-level predictive understanding of the origins and controls on intergranular and surface film structures and properties would enable efficient manipulation of input parameters in order to achieve a desired functionality of the end product. Finally, the more general phenomon of premelting at grain boundaries and surfaces is discussed, driven by temperature and compositional gradients, juxtaposition of particles with different crystallographic orientations or bulk properties, and the interplay of forces at their interface that induces the formation of a thin liquid film at a temperature below the Tm of the bulk phase. It is shown that manipulation of temperature and compositional gradients in such systems might be used to redistribute nanoparticles embedded within a polycrystalline material during warming, or from a particle suspension in a liquid during cooling.

An intriguing

consequence of premelting in polycrystalline ice is the interpretation of paleoclimate from the record of trapped water, trace elements and gases in continental glaciers. If neglected, the consequences of premelting phenomena can lead to highly erroneous interpretations of the evolution of the Earth’s atmosphere, hydrosphere and climate spanning geologic time scales.

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4.1.1 Proton Exchange Membranes for Hydrogen Fuel Cells In a hydrogen fuel cell, H2, is catalytically split into protons and electrons at an anode (usually Pt nanocatalyst on a carbon support), and the protons traverse a proton-permeable membrane, where they are catalytically recombined at a cathode with O2 and electrons to form water. The electrons perform work in an external circuit, such as powering a hybrid vehicle or static power generator.

Particularly for transportation applications, novel proton exchange

membranes (PEMs), that serve as proton-conductors as well as electrical insulators and barriers to fuel/oxidant mixing, are critically needed for advanced hydrogen fuel cells that operate efficiently and reliably at -40 to 130°C and relative humidities <<100% (Eikerling et al., 2006; Kreuer et al., 2004). The performance of such materials is dictated by their nanoscale structure, and thus the rational design of advanced membranes requires control and understanding of membrane structure and dynamics at the nanoscale. Heretofore, the influence of LRIs such as vdW-Ld, AB, solvation and proton donor/acceptor effects, as well as Coulombic interactions and dipole coupling between charged functional groups (such as sulfonate) and charged inorganic particulate additives, has been inadequately applied in explaining the observed structural and performance characteristics, or in the design of new classes of membranes. Exploiting the unique phenomena resulting from reactive interactions in such a complex, multicomponent, multiscale system represents a scientific grand challenge. Nafion, the industry standard PEM (Mauritz and Moore, 2004), exhibits poor performance at >80°C and <100% relative humidity. It is by no means the only ionomer being considered for PEM fuel cells (Harrison et al., 2005; Hickner et al., 2004, 2005), but is illustrative of the general problem of optimizing the required performance characteristics of ionomer membranes.

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Nafion is a statistical copolymer of tetrafluoroethylene and

tetrafluoroethylene substituted with pendant perfluoroether chains terminated with sulfonic acid groups. This material is highly polydisperse, molecular weight is not well known, and placement of the sulfonic acid groups along the backbone is not readily controlled. Although statistical copolymers usually do not form multiphase morphologies, in the case of Nafion the very high incompatibility between the two types of units does result in a nanometer-sized phase-separated morphology. Figure 36, illustrates the (hypothetical) complexity of Nafion-like random copolymer membranes at atomic to macroscopic scales.

Attempts to model structure and

dynamics of such membranes at these scales have thus far met with limited success (Kreuer et

al., 2004; Jang et al. 2004; Blake et al., 2005) and attempts to optimize their performance have been necessarily Edisonian. It is known that the type of morphology formed by uncharged diblock copolymers reflects, to a very good approximation, only the volume fraction of the two components (Khandpur et al. 1995; Bates and Frederickson, 1999). The excluded-volume and componentspecific affinity effects of inorganic nanoparticles on diblock copolymer morphology, chemical and mechanical stability have been clearly demonstrated for the simpler case of nanoparticleguided self-assembly of uncharged block copolymers (Balazs et al., 2006). Such approaches have not been extensively applied to pure ionomer or ionomer/inorganic composite membrane systems. The addition of inorganic particles (oxides and other compounds of Al, Mo, P, Si, Ti, W, Zr, etc.) to Nafion (and to a lesser extent other PEMs), can dramatically improve PEM fuel cell power output, membrane water uptake and retention and membrane tensile strength, while reducing polymer decomposition and fuel, oxygen and water transport (Alberti and Casciola, 2003; Alberti et al., 2005; Chalkova et al., 2006; Licoccia and Traversa, 2006).

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Inorganic

additives generally increase the glass transition temperature of the polymer (Adjemian et al., 2006), suggesting a correlation with improved high temperature performance.

Surface

functionalization of inorganic additives provides the opportunity to tailor the surface to achieve desired characteristics (Gomes et al., 2006; Kim et al., 2006). Since the polymer functional groups are highly acidic, releasing H+ to form sites of fixed negative charge, one could reasonably postulate that inorganic phases that become positively- or negatively-charged at the low-pH operating conditions might alter PEM performance through electrostatic interactions with the functional groups. Inorganic additives also exhibit a wide range of bulk dielectric constants (ε), such as 120 for rutile (α-TiO2) to 4.6 for quartz (α-SiO2) (Sverjensky, 2001). Thus, both electrostatic and vdW-Ld interactions of inorganic nanoparticle and macroparticle additives with the charged and uncharged regions of ionomer membranes may play important roles in dictating the structure, dynamics and performance characteristics of composite membranes for fuel cell and many other applications.

4.1.2 Intergranular and Surficial Films Nanometer-thick intergranular films or IGFs have been widely observed in structural and functional ceramics, and Clarke originally proposed that these IGFs exhibit an equilibrium thickness (Clarke 1987; Clarke, Shaw et al. 1993).

The observations of these IGFs are

summarized [See a recent critical review (Luo 2007) and references therein] as follows: -

IGFs exhibit a self-selecting (equilibrium) thickness for a given set of equilibration conditions, and the equilibrium thickness can be altered by changing the temperature, chemical potentials, and the capillary/applied pressure.

-

The equilibrium thickness can represent either a global or a local minimum in excess free energy.

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-

Dihedral angles are nonzero where IGFs meet glass/liquid pockets, indicating that the excess film energy is lower than the sum of the two crystal-glass/liquid interfacial energies.

-

The average composition of an IGF differs markedly from that of the bulk liquid phase, and it can often lie within a bulk miscibility gap.

-

Quasi-liquid IGFs can be stabilized at subsolidus temperatures.

-

Partial structural order and through-thickness compositional/structural gradients are predicted from molecular dynamics simulations and diffuse-interface models, and their existence has been confirmed by aberration-corrected STEM.

-

IGFs form at virtually all general boundaries (but not at low-energy small-angle or coincident boundaries). In Si3N4, the thickness of IGFs formed at random boundaries does not significantly depend on the boundary crystallography, although some influences of the misorientation are expected from diffuse-interface models. Surficial amorphous films or SAFs of similar character have been observed (Luo and

Chiang 2008). Although fewer systems have been studied, systematical data have been collected for two SAF systems, providing insights into understanding analogous IGFs (where systematical experiments of a similar level have not been conducted). These observations are reviewed in Section 3.2.1 as instructive systems. In a phenomenological model, the excess film free energy is given by Equation 34.

G x (h) = (γ 1 + γ 2 ) + (∆Gvol ⋅ h) +

−A + σ elec (h) + σ short −range (h) + ... 12πh 2

The term (γ 1 + γ 2 ) represents the sum of the excess free energies of two independent (well separated) interfaces [ (γ 1 + γ 2 ) = 2γ cl for an IGF or (γ 1 + γ 2 ) = γ cl + γ lv for an SAF]. ∆Gvol is a volumetric free energy for forming a hypothesized uniform liquid film from a mixture of

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equilibrium bulk phases. When the film is thin, additional interfacial interactions arise, which include a vdW-Ld force, an electrostatic double-layer interaction, and short-range interactions of structural and chemical origins. Capillary and applied pressures, if they are present, also affect film thickness. An "equilibrium" thickness corresponds to a global or local minimum in excess film free energy versus thickness. This model, which was initially proposed by Clarke (1987), can be viewed as a high-temperature colloidal theory, in which ∆Gvol ⋅ h is an additional significant attractive interaction at subsolidus conditions (being analogous the volumetric term in premelting theories). Recently, significant progresses have also been made in quantifying vdWLd forces (French, Cannon et al. 1995; French 2000; Avishai and Kaplan 2005; van Benthem, Tang et al. 2006). There is a critical need to qualify other interfacial interactions. Further discussions of interfacial interactions can be found in a recent review (Luo 2007). Alternatively, these nanometer-thick IGFs and SAFs can be understood to be multilayer adsorbates with compositions set by bulk chemical potentials (Cannon and Esposito 1999; Cannon, Rühle et al. 2000).

More sophisticated models should consider through-thickness

structural and compositional gradients, which have been implemented using diffuse-interface theories (Bishop, Cannon et al. 2005; Bishop, Tang et al. 2006; Tang, Carter et al. 2006). It is proposed that these IGFs and SAFs can be understood from coupled premelting and prewetting transitions in binary diffuse-interface models (Luo, Tang et al. 2006; Tang, Carter et al. 2006) that were extended from the critical point wetting model (Cahn 1977). In addition, molecular dynamics modeling (Garofalini and Luo 2003; Su and Garofalini 2004; Rulis, Chen et al. 2005; Zhang and Garofalini 2005), grand-canonical Monte Carlo simulations (Hudson, Nguyen-Manh et al. 2006) and first-principle methods (Shibata,

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Pennycook et al. 2004; Chen, Ouyang et al. 2005; Rulis, Chen et al. 2005; Ching, Chen et al. 2006) have been employed to study IGFs. A grand challenge is to develop quantitative and realistic models for predicting the stability of these IGFs and SAFs. In general, systematical measurements of the interfacial solute excesses or film thickness as a function of temperature and chemical potentials are required to validate interfacial thermodynamic models.

Despite wide observations of IGFs, such

measurements have not been conducted because of the difficulties in controlling impurities in ceramics and efficiently preparing TEM specimens. Lack of systematic data contributes to the lack of quantitative models.

Thus, there is a critical need to devise new and efficient

experimental schemes. Due to the unknown effect of cooling, it is also beneficial to conduct hotstage TEM or other in-situ experiments. On the other hand, SAFs offer a good platform to conduct certain critical experiments that are difficult to conduct for IGFs, e.g., hot-stage synchrotron X-ray or neutron scattering experiments. Moreover, vdW-Ld forces, which are always attractive for IGFs of symmetrical configurations, can be repulsive for SAFs. Stable subsolidus SAFs have been found in systems with repulsive vdW-Ld forces and future experiments to probe film stability and wetting transitions in these systems will provide insights into understanding the thermodynamic stability of not only SAFs but also IGFs. The technological importance of SAFs and IGFs has been recently reviewed (Luo 2007). IGFs play important roles in fracture toughness, strength, fatigue, creep resistance, and oxidation of Si3N4 and SiC based structural ceramics, mechanical properties and erosive wear behaviors of Al2O3, superplasticity of ZrO2, tunable conductivities for ruthenate based thick-film resistors, non-linear I-V characteristics for ZnO-Bi2O3 based varistors, and functions of (Sr, Ba)TiO3 based

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perovskite sensors and actuators.

Furthermore, IGFs have been found in a host of other

materials, from synroc to AlN substrates to high Tc superconductors, with attendant detrimental implications on corrosion resistance and thermal or electrical conductivity. Understanding and control of SAFs are also technologically important, e.g., in engineering supported oxide catalysts or ultra-thin dielectric films. The formation of nanometer-thick SAFs can affect the shape and growth kinetics of nanoparticles and nanowires. Furthermore, IGFs have important technological roles in materials fabrication because of their unique implications in grain boundary diffusion and migration kinetics. For example, the presence of IGFs or similar disordered grain boundaries can promote rapid grain boundary migration. This mechanism has been confirmed for doped Al2O3 (MacLaren, Cannon et al. 2003) and suggested for Al-Ga (Weygand, Breichet et al. 1997; Gottstein and Molodov 1998). Most recently, Dillon et al. revealed the existence of multiple distinct grain boundary structures (IGFs and derivative structures) with increasing structural disorder and mobility in doped Al2O3, which explained the mysterious abnormal grain growth mechanism in this system (Dillon and Harmer 2007; Dillon, Tang et al. 2007). In a broader context, understanding and control of IGFs (as well as SAFs) will lead to great opportunities for improving and customizing properties of materials or synthesizing new materials.

This is due to 1) the large property changes that accompany the formation of

nanoscale quasi-liquid interfacial films and 2) the fact that such interfacial structures can be retained on cooling. Thus, it is beneficial to develop quantitative grain boundary complexion (phase) diagrams to represent the stability of IGFs and derivative GB complexions (Dillon, Tang et al. 2007). Then, it becomes possible to design a) fabrication recipes utilizing the most appropriate grain boundary structures during processing (e.g. utilizing quasi-liquid IGFs for low-

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T sintering) and b) heat treatments to tune the final grain boundary structures for desired performance properties (e.g., dewetting quasi-liquid IGFs to improve creep resistance). The necessity of developing grain boundary complexion diagrams is demonstrated by recent research of solid-state activated sintering.

Studies using ZnO-Bi2O3 (Luo, Wang et al.

1999) and W-Ni (Luo, Gupta et al. 2005; Gupta, Yoon et al. 2007) as model ceramic and metallic materials showed that nanoscale quasi-liquid IGFs form well below the bulk eutectic/solidus temperature, where the bulk liquid is not yet stable. Nonetheless, short-circuit diffusion in these subsolidus quasi-liquid IGFs leads to subsolidus activated sintering in these systems, which are phenomenologically similar to liquid phase sintering but can initiate at as low as 60% of Tsolidus. It is therefore concluded that bulk phase diagrams are not adequate for designing optimal activated sintering protocols. On the other hand, a recently developed quantitative thermodynamic model can predict grain boundary disordering and related subsolidus activated sintering behaviors for five tungsten based binary alloys (Luo and Shi 2008 ). This example demonstrates the opportunities.

4.1.3 Premelting Dynamics As discussed briefly in Section 1.1.3, and at greater length in 2.3.1, Lifshitz theory has very successfully predicted the nature of the surface melting of many materials; we specifically discussed the case of water and ice as an instructive system. However, several aspects of these phenomena remain worthy of further study, potentially with a view to using LRI in a novel way. The premelting of a material refers to the persistence of a film of its liquid phase at temperatures below the normal melting temperature. Most commonly discussed are the Gibbs– Thomson and Colligative effects. The former is a consequence of a solid phase being convex to its melt phase and thus having a lower freezing point than the bulk, and the latter originates in

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the lowering of the chemical potential of a solvent in the presence of a solute. The melting of most solids is a first-order phase transition, accompanied by discontinuous changes in bulk quantities at the transition point. However, all crystals, be they in contact with their vapor phase or another material, have surfaces where the process of melting is initiated: if there were a layer of liquid at the surface, at temperatures below the bulk melting point Tm, then there is little need to activate the melting process. Such a deduction was made early [by Tamman & Stranski, recently reviewed in Dash et al. 2006] on the basis of the inability to superheat crystals. The ease with which liquids can be supercooled, tells us that the melting process is inherently asymmetrical about the transition point. Interfacial premelting occurs at the surfaces of solid rare gases, quantum solids, metals, semiconductors and molecular solids and is characterized by the appearance of an interfacial thin film of liquid that grows in thickness as the bulk melting temperature, Tm, is approached from below [Dash et al. 2006]. The relationship between the film thickness and the temperature depends on the nature of the interactions in the system. When interfacial premelting occurs at vapor surfaces it is referred to as surface melting and when it occurs at the interface between a solid and a chemically inert substrate it is called interfacial melting, and when at the interface between two grains of the same material it is called grain boundary melting. When films at such solid surfaces diverge at the bulk transition the melting is complete, but where retarded potential effects intervene and attentuate the intermolecular wetting forces the film growth may be blocked and thereby be finite at the bulk transition. This latter circumstance, in which the behavior is discontinuous, is referred to as incomplete melting. Because near the bulk transition we can view these phenomena as wetting transitions (surface melting is a special case of triple point wetting), the role of LRIs, and particularly long range van der Waals effects, has a broad

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context and setting which is particularly relevant to the role of geometry in these volume-volume interactions [Dantchev et al. 2007; Lamoreaux 2005]. We now consider the dynamics of premelting liquid driven by variations in temperature and/or composition. The topic itself occupies a curious interfacial position between condensed matter physics materials science, chemistry and geophysics. Indeed, although the physics of the surface and that of the bulk are most often taught and studied in isolation, it is the confluence of dimensionality and phase behavior found at the surface that provides a wide-ranging area of exploration in science and engineering. What follows summarizes aspects of a recent review [Wettlaufer & Worster, 2006]. There are two intrinsic aspects of surfaces that are familiar to those working in materials broadly; wetting phenomena and thermophoretic and Marangoni flows.

