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Deterministic Order in Surface Micro-Topologies through Sequential Wrinkling Jie Yin, Jose Luis Yagüe, Damien Eggenspieler, Karen K. Gleason,* and Mary C. Boyce* Wrinkling surface patterns in soft materials have become increasingly important over a broad range of applications, including stretchable electronics,[1,2] thin film material properties measurement,[3] tunable adhesion[4,5] and wettability,[6,7] electrospun fiber surface topologies,[8] plant morphogenesis,[9] micro fluidic channels,[10] and photonics.[11] Wrinkled surface topologies occur when out-of-plane bending of the coating is energetically favored over compression. This phenomenon is the planar equivalent to the well-known problem of buckling of a beam on an elastic foundation. Bowden et al.[12] first observed this wrinkling phenomenon on the micro-scale using thermal deposition of a 50-nm-thick gold film on a polydimethylsiloxane (PDMS) substrate, where the expansion mismatch of the two materials was used to generate compression within the film. Subsequently, extensive experimental[13–18] and theoretical studies[19–23] have explored multifunctional micro/nano-scale surface patterns by harnessing spontaneous buckling of bilayer composite systems composed of a wide range of hard and soft materials.[13–17] Upon constrained thermal expansion or swelling of a thin film by a compliant substrate, equi-biaxial compressive strains are induced in the film producing 2D (two-dimensional) wrinkled herringbone patterns with a 90° jog angle. For this equibiaxial strain case, the herringbone possesses a deterministic short wavelength along one direction satisfying a minimum energy condition but an undetermined long wavelength along the other direction[24] (see Figure 1 for the definition of both wavelengths and jog angle). In addition, equi-biaxial strain induced herringbone morphologies are experimentally observed to occur only in small regions of the film, where large areas consist of disordered labyrinth patterns with randomly oriented wrinkles.[11,12,18,24] Upon a sequential release of equi-biaxially stretched PDMS film with an oxygen plasma treated surface layer, Lin and Yang[25] reported the formation of an ordered herringbone pattern with jog angles of 90° while its counterpart, simultaneous release of prestrain, leads to a labyrinth pattern.

Prof. M. C. Boyce, Dr. J. Yin,[+] Mr. D. Eggenspieler Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA E-mail: [email protected] Prof. K. K. Gleason, Dr. J. L. Yagüe[+] Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA E-mail: [email protected] [+] These authors contributed equally to this work.

DOI: 10.1002/adma.201201937

Adv. Mater. 2012, DOI: 10.1002/adma.201201937

The transition from disordered to ordered patterns by means of sequential loading opens a new avenue for creating 2D ordered wrinkling patterns. However, the underlying wrinkling mechanism has yet to be identified and quantified, and hence the predictive design of ordered topologies remains a challenge. In this paper, we explore the deterministic design of ordered wrinkled topologies through a sequential wrinkling strategy. The success of the proposed process is demonstrated in example systems of thin polymeric films synthesized from monomers including ethylene glycol diacrylate (EGDA) and 2-hydroxyethyl methacrylate (HEMA) on PDMS substrates. In this investigation, the initiated chemical vapor deposition (iCVD) technique[26] is used for the first time for the deposition of thin polymeric coatings without use of solvents to obtain wrinkles. Prior deposition approaches employed to produce stiff stressed films on soft substrates included thermal evaporation deposition,[12] plasma oxidation,[25] focused ion beam (FIB) exposure,[27] and UV-curing.[28] iCVD yields a conformal thin coating on virtually any substrate, giving a controllable thickness and tunable structural, mechanical, thermal, wetting, and swelling properties.[29] Here, using the iCVD technique, a variety of ordered deterministic herringbone patterns are created through the wrinkling of polymeric coatings on PDMS substrates and also, the sequential buckling mechanisms underpinning the ordered patterns are revealed. Furthermore, a simplified theoretical model is developed to predict the geometry of the ordered herringbone pattern. In addition to providing the ability to deterministically yield ordered surface topologies, the method also provides a tool to measure the elastic modulus of the thin film. Figure 1 shows a schematic illustration of the wrinkling procedures and the resulting wrinkling patterns obtained upon simultaneous and sequential release of biaxial stretching prestrains. Upon simultaneous release of equi-biaxial strain of εx = εy ≈10%, disordered labyrinth patterns are observed on p(EGDA) coating (t = 100 nm) (Figure 1a), such a labyrinth pattern is more energetically favorable upon the release of the strain energy in all directions. The transition from disordered to ordered patterns is observed through the sequential release of the equi-biaxial prestrain in one direction followed by the release of the strain in the other direction. Figure 1b shows an ordered herringbone pattern with a jog angle of 90° for p(EGDA) coating (t = 200 nm) created upon the sequential release of an equi-biaxial strain of ≈20% and such a pattern persists over a large area (>1 cm2 where a ≈ 2 mm2 region of this large area is shown later in Figure 3c). The ability to control the jog angle α is obtained through the sequential release of non-equi-biaxial prestrain (εx ≠ εy). Figure 1c shows an ordered herringbone pattern with α larger than 90°, where the larger prestrain (εx ≈20%) is first released and then the smaller prestrain (εy ≈10%) is released. We note

