Simultaneous Observation of Attractive Interaction, Depletion Forces

Ian D. Charlton and Andrew P. Doherty*. School of Chemistry, DaVid Keir Building, The Queen's UniVersity of Belfast, Stranmillis Road,. Belfast, North...
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J. Phys. Chem. B 2000, 104, 8061-8067

8061

Simultaneous Observation of Attractive Interaction, Depletion Forces, and “Sticky” Encounters between AOT Reverse Micelles in Isooctane Using Microelectrode Voltammetry Ian D. Charlton and Andrew P. Doherty* School of Chemistry, DaVid Keir Building, The Queen’s UniVersity of Belfast, Stranmillis Road, Belfast, Northern Ireland, UK BT9 5AG ReceiVed: July 7, 1999; In Final Form: June 20, 2000

Microelectrode voltammetry has been used to measure the long-time self-diffusion coefficients (Ds) of AOT (AOT ) sodium bis-2-ethylhexylsulfosuccinate) reverse micelles in isooctane using K3Fe(CN)6 as a micelleimmobilized electroactive probe. Ds values were found to be a function of both reverse micellar volume fraction (φmic) and probe concentration. The results show that increasing the probe concentration results in a decrease in Ds, suggesting an increase in attractive intermicellar interaction upon addition of probe. This has been interpreted in terms of attenuated surfactant tail-group reorganization facilitating interpenetrating of the surfactant tails. Increasing the micellar volume fraction is seen to diminish attractive interaction which indicates the presence of entropy-driven solvent mediated depletion forces. Self-diffusion coefficients at the limit of zero probe concentration (D′s) were found to be micellar volume fraction dependent, and the behavior conformed to the linear interaction theory for interacting micellar systems giving an attractive intermicellar interaction parameter of -2.33. Extrapolation to infinite dilution (i.e., φmic f 0, the limit of zero interaction) reveals a reverse micellar long-time self-diffusion coefficient (D0s ) of 6.13 ( 0.07 × 10-7 cm-2 s-1, which gives a corresponding micellar hydrodynamic radius of 7.5 ( 0.02 nm. This value is approximately a factor of 2 greater than the know micellar size, and the behavior is interpreted in terms of adhesive “sticky” intermicellar interactions indicating the measurements of micellar cluster diffusion.

Introduction Reverse micelles may be defined as supramolecular selfassembled aggregates of nanoscale dimensions with hydrophobic moieties extending outward to an apolar solvent (e.g., isooctane) and hydrophilic groups converging in toward a polar region (a separate pseudophase) of another solvent such as water. In effect, the structure is the reverse of that which is normally encountered for micelles in aqueous phases.1 The use of reverse micellar structures has become increasingly popular recently for a number of applications, in particular, as nanoreactors for polymerizations,2 chemical reactions,3 electrocatalysis,4 and as hosts for enzyme kinetic studies.5 The highly rigid structure of reverse micellar systems has also been exploited to template the production of size controlled nanoparticles of metals6 and alloys.7,8 In addition, it is known that at low water concentration there is a fixed layer of water in the micellar interior which appears to be bound to the charged headgroups;2,4,9-12 therefore, a reverse micelle nanostructure can be used in membrane mimetic studies to probe water structure and physiological activity at biological membranes and proteins.2,13 Probably the most extensively studied reverse micellar system is sodium bis-2-ethylhexylsulfosuccinate (AOT) due to its ability to solubilize9,14 large amounts of polar solvent (typically water) in apolar solvents without need for a stabilizing cosurfactant.15 The typical range of the critical micelle concentration (cmc) for AOT is between 5 × 10-4 and 5 × 10-3 mol dm-3 and is solvent dependent,10,16,17 while the shape of the aggregates is essentially spherical.14,18-21 The size of AOT reverse micelles is highly dependent on the concentration of each constituent;14 * Fax +0044 (0) 890 382117; e-mail, [email protected].

however, it is recognized that the aggregate size is typically characterized by the concentration ratio W (where W ) [H2O]/ [AOT]) rather than the actual concentrations.14 The size of AOT reverse micelles (i.e., the hydrodynamic radius (R0h) has been shown by an array of different techniques to be given by the empirical formula in eq 1.22-24

R0h ) 1.5 + 0.175W

(1)

