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Nanostructured Fluids Based on Propylene Carbonate/ Water Mixtures Gerardo Palazzo,*,† Daniela Fiorentino,† Giuseppe Colafemmina,† Andrea Ceglie,‡ Emiliano Carretti,§ Luigi Dei,§ and Piero Baglioni§ Consorzio Interuniversitario per lo sviluppo dei Sistemi a Grande Interfase (CSGI), Firenze, Italy Received February 24, 2005. In Final Form: April 29, 2005 The microstructure of aggregates formed by sodium dodecyl sulfate (SDS) and 1-pentanol in mixtures of water and a polar aprotic solvent (propylene carbonate, PC) was investigated by means of pulsed gradient spin-echo NMR, dynamic light scattering, viscosity, and conductivity measurements. PC partitions itself between micelles and aqueous bulk. The fraction of micellized propylene carbonate remains constant along PC-dilution, and the phase separation takes place when the composition of continuous phase attains the PC/water miscibility gap. The micellized PC is present mainly in the micelle’s palisade and strongly increases the total interfacial area, thus acting as a cosurfactant. At high PC content, the system is composed by very small aggregates (around 10 Å in radius) made by few SDS molecules (10-6) and PC and pentanol. The resulting system can be described as a nanostructured fluid with a huge interfacial area and a small dispersed phase.

1. Introduction Aqueous solutions of surfactants are so extensively used in detergency that the word surfactant is often used as a synonym of detergent. Household and fabric detergency are the archetypes of removal of undesired substances (soil) from solid surfaces. In such cases, for economic, health, and environmental reasons, there is the constraint of using neat water as solvent, mechanical agitation is allowed (and usually encouraged), and the final task is the removal of the widest class of adsorbed substances. There are, however, other applications of surfactants in detergency where constraints and scopes are markedly different. A typical example is the removal of polymers from frescoes, paintings, and others works of art. Polymers have been (unsuitably) used as consolidants, protectives, adhesives, and varnishes to restore wall paintings, stones, archeological items, and so forth.1 Unfortunately, after a few decades, both thermal and photochemical depolymerization lead to the loss of the works of art due to the loss in transparency and mechanical stress of the polymer coating.2,3 Actually, the first step in the conservation/ restoration process is often the removal of aged polymers coming from a previous treatment. Of course, the cleaning of a work of art is very different from household cleaning: the economical constraints are * Author to whom correspondence should be addressed. E-mail: [email protected]. † Dipartimento di Chimica and Laboratorio di Ricerca per la Diagnostica dei Beni Culturali, Universita` di Bari, via Orabona 4, I-70126, Bari, Italy ‡ Dipartimento STAAM, Universita ` del Molise, v. De Sanctis, I-86100 Campobasso, Italy § Dipartimento di Chimica, Universita ` di Firenze, via della Lastruccia 3, I-50019 - Sesto Fiorentino (FI), Italy (1) Horie, C. V. Materials for Conservations Organic Consolidants, Adhesives and Coatings; Architectural Press: Oxford, 1987; pp 103112. (2) Feller, R. L. In Accelerated Agings Photochemical and Thermal Aspects; The Getty Conservation Institute: Los Angeles, 1994; pp 6390. (3) Morimoto, K.; Suzuki, S. J. Appl. Polym. Sci. 1972, 16, 2947. Feller, R. L. Bull. Inst. R. Patrim. Artist. 1975, 15, 135. Hennig, J. Kunst. Fortschriftsber. 1978, 7, 13.

(hopefully) released, mechanical agitation is not allowed, and the selective removal of the polymer coating, leaving untouched other adsorbed substances (i.e., the painting itself), is mandatory. Health and environmental constraints are always stringent because often we are dealing with hundreds of square meters of porous surfaces located in closed rooms. Therefore, the direct washing with huge amounts of organic solvents able to dissolve the coating is not feasible. We have previously shown that oil-in-water (o/w) microemulsions made of a large part of water and a minute amount of surfactant, cosurfactant, and suitable oils are very effective in restoration of wall paintings.5 Of course, the choice of the ‘oil’ depends on the class of polymers to be removed. For acrylic polymers, orthodox o/w microemulsions have been successfully used.5 However, vinyl polymers are insoluble in apolar oils, and rather more polar solvents should be used for this purpose. Propylene carbonate (PC) is an excellent solvent for vinyl polymers,4 and this was the rationale for a screening of many PC-containing systems as solubilizing agents for vinyl polymer patinae.5 The only formulation that succeeded in removing the coating was a four-component system made of the anionic surfactant sodium dodecyl sulfate (SDS), 1-pentanol as cosurfactant, PC, and water. More than 260 m2 of a fresco by Pozzoserrato (16th century)6 have been cleaned from a vinyl polymer coating with this formulation.5 However, the mechanism of coating removal and the microstructure of the system were still a puzzle. PC is soluble to large extent in water (∼20 wt%), and the amount of PC used in the formulation is only slightly above its solubility in water. This notwithstanding, PC/water mixtures were unsuccessful in removing any coating. For this reason, we have undertaken the present characterization of the microstructure of the SDS/ pentanol/PC/water system. (4) Horie, C. V. Materials for Conservation - Organic Consolidants, Adhesives and Coatings; Architectural Press: Oxford, 1987; pp 103112. (5) Carretti, E.; Dei, L.; Baglioni, P. Langmuir 2003, 19, 7867. (6) Frescoes decorating the external walls of the Santa Maria dei Battuti Cathedral in Conegliano (Treviso) in Northeastern Italy.