While these are

important and indeed present in a host of settings, the phenomenon of premelting dynamics makes some contact with these phenomena but is indeed quite distinct in its origin and consequences; The fluid dynamics of interfacially premelted fluid—the focus here—would not exist in the absence of interfaces, but it requires neither contact lines nor gradients in the coefficients of surface energy. During complete interfacial premelting under long ranged forces that are of a power law form, the film thickness, d, is related to the temperature T through d = λ(Tm − T )−1/ ν , in which λ and ν are positive constants, the latter is an integer that depends on the nature of the interactions driving melting of the system. Thus, the melt layer increases with temperature and becomes macroscopically thick as the bulk melting temperature is reached. The dynamical consequences emerge from the fact that the LRIs provide the field energy per molecule that shifts the equilibrium domain of the liquid phase into the solid region of the bulk phase diagram [Dash et

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al., 2006; Wettlauer & Worster, 2006]. In consequence, for an interfacial film of thickness d, the shift is written Equation 35. µd (T, p, d) = µl (T , p) + U ′( d ) = µS (T, p) , where µl (T, p) and µS (T, p) are the bulk chemical potentials of the liquid and solid respectively

and U ′( d ) is the derivative, with respect to d, of the underlying effective interfacial free energy

U ( d ) which itself depends on the nature of the intermolecular interactions in the system. Hence, for example in the case of nonretarded vdW-Ld forces, a phenomenological description is Equation 36.

U ′(d ) =

2 ∆γσ 2

ρl d 3

,

where σ is of order a molecular length, ρl is the liquid density and ∆γ is the difference between the interfacial energy of the dry interface between the solid phase and the third phase, be it the vapor, a wall, or a different orientation of the solid phase. The coefficient in the equation above is related to the Hamaker coefficient A˜ by A˜ /12π = ∆γσ 2 . Thus we see that interfacial melting occurs when A˜ < 0, so that there is a force of repulsion—disjoining pressure or thermomolecular

pressure—between the media bounding the liquid film, written here for nonretarded vdW-Ld forces. When the external pressure applied to the third phase, such as a wall, pw equal to that applied

to

the

solid

pS ,

balances

the

thermomolecular

pressure pT = − A˜ /6πd 3 ,

then pw = pS = pT + pl , where the hydrodynamic pressure is pl . Combining this with the GibbsDuhem relationship, which can be applied on each side of a solid-melt interface, allows one to show in general that when the system is in equilibrium at temperature T then

pS − pl = pT =

ρ S qm

(Tm − T ) , Tm where ρS is the density of the solid and qm is the latent heat of fusion [Dash et al., 2006; Equation 37.

Wettlaufer & Worster, 2006]. We imagine fixing the pressure in the bulk solid phase and increasing the temperature toward Tm from below; the film thickens, the repulsive

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thermomolecular pressure decreases and hence the hydrodynamic pressure increases, driving unfrozen liquid from high to low temperatures. It is important to emphasize that the transport of unfrozen liquid is driven by thermomolecular pressure gradients brought about by temperature gradients and not capillarity. The existence and dynamics of premelted films is central to the sintering, coarsening, transport behavior and many other bulk phenomena within polycrystalline materials and at the surface of single crystals. There are a plethora of examples in which it is clearly operative but a dearth of experimental and theoretical tests. In the next subsection we discuss a number of these but refer the reader to the reviews by Dash et al., [2006] and Worster & Wettlaufer [2006] for a more thorough treatment.

4.1.3.1 Manipulation of premelting dynamics To enhance the ready sintering of any material it has long been known empirically that to bring the system close to its melting point is advantageous. We can now understand that this is due to the enhanced liquidity of the system originating in the three principal effects of premelting; intermolecular forces, interfacial curvature and impurities. From the description of the previous section it is clear that a gradient in the temperature gradient parallel to the surface is responsible for a gradient in the film thickness and hence a gradient in the thermomolecular pressure. Thus, if the film is sufficiently thick, it can be treated as a thin viscous fluid and its flow described by lubrication theory. The effect can be responsible for trapping of particles at a bulk solidification front [Rempel & Worster, 2001] and, so long as the temperature gradient is maintained, gives rise to subsequent motion of the particle within the solid after it is trapped. Indeed, a simple analysis reveals that the force on the particle can be

r r written in a manner directly analogous to Archimedean buoyancy, FB = −mS G , where mS is the

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r r mass of solid displaced by the particle against which is premelts, and G = ∇(∆µ) , is the gradient in the generalized departure of the system from bulk coexistence, ∆µ ∝ Tm − T which is determined here by a departure of temperature from the bulk melting temperature. Therefore, this is referred to as thermodynamic buoyancy [Rempel et al., 2001] and as an example, a particle of a micron in radius moving under the influence of a very weak temperature gradient (0.025

r r K/m) has G ≈ 3g and hence moves at about 1 micron/year for a nanometer scale film thickness. From the materials standpoint, we can control the temperature and temperature gradient of many systems accurately and over a wide range. Hence, there is a great potential to redistribute particles included in a host solid using premelting dynamics. Rather than attempt to control the trapping of particles within the host solid, the idea is to insure that they enter through quenching and then redistribute them by manipulation of the temperature field of the system. The transport properties of unfrozen water in ice polycrystals bears strongly on the redistribution of paleoclimate records, retrieved from the Antarctic and Greenland ice cores, are redistributed by the premelted water [reviewed in Dash et al., 2006]. In fact, as mentioned above, any physical or biological process relying on the presence of the liquid phase will be strongly influenced by grain boundary melting because the surface area of a polycrystal is dominated by grain boundary interfaces. Because soluble species reside principally in the liquid phase, and their diffusivity is orders of magnitude greater in the liquid than in the solid, the fate and evolution of such species is controlled by the volume fraction of liquid in the material. Indeed, a proper homogenization of a two-phase, multi-component polycrystalline ice system shows a wide variety of coupled processes. For example, in a major species controls the (subfreezing) liquid fraction (through the liquidus) and thereby influences the minor species in striking ways [Rempel et al., 2002]. In Figure 37 we see an example of how a major species can

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be deposited in the sample out of phase with a minor species and after some time the minor species is drawn into phase with the major species. It is not solely diffusive equilibration of the liquid bound species, but the coupling between phase fraction and diffusivity that results in a rich dynamical response that can be quantitatively modeled. It appears that such a homogenization of multicomponent polycrystalline materials has not been harnessed for the purposes of tailoring materials properties. The general features of the approach are quantitatively applicable to cases in which the impurities are not efficiently rejected from the solid phase and for isotopic diffusion in a polycrystal [reviewed in Dash et al., 2006]. Thus, it seems a unique area ripe for exploration in a vast array of materials. Manipulation by freezing rate is also a possible modality of using long ranged interactions to control the morphology and properties of a system. For example, it is possible to treat a colloidal suspension as a “binary alloy” and yet at a solidification front premelting can conspire to reject particles from the advancing front to create a range of microscopic patterns depending on concentration [Peppin et al., 2006, 2007]. The variety of patterns observed when two types of suspensions are frozen is evident in Figure 38. While this has been studied in the context of the natural solidification of colloids such as clays, the physics is sufficiently well understood to envisage using the method more broadly across a range of applications, for example in fabrication of microfibers [Zhang et al., 2005].

4.2 Colloids and Self-Assembly 4.2.1 Tailored Building Blocks: From Hard Spheres to Patchy Colloids The programmable assembly of designer colloidal building blocks with engineered size, shape, and chemical anisotropy is the next frontier in the scientific and technological development of soft materials [van Blaaderen 2006]. Establishing this mastery will enable the

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assembly of new photonic, electronic, plasmonic, and photovoltaic devices with unparalleled complexity and precision, akin to that achieved in biological systems. As an important first step towards realizing this goal, several synthetic pathways have been recently reported that offer precise control over colloid geometry at the nanoscale (e.g., ellipsoids, triangular plates, cubes, and tetrapods) and microscale (e.g., unary and binary colloidal “molecules”). Despite this impressive geometric control, all of the building blocks shown in Figure 39 are chemically homogeneous. To date, the ability to spatially encode their surfaces with the desired chemical heterogeneity (or “patchy” structure) remains an elusive goal. Even though recent simulations clearly demonstrate the transformational impact that this would have on their ability to selforganize into unique structures (see Figure 40) [van Blaaderen 2006, Zhang and Glotzer 2004]. To fully harness the potential that spatially and chemically anisotropic colloids, i.e., “patchy particles” provide, the following questions must be addressed. First, how do various particle motifs, e.g., janus spheres, ring-like (or striped), or distinct patches influence colloidal assembly? What role do vdW-Ld, electrostatic, and hydrophobic forces play in controlling their assembly? Finally, how do critical parameters such as patch size and charge density, colloid size, density, and volume fraction, and solution conditions affect their ability to assemble into the desired equilibrium (crystalline) and non-equilibrium (gel or glassy) phases?

4.2.2 Synthesis and Assembly of Designer Colloidal Building Blocks Current research efforts focus on moving beyond the traditional systems by enabling the creation of designer colloidal building blocks, such as colloidal molecules, janus spheres, and other patchy particle motifs. A myriad of particle motifs are envisioned, in which surface chemistry, shape anisotropy, faceting, pattern quantization, and branching are controlled (see Figure 41) [Glotzer and Solomon 2007]. To date, significant progress has been made towards

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the realization of many of these motifs. Below, we highlight those assembly routes that yield chemically heterogeneous (or “patchy”) colloids. Granick and co-workers [Hong, Cacciuto et al. 2006] recently reported a highly scalable synthetic pathway for creating bipolar janus spheres, i.e., particles that consist of oppositely charged hemispheres. Such species, which are likely the simplest example of patchy colloids, exhibit complex interparticle interactions that depend strongly on their mutual orientation. For example, attractive interactions dominate when oppositely charged faces interact with one another, whereas repulsive interactions emerge when the particles rotate in solution such that their like-charged faces are in close proximity (Figure 42a-d). This heterogeneous interaction landscape promotes the formation of colloidal molecules that themselves are patchy in nature (Figure 42e), somewhat akin to globular proteins. Recently, lithographic patterning approaches have been employed to create more complex, patchy colloidal spheres and wires. For example, Mohwald and co-workers [Edwards, Wang et al. 2007] created polystyrene microspheres decorated with gold dots with sp valence (Figure 43). By rendering these patches attractive, one may be able to assemble the spheres into linear particle chains (or strings). Using on-wire lithography, Mirkin and co-workers [Qin, Park et al. 2005] created silver-gold metallic nanowires whose spatial composition can be exquisitely tuned (Figure 43). While neither approach is readily scalable to bulk quantities, they represent the current state-of-the-art in designing chemically heterogeneous building blocks for colloidal assembly.

4.2.3 Challenges and Opportunities Several challenges must be overcome to fully harness the unique opportunities that arise from a “colloids by design” approach. First, novel synthetic pathways must be developed that

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enable the creation of bulk quantities of designer colloidal building blocks of controlled size, shape, and chemical functionality. Second, these pathways must be extended beyond polymeric and silica-based colloids to functional building blocks, such as metals, semiconductors, and complex oxides. Finally, a theoretical and computational framework must be developed that is capable of predicting the phase behavior, structure, and assembly of a diverse array of particle motifs. The fundamental understanding of the behavior of designer colloids that would emerge from such predictive tools would provide the synthetic guidelines for creating building blocks that self-assemble into desired equilibrium (crystalline) and non-equilibrium (gel or glassy) phases, while avoiding undesired (or jammed) states. The “colloids by design” approach offers enormous potential, if the above challenges can be successfully overcome.

Advances in our current synthetic capabilities and fundamental

understanding of long-range interactions at the nanoscale would open new avenues to precisely engineering crystalline and amorphous phases. For example, the elusive goal of producing a diamond crystal with a lattice constant suitable for photonic band gap applications could finally be realized.

Additionally, colloidal gels could be created with controlled connectivity and

elasticity, which may find potential application in the self-assembly of novel Li-ion batteries [Cho, Warbera et al. 2007] or as inks for direct-write assembly [Smay et al. 2002] of highly efficient solar arrays.

4.3 Devices: Electronic, Optical, Sensing 4.3.1 Frontiers in Lithography: What is the Importance of LRIs in Materials? The term “Lithography” in Webster’s dictionary is define as “the process of printing from a plane surface (as a smooth stone or metal plate)”. Here we will give a partial account of the frontier of lithography as applied to the making of small nanometer sized microelectronic

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devices (eg MOS devices LED’s etc). To take the pulse of the frontiers of lithography to make such small devices, we’ve chosen both the forefront of optical lithography and the forefront of non-optical lithography. The optical lithographies we’ve chosen are 193 nm Lithography (both Immersion lithography and double exposure) and extreme ultraviolet (EUV, i.e. soft X-ray). The non-optical lithographies that we’ve chosen are Nano Imprinting and Self Assembly. What we discuss here is related mainly to what we feel illustrates the importance of LRIs and we will not dwell on other important issues that do not pertain immediately to the topic of this review.

4.3.2 193 nm Lithography Immersion and Double Exposure

4.3.2.1 193 nm Immersion Lithography Immersion lithography as in immersion microscopy uses a liquid of higher refractive index to improve the resolution, decreasing the effective wavelength of light corresponding to how high the refractive index of the immersing liquid. Initial systems are based upon material water immersion (n~1.45). Here the primary challenges are as follows: Design of materials with contact angles compatible with high scanning rates, this immediately pertains to the issue of surface tension at material and water interfaces, design of non-extractable resist components, which involves the design of additives that will interact with the resist matrix in such a way as to prevent extraction. The design of barrier coats whose solubility and interaction with the resin do not conflict with the working of the resist. At the forefront of this are self-separating barrier coats. Finally, there is the inherent challenge in meeting requirement of having low Line Edge Roughness (LER), High Resist Sensitivity and High Resolution. This demanding triple requirement has been called the “Triangle of Misery”.