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Figure 1. Schematic illustration of wrinkling through biaxial mechanical strain: a PDMS is first bi-axially stretched, followed by the deposition of an p(EGDA) or p(HEMA-EGDA) copolymer film on the stretched PDMS using iCVD followed by release of the biaxial strain. The transition from disordered (a) to ordered (b,c,d) herringbone patterns with different jog angles is realized by changing from simultaneous to sequential release of biaxial strains. (a) Upon simultaneous release of equi-biaxial prestrain of 10%, disordered surface patterns are formed on p(EGDA) coating with thickness t of 100 nm. (b) Upon sequential release of equi-biaxial prestrain of 10%, the ordered herringbone pattern with a jog angle α of 90° occurs (p(EGDA) coating thickness t = 100 nm). (c) Upon sequential release of the larger strain εy = 20% first followed by release of the smaller strain εx = 10%, the ordered herringbone pattern with a jog angle larger than 90° (α ≈ 110°) occurs (p(EGDA) coating t = 300 nm). (d) Upon sequential release of the smaller strain εx = 20% first followed by release of the larger strain εy = 30%, the ordered herringbone pattern with a jog angle less than 90° (α ≈ 65°) occurs (p(EGDA) coating t = 400 nm). The corresponding FEM simulations are shown on the right column. For clarity, only the film surface is shown.

that simultaneous release of such a biased biaxial prestrain will produce the same ordered herringbone pattern with its jog angle always being larger than 90° regardless of the biaxial strain ratio. However, through sequential release of the smaller prestrain (εy ≈ 20%) first followed by release of the larger prestrain (εx ≈30%), jog angles less than 90° are created as shown in Figure 1d (α ≈65°). It is observed in these experiments that such an ordered pattern persists over a large area. It should be noted that this is the first time that ordered herringbone patterns with jog angles of less than 90° are created. Micromechanical models using the finite element method (FEM) are carried out to reveal the underlying buckling mechanisms as well as the evolution of wrinkling patterns during simultaneous and sequential release of prestrains (see Methods and Supporting Information Section S1). Upon simultaneous release of a small equi-biaxial prestrain of 2.5%, the film undergoes equi-biaxial compression and the resulting herringbone pattern shows a jog angle of 90° (Figure S1a), consistent with herringbone patterns reported in the literature using thermal deposition and solvent swelling approaches.[1,7,27] For sequen-

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tial release of the same equi-biaxial prestrain, the final pattern is obtained through two intermediate steps (Figure 2): first, after release of the prestrain in the x-axis, out-of-plane buckling occurs and a 1D wrinkle forms; second, upon release of the second prestrain in the y-axis, the 1D waves laterally buckle within the plane, forming the herringbone pattern with jog angle of 90° (Figure S2a). The out-of-plane amplitude of the wrinkle remains nearly constant during the lateral buckling (Supporting Information Section S2). Furthermore, simulation shows that for simultaneous release, the long wavelength of the herringbone is not defined by an energy minimum and is indeterminate (Supporting Information Section S1). This finding is consistent with the wide range of long wavelength observed in previous simultaneous release experiments.[23] However, for sequential release, the long wavelength is deterministic, satisfying a minimum strain energy condition (Supporting Information Section S1). A structural mechanics model for the long wavelength is provided later in the paper. At relatively larger prestrains (εx = εy ≥ 5%), the sequential wrinkling strategy provides a robust method for creating ordered