10.1021/la050492z CCC: $30.25 © 2005 American Chemical Society Published on Web 06/09/2005

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Table 1. Density (d), Viscosity (η), Refractive Index (n), and Transport Properties for Binary Mixtures PC/Watera 102 × PC mole fraction (χPC) d/g cm-3 η/mPa s n DW/m2 s-1 DPC/m2 s-1 DPOH/m2 s-1 a

0.0000

0.3623

0.9254

1.9252

3.0466

3.272

4.2408

linear relationship

0.9970 0.890 1.3325 2.3 × 10-9 8 × 10-10

1.0013 0.937 2.3 × 10-9 1.0 × 10-9 -

1.0076 0.959 1.3365 -

1.0182 1.038 1.3415 -

1.0286 1.3450 2.0 × 10-9 1.0 × 10-9 -

1.7 × 10-9 1.0 × 10-9 -

1.0389 1.19559 1.34950 1.7 × 10-9 0.9 × 10-9 6 × 10-10

0.9980 ( 6 × 10-4 + (0.99 ( 0.03)χPC 0.900 ( 7 × 10-3 + (6.9(0.3)χPC 1.3329 ( 3 × 10-4 + (0.40(0.01)χPC

Uncertainty for n is (5 × 10-4 and is (1 for others quantities on the last figure.

2. Experimental Section 1-Pentanol (purity>98.5%), SDS, and PC (purity > 99.0%) were purchased from Merck, Darmstadt, Germany. SDS was purified from ethanol,7 dried under reduced pressure, and stored over dry silica gel; pentanol and PC were used as received. Unless otherwise stated, all the samples where prepared by weighing. Quaternary systems SDS/pentanol/PC/water were prepared by addition of suitable amounts of PC to a stock solution of SDS and pentanol in water in order to have a set of samples with fixed mass ratios SDS/pentanol/water ) 5.0:6.6:88.4, respectively. Conductivity measurements were performed at 25.0(0.2 °C with a CDM230 conductivity meter (Radiometer Analytical) equipped with a four-pole conductivity cell CDC866T (cell constant ) 1.048 cm-1). Viscosity measurements were performed on a Paar Physica UDS 200 Rheometer. A double-gap measuring system has been chosen (diameter, 5 cm; thickness of the gap, 1 mm; amount of sample needed, almost 25 cm3). Density and refractive index measurements were performed with an Anton Paar DMA 4500/ 5000 densimeter and on an Atago absolute refractometer interfaced with a digital thermometer, respectively. All the measurements were performed maintaining the temperature at 25 °C during the whole run. Dynamic light scattering (DLS) experiments were carried out on a Brokhaven Instruments apparatus (BI 9000AT correlator and BI 200 SM goniometer). The signal was detected by an EMI 9863B/350 photomultiplier. The light source was the second harmonic (532 nm) of a Nd:YAG diode pumped laser (Compass 315M diode pump laser, Coherent). Homodyne detection was recorded using decahydronaphthalene as cell matching liquid. The data were collected in multiple sample-time detection, and the autocorrelation function of the scattered light intensity was expanded about an average line width as a polynomial function of the sample-time with cumulants as parameters to be fitted.8,9 As a result of the cumulant analysis, one obtains the average diffusion coefficient of collective motion and the standard deviation of the of diffusion distribution function (see also Discussion). Self-diffusion coefficient measurements have been carried out by the Fourier transform NMR pulsed field gradient spin-echo (PGSE-NMR) method.10 Experiments were performed on a BS587A NMR spectrometer (Tesla), operating at 80 MHz for the proton, equipped with a pulsed field gradient unit (Autodif 504, STELAR s.n.c). The pulse sequence employed was the StejskalTanner11 sequence, 90°-τ-180°-τ-echo, with two rectangular field gradient pulses of strength G and duration δ, separated by a constant interval ∆ ) 140 ms. The echo amplitude recorded at 2τ is given by

A(2τ) ) exp[-2∆/T2] exp[-γ2G2δ2(∆ - δ/3)D] where T2 is the spin-spin relaxation time and γ is the gyromagnetic ratio of a proton. The self-diffusion coefficient of the species under investigation, D, is obtained by an exponential fitting of the above equation to the experimental echo decay collected at fixed G and different δ values. Typical conditions are G ≈ 0.04 T m-1 rad-1 ) 0.25 T m-1 and δ ranged from 2 to 50 ms. The strength of the applied field gradient (G) was determined before each experiment by a separate calibration with pure DMSO. The value of the DMSO self-diffusion coefficient was from the literature.12 The magnetic field was locked by an external D2O lock signal for all the samples. The temperature of the

samples was maintained at 298.0 ( 0.2 K by means of a built-in variable temperature control unit. The accuracy of the selfdiffusion coefficients was within 5%.