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More advanced designs include the use of higher index of refraction fluids to get so called second generation (n~1.6) and third generation immersion fluids (n~1.8). For second generation fluids, the same issues occurs as with water immersion, but since later generation fluids are based upon hydrocarbons, the specific solution can be quite different. The same may be true for third generation fluids however these are less well defined at the moment as no stable or practical recyclable materials have been identified. A better understanding of LRIs is important in 193 nm immersion because of the following considerations: Diffusion of material into immersion fluids from resist, diffusion from exposed to non-exposed areas of additives and photogenerated base acids. Diffusion of photoacid, and other resist components, Interaction of barrier coats and/or formation of self forming barrier coats, Dissolution of polymer exposed areas, Resolution, LER. Adhesion of features with larger aspect ratios. Control of dissolution. Defects. Control of redeposit of material on surfaces after exposure and development. Nanocomposite high index fluids that are stable and retain sufficient fluidity to be usable. Nanocomposite high index resist that are stable but meet the targets for resolution, LER and sensitivity. The second and third generation immersion lithography is discussed in [Zimmerman 2007]. For these types of systems, three types of higher index materials are needed. Lens materials (eg LuAlG), immersion fluids other than water and higher index of refraction resists. Of these, only the immersion fluid and resist are within the scope of this review. Immersion fluids for second generation approaches appear to be feasible and are based on hydrocarbons. For third generation the best materials for stability and transparency at 193 nm are polycyclicaliphatics, however these decompose too rapidly upon irradiation. In this paper it is speculated that the best solution for third generation immersion fluids may be water with added

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metal oxide nanoparticles (5 nm or smaller) with –O-Si-CH2-CN surface functionalization to give water compatibility.

Finally, the design of resists with high index of refraction is also

very challenging and current materials are still very immature and invariably have high absorbance at 193 nm which would make them impractical.

Again, the paper speculates that

resist materials with index of refraction at 193 nm higher than 2.4 would have to resort to the use of nanocomposites with inorganic materials.

4.3.2.2 Double Exposure Double Exposure is a potential resolution enhancement technique which enable lithography at a k1 (i.e. k1 in Raleigh’s equation R= k1λ/NA) less than 0.25. Double exposure is more cost effective than double patterning, but may require the development of novel materials. Either a novel double photon-like process must be used, or some type of material interaction must be available to destroy patterning information in nominally “non exposed area” from the first exposure so it will not be present during second exposure. In double patterning this information is lost during the pattern transfer process, which occurs after the first exposure and prior to the second exposure.

In double exposure, the wafer does not leave the track for

processing. The two exposures are done one after the other. In such materials, the same criteria governed by LRIs outlined for 193 nm single exposure still apply. However, in addition to these, molecular interactions may play a role in what happens photochemically, by affecting the distance different components are from each other to allow desirably photochemical energy transfer and to prevent undesirable photochemical events.

Also interactions which favor the blurring of information created during the first

exposure would be desirable. Simulations show that “Two photon PAG” and “Optical

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Threshold” materials are the approaches most likely to yield a material with the needed throughput for a double exposure resist.

4.3.3 EUV (Extreme Ultraviolet) Here the challenge is in designing resist materials which while meeting absorbance criteria, outgassing criteria, also meet the line edge roughness criteria, dose criteria, resolution targets and in addition do have undue shot-noise due to the high energy of the EUV photons. Similarly to 193 nm lithography, the following factors are still strongly influenced by long range molecular interactions: Diffusion from exposed to non exposed areas of additives and photogenerated base acids; control of dissolution of exposed areas; control of dissolution and defects. In addition because the smaller dimensions targeted, line collapse owing to aspect ratio considerations become even more problematic. Therefore a better understanding of how to improve adhesion of such small features and/or prevent their mechanical breakdown during image processing is very crucial. For example Allen et al. [2007] claim that oligosacharides and silicon-based materials, especially low molecular weight glass-like materials, are best suited. The best designs appear to be ones forming a “rough stone wall,” where small, roughly spherical oligomers form a material in which the oligomeric materials are separated by large distances. This type of molecular arrangement limits acid diffusion which cannot cross the large distance between molecules In [Watanabe 2007] it was found that decreasing polydispersity and molecular weight of polymers gives better LER. Also, they have found that attaching the PAG to the polymer backbone both decreases LER and increases photospeed (2 mJ/cm2. 2nm LER). They were able to resolve down to 50 nm lines and spaces (L/S) without any line collapse. A similar type of approach is described in [Oizumi 2007]. Resists consisting of small molecules (monodispersed)

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protected with acid cleaveable groups (AdMA), blended with a PAG give material which are can be coated into thin films having a Tg of about 120ºC, which upon imaging give features having 3.4 nm LER. In [Fukushima 2007] resist-based, low molecular weight polymers were compared with a PAG added as an independent component or bound to the polymer. It was found that the outgassing of both was comparable, but that the PAG bonded material had less sensitivity and lower LER. (3.5 nm vs 7.8 nm)

4.3.4 Nano Imprinting Nanoimprinting has been growing in importance of the last few years and it is expected to have a much greater impact as time goes on. Such materials [Allen et al. 2007] may have possible applications in hard disk storage. Also, as will be discussed shortly, LED devices have already been made using nano imprinting. In nano imprinting, the interaction of material with surfaces and flow of material into confined geometries need to be better understood.

It is also important to design resistant release

layers not susceptible to physical degradation. In order to design nanoimpriting material that are photocurable (Step and Flash), it is also important to have good understanding of possible interaction of photosentive components and photoproducts with the nanoimpriting resin before and after cure. For instance in [Ito 2007], a “Step an flash” approach is discussed which, unlike those

with epoxy which requires metal containing PAG’s, can use conventional

fluoroaklylsulfonate-based PAG’s. These materials also have low viscosity ideal for better reproducibility of small features. Another issue of concern is properly functioning release layers, as discussed in [Tada 2007]. This paper addressed the issue of the number of times a template can be employed before it starts to deteriorate. One key route of degradation is the deterioration of the release layer (e.g.

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derived from (MeO)3Si- (-O-CF2CF2CF2)n). In this instance, mechanical failure appears to be the main cause of the problem. The issue of resin type and the stability of molded images is also an important consideration. For instance in [Ichiro 2007] a silsequioxane resin (HSQ) resin is spin-coated on a Si substrate. Then a mold-coated fluorinated anti-sticking agent is pressed into the HSQ at RT at very high pressure 5-40 MPa, depending on mold shape. In this instance it was found that when the Ladder Material (OCDT-12 Tokyo Ohka) and Caged HSQ (FOX 16 Dow) materials were compared, the Ladder materials had far more resistance to thermal flow. Recent modeling work is trying to understand how fast certain patterns in molds can be filled by the nano imprinting substrate. Specifically, in [Tanabe 2007] the flow of polymers during nano imprinting was studied.

It was found that two types of features were difficult to

print and took too much time: Small aspect ratios. Simulation shows that lateral flow is needed, and large aspect ratios where fluid resistance larger. Therefore, there is a critical aspect ratio needed to minimize process time. Finally, the making of molds having high resolution is very challenging, as in nano impriting the mask (i.e mold), unlike in optical lithography, must be of the same size of the features it is imaging. Self-assembly, the topic of the last section of this review, is being used to make the mold (i.e. mask) to enable nano imprinting. In the paper, [Yanagishita 2007] highly ordered alumina, upon anodic oxidation, creates periodic holes into which Ni is deposited, creating a Ni mold which can be used to make nanohole arrays into polymer substrate. Such approaches can be used to make LED devices.

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4.3.5 Self Assembly Is self assembly “the Once and Future Technology” whose time may have finally come? Some applications already exist in the manufacture of LED’s. Also, as previously discussed, self-assembly is already been used to form self assembled barrier coats for immersion lithography and molds for nanoimpriting can be made by taking the natural tendency of materials to form periodic structures. The potential for this technology is great, if it

can be better

controlled so that a greater variety of nanometer-sized structures can be made. Of course, LRIs are a central part of any manufacturing scheme involving self-assembly. The synthesis of novel structures which will self-assemble into useful masks either by themselves or on a patterned substrate is also a growing field. In [Nealy 2007] low MW hydroxyl-terminated polyhydroxystyrene is spin coated and heated

on a silicon to yield a

polymer brush. This layer is coated with PMMA photoresist which is patterned and etched. Also, the block copolymer (eg PS-b-PMMA) is spin-coated onto nanopatterned substrate and annealed above Tg to form self assembled surface. Finally, how well materials self assemble may be strongly predicated by the presence of an interacting solvent. For instance, in [Bosworth 2007] poly-α-methylstyrene-β-hydrostyrene diblock copolymer (7k,14k) was used to self assemble with heating. Normally, this material has too high a Tg to be annealed and aligned, however, by using solvent swelling this can be accomplished at much lower temperatures. The type of solvent affects orientation; acetone leads to cylinders, while THF leads to parallel oriented cylinders.

By adding PAG and

tetramethoxymethylglycouril, a crosslinking resist resin is formed which can be developed with cyclohexanone-isopropanol. This and self assembly.

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approach is in effect a hybrid between standard lithography

4.3.6 Frontiers in Lithography 10 Years on In the next few year High Index Fluid Immersion, EUV or Double patterning may become the driving force for optically-driven lithography.

However, all

optically-driven

lithographies have elements in which LRIs play an important role at the interphase between substrates and exposed and non-exposed areas. Consequently, regardless of which technology wins out, if any, a better understanding of such issues will be crucial to enable the best manufacturing of nano devices.

At the very least, self-assembly will play a larger role in such

imaging schemes as it already has for the formation of spontaneous barrier layers and gradients. Depending on how the optically-driven lithographies fare, the non-optically-driven lithographies may either take over or be complimentary to them. Already, the non-optically driven lithographies nano-imprinting and self assembly are becoming more important. In order for their importance to increase, a better understanding of LRIs will certainly be important because here as well, interphases are involved. With regard to how these interphases interact and how material flows between the interphase, both kinetics and thermodynamics are needed to predicate how much can be done with these materials. As elements of self-assembly are already creeping into other fields such as nano-imprinting and immersion, it is tempting to speculate that their importance will continue to grow in the next ten years. Ultimately, self-assembly may allow the direct assembly of functioning devices without the intermediacy of current lithographic manufacturing protocols.

(eg self assembly of

nanoinorganic materials or conducting polymeric structures into functional nano devices.) Regardless of which these scenarios turns out to be true, a better knowledge of LRIs will play a crucial role.

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4.3.7 Emerging Electronic Applications: Active electronic devices made from Single-Walled Carbon Nanotubes Many novel applications of SWCNT have been proposed and demonstrated [Baughman et al. 2002]. The literature is vast and we will mention here only some representative examples in electronics where the control of LRI is likely to play an enabling role. Semiconducting SWCNT channels have been used to contruct field effect transistors they have some of the highest mobilities and can act as ballistic conductors [Tans et al. 1998; Appenzeller et al. et al. 1998; Javey et al. 2003]. While individual devices with superlative performance and some simple circuits have been demonstrated, considerable further progress is required in fabrication, materials, and device design for these devices to find application as general-purpose circuit elements. Important issues include the development of effective gate dielectric materials, fabrication of good contacts between SWCNT and electrodes, large-scale fabrication, demonstration of high-frequency operability, and ability to dope controllably with ‘n’ and ‘p’ type charge carriers. Heinze et al. [2002] showed that CNT-FET operation can be governed by modulation of the Schottky barrier with the metal contact. Wind et al. [2003] measured performance of CNT-FETs with multiple, individually addressable gate segments, suggesting a transition of switching from Schottky-barrier to the nanotube channel.

They

showed that the source-drain current has no dependence on the length of the gate when it is located in the interior of the FET, indicating the transport in the CNT-FET is ballistic over distances of a few hundred nanometers. Javey et al. [2003], by using Pd contacts in CNT-FET, greatly reduced the Schottky barrier resistance and achieved ballistic transport at room temperature. Guo et al. [2002a, 2002b] provided a theoretical study on the electrostatics of ballistic CNT-FET in one and two dimensions by solving the Poisson equation self-consistently

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with carrier statistics. Because of their robustness and small dimensions, carbon nanotubes have proven to be very effective in field emission devices, serving as field concentration points on an electrode from which electrons are easily emitted [de Heer et al. 1995].

They are being

developed for use in field emission displays [Lee et al. 2001]. SWCNT-based channels expose all their atoms to the environment, which has allowed their use as very sensitive sensors [Gruner 2006; Staii et al. 2005; Qi et al. 2003]. Such devices can be gated very efficiently in an aqueous environment, which can lead to their use as sensors for dissolved species, or of the electrochemical environment [Rosenblatt et al. 2002]. An interesting feature of these devices is that the capacitance between the nanotube and liquidimmersed gate electrode is very high, primarily because charge separation is effectively over the very small length scale (~ 1nm) of the electric double-layer surrounding the CNT. Rosenblatt et al. [Rosenblatt et al. 2002] fabricated devices that, using electrolyte gating, achieved low contact resistance, excellent gate coupling, and considerably higher mobility than back-gated CNTFETs. Larrimore et al. [Larrimore et al. 2006] have shown that such devices can be used to measure the change in solution electrostatic potential (for given gate voltage) due to the presence of redox-active species in solution.

With changing concentration of oxidized and reduced

species, they observed a shift in the relation between the conductance and the gate voltage that is logarithmic in the ratio of the concentration of oxidized to reduced species. This observation was explained using the Nernst equation of electrochemistry to relate the electrostatic potential in the solution to the gate voltage.

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4.4 Materials Design and Chemical Construction 4.4.1 Molecular Design The ability to design chemicals, materials and devices is the prized reward for the investment in understanding long range interactions in matter. Designing matter having prespecified properties has enormous practical impact. The physical and chemical properties of pure components and mixtures determine whether they are suitable for particular end uses. The design of a compound, material or mixture for a set of desirable properties is essentially the inverse of property prediction. It is analogous to the identification of molecular structures from spectra. Here we consider paradigms having formal, mathematical design formulations. The generalized design problem is formulated to derive chemical composition, structure and physical state given one or more values of at least one observable property. The generalized design problem may also include one or more constraints. End use properties and constraints may be thermodynamic, kinetic, transport, optical or structural. There may not be a unique solution to the design problem, but this is advantageous. The designer understandably welcomes a reasonable number of feasible alternatives. Design literature is commonly found in three very disparate disciplines. Each discipline typically utilizes different underlying principles for incorporating effects of long range interactions in matter. Chemical group contribution methods are common in the design of chemical compounds and mixtures. Classical force fields describing atomistic interactions and structure are common in structure-based drug design. Classical and quantum-chemical methods are common in materials processing modeling. The solution methodology of many design paradigms can be substantially improved by incorporating accurate descriptions of long range interactions.

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Modern methods used to design chemical compounds and mixtures require iterative structure generation and property estimation. There are several methods for generating and searching compounds. Structures may be composed exhaustively, randomly, opportunistically, or heuristically by resorting to expert systems. For discussion of expert systems see Gani and Brignole, 1983; Gani et al., 1991; Pretel et al., 1994; Constantinou et al., 1995; Joback and Stephanopoulos, 1995; Mavrovouniotis, 1995; Venkatasubramanian et al., 1994, 1996; Harper and Gani, 2000; and Vaidyanathan and El-Halwagi, 1994.

Reviews of mathematical solution

techniques are available in Achenie et al., 2003; and Mavrovouniotis, 1996. A generate-and-test strategy must be efficient to permit consideration of a large subset of feasible molecular structures. Recent approaches incorporate the evaluation of chemical group contribution to the desired property within a combinatorial branch-and-bound optimization formulation generating feasible structures (Friedler et al., 1998; Karunanithi et al., 2006; and Vaidyanathan and ElHalwagi, 1996.) Mathematical programming methods can be applied to a problem in which the objective function expresses the distance to the target and the entire compound search space is considered in a systematic and deterministic manner.