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COMMUNICATION Figure 2. The evolution of herringbone jog angle with the sequential released biaxial strain ratio ε2nd/ε1st. Left column: intermediate wrinkling patterns during the second release of smaller prestrain (εx = 2.5%) followed by the first fully released prestrain(εy = 2.5%). Right column: intermediate wrinkling patterns during the second release of larger prestrain (εy = 5%) after the first release of smaller prestrain (εx = 2.5%).

herringbone patterns in contrast to the simultaneous release of equi-biaxial prestrain. Simulation shows that for simultaneous release, when the prestrain is increased to 5% (Figure S2c) or 10% (Figure 1a), the herringbone pattern becomes distorted and thus disordered. This is consistent with the labyrinth patterns observed in corresponding experiments under a prestrain of 10% (Figure 1a). However, upon sequential release of the prestrain, the ordered herringbone pattern persists even at a relatively large strain of 10% (Figure S2g) and 20% (Figure 1b), which agrees with our experimental observation (Figure 1b). A jog angle α = 90° is universally found for all equi-biaxial strain induced wrinkling, which implies that the jog angle is independent of the material properties of the system and only related to the ratio of the bi-axial strain state. Hence, altering the strain state provides the ability to manipulate the jog angle as shown in Figure 2, where the biaxial strain ratio is defined as the ratio of the second released strain ε2nd to the first released strain ε1st. For the same non-equi-biaxial prestrains (e.g. εx = 2.5% and εy = 5% shown in Figure 2), simulation shows that releasing the larger prestrain first leads to final herringbone patterns with α > 90°, which agrees with the experimental observation (Figure 1c). Releasing the smaller strain εx = 2.5% first and then releasing the larger strain εy = 5% leads to final herringbone patterns with α < 90°. As the second strain εy2nd increases from 0 to 5%, when εy2nd/εx1st < 1, intermediate herringbone patterns with α > 90° are first formed; when εy2nd/εx1st = 1, α = 90°; when εy2nd/εx1st > 1, α < 90° (right column of Figure 2). This trend agrees with the experimental observation for sequential release of the non-equi-biaxial prestrain as shown in Figure 1d and the jog angle decreases with an increase in the biaxial prestrain ratio. From the angle information in Figure 2, an Equation for predicting α can be approximated as     3 α ≈ π − 2 tan−1 ε2nd ε1s t 5 (1) which provides a design guideline for quantitatively controlling 2D herringbone patterns.

Adv. Mater. 2012, DOI: 10.1002/adma.201201937

The formation of the herringbone pattern due to sequential unloading is deterministic and provides a minimum energy configuration (see Supporting Information Section S1). As schematically illustrated in Figure 3a, the theoretical prediction for the deterministic geometry of herringbone patterns (Figure 3b) is obtained through a simplified model: • First, release of the first strain produces the 1D wrinkle pattern; each wrinkle can be considered to be a composite beam with a one-half sinusoidal cross-section (composed of the coating film and underneath substrate) bonded to an elastic foundation, where the cross-sectional shape is determined from the wavelength λ and amplitude A of the 1D wrinkles[21]] upon the first strain release ε1st, λ=

1   2π t E¯ f 3 E¯ s 3 1 + ε1s t

(2)

  t ε1s t εcr − 1 (3) A= √ 1 + ε1s t   where E¯ f = E f (1 − ν 2f ) and E¯ s = E s (1 − νs2 ) are the plane strain modulus of the film and substrate with f and  ν2 νs being the respective Poisson’s ratio. ε cr = 3 E¯ s E¯ f 3 4 is the critical buckling strain of the 1D wrinkle and εcr = 0.37% for p(EGDA) coating. Equations (2) and (3) are validated for the wrinkling of p(EGDA) coating on PDMS (Figure 4a, 4b, and S4), which provides a predictive methodology to design the 1D wrinkled morphologies by tailoring the film modulus and thickness, and substrate modulus as well as prestrain.