3. Results 3.1. Preliminary Investigations on the PC/Water and SDS/PC/Water Systems. PC exhibits anomalous solvent properties, being highly polar13,14 (dielectric constant ) 65.1; dipole moment 4.94 D) and having limited miscibility with water15 at the same time. At room temperature, the binary system propylene carbonatewater shows a wide miscibility gap in the range 20-92 PC wt%.15 Detailed investigations on the physicochemical properties of mixtures PC/water are still lacking. In Table 1, the values of density (d), viscosity (η), and refractive index (n) determined in the present study in mixtures of PC and water are listed. All three properties behave as linear functions of the PC mole fraction, χPC, (see last column in Table 1) within the whole single-phase waterrich domain (0 e χPC e 0.042). Also shown in Table 1 are the values of self-diffusion coefficients of water (DW) and propylene carbonate (DPC). The water diffusion decreases slightly upon PC loading, passing from 2.3 × 10-9 (neat water) to 1.7 × 10-9 m2 s-1 (PC ) 20 wt%; the water-rich side of miscibility gap). In contrast, the PC diffusion is essentially constant (DPC = 1 × 10-9 m2 s-1) in the investigated range of composition. The last row of Table 1 is assigned to the pentanol selfdiffusion coefficient (DPOH), measured when trace amounts of alcohol (1 wt%) are dissolved in pure water and PC/ water mixtures. For this compound as well, the selfdiffusion coefficients are scarcely affected by the PC loading, decreasing from 8 × 10-10 (neat water) to 6 × 10-10 m2 s-1 (maximum PC loading). From Table 1, we learn some key points that will be useful in handling four-component systems: upon PC loading, the viscosity increases while the diffusion coefficient of PC remains constant, furthermore the increase in solution density is satisfactorily described by the ideal mixing model. The influence of propylene carbonate on the selfassembly of SDS was investigated by means of conductivity (χ, specific conductance) measurements. Figure 1 shows χ vs c plots (c being the SDS concentration) representative (7) Baglioni, P.; Rivara-Minten, E.; Dei, L.; Ferroni, E. J. Phys. Chem. 1990, 94, 8218. (8) Corti, M. In Physics of Amphiphiles, Micelles, Vesicles and Microemulsions, Proceedings of the International School of Physics “Enrico Fermi”; Corti, M., Degiorgio, V., Eds.; North-Holland Physics Publishing: Amsterdam, 1985; pp 122-151. (9) Chu, B. Laser Light Scattering: Basic Principles and Practice, 2nd ed.; Academic Press: New York, 1991. (10) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1. (11) Tanner, J. E.; Stejskal, E. O. J. Chem. Phys. 1968, 49, 1768. (12) Holz, M.; Mao, X.; Seiferling, D.; Sacco, A. J. Chem. Phys. 1996, 104, 669. (13) Simeral, L.; Amey, R. L. J. Phys. Chem. 1970, 74, 1443. (14) Payne, R.; Theodorou, I. E. J. Phys. Chem. 1972, 76, 2892. (15) Catherall, N.; Williamson, A. J. Chem. Eng. Data 1971, 16, 335.

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Figure 1. Specific conductivity (χ) vs SDS concentration (c) for SDS dissolved in water and PC/water solution (PC ) 16wt%). Continuous curves denote the fit of experimental data to the function: χ(c)) A1c + σ(A2 - A1) ln(1 + e(c-cmc)/σ)/(1 + e-cmc/σ) proposed in ref 17. The terms A1 and A2 represent the slope of the χ profile below and above the cmc, respectively. The term σ is a measure of the width of the transition from monomers to micelles. For water, the best fit parameters are A1) 7.2 × 10-2 µS cm-1 mM-1; A2) 2.8 × 10-2 µS cm-1 mM-1; σ ) 0.68 mM; cmc ) 7.8 mM. For PC/water, the best fit parameters are A1) 6.1 × 10-2 µS cm-1 mM-1; A2) 5.3 × 10-2 µS cm-1 mM-1; σ ) 0.71 mM; cmc ) 16.1 mM. The location of cmc values is highlighted by vertical dotted lines.

of the SDS behavior in neat water and in PC/water mixture (χPC ) 0.0325).16 The break in the χ vs c plot (see Figure 1) is clearly evident in the case of SDS in water. When a mixture of PC and water (PC ) 16 wt%) is used as solvent, the conductivity curve exhibits a weak curvature, as shown in Figure 1. This behavior, often found for surfactant with small aggregation number, make difficult a safe determination of cmc. For this reason, the cmc values have been evaluated by fitting the whole data set to the function proposed by Carpena et al.17 (see also caption of Figure 1). It turns out that the cmc in water is 7.8 ( 0.2 mM, in good agreement with the known cmc value (8 mM),18 while it is almost double (16.1(0.4 mM) in the presence of PC. Furthermore, in PC/water the slope of the χ profile above the cmc is higher than that found in pure water Neglecting interionic interactions, such a slope is given by19

() dχ dc

>cmc

)

[

]

2 eF NaggR R + 6πη Rmic RNa+

(1)

where F (the Faraday constant), e (the elementary charge), and RNa+ (the effective sodium ion radius) are independent from the micelle features. In contrast, Nagg (the number of surfactant molecules forming a micelle), R (the degree of counterion dissociation), and the hydrodynamic micellar radius (Rmic) depend on the type of surfactant and on concentration. For binary systems (surfactant plus water), dimensional arguments19 suggest that the micellar size scales as the cube-root of the aggregation number (Rmic∝ (16) Shanks, P. C.; Franses, E. I. J. Phys. Chem 1992, 96, 1794 and references therein. (17) Carpena, P.; Aguiar, J.; Beranola-Galva`n, P.; Carnero Ruiz, C. Langmuir 2002, 18, 6054. (18) Van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physicochemical properties of selected anionic, cationic and nonionic surfactants; Elsevier: Amsterdam, 1993; Chapter I.1. (19) Evans, H.C. J. Chem. Soc. 1956, 579.

Figure 2. Self-diffusion coefficients of PC, pentanol, and SDS measured along a PC dilution line. The mass ratio SDS/ pentanol/water is 5.0:6.6:88.4. Also shown are, in the case of samples doped with tetramethylsilane (TMS), the TMS selfdiffusion coefficients. The continuous lines are the predictions for PC and pentanol diffusion according to eqs 2 and 3 (see text for details).