These methods are discussed by

Macchietto et al., 1990; and Duvedi and Achenie, 1996. Approaches to estimate property values from chemical structure include quantum-chemical computations of molecular orbitals, group contribution methods, and direct correlations between property values and molecular features. Group contribution methods represent the most common method to link pure component structure and property. Many investigators have worked on these approaches. They include Fredenslund et al., 1977; Larsen et al., 1987; Lyman et al., 1990; Benson, 1989; Van Krevelen, 1990; Domalski and Hearing, 1988; Joback and Reid, 1987; Mavrovouniotis, 1990; Reid et al., 1987; Marrero and Gani, 2001; and Kang et al., 2002. Detailed structural precision is required

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for confident assessment of the objective function. Recent work presents optimal design of chemical structure while addressing the unavoidable uncertainty in the property-prediction accuracy (Tayal and Diweker, 2001). The scope of products of interest in the chemical and materials engineering context is very broad as it includes both pure materials as well as mixtures. The size of the search space increases dramatically in multicomponent systems. Further the property models for mixtures involve additional complexities modeling interactions between components. The Universal Quasichemical Functional Group Activity Coefficients (UNIFAC) models (developed by Fredenslund et al. (1975, 1977), Prausnitz (1990), Prividal and Sandler (1990), Voutsas and Tassios (1996), Weidlich and. Gmehling (1987) Gmehling et al. (1993), and Larsen et al. (1987)) and the Universal Quasichemical Activity Coefficient (UNIQUAC) models (developed by Abrams and Prausnitz (1975), Gmehling et al. (1982), Magnussen et al. (1981), and Sandler et al. (1986)) are widely used in the chemical industry to describe activity coefficients, excess enthalpies, azeotropy, vapor-liquid, liquid-liquid, solid-liquid equilibria of mixtures. It is far more difficult to guide a multicomponent design search, however there are very strong incentives for systematic mixture selection. Designed mixtures can be tailored more precisely to the needs of a process.Design based on group-contribution property models entail the same general sequence of steps. The property specifications are formulated and the basis set of acceptable groups is selected. Then, the set of feasible candidate compound structures is formed. Once the property values of the candidates are determined, the candidates are screened to select a final set of compounds. An important step in all methods is the pruning of infeasible or chemically implausible structures. Group contribution methods are inherently entirely parameterized around long range interactions. Each pure compound or mixture is modeled as a mixture of predefined independent functional groups. The system interaction energy equals the

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Boltzmann-weighted sum of group interaction energies. The many group interaction parameters are fitted to the experimental data of systems containing the same structural groups. The many mathematical programming techniques for chemical design optimization are well established for use with group contribution methods, yet there are many limitations. The interaction parameters between all groups in the mixture must be known to make property estimations. Group contribution methods are not applicable to mixtures that contain new functional groups and their applicability to compounds very different from those used in the original training set is questionable. In addition, overall molecular structures are not considered, hence there are severe difficulties differentiating between configurational isomers and conformational rotamers. The interaction energies are not fundamental as the same model and parameter set cannot be used to predict multiple thermodynamic properties or both vapor-liquid and liquid-liquid equilibria. Implicit continuum solvation theories are established alternatives to the group contribution methods for estimating thermodynamic properties and have been applied to material design problems. A novel conductor-like screening model (COSMO) was recently developed by KIant and Schuurmann (1993) which considers a molecule’s structure and the surrounding polarization charges from a perfectly conducting solvent computed by quantum chemical theory. Thermodynamic properties are computed from the statistical thermodynamics of the: polarization charges’ interaction energies, molecular cavity formation energy and van der Waals interaction energy, resulting in the COSMO-RS (where RS stands for real solvent) model (see Klamt (1995, 2005)). The methodology continues to be refined and reformulated by various investigators (Klamt et al. (1998), Klamt (2000), Lin and Sandler (2002), Lin et al. (2004), Grensemann and Gmehling (2005), Wang et al. (2005), and Wang and Sandler (2007)). The fully self-consistent thermodynamic model permits calculation of solution activity coefficients, excess enthalpies,

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azeotropy, vapor-liquid, liquid-liquid, solid-liquid equilibria of mixtures for single and multicomponent systems. There are rather severe advantages to this approach over group contribution and classical forcefield methods. A molecule’s electronic structure and polarization environment are carefully and accurately considered using a detailed quantum chemical calculation. Hence the effects of configurational isomerism and conformational rotations are accurately considered. Once this is done for the individual molecule a single time, the results are now pressumed applicable for any mixture or condensed state without recalculation. The statistical thermodynamic calculations are analytically exact, hence high precision is obtained without the time-consuming ensemble averaging. Since the statistical thermodynamical calculations are very fast, property predictions can be calculated very efficiently. The same parameters are used for vapor-liquid, liquid-liquid and liquid-solid equilibria. The more recent refinements are comparably accurate relative to the established group contribution and classical force field methods. The COSMO models take very careful consideration of fundamental long range interactions including electrostatics, electrodynamics and medium polarizability. COSMO design is a molecular design methodology to find an optimal selection of mixture components given an objective function in terms of thermodynamic properties. Lustig has reported on this several times (2007, submitted; Lustig et al. 2006). A genetic Monte Carlo algorithm inverts the COSMO-SAC (where SAC stands for surface activity coefficient) model by mutating the COSMO polarization charges and allowing selective evolution of mutations to optimize the problem objective function (Lin and Sandler, 2002). The methodology has been demonstrated for designs of ionic liquids where the diversity of options for charge centers, chemical group functionality, valency and molecular configuration presents the most significant obstacle to their

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selection. This is a unique design methodology which directly utilizes the basic long range interactions. Another aspect of molecular design comprises computational tools used to analyze protein active sites and suggest compounds that may bind to these sites. This area has been called “ligand design”, “inhibitor design”, “structure-based drug design”, “rational design” and “de novo design” somewhat interchangeably. Reviews are available in this broad area from Murcko (1997a, 1997b), Bohm (1993), Lewis and Leach (1994), Clark et al. (1997), Good and Mason (1996), and Balbes et al. (1994). A design basis is enabled given a three-dimensional, atomistic protein structure, usually derived from experimental spectroscopy. The design methodology comprises several steps. First, constraints are defined on either the active site, receptor site, homology models, receptor models, pharmacophore models. The constraints are most frequently steric to ensure binding contacts at one or more sites and restricted to preferred chemical functionalities. Second the full structures of candidates must be generated. Third, compliance with constraints and fitness with an objective must be evaluated for each structure. Given a first pass screening, more rigorous verification is performed for the best designs by more accurate methods. Published methods are fraught with several difficulties. Most methods do not consider or find all possible fragments and molecules which satisfy the binding geometry criteria. Generally molecular generation methods are inefficient as they produce structures which would be either chemically unstable or fit poorly in the cavity. Methods generally do not account for structural relaxation of either the host or binding structures. Methods generally account for neither relaxation in solvent structure around the cavity nor the influence of such effects on the protein. The design process generally requires a large amount of human intervention to interpret the ligand-cavity fit and binding. Such intervention normally requires strong qualifications in

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both synthetic and computational chemistry. Molecular structures and intermolecular energies are derived from classical force field models. As such long range interactions are approximated crudely in terms of separate electrostatic and London dispersion models. Static partial charges and van der Waals constants are assigned to each atom, where such assignments for each atom can be specifically classified according to the functional group or neighboring atoms in which the atom is bonded. Given the large sequence of design steps and number of candidate structures normally considered, only such simplified long range interaction models are currently practical, even if they prove to have limited accuracy. Computer-aided materials design is now an actively used tool in materials science. Recent developments in the use of electronic theory have been able to explain many experimental results and to predict the physical properties of materials before actually synthesizing them. In common with computational chemistry, there are three major levels of theory for atomistic simulations of materials: first-principles quantum mechanics, semi-empirical quantum mechanics, and quasi-classical methods such as force field approaches.

Density

functional theory has become the prominent first-principles approach for detailed atomistic investigations of materials. Accurate predictions of geometric structures and total energies for systems up to about 100 atoms have become the corner stone for the success. The major challenge is now the simulation of dynamic phenomena on the quantum level over time intervals long enough to provide statistically meaningful results. Reliable predictions can now be made for a wide range of problems, such as band structure and structural and thermodynamic properties of compound semiconductors. To date, materials design literature is essentially a restatement of property prediction or atomistic simulation of materials processing. A good selection of design literature can be found in Ito (1995, 1998), David et al. (2007), Jones et al. (2007), Nakano et al.

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(2007), and Katayama-Yoshida et al. (2007). The generalized materials design problem formulated to derive chemical composition and physical state given one or more values of at least one observable property is not yet widely practiced.

4.4.2 Materials Design From a fundamental point of view, the idea of materials or – more generally – compound design corresponds to the inversion of the mapping between a given system and its properties. Mapping system to properties is the conventional scientific approach aiming at the elucidation, understanding, and prediction of the interplay of the intervening forces which underlie the observed phenomena. Historically, a vast plethora of theoretical approaches and models emerged, all with the final purpose to sufficiently accurately predict all properties which are exhibited by any given systems. Design approaches try to accomplish the reverse, i.e. to predict the system which will exhibit given target properties. In order to screen at least significant parts of chemical space in silico, empirical but very cost effective approaches to the generation of diverse compound libraries and the rapid screening of their mapping, have been devised and deployed for pharmaceutical applications and drug discovery with some success. These methods are also known as Quantitative Structure Property Relationships (QSPR) (von Schleyer et al. 1998) In 1998 Ceder et al. employed first-principles calculations in order to heuristically “guide” their materials design for lithium batteries, while Besenbacher, Norskøv and coworkers (Besenbacher et al.,1998) made use of such calculations for surface alloy catalyst design. The same group (J’ohannesson et al.,2002) also investigated the use of genetic algorithms, and successfully applied them more recently to the design of ruthenium catalysts for the synthesis of ammonia (Honkala et al.,2005).

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More interestingly, however, Wang and Zunger (1993) already considered the problem of searching those electronic wavefunctions which exhibit a specific target eigenvalue. Later, Franceschetti and Zunger (1999) discussed the inversion of the mapping of atomic configurations to electronic structure through iterative minimization of an object function,

, by variation of

position and identity of atoms . See also Dudiy and Zunger (2006) for a recent application of this inverse band structure approach to the problem of impurity design in alloys. A variational elementary particle number Ansatz towards the minimization of the penalty functional, measuring the deviation of the instantaneous property from the target property, was proposed by von Lilienfeld et al. (2005). It is based on the framework of a molecular grandcanonical ensemble density functional theory notion which accounts not only for non-integer variations in electron-number,

, but also in proton distribution, Z (r ) Within Kohn-Sham

density functional theory (Hohenberg and Kohn, 1964; Kohn and Sham, 1965; Parr and Young, 1989), all observables can be expressed as a functional of the electron density, n(r), which is, up to a constant, in a one-to-one relationship with

and

. As a result, not only different

stoichiometries and configurations can continuously be transformed into each other, but also gradients, Laplacians, and higher order derivatives with respect to chemical composition are defined. Reverse compound design (RCD) can hence be recast in terms of a particle minimization problem, very analogous to the numerical optimization of the coefficients defining an electronic wavefunction when determining the ground state energy. Through variation of chemical composition, this scheme showed consistently promising results for controlling inter- molecular energies energies of hydrogen-bonded complexes, Fermi levels of molecular electronics model systems (von Lilienfeld and Tuckerman, 2007; Marcon et

al. 2007) as well as binding energies of drug candidates. Wang et al. (2006) proposed a very

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similar method, namely to minimize an object functions in the coefficient space spanned by a linear combination of atomic potentials which represent the external potential in the electronic molecular Hamiltonian. This idea was successfully applied to tuning polarizabilities as well as hyperpolarizabilities, and lowest occupied molecular orbital eigenvalues (Keinan et al. 2007). Also, very recently Herrmann et al. (2007) applied ideas analogous to the one of Wang and Zunger to the problem of identifying those vibrational modes in a complex compound which exhibit certain vibrational levels. A very important problem, however, remains unaddressed in all of the aforementioned approaches. Namely, that the chemical space, i.e., the property penalty hyper space, spanned by all the stable combinations of

and

, typically

, is very high-

dimensional due to all the combinatorial possibilities to arrange the different nuclei of the periodic table in real space. Already when ignoring the configurational degrees of freedom and considering solely the stoichiometrical particle space the dimensionality of chemical space amounts to 110 Nn + 1 . Where 1 stands for

,

for the number of nuclei, and 110 for their

atomic number. Furthermore, the computational cost of determining a numerical value of depends, usually non-linearly, on

and

also

, i.e. the extension of the system. Finally,

chemical space is very likely to generally possess regions which are not only smooth but very rough or very flat. It seems probable, that a successful scheme will rely on a smart combination of various algorithmic, mathematically diverse, ingredients, such as derivative-based, genetic, molecular dynamics, Monte Carlo, dimensionality reduction, or artifical intelligence techniques. As a concluding remark it appears noteworthy that successful design algorithms will have to meet three pre- requirements. (i) The accuracy of the mapping, be it through QSPR, empirical force-fields, or ab initio electronic structure methodology, must be sufficient in order to generate

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the correct ranking of observables as they approach the target observable. (ii) Chemical configuration (isomers) and composition (stoichiometry) must be variables. (iii) A robust optimization algorithm must be devised for the efficient exploration of relevant areas in chemical space. If compound design is to be performed beyond a mere screening approach this requirement precludes the usage of force-fields which assume fixed composition, connectivities, or conformations. Of particular interest for compound design would be to employ interatomic potentials that reliably predict properties in all phases for compounds consisting of all elements in the periodic table with the sufficient accuracy to perform compound design (see Pettifor and Cottrell, 1992). First attempts towards “reactive” forcefields were made (van Duin et al. 2001), but still lack convincing evidence in terms of reactivity as well as accuracy, for general applications which do not closely resemble the training systems. Alternatively, first-principles approaches do not only elegantly circumvent the problem of parameterizing internuclear potentials but also open the door towards the inclusion of electronically excited, magnetic or chemically reactive states properties into the object functional. They are computationally, however, still orders of magnitudes more demanding. Finally, as a prominent example of application we name the problem of molecular crystal engineering, as long as the ab initio prediction of molecular crystals is too unreliable, the in silico engineering of crystal properties remains elusive.

For discussion of molecular crystal

engineering see Desiraju (2007), Dunitz and Scheraga (2004), and Day et al. (2005).

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4.5 Local Studies of Long-Range Interactions by Scanning Probe Microscopy Long range interactions (LRI) including van der Waals (vdW) and electrostatic forces control multiple phenomena ranging from the self-assembly of the molecules on surfaces, colloidal crystals, conformation and structure of proteins on all structural levels, and functionality of living cells. Understanding these phenomena necessitates the development of experimental strategies to probe static and dynamic aspects of LRI on the relevant time, energy and length scales. This is a first step towards understanding the emergent behavior in complex systems controlled by LRIs, and hence developing pathways for control and utilization of LRIs. Scanning Probe Microscopy (SPM) [Kalinin & Gruverman 2006]

offers a natural

pathway for probing LRIs on the nanoscale directly. To date, a number of excellent reviews and books summarize applications of SPMs for polymers, biological systems, ferroelectrics, and other materials and devices [Butt et al. 2005; Hofer et al. 2003; Foster & Hofer 2006]. In the last decade, SPM-based force spectroscopy and optical tweezers technology have given rise to new areas of scientific enquiry, including thermodynamics and kinetics of single molecule reactions, [Ritort 2006] which stimulated the development of novel areas of statistical physics [Jarzynski 1997]. In condensed matter physics, SPMs observations of spatial variability of superconductive gap in high temperature superconductors [McElroy et al. 2005] and charge ordered states in manganites [Renner et al. 2002] and rutenates [Matzdorf et al. 2000] have provided new clues to the physical properties of strongly correlated oxides. Given the large number of reviews, and constantly emerging novel applications of SPM, in this section we aim to describe the general principles of SPM as applied to LRIs, summarize some of the outstanding challenges in the field, and outline some of the possible pathways for development.