• Second, upon release of the second pre-strain, the composite beams are taken to buckle under the constraint of being bonded to the compliant substrate. Using the expression for the in-plane bending for a composite column on an elastic foundation (Equation (S3)), the long wrinkle wavelength λl (Figure 3b) and the critical sequential buckling strain εlcr upon the release of the second prestrain ε2nd can be obtained

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Figure 3. (a) Schematic illustration of lateral buckling of beams with sinusoidal cross section rested on substrates. The composite wavy column shown on the left takes the same wavelength and amplitude as those formed by the first release of prestrain along y-axis. When subjected to uni-axial compression along x-axis, straight columns laterally buckle into sinusoidal shapes along x-axis shown on the right. (b) Schematic illustration of parameters (wavelength, amplitude and jog angle) characterizing the geometry of a herringbone pattern. The out-of-plane profile is represented by z (x, y) = As cos {2π/λm (y +Al cos (2πx/λl))}, where As and Al are the out-of-plane amplitude of short wave along y-axis and in-plane amplitude of long wave along x-axis, respectively. λm and λl are the intermediate and long wavelengths defined as the distance between two adjacent jogs along the y-axis and x-axis, respectively. Two dependent parameters are the short wavelength λs (the perpendicular distance between two adjacent contours) and the jog angle α with λs = λm sin(α/2) and α = π - 2tan−1(π2Al/ 2λl). SEM images of herringbone patterns over macroscopic areas created through (c) sequential release of equi-biaxial prestrain of 20% on 200 nm p(EGDA) coating (SEM area: ≈ 1 mm × 0.8 mm), (d) sequential release of non-equi-biaxial prestrain with ε1st = 20% and ε2nd = 30% on 400 nm p(EGDA) coating (SEM area: ≈ 1.5 mm × 1.2 mm)

through classical buckling perturbation analysis (see Section S5 in the Supporting Information for details), which are found as when considering the finite deformation of the column  14  λl = 2.06π t 1 − ν 2f

l εcr

0.05π =

1 − ν 2f

 ¯ 12  1s t  g ε Ef ¯ 1 + ε2nd 3Es

 ¯ 23   3Es h ε1s t E¯ f

(4)

(5)

g(ε1st) and (ε1st) are defined as 



h 1/4     1s t   1s t and h ε1s t = g 2 ε1s t εcr − 1 = 3 ε − εcr π + 1 g ε

where

(see Supoorting Information Section S5). For small prestrain (e.g. ε1st < 5%), g(ε1st) can be approximated as 1 with the error less than 5%. Equation (4) shows the long wavelength is proportional to the coating thickness t since εcr is independent of the film thickness t. In addition, λl decreases with increasing second prestrain. The critical sequential buckling strain (Equation (5)) is found to be independent of the film thickness and to be dependent of the first released prestrain. From the

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geometry of a herringbone pattern, the lateral amplitude Al is governed by the jog angle and the long wavelength, i.e., Al =

2λl cot (α/2) π2

(6)

Equation (6) demonstrates that Al is proportional to λl and thus is proportional to t. In addition, Al is dependent of the jog angle and thus the strain ratio. Specially, when the jog angle is equal to 90°, Al becomes 2 λl/π2 and the value of Al is smaller than that of λl (i.e., Al ≈ 0.2λl). The theoretical model is further examined in simulations and experiments. Figure 4 shows the wavelength and amplitude of herringbones created through sequential release of equi-biaxial prestrain as a function of different coating thicknesses. As shown in Figure 4a, the linear increase of the long wavelength with coating thickness in Equation (4) agrees well with the experiments of p(EGDA) coating on PDMS substrate and related FEM simulations. The level of agreement between experiment and simulation is excellent when t ≤ 400 nm. The model prediction for the thickest coating (t ≈ 540 nm) is about 13% larger than that found in the experiment. The error in thickness measurement increases with thickness (see

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COMMUNICATION Figure 4. The comparison between FEM, theory, and experiments for multiple wavelengths (a) and amplitudes (b) of herringbones and 1D wrinkles for different p(EGDA) coating thickness upon sequential release of equi-bi-axial prestrain of 10% or release of uni-axial prestrain of 10%. SEM images of wrinkled p(EGDA) coating with thickness of 200 ± 8 nm (c), 400 ±12 nm (d), and 540 ± 20 nm (e). (f) SEM images of wrinkled p(HEMA-EGDA) coating with thickness of 300 ±10 nm upon sequential release of equi-bi-axial prestrain of 10%.