Nagg1/3), and the decrease of (dχ/dc) above the cmc20 can be accounted for only by dressed micelles, i.e., by micelles that are not fully dissociated (R < 1). However, in the presence of a third component that might be taken up by the micelle, the aggregate size (Rmic) will be not a function of Nagg only but also of the amount and location of bound cosolvent. Therefore, the increase in the slope of the χ curve above the cmc, observed by switching the solvent from water to PC/water solution, might be accounted for by an increase in R and/or an uncorrelated decrease in Rmic. 3.2. The SDS/Pentanol/PC/Water System. The structural characterization of the formulation that exploits the best performances is not an easy task to afford. Basically, we are in the presence of partition equilibria between the continuous and dispersed phase that involve three chemical species, viz. SDS, pentanol, and PC. Under favorable conditions, partition equilibria in surfactant systems can be profitably investigated by means of the PGSE-NMR technique. Under all the conditions explored in the present work, the recorded echo decays are single-exponential, so that all the information can be safely condensed in a single diffusion coefficient. The self-diffusion coefficients of SDS, pentanol, and PC, measured along the PC dilution path of aqueous solutions (SDS/POH/water), are shown in Figure 2 as function of the overall PC amount. Hereafter, we will indicate the system composition by the percentage of PC evaluated on the overall sample weight (the mass ratios SDS/POH/water being fixed at 5.0:6.6:88.4, respectively), while the relative amounts of water and PC will be described by the PC mole fraction evaluated only with respect to PC and water (χPC ) PC moles/(PC moles + water moles)). As stated above, PC, pentanol, and SDS are expected to partition themselves between aqueous bulk and aggregates. Since the experimental PGSE decays are always strictly monoexponential, the molecular exchange is fast (20) The slope below the cmc is given by eq 1 with R ) 1, N ) 1 and the effective radius of dodecyl sulfate ion instead of the micellar radius.

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compared to the experimental time scale (about 0.1 s).21 Under this condition, the self-diffusion coefficient probed by the PGSE-NMR experiment is an apparent diffusion coefficient given by22

Dapp ) PfreeDfree + (1 - Pfree)Dmic

(2)

where Pfree is the fraction of molecules moving in the aqueous bulk with diffusion coefficient Dfree, and Dmic is the self-diffusion coefficient of the micelle. In the case of SDS, the results of Figure 1 suggest that the fraction of monomeric surfactant is about 16 mM; this is much less than the overall SDS concentration (∼0.18 M). Therefore, the term Pfree ) cmc/c is about ∼0.1, and the contribution of free SDS to the observed diffusion is expected to be small. This hypothesis was tested by measuring the self-diffusion coefficients of TMS in solutions doped (∼1%) with trace amounts of this waterinsoluble compound. The results, shown in Figure 2 as large closed diamonds, coincide with the measured DSDS. This proves that, in the range of composition explored, SDS is a good probe of micellar diffusion (Dmic ≡ DSDS). In the case of pentanol and PC, the contribution of molecules dissolved in the aqueous bulk to the observed diffusion cannot be neglected. Since Dmic) DSDS, one can evaluate, through eq 2, the fraction of free molecules, as long as the parameter Dfree is known. Since the diffusion coefficient of PC measured in the binary system waterPC is ∼10-9 m2 s-1 (Table 1), we have used this value as Dfree in the case of PC. The fraction of free PC evaluated from the data of Figure 2 through eq 2 is almost the same for the 17 compositions explored (〈Pfree〉 ) 0.60 ( 0.01). Once Pfree is known, one can easily evaluate the composition of the aqueous phase. In Figure 3A, the actual composition of aqueous bulk (expressed as χPCfree) moles of PC free/[moles of PC free plus moles of water]) is reported as a function of the stoichiometric composition of aqueous phase (expressed as χPC ) moles of PC/[moles of PC plus moles of water]). It is clear that the real PC mole fraction in the aqueous phase is always lower than the mole fraction inferred from the overall PC and water content. Of course, this reflects the presence of a relevant fraction of PC bound to the micelles. A stated above, the whole data set is well described by a constant Pfree value:

Pfree XPCfree ) 1 - χPC Pfree + χPC

(3)

since χPC ,1, the data closely follow a straight line with null intercept and slope ) Pfree (i.e., χPCfree ≈ PfreeχPC). In Figure 3, the prediction of eq 3 with Pfree ) 0.60 (solid line) suggests that at the maximum PC solubility in the fourcomponent system (vertical dotted line) the aqueous phase attains the solubility gap of PC/water system (horizontal dashed line). In Figure 2 is reported as solid line the self-diffusion coefficient of PC calculated from eq 2 under the assumption of Pfree) 0.6 and Dfree)1 × 10-9 m2 s-1. It is clear that such an assumption describes satisfactorily the experimental behavior. In the case of pentanol, we have assumed a fixed Dfree value equals the self-diffusion coefficient of pentanol in (21) In the case of slow exchange, the observed echo decay is the superimposition of the decays due to molecules in the two sites (i.e., it is two-exponential). (22) Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1983, 87, 4756. Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1984, 88, 5391.