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4.5.1 The SPM approach The quintessence of an SPM approach is a combination of local probe bearing a specific aspect of studied functionality (e.g. charged [Nonnemmacher et al. 1991] or chemically functionalized [Noy et al. 1995] probe) combined with positioning system that locates it at a selected location with respect to the studied system, and detection system that measures forces or currents on or other interactions through the probes, thus linking nanoscale probe-surface interactions to the macroscopic world. The progress in SPM capacity to probe the relevant phenomena is directly linked to the performance and functionality of these elements. Positioning systems, while sometimes presenting a serious challenge to engineering, are well understood and developed. Platforms that allow drift-free localization of probe with respect to the surface (e.g. lateral drift of smaller then 1-10 A in 1 hour) have been developed in the context of low-temperature Scanning Tunneling Microscopy and Atomic Force Microscopy and could be extended to ambient/liquid environments should the need for this become obvious enough to justify increased financial and design requirements. The detector systems used in SPM, i.e. current amplifiers in Scanning Tunneling Microscopy or optical position sensor/cantilever/electronics force detectors in Scanning Force Microscopies have intrinsic limitations on bandwidth and sensitivity enforced by fundamental physical limits (e.g. thermomechanical noise, laser shot noise, Johnson noise, etc). However, these fundamental limits are typically not achieved, and the noise is dominated by the microscope electronics or environment. Notably, the noise level of an SPM system is the fundamental factor that determines both the detection limit and spatial resolution of the image (more precisely, information limit of the technique) [Kalinin et al. 2006]. Correspondingly, the strategies for improving SPM performance invariably include low acoustic and electronic noise

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environments ranging from acoustic hoods and active vibration damping systems to specially designed low-noise buildings. Minimization of the electronic noise of SPM electronics and laser noise present another venue for technique development. Recent introduction of low-noise detector systems by H. Yamada group has allowed significantly increase the resolution in noncontact AFM [Fukuma et al. 2005]. Data processing electronics in cantilever-based scanning probe microscopies should be mentioned specifically, since it links the ~0.1-10 MHz time scale of the cantilever oscillations to the ~1 kHz time scale of feedback loop operation or single pixel acquisition. This stage selects relevant time-averaged aspects of cantilever response (e.g. amplitude and phase for lock-in detection, resonant frequency and amplitude for phase locked loops), and plays a dual role of making the acquired information volume manageable (1 data point/pixel, rather then 10,000) and at the same time limits the information obtained from the experiment. The data processing options are strongly affected by the environment – dynamics and detection limits for the cantilever in vacuum, ambient, and liquid environments are vastly different. For example, the high-quality factors of cantilevers in vacuum severely limit the use of the amplitude-based lockin detection methods, and necessitate the use of PLL-based frequency tracking. Finally, the probe is the heart of an SPM experiment. Probe functionality determines both the measured functionality (e.g. chemical functionalization, magnetization, charge, temperature), and spatial resolution at which the properties can be measured. There is typically an inverse relationship between resolution and sensitivity, necessitated by the constant detection level of the system. The performance of an SPM probe is always limited by the design and fabrication process. For example, electrostatic interactions can be measured on arbitrarily small length scale if a conductive metallic sphere with known and controlled potential can be placed at arbitrary

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location and force on it can be measured. Practically, the probe represents the apex of the conductive cone that can be fabricated. Hence, the local part of electrostatic forces is measured jointly with the signal from the conical part. The optimal probe size, R, can then be determined as the one for which electrostatic force is larger then response from the conical part for experimentally accessible range of probe-surface separations (of order or R) [Jacobs et al. 1998].

4.5.2 Types of SPM measurements The multitude of the existing SPM methods necessitates the development of appropriate classification methods. One approach to classification is based on the type of the experimental apparatuses – e.g. STM utilizing the conductive metal tip, AFM utilizing the tip on a force sensitive cantilever, or nanoindentation. Alternatively, SPM methods can be classified based on measured functionality, frequency region of operation, modulation approach, etc. From the perspective of LRI measurement functionality, there are two parameters that can be controlled in an SPM experiment, namely tip-surface separation and probe bias. Detected are the probe current and force components acting on the probe. Hence, the SPM imaging mechanism can be represented as force-distance-bias surface Fc = Fc (h, Vtip , µ ) , where h is the tip-surface separation (for non-contact methods) or indentation depth (for contact), Vtip is probe bias, and µ are parameters describing chemical functionality of the probe [Figure 44]. Note that the cantilever detection system adopted in most commercial SPMs implies that full force vector, Fc , cannot be measured directly. Rather, flexural cantilever displacements measure a superposition of normal and longitudinal (along the cantilever axis) force components, while torsional displacements are sensitive to lateral force components. Practically, the fact that torsional and longitudinal spring

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constants are larger then vertical implied that flexural response is dominated by normal force component. One of the primary challenges in SPM probing of the LRI is the decoupling between multiple interactions simultaneously present in the tip-surface junction that all contribute to the forces, Fc . One approach to measurement of LRI is based on measurement force at several separations from the surface. The alternative is offered by modulated methods, in which a specific functionality of the probe is modulated, and the oscillatory response is detected. This allows both to probe a subset of tip-surface interactions (e.g. oscillating electrostatic potential does not affect VdW forces), minimize noise level by getting away from 1/f corner and utilizing resonance enhancement, and probe linear response dynamics though measurement of both amplitude and phase of response. Practically, only some aspects of probe functionality can be modulated at rates of >1 kHz, required for imaging. These include position, h (e.g. acoustic driving) or force, Fc (e.g. magnetic driving) and electrical bias, Vtip . Chemical functionality, hydrophobicity, etc. and other chemical functionalities, µ , do not offer obvious universal strategies for modulation, even though optically- and bias induced transformations provide some possibilities. Below, we briefly discuss SPM techniques based on whether the separation between different interactions is achieved through force-based measurements, or voltage modulated measurements.

4.5.2.1 Direct force measurements The most straightforward application of SFM to probe long-range interaction forces is direct measurements of static (DC) force between functionalized probe and the surface using the cantilever position detection. The experimentally achievable force sensitivity levels is of order 1-

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10 pN are sufficient to probe a single hydrogen bond [Rief et al. 1997]. The projections made in the pioneering work by Binning and Rohrer suggest that forces down to 10-18 N can be measured, and steady progress in this direction is achieved in the context of e.g. Magnetic Resonance Force Microscopy [Rugar et al. 2004]. In measuring tip-surface forces, a requirement in addition to force or deflection sensitivity is the measurement of the relative positions of the surface, i.e. surface topography. In an SPM experiment, the force-interaction is used both to determine the position of the surface and to measure effective interactions, hence necessitating strategies to differentiate the two. One such approach is based on direct measurement of force-distance curves at each point yielding 3D data set. These sets can be analyzed to provide 2D maps of various properties. On of the most exciting examples of this approach is molecular unfolding spectroscopy, in which force-distance curves obtained at different rates contains information on thermodynamics and kinetics of forceinduced reaction on a single molecule level. Alternatively, the force distance curves can be used to determine local adhesion, indentation modulus, or long-range electrostatic interactions. Chemical fictionalization of the probe allows controlling the nature of tip-surface interaction and probe hydrogen bonding and acid-base interactions. The review by H.J. Butt et al [2005] provides an in-depth and detailed account of force-based studies of materials. The direct force measurements at each point brings a dual challenge of large data acquisition times and relatively low pixel density, and the necessity to analyze the large 3D arrays of data to extract relevant parameters that can be plotted as 2D maps. An alternative approach for measuring LRIs is based on the decoupling topography from measured force component either through (a) height variation, (b) use of force-modulation approaches, (c)

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methods using fast spectroscopy, or (d) detection through complementary mechanical degrees of freedom. The example of the height variation approach are well-known double-pass or interleave modes. In these, the first AFM scan is used to determine the position of the surface, i.e. condition at which measured signal, R (h, V0 ) = R0 , where R0 is a set-point value. The feedback signal, R , can be static deflection for contact AFM, oscillation amplitude for amplitude-based detection signal, or frequency shift for frequency-tracking methods. The second scan is performed to determine interactions at different distance and bias conditions to measure R = R(h + δ , V1 ) . As a typical example, magnetic and electrostatic force microscopies utilize the fact that these forces are relatively long ranged and weak compared to the VdW interactions. Hence, once the position of the surface has been determined, force measurement at significant ( δ = 10-500 nm) separation yield magnetic (if probe is magnetized) or electrostatic (if probe is biased) force components. The alternative approach to force detection is based on the ac modulation approaches, e.g. Atomic Force Acoustic Microscopy, force modulation, and similar methods. In these, the condition of R (h, V0 ) = R0 is used to determine the position of the surface, and modulation of the probe height or bias is used to obtain additional information on the distance- or bias derivative of the force-distance-bias surface. For example, in the small signal approximation the AFAM signal is related to (∂h ∂F )V =const . In addition to providing additional information (i.e. not only the force curve, but also its derivative), the modulation methods allow to increase sensitivity by moving away from 1/f noise corner, and control effective cantilever stiffness through the inertial stiffening, i.e. the dynamic range of the measurements. This decoupling can be performed dynamically, e.g. response phase and amplitude in AFM phase imaging (amplitude yield

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information on topography, and phase yields information on elasticity and adhesion). The emergence of dual-modulation modes [Proksch 2006] have allowed to increase the sensitivity of modulation methods by lifting the restrictions imposed by weak dissipation that confines the phase changes to a relatively small region of phase space of the system. A number of approaches for LRI detection are based on the data processing beyond simple lock-in or PLL detection. For example, the use of the functional agent coupled to the probe with a flexible linker combined with separate detection of the signal from top and bottom of trajectory forms the basis of molecular recognition imaging [Raab et al. 1999]. A number of methods have been developed to sample a larger region of the force-distance phase space of the system beyond small-signal approximation, e.g. Pulsed Force Mode [Miyatani et al. 1997]. Finally, different interactions can be decoupled using flexural and torsional degrees of freedom of the probe, with normal force mapping the topography, and friction forces sensitive to adhesion and chemical interactions. In lateral force microscopy [Mate 1987], the topography is detected from the normal force signal, while friction force detected from the lateral signal provides the information on the short range tip-surface interactions sensitive to local chemical composition, molecular orientation, etc. Recent development of harmonic detection method [Sahin et al. 2007] allows the reconstruction of tip-surface interactions based on decoupling between torsional and lateral oscillations.

4.5.2.2 Voltage modulation approaches in ambient and liquid The efficient approach for decoupling of the vdW-Ld and electrostatic components of LRI is based on the use of voltage modulation. While the use of force or distance modulation measures the gradients of both vdW-Ld and electrostatic forces, the voltage modulation allows the electrostatic interactions to be probed selectively. Electrically modulated SPM in ambient

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and ultra high vacuum environments are very well established. These include Kelvin Probe Force Microscopy (KPFM) with amplitude (measured force) and frequency (measures force gradient) feedback, and Piezoresponse Force Microscopy. The applications of these modes are well known in areas as diversified as local work function imaging [Henning et al. 1995], mapping electrostatic potential in operational devices [Shikler et al. 1999], and sub-10 nm structural imaging of calcified tissues based on piezoelectricity [Kalinin et al. 2005] [Figure 45]. The spatial resolution and sensitivity of these methods are dictated by environmental limitations and nature of tip surface interactions to ~1 mV and ~30 nm for KPFM and 1 pm/V and ~5 nm for PFM. Further progress in areas such as high resolution imaging, probing macromolecular transformations, or cellular and sub-cellular electrophysiology necessitates implementation of electrically modulated SPM in liquid conductive environments. The key task here is the capability to control dc and ac electric potential on small length scales. The conductivity of solution, stray currents, and electrochemical reactions present significant obstacles, which result in a dearth of experimental effort in this direction. Experimentally, it was shown that the use of sufficiently high ac frequencies accessed though direct imaging or frequency mixing down conversion allows probing ac behavior (local ac field is localized) [Figure 46] [Lynch et al. 1006; Rodriguez et al. 2006]. At the same time, dc fields are not localized in most solvents [Figure 47] [Rodriguez et al. 2007]. The development of insulated and shielded probes [Rosner and van der Weide 2000; Frederix et al. 2005] offers a pathway to future progress (e.g. k = 0.01 – 1 N/m, area ~10-100 nm, conductivity ~30Ohm vs gold) in this area that will open broad access to these phenomena, and necessitates the development of appropriate theoretical models.

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4.5.2.3 Functional Probes In the last several years, a number of approaches for imaging are emerging base don probes carrying more complex local functionalities, including the field effect transistors [Park et al. 2004], electrochemical probe, etc. While the field is still in the nascent state, there is clearly tremendous potential for progress.

4.5.2.4 Probing dissipative dynamics Understanding long-range interactions ideally requires probing not only the conservative, but also the dissipative part of the force. SFM offers a natural approach to probing local dissipation by comparing the quality factor of the cantilever interacting with the surface and away from the surface. Assuming that the internal dissipation of a cantilever does not change and that environmental dissipation changes only insignificantly, the changes in Q-factor will be due only to the tip-surface dissipation. Simple estimates suggest that detection limits set by the thermomechanical noise are of the order of 3 10-17 W (experimentally achieved limit is ~0.03-0.1 pW) [Proksch 1999]. However, until recently the dissipation probing in SPMs has been limited. Indeed, cantilever dynamics in the vicinity of the resonance in the simplest harmonic oscillator approximation is described by three parameters – resonance amplitude, resonance frequency, and Q-factor. Experimentally, SFM based on sinusoidal modulations, which are now the vast majority of experimental platforms, measure only 2 independent parameters, i.e. amplitude and phase in lock-in detection and resonance frequency and amplitude for phase-locked loop based frequency tracking methods. Hence, dissipation is not addressed directly. Practically, with a single frequency modulation, dissipation can be determined if the driving force acting on the system is known. This provides an additional constraint on the signal, the assumption implicitly

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used by Cleveland [1998] and Garcia [Tamayo and Garcia 1998]. In the frequency tracking methods [Albrecht et al. 1991], the presence of an additional constraint implies that the response amplitude is inversely proportional to the Q-factor. These approaches were implemented by several groups to study magnetic dissipation [Proksch et al. 1999; Gruter et al. 1997], electrical dissipation [Denk and Pohl 1991], and mechanical dissipation on atomic [Kantorovich and Trevethan 2004] and molecular levels [Farrell et al. 2005]. However, this approximation is applicable rigorously, in a limited number of cases, e.g. magnetic driving (if sample is paramagnetic) or acoustic driving with flat (no dispersion) transfer function. Even for acoustic driving by the piezo, adopted in most SPMs, the non-idealities in the transfer function of the piezodriver lead to the qualitatively incorrect results in e.g. MFM dissipation studies [Proksch 2007]. For methods based on electric excitation, the relationship between the driving voltage and local force is position dependent, and this dependence is convoluted with cantilever response function, and the two cannot be distinguished at single frequency measurement. Simple frequency sweeps or ring-down measurements are usually time consuming, and thus have only limited applicability to imaging applications. Recently, the advent of multiple-modulation methods such as Dual AC [Rodriguez et al. 2007] and band excitation [Jesse et al. 2007], that open pathway for simultaneous probing of finite region of Fourier space, offer a potential path forward [Figure 48]. 4.5.3

Future developments In formulating the possible pathways the SPM field will develop, it is probably

reasonable to distinguish the short-term improvements, the need for which is obvious and which are within the engineering capabilities (albeit the financial aspect of pursuing those is not immediately obvious), the medium-range goals that represent significant experimental and

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engineering challenges, but which are (a) either necessitated by practical needs, or (b) enabled by engineering developments, and serendipitous directions that are either unpredictable, or are believed to be impossible in the context of existing technology. The short term goals as applied for SPM include more stable SPM platforms, reducednoise detectors, and functional SPM probes including shielded, insulated, multiple electrode geometries, etc. The novel probe concepts and prototypes appear regularly in academic and national lab environment; however, their transfer to mass-production is always a problem. Similarly, detection systems beyond cantilever (which mixes longitudinal and normal force components) that allow 3D vector force measurements have been reported [Dienwiebel et al. 2005]. Note that the importance of the mass production should not be underestimated – e.g. the explosive growth of AFM applications since 90’s is related to the introduction of the etched Si probes that can be fabricated in large volumes reproducibly [Figure 49]. The obvious medium-range goals for SPM development necessitated by applications are high-frequency probing beyond ~10-100 kHz limit imposed by amplifier bandwidth-gain product for STM and ~1-10 MHz for AFM. The second requirement is the chemical identification of the species below the SPM probe, i.e. chemically specific imaging. The possible pathways for these include combining SPM with microwave and optical measurements, in which SPM tip acts as a local passive antennae (e.g. amplifies signal in SERS mode, or breaks the evanescent wave condition in TIRF), or is used for detection. In the latter case, the use of amplitude modulated or pumped probe measurements allows linking the time scales of optics or microwaves to the time scale of SPM detection system. These methods can bring into reality the capability to probe ultrafast phenomena and chemical identification below the tip.