Supporting Information Section S6) and largely accounts for the discrepancy between model and experiment. The intermediate wavelength λm is equal to the 1D wrinkle wavelength λ in Equation (2) (i.e., λm = λ), which agrees with both experiments and FEM simulation. The geometrically dependent short wavelength λs is given by λs = λm sin(α/2), which is consistent with simulations. Figure 4b shows the value of lateral amplitude Al is about 4–5 times larger than that of out-of-plane amplitude of 1D wrinkle. The linear increase of Al with the coating thickness in Equation (6) is consistent with experiments. The deterministic long wavelength predicted by Equation (4) through sequential release of biaxial prestrain can find potential applications in the measurement of material properties of the thin film coatings. Since both the intermediate wavelength λm and the long wavelength λl are proportional to the film thickness t, for small equi-biaxial prestrain, the ratio of λl/λm gives  1  1 E¯ f 6  λl ≈ 1.03 1 − ν 2f 4 (7) λm 3 E¯ s The above Equation shows that the wavelength ratio is only related to the modulus ratio between the film and substrate. Thus through the measurement of the ratio of λl/λm, the modulus of the film Ef can be estimated as  6  6 λl λl 2.51 E¯ s 0.31 E¯ s Ef ≈

≈

(8) λ λ m s 1 − ν 2f 1 − ν 2f Measurement of thin film properties through measurement 3 of the 1D wrinkle wavelength (i.e., E f = 3(1 − ν 2f ) E¯ s (λ/2π t ) 3 from Equation (2)) has been used by others but the film thickness must be known. However, for very thin films, the

Adv. Mater. 2012, DOI: 10.1002/adma.201201937

thickness is difficult to measure and hence gives substantial measurement error. Through the sequential release of the load, the film property can be obtained by only measuring the two wrinkle wavelengths without the measurement of the film thickness. As one example for demonstrating the measurement of film modulus through sequential wrinkling, a HEMA-EGDA copolymer with a relatively lower Young’s modulus is deposited on PDMS substrate with coating thickness of 300 nm. Upon the sequential release of equi-biaxial prestrain of 10%, a herringbone pattern is observed in the hydrophilic swellable layer (Figure 4f), where the intermediate wavelength is λm = 9.2 ± 0.6μm and long wavelength is λl = 20.2 ± 1.1μm and the ratio of two wavelengths gives λl/λm ≈2.2. By assuming a Poisson’s ratio for p(HEMA-EGDA) of 0.4, from Equation (8) the Young’s modulus of p(HEMA-EGDA) Ef can be readily predicted giving Ef ≈183MPa. This value is consistent with the value Ef = 168 ± 24MPa obtained through the measurement of the 1D wavelength (i.e., λm in 2D wrinkles) and the coating thickness (i.e., Equation (2)). Figure 4f also confirms that the wrinkling processes described here can be extended to additional iCVD functional polymeric surface layers. In conclusion, the sequential wrinkling strategy shows great promise for creating deterministically ordered herringbone patterns as well as their application in thin-film property measurement. Compared with the 1D sinusoidal wrinkling patterns, the extra tunable long wavelength and asymmetric herringbone patterns with jog angle different than 90° provides new potential applications in tunable wetting, adhesion, and friction properties, altering boundary layers in fluid flow as well as potential applications in microfluidic channels.