Figure 3. Aqueous bulk composition (χPCfree ) moles of PC free/[moles of PC free plus moles of water]) as a function of the stoichiometric composition of the aqueous phase (χPC ) moles of PC/[moles of PC plus moles of water]). Data have been evaluated from the PC diffusion (Figure 2) by using eq 2 and the values Dfree ) 1 × 10-9 m2 s-1 and Dmic ) DSDS. The solid line represents the fit of data according to eq 3 (best-fit paramenter Pfree ) 0.60). The maximum PC solubility in the four-component system (27.1 wt%) corresponds to χPC ) 0.0691 (vertical dotted line). The maximum PC solubility in the binary system PC/water (PC mole fraction of 0.0420) is read on the χPCfree axis (horizontal dashed line). (B) Micellar volume fraction (φmic) as a function of the stoichiometric composition of aqueous phase.

aqueous solution at high PC content (Dfree) 6 × 10-10 m2 s-1; Table 1). The fraction of free pentanol evaluated under such an assumption is essentially constant (〈Pfree〉 ) 0.53 ( 0.01). Note that we have neglected the small increase in the self-diffusion coefficient of free pentanol upon water loading (evident in Table 1) because the assumption of Dfree) 6 × 10-10 m2 s-1 describes well enough the pentanol diffusion behavior (see Figure 2). The approximation of constant partition of pentanol and PC greatly simplifies the data analysis. By taking into account the partition of PC and alcohol between micelles and continuous phase, it is possible to evaluate the volume fraction of the aggregates, φmic (Figure 3B). Figure 3B reveals that φmic increases upon dilution of the system with PC. Moreover, the continuous phase composition and its viscosity are easily calculated from the system’s composition. The higher the overall loading of PC becomes, the higher its concentration in the aqueous bulk becomes. This means a monotonic increase in the bulk viscosity. With this in mind, the only explanation for an increase of DSDS upon PC loading is a parallel decrease in the aggregate’s size. To have insight on this point, DLS measurements have been performed on selected samples. On the present system, DLS experiments are more delicate than PGSENMR. They furnish a diffusion coefficient, DDLS, as well,

Nanostructured Fluids

Figure 4. Diffusion coefficients as a function of the overall PC content (mass ratio SDS/pentanol/water ) 5.0:6.6:88.4). Closed circles are the collective diffusion coefficients probed by DLS; closed squares are the self-diffusion coefficients of the micelle probed by PGSE-NMR using SDS as diffusion probe. The singleparticle diffusion coefficient, D0, was evaluated from the abovereported quantities as described in the text. Note that in absence of PC the three diffusion coefficients almost coincide.

but the signal-to-noise ratio is proportional to the difference in refractive index between aggregates and continuous phase (optical contrast).8,9 A consequence of the PC and pentanol partition is that the optical contrast becomes small. Indeed, we found that the signal-to-noise ratio of the intensity correlation function becomes quite low upon PC loading; thus, long averaging times are required and the uncertainty associated to DDLS is high (10-25%, see Figure 4). The diffusion coefficient observed in DLS experiments, in the four-component systems are always larger than the DDLS value found in the absence of PC (see Figure 4). This agrees well with the scenario of aggregates that, in the presence of PC, are smaller than those found in neat water. As shown in Figure 4, the DDLS values are systematically higher than the micelle self-diffusion coefficient probed by PGSE-NMR (DNMR). This is because the two parameters have different physical meaning and should coincide only in absence of interparticle interactions23,24 (a point that will be afforded in detail in the Discussion). There are several evidences indicating that the addition of pentanol to SDS in water induces a sphere-to-rod transition in a micellar shape.25-28 Our diffusion data are consistent with these previous finding. Indeed, we measured DSDS ) 1.0 × 10-10 m2 s-1 in the SDS/water system (5:88.4 by weight) while the addition of pentanol (6.6 wt%) reduces DSDS to 2.9 × 10-11 m2 s-1. A similar drop was observed in the DDLS values (∼1 × 10-10 in SDS/water and 4.0 × 10-11 m2 s-1 in SDS/pentanol/water). The addition of propylene carbonate induces a dramatic increase in the micellar diffusion coefficient (Figure 4) that, at high PC content, are incompatible with rodlike aggregates. The simplest explanation is that PC loading induces a shape (23) Cichocki, B.; Felderhof, B. U. Phys. Rev. A 1990, 42, 6024. (24) Cichocki, B.; Felderhof, B. U. J. Chem. Phys. 1991, 94, 556. (25) Lang, J. J. Phys. Chem. 1990, 94, 3734. (26) Stephany, S. M.; Kole, T. M.; Fisch, M. R. J. Phys. Chem. 1994, 98, 11126. (27) Thimons, K. L.; Bradzil, L. C.; Harrison, D.; Fisch, M. R. J. Phys. Chem. B 1997, 101, 11087. (28) Caponetti, E.; Chillura Martino, D.; Floriano, M. A.; Triolo, R. Langmuir 1997, 13, 3283.

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Figure 5. Viscosity of systems with fixed mass ratios SDS/ pentanol/water (5.0:6.6:88.4) and different amounts of PC. The upper axis is the composition (mole fraction) of the aqueous bulk evaluated taking into account the PC partition; the lower axis is the overall PC content. Closed triangles refer to the measured viscosity; closed dots are the corresponding prediction of eq 4 with ν ) 2.5; open triangles represent the viscosity of the aqueous bulk according to the linear relation of Table 1 and PC partition (Figure 3).

transition in the aggregates from slow-diffusing rods to fast-diffusing spherical ones. The viscosity of micellar solutions is very sensitive to the micelle shape. Solutions of highly asymmetrical particles are much more viscous than solution of spherical aggregates (the dispersed phase volume fraction being constant). For dilute dispersions, the influence of particle shape and volume fraction (φ) and of the continuous phase viscosity (η0) is quantitatively accounted for by the following equation:

η ) η0(1 + νφ)