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Complementary to these are developments enabled by the parallel developments of the technology. A remarkable example is development of fast data analysis algorithms due to introduction of commercial fast DAQ cards. In SPM, the typical frequency range of operation for the cantilever is ~0.1-10 MHz (and expected to grow once ultrasmall levers for video-rate imaging are introduced), while pixel time and feedback times are of order of ~1 kHz [Figure 49]. The typical data conversion process from real-time trace of cantilever oscillations to measured signal includes either lock-in processing to extract amplitude and phase, or phase locked-loop to extract resonance frequency and amplitude. In this process, the information on single-time or aperiodic events is essentially lost. Similarly, the capability to respond and control events in the tip-surface junction are limited – i.e. response occurs on the time scale of a single oscillations, and feedback becomes active only after 1000. The development of fast electronics now allows to achieve control of cantilever on a single oscillation, as well as to use much more complex signal processing schemes. While full potential of such methods are impossible to predict, some of the examples will include adaptive control of molecular transformations, probing inaccessible regions of free energy surface, controlling conformation pathways, etc, in analogy of recent studies of spin control by D. Rugar and J. Mamin group [Mamin et al. 2005]. Last by not least, the serendipitous discoveries are impossible to predict, or combine clear need with no feasible pathway to achieve it. Some of the many examples include capability to modulate chemical functionality of the probe in time (note that light-induced processes are slow, since cross-sections are small unless SERS is involved, and electrical modulation affects also electrostatic forces), or using active feedback to lower “temperature” of the probe weakly thermally coupled to environment.

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Finally, the development of multiple probe SPM systems allows truly spectacular potential for probing LRI interactins. The independently controlled SPM probes are currently being developed for STM applications, including classical 4-probe conductivity measurements of surfaces and nanostructures, scanning gate microscopies, or piezoresistive and piezogalvanic measurements in nanowires and nanotubes. The adoption of the force-based multiple-probe SPMs will provide multiple opportunities in studying long-range interactions, including many body effects, local potential and fields, etc. Finally, what is the key capability that SPM studies of LRI can bring to the community? In my opinion, one of the least understood and least used aspect of nanoscale is the conversion between electrical and mechanical phenomena beyond simple capacitive forces. There are common in inorganic materials – e.g. 1/3 inorganic compounds are piezoelectric. Furthermore, electromechanical coupling is ubiquitous in biological systems, underpinning processes from hearing to motion to cardiac activity, and soft condensed matter systems such as polyelectrolytes, redox-active molecules, ferroelectric polymers, etc. However, electromechanical properties are traditionally difficult to access even in the macroscopic systems due to the smallness of corresponding coupling coefficients. On the nanoscale, even thin film measurements have become possible only with the introduction of double-beam interferometer systems in 90ies. This is in drastic contrast to mechanical and transport measurements, that evolved continuously from macro to nanoscale. SPM methods combining high field localization and sensitivity to extremely small mechanical response offer unique capability to study electromechanical coupling on the nanoscale. While introduced only in ~1996 in ferroelectric community, these methods has become the mainstay for characterization of ferroelectric materials, and applicability to piezoelectric biopolymers and III-V nitrides and imaging in liquid has recently been

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demonstrated. In the future, it will open the pathway for probing and controlling electromechanical conversion on a single molecule level and harnessing these for device applications [Figure 50 Figure 51].

4.6 Scattering Probes of LRIs 4.6.1

Probing LRI’s at interfaces using X-ray scattering The worldwide availability of synchrotron X-ray and neutron scattering user facilities

(Brown et al., 2006) has made it routinely possible to determine the structure and dynamics of both free and buried interfaces at sub-angstrom to millimeter length scales (Fenter and Sturchio, 2005) and femtosecond to millisecond time scales (Rheinstädter et al., 2006). Advances in computational theory, algorithms and processing power are beginning to permit quantitative comparison of atomic and molecular interactions in condensed phases over similar length and time scales (Cygan and Kubicki, 2001; Schoen and Klapp, 2007).

This convergence of

capabilities offers unprecedented opportunities for exploring LRIs at the nanoscale for materials science and engineering. Electromagnetic radiation is elastically or inelastically scatterd by the electrons surrounding atomic nuclei, and the penetrating power of X-rays has long been applied in imaging biological and materials structures. The physics of interaction of electromagnetic radiation with atoms is precisely known, permitting crystalline structures to be determined with extreme precision.

Synchrotron X-ray sources provide highly-intense beams, the energies and

polarizations of which are highly tunable. These enhancements over conventional X-ray sources permit a wide range of unique studies of condensed matter, as recently reviewed for earth science applications by Fenter et al (2002) and papers therein. The high intensities and wide range of wavelengths available from synchrotron sources permit determination of local ordering, even in

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glasses and other amorphous or poorly-crystalline materials (Egami, 2004, 2007).

X-ray

absorption and fluorescence provide direct identification of the specific elements interacting with the beam, and methods such as absorption fine structure, near-edge and photoelectron spectroscopy can be used to determine the valence state of the target element and its nearestneighbor distributions and elemental compositions (Wada et al., 2007; Glover and Chantler, 2007; Evans et al., 2003). 3-D tomographic imaging of structures and elemental distributions within condensed matter is now routinely performed at synchrotron light sources (Sutton et al., 2002), even at high temperatures and pressures (Wang et al., 2005). Synchrotron X-ray methods for probing elemental distributions at interfaces have been highly-developed in recent years. Grazing-incidence small angle scattering and absorption fine structure can give precise information on the bonding configuration of sorbed ions and the distribution and orientation of nanoparticles on solid substrates (Waychunas, 2002, Waychunas et al., 2006; Saint-Lager et al., 2007). Crystal truncation rod studies can provide 3-dimensional information, at sub angstrom resolution, on the relaxation of crystalline surfaces and the distributions of water and ions in liquid electrolytes at the crystal-water interface (Lee et al., 2007; Catalano et al., 2007; Zhang et al, 2007). Some examples for cations on the rutile (110) surface are described elsewhere in this publication. Resonant anomalous reflectivity can probe a wide length-scale on either side of a crystal/fluid interface and can give information on the distribution of elements not specifically oriented relative to the underlying crystal structure (Fenter et al., 2007; Park and Fenter, 2007).

Reflectivity studies have also revealed the

interaction of water with hydrophobic surfaces (Poynor et al., 2006). X-ray standing wave studies can also probe the distribution of fluorescent trace elements at interfaces with crystalline phases, also at subangstrom resolution, and distinguish the ordered fraction of the total

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distribution of the trace element, relative to the underlying crystal structure (Zhang et al., 2004a,b).

Buried interfaces between dense solids have also been probed by non-specular

scattering and absorption spectroscopy (Lutzenkirchen-Hecht et al., 2007) Though third-generation synchrotron sources provide sufficient intensity to overcome large attenuation effects in condensed matter, attenuation is proportional to density and atomic number, making even the detection of oxygen, carbon and lighter elements difficult. Neutrons, on the other hand, are scattered by atomic nuclei, which occupy an exceedingly small volume of even the densest phases, such that neutrons can penetrate many centimeters of dense matter. This makes high pressure/temperature studies readily possible, and important advances in deepearth petrology and materials are being made at neutron diffraction facilities (Matthies et al., 2005; Suzuki et al., 2001). The coherent scattering length can be positive or negative, depending on whether the interaction with the nucleus is attractive or repulsive. Furthermore, the scattering lengths are a complex function of the atomic weight (rather than atomic number), and thus different isotopes of the same element interact differently with neutron beams, and the light elements interact strongly with neutrons, making detection independent of atomic number (Bee, 1988; Kreitmeir et al., 2007).

Hydrogen, which is nearly impossible to detect by X-ray

scattering, has a coherent neutron scattering length comparable to heavier elements, and a very large incoherent scattering length, useful for probing the dynamics of hydrogen-bearing compounds.

The coherent scattering lengths of hydrogen and deuterium are opposite in sign,

making many unique experiments possible. Wenk (2006) provides a recent and thorough review of neutron scattering applications in the earth sciences, highlighting techniques readily applicable to materials science.

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4.6.2

Probing LRI’s at interfaces using neutron scattering Neutron diffraction is highly complementary to X-ray diffraction, since light elements as

well as heavy elements are readily detected (Kim et al., 2007; Goncharenko 2005), and isotope substitution can be used to isolate specific substructures within complex crystals and poorlycrystalline materials exhibiting local order. A unique aspect of neutron scattering is its sensitivity to magnetic substructures within solid phases (Apetri ,et al., 2007; Kimber et al., 2006, Hayward et al., 2005). Isotope substitution can even be used to determine the hydration and complexation structures of ions in homogeneous liquids (Enderby, 1995; Neilson et al., 2002; Muenter et al., 2007). Neutron wide angle, small angle and ultrasmall angle scattering has been extensively used to identify structures (scattering density contrasts) in complex fluids, polymer blends and solid phases angstrom to millimeter length scales. This technique is also widely employed in determining surface fractals, particle size distributions and pore-filling characteristics of ceramics, metals and mesoporous materials (Rother et al., 2007; Kaewsaiha et al., 2007; Ficker et al., 2007). Another unique feature of neutron scattering is the strong incoherent scattering of hydrogen which results from the gain or loss of energy of incident neutrons interacting with the same hydrogen nucleus within a sample at different times. Neutron inelastic (INS), quasielastic (QENS) and spin-echo (NSE) spectroscopies can be used to probe dynamics ranging from vibrational densities of states, to translational and diffusional dynamics of water molecules and other hydrogen-bearing molecules in bulk systems and as surface coatings at open or buried interfaces (Cole et al, 2006). QENS has been extensively employed in studies of the dynamics of bulk water (e.g., Teixeira et al. 1985 ) and water confined within nanoscale pores in a variety of inorganic substrates, predominantly various silica matrices, such as Vycor ad Gelsil glass and

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MCM zeolites (Bellissent-Funel et al. 1993, 1995; Zanotti et al. 1999; Takamuku et al. 1997; Takahara et al. 1999, 2005; Mansour et al. 2002; Faraone et al. 2003a,b; Liu et al. 2004; Crupi et al. 2002a,b) and thin films on the surfaces of metal oxide nanoparticles (Mamontov 2004, 2005a,b). These studies demonstrate that water in such nanoscale environments is very different from bulk water, exhibiting liquid-like dynamic motions at temperatures far below the freezing temperature of bulk water. Coupling QENS with large-scale classical MD simulations, Mamontov et al. (2007, 2008) showed that water sorbed on the surfaces of rutile-structured TiO2 and SnO2 is very similar structurally to the interface between the oxide surfaces and bulk liquid water. Dynamic motions are dominated by a.) fast (1-10’s of picosecond time scales) rotational motions of water molecules

within their hydrogen-bonded cages, which is not significantly affected by the

position of individual water molecules within the sorbed layer structure; b.) coupled rotationtranslation motions of water molecules with undersaturated hydrogen bonding environments in the outermost hydration layer (10’s -100’s of picoseconds), and translational jumps of inner hydration waters that have full hydrogen bonding networks (10’s-1000’s of picoseconds). The latter exhibit a distinctly non-Arrhenius temperature dependence, with a fragile-strong transition in the ~200K range. Because QENS is sensitive only to the hydrogen motions, MD simulations are highly complementary, since they can track the dynamics of water and other elements in the system simultaneously.

The average bonding configuration of L1 chemisorbed and L2

physisorbed water molecules on the rutile <110> surface is illustrated in Figure 52. Figure 53 shows the oxygen atom trajectories of individual water molecules which started in the L1 and L2 sorption layers (Mamontov et al., 2008). L1 water is essential non-translating over the 10 nanosecond time period illustrated, while L2 water molecules fully-hydrogen-bonded to L1 and

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L3 molecules undergo periodic translational jumps into L3, where they then exhibit the much faster coupled translation-rotation motion mentioned above. The characteristic relaxation times of the fast and slow diffusion components of the surface waters, extracted from the QENS experiments on TiO2 and SnO2 nanopowder surfaces at the Disk Chopper Spectrometer (DCS) at the Center for Neutron Science, National Institute of Standards and Technology (NIST), are compared with the corresponding values extracted from the MD simulation at 300K in Figure 54 (Mamontov et al., 2007). Thus, the neutron scattering experiment serves to support the validity of the classical simulation, which employed the very simple, rigid and non-polarizable SPC/E water model, while the MD results aid in the molecularlevel interpretation of the scattering experiment.

4.7 Self-Assembling Electrochemical Devices: Li-Ion Batteries from Heterogeneous Colloids Self-assembly, utilizing intrinsic or applied forces, is a widely-accepted concept for the design of novel materials and composites over a wide range of length scales. By contrast, the self-assembly of subassemblies and complete devices has been more challenging, although key examples exist [Whitesides & Grzybowski 2002; Whitesides and Boncheva 2002; Gur et al. 2005; Huang et al. 2001; Rueckes et al. 2000; Colvin et al. 1994]. Recently, it has been demonstrated [Cho et al. 2007] that electrochemical junctions can be formed between conductive device materials using combined vdW-Ld and AB interactions, and in an additional step, that the simultaneous implementation of repulsive and attractive interactions can be used to fabricate complete colloidal-scale self-organizing and self-wiring devices. These concepts have been demonstrated in prototype self-organizing lithium rechargeable batteries.