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6

Experimental Section

Supporting Information

Preparation of PDMS sheet: PDMS preparation was done using the Sylgard 184 Silicone Elastomer Kit from Dow Corning. The elastomer and curing agent were thoroughly mixed at a mass ratio of 10:1 and poured into petri dishes with a PDMS layer of about 2mm. The petri dishes were put in a dessicator to degas for 45 minutes and then cured in an oven at 70 °C for one hour. Cross-shaped PDMS films 6 cm long and 2 mm thick were cut using Epilog laser cutter for the experiments. The samples were placed in a home-made sample holder for biaxial stretching. Legs of the PDMS were introduced between jaws and through the use of screws stretched to a specific elongation. iCVD deposition of polymer coating: A layer of trichlorovinylsilane (97%, Sigma) was used as adhesion promoter between PDMS and p(EGDA). First, a plasma oxygen treatment for PDMS surface activation was carried out in a plasma cleaner (Harrick Scientific PDC-32G) at 18 W for 30 s. Immediately, the biaxially stretched cross-shaped PDMS film was introduced in an oven at 40 °C under vacuum and exposed to trichlorovinylsilane vapours for 5 min. iCVD polymerizations were conducted in a custom-built cylindrical reactor (diameter 24.6 cm and height 3.8 cm). EGDA (98%, PolySciences) was heated to 60 °C and was introduced into the reactor at a flow rate of 0.5 sccm by using regulated needle valves. Tert-butyl peroxide (TBPO) (98%, Aldrich) and nitrogen were fed into the chamber at a flow rate of 1.5 sccm and 1.0 sccm respectively through a mass flow controller (MKS Instruments). ChromAlloy O filaments (Goodfellow) were resistively heated to 260 °C. The distance between the filaments and the stage was kept at 2 cm. The stage was back-cooled by water using a chiller/heater (Neslab RTE-7) and the temperature was set at 25 °C. Polymer thickness was monitored in situ by laser interferometry (JDS Uniphase). After the polymer deposition, the system was released slowly and simultaneous or sequentially to obtain the desired pattern. For p(EGDA-HEMA) copolymer, the flow rate ratio is controlled as 0.5 to 0.25 sccm. Characterization of wrinkled patterns and film thickness: The surface topography was studied using a Hitachi TM3000 Tabletop scanning electron microscopy (SEM). Film thicknesses were monitored in situ by interferometry with a 633 nm HeNe laser source (JDS Unipahse) using silicon wafers as substrates. After the iCVD coating, the film thickness was measured using Variable-angle ellipsometric spectroscopy (VASE, M-2000, J. A. Woollam) Characterization of mechanical property of p(EGDA) coating: In order to test the material properties, self-free-standing films of p(EGDA) were obtained through two steps: first, the films with certain thickness were deposited on a sacrificial layer; second, a self-free-standing film was obtained by dissolving the sacrificial layer in the deionized water. Films with 3.5 μm thickness were chosen since the films must be thick enough to be self-standing. Since those samples were very thin and brittle, a cardboard frame was used to handle them: the frame was first glued to the sample before dissolving the sacrificial layer in water. Then the cardboard frame was cut just before the test once both ends of the samples were amounted in the jaws of the Q800 DMA. 1%/min strain rate ramps were performed on EGDA films at room temperature. The stress-strain curve for a typical result of this test was shown in Figure S5. The measured stiffness of the p(EGDA) film is 775MPa, which is higher than the average value reported in the literature for solutionsynthesized p(EGDA). This difference has been demonstrated to arise due to reactivity differences in the two methods;[30] see also Supporting Information, Section S7. Micromechanical FEM simulation: The coating is modeled as a linear, isotropic and elastic material with the measured Young’s modulus of Ef = 775 ± 30 MPa and a Poisson’s ratio νf ≈ 0.4 of a self-standing p(EGDA) film. The PDMS substrate is a non-linear elastic elastomeric material and modeled as a hyperelastic almost incompressible Neo-Hookean material with measured Young’s modulus Es = 0.45 ± 0.02 MPa and Poisson’s ratio νs = 0.49.

Supporting Information is available from the Wiley Online Library or from the author.

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Acknowledgements The authors thank the King Fahd University of Petroleum and Minerals in Dharan, Saudi Arabia, for funding the research under the grant No. 016403-011 reported in this paper through the Center for Clean Water and Clean Energy at MIT and KFUPM. J. L. Yagüe thanks the Grupd’Enginyeria de Materials at IQS-Universitat Ramon Llull in Barcelona, Spain, for his Postdoctoral Fellowship. Received: May 15, 2012 Revised: July 17, 2012 Published online: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

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