(4)

where the intrinsic viscosity, ν, depends only on particle shape and can be evaluated through the Simha equation.29 For spheres, ν assumes its lowest value (2.5) and eq 4 reduces to the well-known Einstein equation. The influence of PC loading on sample’s viscosity is shown in Figure 5. Upon addition of PC, η first decreases up to a minimum (located at PC ≈ 10 wt%) then increases. One should keep in mind that any increase in the overall PC content corresponds to an increase in the dispersed-phase volume fraction and in the PC concentration in the continuous phase. Although the micelle volume fraction of the present system (φ g 0.1) is above the range of quantitative agreement with eq 4, this last should still describe the system’s behavior in a qualitative way. The knowledge of PC partition, obtained from PGSE-NMR, permits us to evaluate the composition of the aqueous bulk (reported as χPCfree in the upper horizontal axis of Figure 5) and therefore the η0 values (through the relationship of Table 1). On the other hand, knowing the amount of pentanol and PC present in the SDS micelles, the micellar volume fraction can be calculated as well. Both η0 and the viscosity calculated according to the Einstein equation (eq 4 with ν ) 2.5) are shown in Figure 6 together with the experimental η values. It is clear that the cumulative effect of increasing φ and η0 by PC loading qualitatively accounts (29) Simha, R. J. Phys. Chem. 1940, 44, 25.

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Figure 6. Molar conductivity (closed dots, left axis) and Walden’s product (open dots, right axis) as a function of overall PC content.

Palazzo et al.

tivity at infinite dilution of SDS in water (Λ0 ) 72 S cm2 mol-1)30 is higher than the Λ value measured without PC. This means that ion-ion interactions are effective at the high SDS concentration investigated in the experiments of Figure 6. However, Λ decreases upon PC dilution. This is quite unexpected (at least in water) because a decrease in ionic strength decreases the interionic interactions and thus should result in an increase in molar conductivity. It seems, therefore, that ion-ion interactions, though present, are not responsible for the slope of the Λ vs PC wt% plot. According to eq 1, other parameters are responsible of the observed conductivity behavior. The most obvious candidate is the viscosity of the continuous phase because we already know that it increases upon PC loading. According to eq 1, the product Λη is expected to remain constant as long as the charge carriers do not change their size and effective charge; this is known as Walden’s rule.31 In Figure 7 is also plotted the Walden’s product (Λη) as a function of the system composition. It is clear that Λη remains constant only for PC concentrations higher than 10 wt%. In the range 0-10 PC wt%, Λη increases with PC loading, and (taking in mind the evidences coming from PGSE-NMR, DLS, and viscosity measurements) this suggests a decrease of the Nagg/Rmic ratio. For high PC concentrations, Walden’s rule holds, so that the Nagg/Rmic ratio remains almost constant. 4. Discussion

Figure 7. Hydrodynamic radius (Rmic) and thickness of hardcore shell (t) as a function of the overall PC content. Parameters were evaluated as described in the text. The horizontal dotted line denotes the length of SDS molecule.

for the ascending branch of the η vs PC wt% plot but is inconsistent with the decrease in viscosity found in the PC-lean region. According to eq 4, such a decrease can be accounted for only by a decrease in the Simha coefficient, ν. In other words, the initial decrease in viscosity, upon PC loading, is consistent with a parallel evolution of the aggregate shape, from rodlike to spheres. When a given amount of SDS/pentanol/water is diluted by PC, the solution conductivity decreases in a monotonic way (not shown). Since the PC addition results in a dilution of electrolytes (SDS) the molar conductivity (Λ ) χ/c) is a useful parameter to describe the conductivity behavior of the system. As shown in Figure 6, Λ remains almost constant up to 5 wt% in PC and decreases for higher PC loading. Equation 1 furnishes the essential background for a crude analysis of the conductivity data (since Λ ) χ/c, the molar conductivity is described by the right-hand term of eq 1). The data of Figure 7 refer to a concentrated system where interion interactions that are not accounted for by eq 1 are present. Actually, the equivalent conduc-

As a whole, the above-described results agree in a unified description of PC effect on micelles formed by SDS and a fraction of pentanol. It appears that, upon PC loading, the micelles diffuse faster, likely because they decrease in size. Viscosity and conductivity measurements are consistent with such an interpretation. By describing the system’s behavior in terms of aggregate’s size, one could attain a better insight. Such a description is very delicate in the present case because we are dealing with a concentrated electrolyte system based on PC/water mixtures as the continuous medium. A quantitative analysis of results coming from any technique is somehow model-dependent. However, there is a hierarchy in this dependence. Macroscopic properties such as viscosity and conductivity are strongly model-dependent, so that, also in case of the well-known solvent water, their interpretation at high concentration is difficult (sometime ambiguous as well). Thus, any attempt of detailed analysis in the case of PC/water mixture is hopeless. Techniques that probe molecular properties are more promising. PGSE-NMR experiment probes the self-correlation function and furnishes a self-diffusion coefficient DNMR that is related to the mean-square displacement of the spin-bearing particle in the experimental time-scale τ.32 On the other hand, DLS probes the autocorrelation function and furnishes a diffusion coefficient DDLS that is related to the collective motion. Both DNMR and DDLS are concentration dependent, and we can write (first-order approximation in volume fraction)23,24

DNMR ) D0(1 + λNMRφ)

(5A)

DDLS ) D0(1 + λDLSφ)

(5B)

Of course, in the limit of infinite dilution, DDLS ) DNMR ) D0. λDLS and λNMR depend on particle’s size and shape (30) Kay, R. L.; Lee, K. S. J. Phys. Chem. 1986, 90, 5266. (31) Walden, P. Z. Phys. Chem. 1906, 55, 207. (32) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Clarendon Press: Oxford, 1991.