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With the advent of nanotechnology, numerous devices have been demonstrated that are based on contact-junctions between components, including bi-stable carbon nanotube memory, diodes, light-emitting diodes (LEDs), logic gates, and solar cells [Gur et al. 2005; Huang et al. 2001; Rueckes et al. 2000; Colvin et al. 1994]. It is likely that attractive vdW-Ld forces provide the intimate contact between materials that allows electronic transport across these nanoscale ohmic and pn junctions. In contrast, bipolar electrochemical devices such as batteries, fuel cells, electrochromic displays, and certain types of sensors are based on the separation of electronically conducting electrodes by ionically conducting but electronically insulating electrolytes. Electrode materials of the same type (e.g., cathode or anode) simultaneously need to be continuous connected to their respective current collectors. In principle, the simultaneous control of repulsive and attractive forces can enable the “bottom-up” self-organization of dissimilar colloids into complete bipolar devices as conceptualized in Figure 55. Although current theories provide general guidelines for materials selection, the paucity of physical properties data for lithium-active compounds required direct experimentation. Using liquid-cell atomic force microscopy (AFM) and graphite tips (in the form of mesocarbon microbeads, MCMB), numerous solid compounds and solvents were screened to identify cathode/solvent/anode combinations between which repulsive interactions exist.

Figure 56

illustrates typical results in which four solvents and five different solids were characterized, and show a range of interactions from strongly attractive to strongly repulsive. Detailed analysis showed that these interactions cannot be explained on the basis of vdW-Ld forces alone, but rather they indicate a strong and occasionally dominant role of AB interactions. Using LiCoO2 as the positive and graphite as the negative electrode material, and solvents providing a repulsive interaction

(modified to obtain a lithium conducting electrolyte), self-assembling batteries

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exhibiting reversible Faradaic storage were demonstrated (Figure 57). This general approach to colloidal-scale self-assembly of heterogeneous colloids could clearly be extended to a range of bipolar device types, and would benefit greatly from improved fundamental understanding of the long-range interactions between device materials.

5 Findings and Recommendations: LRI in NS Workshop From the workings of natural systems, by trial-and-error synthesis of new materials, by playing on the stochastics of the very small, by applying the mechanics of the very large, by mimicking the design of biological models, by learning to work between the atomic microscopic and the materials macroscopic, we are creating a new science and engineering of "nanoscale" forces that act at range between the Angstrom-atomic and the micrometer-macroscopic. In this undertaking, there is healthy tension between the need to learn basic interaction fundamentals and the drive to realize practical powers of nanoscale forces. The particularities of solvation, fluctuation, structure, and electromagnetic fields acting at nanometer distances immediately compel us to learn new physics and chemistry as well as motivate us to design materials to new degrees of detail. The concept of harnessing nanoscale forces evokes images of tiny low-energy control systems, "colloids-by-design" of controlled size, shape, and chemical functionality for catalysts; electronic devices, micromachines, and materials of "super-diamond" strength; prototypical batteries and capacitors of high energy density, solar arrays, photocatalysts, and high efficiency fuel cells are already being synthesized and tested. Most tantalizing is the potential mimicry of biological systems for energy conversion, harnessing of electromagnetic fields, efficient direct imaging, self-reproduction, and self-organization.

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Systematic progress and leaps of invention both require a knowledge of interactions beyond what we now possess. Intelligent recognition of this gap in determining research support can remove heavy impediments to invention. Of greatest need in building a systematic science of nanometer-scale materials is to achieve reliable understanding and manipulation of their organizing forces.

5.1 Recent Scientific Advances In LRI in NS Perhaps the most pleasant result from the reports on basic science had to do with electrodynamic (London dispersion, van der Waals, Hamaker, Casimir, Lifshitz) forces. There has been rapid progress in formulations in geometries relevant to nanoscale systems. There is encouraging work on quantum mechanical computation of the material polarizabilities that animate these forces. There is also good progress in techniques to collect spectra needed for quantitative formulations. Paradoxically, on the nanometer scale that was the focus of this workshop, the classic coulomb and double-layer electrostatic forces that are widely encountered in most assembly processes are dauntingly intractable, this despite the brilliant statistical mechanical analyses that are being carried out on various idealized systems. Long-range electric fields were, until the Debye-Huckel theory, the bane of early studies of dilute salt solutions. The correspondingly strong electric fields near ions still pose qualitative problems. Their polarizing forces are so strong as to reorganize water solvent so that continuum models break down. Ionic fields are so powerful as to approach those known to break down dielectrics. The chemical details of the ion orbitals enforce strict geometric conditions on surrounding waters. Even the polarizability of different ions creates charge-fluctuation forces as well as additional dielectric forces that are too

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often neglected. For these reasons, energies of individual ion solvation as well as ion interaction and ion approach to interfaces all occur under the dominance of high electric fields. In the area of "polar" acid/base and H-bonded systems, there has been good progress on specific problems but still little understanding of the powerful "hydration" forces that dominate interactions at ~nm separations or even of the solvation of ions. As with electrostatics there is an intrinsic connection between field-based and structural forces; and again as with electrostatics, there are few rigorously formulated and computed cases. Over all these considerations is the obvious fact that real materials are organized by combinations of LRIs. They vary differently with solution conditions. The balance between them varies even more. The different degree of rigor and accuracy with which they can be computed daunts attempts for reliable combination and balance.

5.2 Challenges and Needs in LRI in NS Given the breathtaking examples presented at the initial gathering and here in review, it is at first difficult to see the defects and deficiencies impeding vigorous progress. The first point is the unevenness of that progress and the need to locate areas requiring new ideas and practices although not currently the focus of active effort. There is a striking disparity in the level of accuracy with which we can speak of the different kinds of interactions reviewed here. The general impression is that all kinds of interactions must be simultaneously connected. When it comes to combining component forces in order to work with real systems, the chain of reasoning is as strong as its weakest link. That is to say, interactions are treated with such different degrees of approximation that their combination limits the strength of the enterprise to its most poorly understood component. We need reliable intermolecular force fields for computation. We need sufficient understanding to

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model many-body interactions. Particularly when working in the "nano" range, we must learn how to formulate effective interactions for various length scales. Electrostatic and solvation interactions involve polarization, hydration, dielectric saturation, and structural components that carry us far beyond the continuum-dielectric models that are still most popular. Reversing the scene of a half-century ago, it is the far more sophisticated theory of electrodynamic – van der Waals, Lifshitz, Casimir – forces that earns reliability.

Electrostatic and hydrogen-bonding polar interactions still frustrate quantitative

evaluation. There are not enough test systems where measured forces are examined in sufficient detail that it is possible to test and validate quantitative theories and experimental procedures. Even within the world of computation and simulation there are not enough criteria procedures where results of the same problem can be compared so as to test different algorithms. There are even impediments in language: physicists think in terms of electrostatics and electrodynamics that sometimes do not easily relate to the chemist’s structural approach. The need for merger of approaches is being systematically met on many fronts. Casimir forces are being formulated for arbitrary geometries. Simple analytical approximations are emerging that establish limits on behavior for different governing physics. There is an emerging, if overdue, recognition that it is necessary to join molecular dynamics with more accurate dispersion forces, generalized density functional theory, and quantum chemistry. More rigorous theory and computational algorithms, development of scattering, spectroscopic, and local probes of structure, forces and dynamics at relevant time, space, and energy scales will combine to create practical theoretical tools. In this way one can expect new theoretical principles and practical implementations for real systems. Pushed to a natural limit, this effort will provide indepth understanding of self-assembly for device manufacture.

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How to proceed in this merger while keeping close to real systems? Several kinds of phenomena can prove instructive: collective dynamics, colloidal crystal self-assembly and effective properties of zeolites and porous solids; properties of inhomogeneous liquids; processes driven by the defect interactions; ordered and amorphous interfaces of finite thickness: dimensionality and charge effects; charged defects and ES fields on local phase stability and microscopic mechanisms of phase transitions & front motion; phase transitions in confined geometries – surface films and liquids; concentrated solutions. From these we may expect new theoretical principles & implementations for real systems; the possibility of constructing “colloids by design” -- scalable synthetic methods that control size, shape, and chemical functionality of colloidal building blocks; the development of predictive tools for phase behavior, structure, and assembly for diverse motifs; the capability to control two- and three-dimensional electric & magnetic fields at nanoscale In this way, we expect to be able to merge not only physics, chemistry, and materials science and engineering approaches but also computational, experimental, and chemical methods for realistic interpretation and prediction.

5.3 Transformative Opportunities from LRI in NS The magic of the nanoscale – mixing the macromolecular with the macroscopic – creates a learning path to create new materials organized by "long-range forces". Even with the current rough ideas of colloid organizing forces, nanometer-size colloids or "tailored building blocks" are being synthesized with reliable uniformity so as to be suspended/manipulated to create instructive assemblies. •

The range of such materials is still limited.

•

Theory and computation do not yet serve to describe or to design desired assemblies.

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•

Synthetic pathways are not yet suited to large supply.

Given needed support, the first two impediments will likely yield to current effort. The third, synthesis, needs bolder study but is not beyond achievement given the rapid progress in the theory and measurement of colloidal forces. Lithography, pattern formation in thin liquid films, design of materials with temperature sensitive vdW-Ld forces, and ion-conducting membranes show similar promise.

Among the many tantalizing applications of carbon nanotubes as

substrates for assembly and for elements in construction is the qualitative change to be expected from minor changes in carbon-carbon network. Given the dozens of windings in carbons along the cylindrical shell it becomes clear that some CNT's are simply dielectrics while others are conductors and still others are semiconductors whose electrical and charge-fluctuation properties can be switched by small changes in temperature. Obstacles to progress are the difficulties in synthesis of precisely defined CNT's as well as means to manipulate and watch them. None of these presents a major obstacle in principle, but practical procedures are nowhere within sight. Batteries and high storage capacitors are perennial favorites on the must-make list for energy transforming materials. New materials such as the microbatteries from assembled A-B colloids described at the workshop and capacitors from highly polar non-reactive materials might begin to satisfy desiderata such as high energy density, non-toxicity, durability and inexpensive synthesis. Low friction contact surfaces by "repulsive" vdW-Ld forces. Manipulation of material polarizabilities creates the possibility of switchable friction between bodies whose polarizabilities can be changed by applied fields. The existence of such repulsion between surfaces has recently been reported. There is good reason to expect rapid progress in material design.

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One transformative opportunity is primarily educational. How to bring sophisticated ideas to general practice?

These are "perception and momentum" issues where there are

remarkable gaps between what can be done with current state of the art theory and what is done by "end-user" practitioners? What mechanisms will allow us to diversify our thinking so as to benefit from the expertise of others. There is a puzzling focus on one kind of interactions, electrostatics, say, with relative neglect of vdW-Ld and AB. Most systems have a combination of all charges even when they perceive they can ignore/turn them off. When top experts in a given field still have trouble communicating and resolving differences even between "Casimir" and "Lifshitz," how do we expect practical end-users to be able to use electrodynamic forces. Better education among mature colleagues as well as young scientists and engineers could forestall more decades of ideological separation. Perhaps the demands of the new science of long-range interactions can make us "scientists" again rather than specialists in arcane practice.

6 Conclusions Evidence gathered for this report reveals not only abundant creativity in the design of devices but also inspiring research on physical forces governing organization on the nanometer scale. Careful consideration of this research also shows clearly an unevenness in our grasp of the basic organizing forces. Perhaps the greatest surprise is the inadequacy of theories of polar and electrostatic interactions compared with the present-day sophistication in formulating and computing charge-fluctuation forces. We cannot avoid these areas of ignorance. Electrostatics and polar interactions need conceptual advances. There is still no good algorithm to handle the strong electric fields near ions nor any language to include the powerful solvation forces surrounding even the simplest molecules.

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Realizing that few systems operate by only one kind of interaction, we are faced with the paradox that the most sophisticated and accurate theory about one kind of force is vitiated when combined with less reliably formulated interactions. The panel was unanimous in its ardent plea that attention and significant research support be devoted to fundamentals. With better force measurement, theoretical formulation, and potentials for computer simulation, design of materials will accelerate and likely move faster than is possible with trial-and-error approaches. A second fundamental need is in education. Bluntly put, don't duck the areas of ignorance. The emphasis must shift to learning-to-learn: better modes of teaching about forces as the need to learn them is recognized; better preparation in the basics of several sciences so as to remove the daunting fear of new learning after graduation. The possibilities – by supplementary coursework, by computer facilities, by specialized texts that are written at a friendly level – can then be realized in many ways. Then, third and greatest, the heavy work of designing and making materials, testing them, and creating synthetic pathways to provide needed supply. While theory and computation still fall short, the creation of materials is simultaneously a source of testing design ideas and of providing samples with systematically varied properties for systematic construction. It would qualitatively improve this iteration if material synthesis were made more accessible. With the magnificent facilities now being developed in national centers, even DoE nanoscience centers, people will have new possibilities for design and application of design ideas. Training and linking programs that facilitate use of existing facilities is an economically practical strategy. A neglected source of creativity was seen in the act of the meeting itself. At all times during exchanges, during presentations of recent work, during discussions of what people needed to learn, there was an ardor in the learning being experienced by the participants themselves.

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One person, from a major DoE national lab, told the organizers, "I couldn't figure out why you even invited me. Now, I'm learning more than I could have expected, and I find people eager to talk. Thanks for asking me. This meeting has created new collaborations for me and has changed the way I will work." Perhaps meetings that force people to focus on a problem they are not

studying, but still a problem needing solution, will bring out creative spirits of the kind that were so happily evident at our workshop.

7 Acknowledgements The authors would like to acknowledge Harriet Kung of the Division of Materials Sciences and Engineering, one of the research divisions in the Office of Basic Energy Sciences of the U.S. Department of Energy and Frances Hellman, chairperson of the Council for the Division of Materials Sciences and Engineering for sponsoring the LRI in NS workshop. Christie Ashton and Sophia Kitts for organizational assistance and Barbara French for assistance in edting the manuscript. And to all of the participants who provided their time and energy and most importantly their intellectual insights with out which this would not have been possible.

8 Figures

Figure 1. Planar configurations for Hamaker coefficient computation for two optically isotropic materials.

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Figure 2. ab initio dielectric functions for [6,5,s] and [9,3,m] CNTs in the radial and axial directions.

Figure 3. van der Waals London dispersion spectra for [6,5,s] and [9,3,m] CNTs in the radial and axial directions.

Figure 4. Casimir force per unit length between two cylinders (black) vs. the ratio of sidewall separation to cylinder radius h/R, at fixed a/R = 2, normalized by the total PFA force per unit length between two isolated cylinders.

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Figure 5. Role of acid-base interaction in Polymer Adsorption. The adsorption of a basic polymer, poly-methymethacrylate (PMMA), on to an acidic silica is maximum when the adsorption occurs in a neutral solvent, carbon tetrachloride. However, when the adsorption occurs in either acidic or basic solvent, the adsorption is reduced as the solvent interacts either with PMMA or silica. Taken from Fowkes 1983. Percolating Network of Material 1 A121 > 0 (attraction)

Material 1: anode storage compound

A123 < 0 (repulsion)

Load/source

Bipolar Junction

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Figure 6. Colloidal scale self-organizing lithium ion battery concept, demonstrated in graphite – LiCoO2 system making use of acid/base forces for junction formation and particle assembly). F F OH

F

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Figure 7. Examples of fluoropolymers which may serve as a γ+ reference solid to be used for the analysis of monopolar surfaces and liquids interactions.

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Figure 8. Hamaker Coefficients for [9,3,m] and [6,5,s] CNTs with Gold in a water medium.

Figure 9. Hamaker Torques for [9,3,m] and [6,5,s] CNTs with Gold in a water medium in the near and far limits.

Figure 10. A 17-base pair DNA model constructed using AMBER program.

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Figure 11. The calculated TDOS of the b-DNA model with 32 Na counter ions added using the OLCAO method. The calculation shows this model has a n insulating gap of about 2.0 eV.