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and on interparticle interactions in different ways and, for a given ensemble of particles, are univocally defined. Looking to the inverse problem, once the system is defined, DDLS and DNMR are sufficient to determine λDLS or λNMR and so D0. A case easy to handle is that of monodispersed, spherical particles interacting by an effective repulsion potential. In this case, the whole interaction potential can be considered to be the sum of the hard body component plus an effective repulsive tail. With a rough approximation, this tail can be represented by a rigid interaction shell of thickness t. The particle interaction is approximated as an hard-core repulsion at a center-to-center interparticle distance 2(Rmic + t) which is always longer or equal to the hydrodynamic diameter 2Rmic.23,24 The above-described model was proven to describe in a consistent way the diffusion behavior of spherical micelles formed by ionic surfactant at low ionic strength (where electrostatic repulsion dominates the interparticle interaction).33,34 As described in detail in the literature (see, for example, ref 34), in this case, λDLS and λNMR are functions only of the normalized hard-core radius x1)(Rmic + t)/Rmic. The diffusion coefficients coming from DLS and PGSENMR were thus processed according to guidelines outlined above. Each pair of DDLS and DNMR values shown in Figure 4 give rise to a pair of D0 and x1 values. For each composition, the D0 value (shown in Figure 4) and the viscosity of continuous phase (evaluated from the PC partition) permit the evaluation of the hydrodynamic radius of the micelle according to the Stokes-Einstein equation

D0 )

KT 6πη0Rmic

(6)

Finally, each pair of Rmic and x1 values results in a value of the effective hard-core interaction shell t. The dependence of Rmic and t on PC loading is shown in Figure 7. The former parameter can be profitably compared with the length expected for a SDS molecule. The length of the dodecyl tail is 16.7 Å (calculated according to Tanford35), and the contribution of the polar headgroup was evaluated as twice (3vHG/4π)1/3, where the molecular volume of the NaSO4 moiety of SDS (vHG) is36 67 Å3, so that we estimate the overall length of SDS molecule to be 22 Å. In the absence of PC, the hydrodynamic radius is large (70 Å, 3-fold the length of SDS) but decreases dramatically upon addition of PC and finally steadies (22-15 Å, already at PC ) 5 wt%. Dimensional arguments indicate that, as long as the surfactant polar head area remains constant, the micellar size must increase upon increasing the ratio nPC/nSDS in the micelle (nPC and nSDS being the mole number of PC and SDS, respectively), and this result is independent from the aggregate shape. Therefore, the results of Figure 7 can be rationalized only by assuming that the mean interfacial area per SDS molecule depends on the amount of propylene carbonate. The hypothesis that PC acts as cosurfactant is consistent with its role in tuning the aggregate shape, inferred from viscosity data in the previous section. The data of Figure 7 strongly suggest the presence of a PC-induced transition from rodlike to spherical micelles. Indeed, in absence of PC, the Rmic value (33) D’Archivio, A. A.; Galantini, L.; Tettamanti, E. J. Phys. Chem. B 2000, 104, 9255. Galantini, L.; Pavel, N. V. J. Chem. Phys. 2003, 118, 2865. (34) Galantini, L.; Giampaolo, S. M.; Mannina, L.; Pavel, N. V.; Viel, S. J. Phys. Chem. B 2004, 108, 4799. (35) Tanford, C. J. Phys. Chem. 1972, 21, 3020. (36) Reiss-Husson, F.; Luzzati, V. J. Phys. Chem. 1964, 68, 3504.

is hardly consistent with a spherical geometry and strongly supports the presence of elongated micelles; at variance at high PC content, the hydrodynamic radii are close to the surfactant size, as expected for spherical micelles. We can gain a better insight on the cosurfactant action of propylene carbonate by evaluating the mean area per SDS molecule. This can be easily done by assuming that the aggregates are spherical. Of course, such an assumption is sound for high PC loading only. The volume of a spherical micelle vmic is given by

vmic )

4πRmic3 3

(7)

Since the radius entering eq 7 is a hydrodynamic radius, vmic takes into account the pentanol, PC, and surfactant molecules present in the micelle, as well as the hydration water layer. Neglecting this last contribution, the total volume of self-assembled components (Vmic) is given by the volume of a single micelle times the number of micelles (nmic):

Vmic ) nSDSvSDS + nPCPPCmicvPC + nPOHPPOHmicvPOH ) nmicvmic (8) where ni and vi are the mole number and molar volume, respectively, of the i-th component and Pimic denotes the fraction of the i-th component present in the micelle (it is assumed to be 1 in the case of SDS). Since the total micellar volume, Vmic, is known from the system composition and from partition equilibria and the hydrodynamic radius was previously determined, one can easily evaluate the number of micelles and the aggregation number referred to the surfactant only (Nagg ) number of SDS molecules present in a micelle)

Nagg )

nSDSNav nmic

(9)

where Nav denotes the Avogadro’s number. The average area occupied by a surfactant molecule at the surface of the sphere is

ASDS )

4πRmic2 Nagg

(10)

Note that eq 10 define an average polar head area (ASDS) evaluated at the hydrodynamic shear surface of micelles, i.e., the surface enveloping the solvated sulfate groups of the micellized detergent ions, and that the calculations are insensitive to the location of the components within the micelles. The dependence of both aggregation number and average polar head area on system’s composition is shown in Figure 8, where a 4-fold increase in the SDS polar head area is evident. This is an unambiguous indication that PC acts as a cosurfactant and suggests that it is mainly located at the polar/apolar interface. Accordingly, at high PC loading, the number of SDS molecules per micelle is very low (20-6, Figure 8) when compared with the aggregation number reported for the SDS/water system (∼70),18 confirming that most of the interface is made by PC (and pentanol) molecules. We can compare the results coming from diffusion measurements and the independently measured conductivity as follows.

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Palazzo et al.

Figure 8. SDS aggregation number (closed triangles, left axis) and mean area per SDS molecule (open circles, right axis) evaluated according eqs 13 and 14, respectively.

Figure 9. Comparison between Walden’s product (closed dots, right axis) and the term ηNaggDNMR (open dots, left axis). For details, see the text.

Equation 1 can be rewritten as

eFR eFR2 ηΛ ) ηDmicNagg + KT 6πηRNa+

(11)

where Dmic is the self-diffusion coefficient of the micelles measured by PGSE-NMR. The above equation foretells that ηDmicNagg should be proportional to Walden’s product as long as the degree of micelle dissociation and the effective radius of Na+ remain constant. As shown in Figure 9, this holds only for high PC content (>15 wt%). In particular, in the water-rich region, the trends of ηΛ and ηDmicNagg are opposite. Both Dmic and Λ are experimentally observable (so they are model independent); furthermore, the viscosity enters both sides of eq 15. Therefore, the best candidate for the observed discrepancy is the aggregation number, which was evaluated under the assumption that the micelles are spherical. Figure 9 confirms that such an assumption is a good description

of micellar shape for PC content higher than 15 wt%. In contrast, in the water-rich region, ηDmicNagg fails to describe the conductivity behavior, likely because the evaluation of Nagg via eqs 8-11 overestimates the aggregation number in the case of rodlike micelles. Accordingly, any evolution toward spherical micelles produces an artifactual drop in the estimated aggregation number that obscures the increase in Dmic experimentally seen (Figures 2 and 4). Therefore, the comparison between conductivity and diffusion-based data fully support the rod-to-sphere transition inferred in the previous section. Such a change in micelle shape is a consequence of the cosurfactant action of PC. By increasing the interfacial area, PC increases the spontaneous curvature of the interfacial film, thus making spherical structures more stable than cylindrical ones. Such a “cosurfactant action” is in agreement with a lucid study on the phase behavior of the ternary system PC/water/Pluronic F127, demonstrating that PC is mainly active by increasing the interface between the PEO-rich and the PPO-rich domains, while only 20% of PC participates in the PPO-rich domains.37 To conclude this discussion, there is another parameter that deserves some comments: the thickness of the hardcore interaction shell, t. This is an adjustable parameter that encapsulates some features of the intermicelle repulsion potential. As shown in Figure 7, it is almost null in absence of PC and suddenly jumps to ∼20 Å when trace amounts of PC are added to the system. For further PC loading, t decreases monotonically, so that it vanishes at the highest PC concentration explored (20 wt%). As discussed above, in the water-rich region, the micelles are rodlike and the analysis of diffusion data (based on a spherical symmetry) could not furnish safe results. However, from PC content, 10-15 wt% up to the phase separation the hard-core interaction model (and thus the results of Figure 7) should represent the physics of the micellar system. The striking feature of Figure 7 is that, while at low PC content t is quite large (as expected for ionic micelles), it decreases continuously upon PC addition, finally leading to a behavior (t ) 0) expected for nonionic surfactant (or for ionic micelles where the electrostatic interactions are fully screened). The hard-core interaction thickness, t, is a phenomenological parameter; in a recent paper, Galantini et al. have compared the results obtained by analyzing PGSE-NMR and DLS data according to the hard-core interaction model and to the standard DLVO theory.34 They have found, in the system subject of their study, that the parameter t is empirically correlated to Debye’s screening length. From this point of view, one can speculate that a decrease in the local dielectric constant due to the high concentration of PC surrounding the sulfate groups can decrease the effective Debye’s length and thus t. A further point is that the increase in the average polar group area of SDS and the decrease in the aggregation number lead to a sensible reduction in the interfacial charge density that should result in a attenuation of the electrostatic repulsion. These effects should be probed by changes in the degree of counterion dissociation, a parameter that can be determined by Na-PGSE-NMR experiments (already scheduled). Conclusions In the present study, we demonstrate that, when PC is added to the rodlike micelles made by SDS and pentanol (37) Ivanova, R.; Lindman, B.; Alexandridis, P. Langmuir 2000, 19, 9058.

Nanostructured Fluids

in water, it partitions itself between micelles and aqueous bulk. The fraction of micellized propylene carbonate remains constant along PC dilution, and the phase separation takes place when the composition of continuous phase attains the PC/water miscibility gap. The micellized PC strongly increases the total interfacial area, thus acting as a cosurfactant. The dependence of micelle size (obtained by comparing DLS and PGSE-NMR results) on PC content indicates (i) the propylene carbonate is present mainly in the micelle’s palisade; (ii) the cosurfactant action of propylene carbonate induces a rod-to-sphere transition; and (iii) at high PC content, the system is composed by

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very small aggregates (around 10 Å in radius) made by few SDS molecules (10-6) and PC and pentanol. The resulting system can be described as a nanostructured fluid with a huge interfacial area and a small dispersed phase. Acknowledgment. This work was supported by the MIUR of Italy (PRIN 2003 NANOSCIENZE PER LO SVILUPPO DI NUOVE TECNOLOGIE) and by the Consorzio Interuniversitario per lo sviluppo dei Sistemi a Grande Interfase (CSGI-Firenze). LA050492Z