Figure 12. The calculated imaginary dielectric functions for the b-DNA model of Figure 10.

Figure 13. The canonical base pairs adenine:thymine (A:T) and guanine:cytosine (G:C). The arrows indicate where each nucleobase would be singly-bonded to one of the helically encircling phosphodiester strands. In the study under review the dangling bonds were terminated with hydrogen as shown. The dashed lines show the Watson-Crick hydrogen bonding scheme between the nucleobases. Color code: green, N; red, O; black, C; white, H.

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Figure 14. A typical stacking configuration used in this study. The two base pairs are attracted by the vdW-Ld interaction. In the lowest energy configuration they undergo a helical twist as shown, which reduces the Pauli repulsion. This is the so-called AT:AT step, where the first AT labels the nucleobases going up one strand (in this diagram the right one), while the labels to the right of the colon correspond to going down the other. For Watson-Crick pairs the labels after the colon are redundant, and often omitted.

Figure 15. Stacking energy vs. twist angle for the indicated base pair steps. The notation for labeling these steps is explained in the caption of Fig. at_at.png.

Figure 16. Comparison of the stacking energy of a special DNA and RNA step vs. twist angle, showing the effect of the methyl group on thymine (DNA) vs. the hydrogen termination on uracil (RNA).

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Figure 17. Comparison of vdW-DF and a CCSD(T) based method. The ordinate is the stacking energy at a fixed twist angle of 36°. The abscissa labels indicate the base pair involved, using the more economical notation mentioned in the caption of Fig. at_at.png.

Figure 18. The osmotic coefficient is the ratio between the osmotic pressure expected if all counter-ions of the polyelectrolyte were "free" as released salt. Osmotic coefficients not vanishing at equimolarity of charge reflects non electrostatic swelling of the polyelectrolyte complexes, a combination of polyelectrolyte intrinsic rigidity and repulsive hydration forces [reproduced from Carriere 2006].

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Figure 19. In the absence of added salt, charged cationic bilayers in the presence of chaotropic counter-ions such as bromide show a coexistence of two lamellar phases at a an osmotic pressure of a few atmospheres. Graph shows Maxwell construction in the pressuredistance representation demonstrating equilibrium between phases. Experimental determination of tie-lines gives a precise estimation of counter-ion binding combining with hydration forces. (Zemb 1992).

Figure 20. The excess osmotic pressure for various confined solutes as a function of the separation between confinig surfaces.

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Figure 21. Representative impurity-based quasi-liquid interfacial films.

Figure 22. Left, a photograph of four veins intersecting at a node between four grains in polycrystalline ince near the bulk melting temperature. Right, schematic of the vein/node network.

Figure 23. Film thickness (nm) versus undercooling (K) at the interface between ince and water vapor. The various curves show different concentrations Ni of a 1:1 electrolyte Ni = 6 x 10-4 (long dashed line), 6 x 10-3 (dash-dot line), 0.06 (solid line), 0.18 (small dashed line), and 6 (dotted line) in moles NaCl per square meter.

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Figure 24. A photograph of the two phase nature of the ice formed from salt water. This is a section that is perpendicular ot the growth direction (ther numbers on the scale indicate centimeteris). Note the linear “substructure” which separates the solid (white) from the brine. This coexists with the channels (or holes) that form due to convective instabilities and thread the material parallel to the growth direction.

Figure 25. Protonation constants of bridging (Ti2O-0.516) and terminal (TiOH-0.483) oxygens on the rutile <110> surface calculated using ab initio-optimized bond lengths and surface atom partial charges as input into eq. (3). An OII ion resides the corners of each coordination polyhedron, which also contains a central TiIV ion.

Figure 26. ~1m SrC2 solution (in SPC/E water) at 25°C at liquid density sandwiched between rutile <110> surface slabs. Oxygen (red) and titanium(grey) atoms are minimized for clarity. Sr2+ ions (magenta), Cl- ions (teal), hydrogen atoms (white). Left - Uncharged, ‘nonhydroxylated’ surfaces (Predota et al., 2004b) with full 40 Å water layer shown. Note strong layering of near-surface water, an inner layer of chemisorbed water molecules atop bare 5-fold titanium ions and a distinct second layer associated with the bridging oxygens. Right – negatively-charged (-.2 C/m2), ‘hydroxylated’ surface attracts Sr2+ ions into ‘inner sphere’ sorption sites, displacing second layer water molecules and interacting directly with bridging and terminal oxygens. Page 4.5.2—179 of 213

Figure 27. ‘Inner sphere’ sorption site geometries on the rutile <110> surface identified by synchrotron X-ray standing wave and crystal trunctation rod studies. Red – oxygen atoms, blue – titanium atoms, green – ions sorbed at the ‘tetradentate’ site (Rb+, Sr2+, Y3+), black – ‘monodentate’ and ‘bidentate’ sites preferred by transition metal cations (Zn2+, Co2+).

Figure 28. Sorption heights (Å) of cations above the Ti-O surface plane of rutile <110> versus bare cation radius (Marcus, 1997) for ions in the tetradentate, monodentate and bidentate sites (Fig. 3) determined by X-ray and computational approaches.

Figure 29. Phase diagram of hard sphere colloids. Micrographs and schematic plots of g® for representative colloidal dense liquid, crystal, and glass suspensions.

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Figure 30. Schematic phase diagram for colloids as a function of potential U/kT and φ. The solid line is the boundary for the non-equilibrium solids and the dashed line the boundary between equilibrium and non-equilibrium behaviour.

Figure 31. Ionic crystal (CsCl) assembled from oppositely charged colloidal microspheres.

Figure 32. (a) Confocal 2D image of the biphasic colloidal mixture containing attractive (surface-modified) and repulsive (bare) particles For this sample φatt = φrep =0.05. (b) MSD of the respective populations.

Figure 33. (from Reference Richard 2003) Cryo-transmission electron microscopy of surfactants around carbon nanotubes show that they can form a variety of structures (need permission).

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Figure 34. (a) Atomic force microscopy image of DNA-CNT deposited on a mica surface following separation and length fractionation. (b) Absorption spectra of three fractions following ion-exchange chromatography of a starting mixture. Note in particular the separation achieved of the (9,1) and (6,5) nanotubes that have nominally the same diameter and bandgap (c) A starting dispersion (black) and three sorted fractions rich in metallic SWCNT (pink) and semiconducting SWCNT (green) with different diameters. (d) Proposed structure of the DNA-CNT hybrid.

Figure 35. Centrifugation of surfactant (sodium cholate) -dispersed SWCNT in a density gradient has been demonstrated to result in their separation. It has been proposed that the effective density of the surfactant-SWCNT hybrid increases with increase in diameter and on the electronic character of the SWCNT.

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Figure 36. Hypothetical Nafion membrane self-assembly (from Eikerling et al., 2006)

Figure 37. The time evolution of two periodic profiles of bulk (salt concentration in the solid plus liquid system) solute fileds deposited on a polycrystalline ice sheet asynchronously (From Rempel et al., 2002]. The initial profiles are labeled “0” with the minor species in black and the major species in red. The units are dimensionless, with the horizontal axis being the distance along the sample, but the essential point is that the major species, CB2, controls the liquid fraction and it drives the minor species, CB1, into phase with it on a time scale sufficiently rapidly that its original profile is unchanged.

Figure 38. Colloidal suspensions frozen upward in a cell that is free at its upper end [From Pepin et al., 2006, 2007]. Clearly the structure of the ice (dark regions) depends on the conditions of freezing and the particle concentrations. While (a) and (d) exhibit ice dendrites that align colloids in (c) and (f) a polygonal structure forms and there are mixed states between the two geometries initiated by sidebranching as shown in (e). Online movies can be seen accompanying Peppin et al., 2006.

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Figure 39. Images of synthetic nanoscale and microscale building blocks with controlled architectures: (a) Fe2O3 ellipsoids [Wang H., Brandl F. et al 2006], (b) Ag triangular plates [Sun Y., Mayers B. et al. 2003], (c) Ag cubes [Sun and Xia 2002], (d) CdSe tetrapods [Manna L., Scher E.C. et al 2000]), (e) tetrahedral cluster of polystyrene microspheres (844 nm in diameter) (e.g., unary [Manoharan V.N., Elsesser 2003], and (f) binary cluster of silica microspheres (2.3 µm and 0.23 µm in diameter, where the number of larger particles equals 8 [Cho, Li, et al. 2005])

Figure 40. Schematic representations of model patchy particles and their predicted equilibrium structures (side and face views) formed via self-assembly: (a) particles with four circular patches (in red) assembled at a dimensionless temperature of kt/ε = 1.0, and (b) particles with a ring-like patch (in blue) arranged on an equatorial plane assembled at kt/ε = 0.5. [Adapted from Zhang and Glotzer 2004]

Figure 41. Schematic representation of the myriad of designer colloides categorized by (a) surface chemistry anisotropy, (b) aspect ratio, (c) faceting, (d), pattern quantization, and (e) branching. [Adapted from Glotzer and Solomon 2007].

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Figure 42. Schematic illustrations (A-B) and predicted interparticle potential energy landscapes (C-D) for the pairwise interaction of bipolar Janus spheres in solution, and (E) fluorescence and simulated images of colloidal molecules assembled from these species alongside their predicted charge distribution. [Adapted from Hong, Cacciuto et al. 2006]

Figure 43. Scanning electron micrographs of lithographically patterned colloids (left) and nanowires (right). [Left and right images taken from [Edwards, Wang et al. 2007] and [Qin, Park et al. 2005], respectively]

Figure 44. Fig. 1. (a) Force-based SPM can be conveniently described using force-distance curve, showing the regimes in which contact (C), non-contact (NC), intermittent contact (IC), and interleave imaging are performed. Also shown are domains of repulsive and attractive tip-surface interactions. (b) Voltage modulation SPMs can be described using force-distance bias surface. In the small signal limit, signal in techniques such as Piezoresponse Force Microscopy, Atomic Force Acoustic Microscopy, Electrostatic Force Microscopy and Kelvin Probe Force Microscopy is directly related to the derivative in bias or distance direction.

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Figure 45. Fig. 2. Voltage modulation measurements of long range interactions. (a) Surface topography and (b) Kelvin Probe Force Microscopy image of ferroelectric domains on BaTiO3 surface. KPFM image clearly distinguishes antiparallel domains due to the difference in surface charge. (c) Surface topography and (d) KPFM image of the laterally biased BiFeO3 surface. KPFM image illustrates potential drops on the poorly-conductive grain boundaries. (e) Surface topography and (f) Piezoresponse Force Microscopy image of white blood cell.

Figure 46. Fig. 3 (a) Topography, (b) PFM amplitude, and (c) PFM phase images of ceramic PZT in liquid illustrating high-frequency electromechanical detection in aqueous environmnet. (d) Scanning electron microscope images of (d) a standard tip and (e) an insulated, conducting probe.

Figure 47. Fig. 4. Schematics (a,c,e) and PFM phase images (b,d,f) of switching in (a,b) local, (c,d) fractal, and (e,f) non-local cases. The size of switched region illustrates the spatial extent of the electric field. The localized switching was observed only in ambient environment, while fractal-like clusters are observed in methanol and isopropanol. In aqueous solutions and DI water, only non-local switching is observed, indicative of nonlocalized dc electric field.

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Figure 48. Fig. 5. Excitation (blue) and response (red) signals in standard SPM techniques in (a) time domain and (b) Fourier domain. Excitation (blue) and response (red) signals in band-excitation (BE) SPM in (c) time domain and (d) Fourier domain. In the simple harmonic oscillator approximation, system response near the resonance is described by resonant frequency (related to force gradient acting on the probe, or contact stiffness), amplitude (related to force), and Q-factor (related to dissipation). Only two parameters can be measured at a single frequency, while the frequency dependent system response is inaccessible. In BE, the system response is probed in the specified frequency range (e.g. encompassing a resonance), as opposed to a single frequency in conventional SPMs.

Figure 49. Fig. 6. Roadmap for development of SPM probes and imaging modes. Shown is the probe evolution from simple etched STM tip (current probe) to AFM cantilever (force and current) to 3D probes with a force sensing integrated readout and active tip (FIRAT) and shielded probes. In parallel, data acquisition methods evolved from static detection (STM and contact AFM) to constant frequency (Intermittent contact AFM, AFAM, etc) and frequency-tracking (non-contact AFM) to more complex waveforms.

Figure 50. Fig. 7. Development of electronic device and information technologies started with from vacuum tubes on centimeter sale and now approaches 1-10 – nm range of modern microelectronics and potential molecular electronics. Similar progress in energy

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technology and molecular engineering requires a capability for electrically controlling and inducing motion on the molecular level.

Figure 51. Fig. 8. (a) Artistic rendition of molecular transformation change in electric field in the tip-surface junction. (b) Corresponding force-bias-distance surface. The redox potential of the molecule is expected to be dependent on the force acting on the molecule.

Figure 52. Hydrogen-bonding configuration of chemisorbed L1 water molecules which sit atop bare 5-coordinated metal atoms at the <110> surface of rutile (α-TiO2) and cassiterite (α-SnO2) as either intact water molecules (left) or dissociated hydroxyl groups (right) at ‘terminal’ (T) and ‘bridging’ (B) surface oxygen sites, and physic-sorbed L2 water molecules hydrogen bonded to the surface groups (Vlcek et al., 2007; Mamontov et al., 2007).

Figure 53. Figure 2. MD simulation results of oxygen atom trajectories above the rutile <110> surface for water molecules that originated in L1 (blue) and L2 (red), as a function of time (Mamontov et al., 2008).

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Figure 54. Figure 3. Characteristic residence times (τ) for fast (rotation-translation) and slow (translation) diffusional components (open symbols) extracted from the QENS scattering from rutile (red) and cassiterite (green) nanoparticles surfaces (open symbols and dashed lines, compared with τ’s extracted form MD (filled symbols) over the same energy transfer range as the NIST DCS (Mamontov et al., 2007). Note that the accessible temperature range of the DCS measurements is well above the fragile-strong transition of the slow translational diffusion component (Mamontov et al., 2008). A

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A323 > 0 (attraction)

Figure 55. Schemes for self-organization of bipolar electrochemical devices, exemplified by using repulsive short-range Lifshitz-van der Waals (LW) interaction (negative Hamaker constant, A123<0) to form the electrochemical junction while simultaneously using attractive LW (A121>0) to form percolating networks of a single active material and/or to selectively adhere to current collectors (A123>0). A) Battery formed from a single particle pair. B) Nanorod-based batteries. C) Layered lithium-ion battery using repulsive shortrange forces to separate LiCoO2 and graphite, while using LW attraction to form continuous percolating network of graphite anode. D) Interpenetrating electrode battery formed from a single heterogeneous colloid, wherein the electrodes form co-continuous percolating networks that are everywhere separated by repulsive force.

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Figure 56. Force curves measured between MCMB probes and five substrates (PTFE, LiCoO2, ITO, Si3N4 and HOPG) in A) acetonitrile, B) m-xylene, C) ethanol and D) methylethyl ketone (MEK; 2-butanone) using liquid-cell atomic force microscope (AFM) show behavior ranging from strong attraction to strong repulsion.

Figure 57. Three-electrode cells using lithium titanate reference electrodes allowed working voltage as well as the potentials at the working (LiCoO2) and counter (MCMB carbon) electrodes to be independently measured. Right figure shows galvanostatic cycling (11th cycle) of a self-organized LiCoO2-graphite rechargeable cell, charging at 100 µA and discharging at –20 µA conducted in MEK + 0.1M LiClO4 + 1 wt% PEG 1500.

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