At W > 10-12, the interior water behaves as bulk water (i.e., density, viscosity, etc.), therefore such systems are defined as microemulsions, whereas at W e 10 the aqueous phase exhibits properties very dissimilar to bulk water and is responsible for some recently exploited phenomena. In addition, at low water content the system is a true reverse micelle with each aggregate behaving as a rigid macromolecule.10 We have shown recently that voltammetry of electroactive probes within such ridged selfassembled supramolecular structures is possible.25 In addition to their practical applications, AOT reverse micelles represent an ideal model structure for studying intermicellar interactions.26 In particular, AOT represents the case where hard-sphere repulsive forces operate with a narrow attractive potential energy well, i.e., the structure may be considered a repulsive core (charged headgroups) with an attractive outer shell (i.e., the tails).26-28 Such systems undergo Brownian motion in the usual fashion and the attractive energy gives rise to “sticky” interactions due to surface adhesion upon collision.27-29 Such sticky encounters result in short-lived droplet clusters that may exchange solubilized material before dissociating into separate droplets.29 The dynamics of such behavior is currently of great interest because of their application as nanoreactors and membrane mimetic systems.

10.1021/jp9923015 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/27/2000

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It is usual to study AOT reverse micellar diffusion and interparticle interaction using scattering techniques such as small-angle X-ray scattering (SAXS),12 small angle neutron scattering (SANS),30 and dynamic light scattering (DLS).31 A modified form of Baxter’s27 hard-sphere model with surface adhesion accounts well for the behavior of AOT systems probed using SAXS, i.e., the negative binding enthalpy associated with “sticky” interactions.26 In defining the indirect correlation function, this model incorporates the stickiness parameter λ to account for the fraction of bound particles (i.e., those undergoing adhesive sticky encounters), where λ ≈ exp(-uw/kBτ) and kB is the Boltzmann constant, τ is a dimensionless temperature term, and uw is the binding enthalpy per particle.26,27 In SANS studies, experimentally extracted structural factors have been compared to model calculations of multicomponent sticky hard spheres where a shallow contact potential is necessary to obtain agreement between experiment and model.32 Similarly, in DLS of AOT systems, the first cumulant and time evolution of the droplet density function can be calculated successfully by assuming the existence of polydispersed fractal clusters formed from droplet attraction.33 We have shown recently34-36 that certain electrochemical techniques may provide valuable information concerning the supramolecular structure, structural evolution, and interparticle interaction in normal aqueous-phase micellar systems. Such techniques yield highly precise transport data which may be acquired simply and unambiguously and analyzed without need for assumptions or parameterized fitting of the data.37 Since AOT reverse micelles exhibit unusual sticky interaction, we now turn our attention to this system in an attempt to probe micellar structure and intermicellar interaction processes using voltammetry. The use of voltammetric techniques relies on the measurement of the micellar Ds values using steady-state diffusion-controlled current (iLim) data. Although electrochemistry may be accomplished easily in aqueous-based micellar systems, the high electrical resistivity of reverse micellar systems (e.g., suspended in isooctane) causes severe distortion of the voltammetric responses by ohmic drop (iR drop), therefore current-voltage data at macroelectrodes are unreliable.38 However, microelectrodes (e 25 µm diameter) draw extremely small currents (pAnA), therefore iR distortion may be substantially circumvented and voltammetric measurements in reverse micellar systems accomplished.25,38 The expression relating iLim at the microelectrode to self-diffusion of electroactive species toward the electrode surface is given in eq 238

iLim ) 4nFrDsC∞

(2)

where n is the number of electrons, r is the microelectrode radius, F is the Faraday constant, and C∞ is the bulk concentration of the electroactive probe. It is important to note that electrochemical experiments yield long-time self-diffusion coefficients because the micellar displacement is much greater than the mean intermicellar spacing, i.e., the diffusion layer thickness at the electrode is in the µm range, whereas the interparticle spacing is typically in the nm range. Such long-time measurements are useful in that they may more easily allow observation of time-dependent effects such as the sticky interactions,39 although these are observed with short-time mutual diffusion coefficient measurements. A detailed discussion of mutual and self-diffusion coefficients may be found elsewhere.40 In this study we examine the self-diffusion behavior of AOT reverse micelles formed in isooctane at different volume fractions using microelectrode voltammetry. We restrict our

measurements to solutions where W ) 10 to ensure that the systems are reverse micelles (i.e., not microemulsions) and because it is known that at this composition the micellar size is independent of the solution preparation process, i.e., sonication, shaking, etc., and is insensitive to changes in temperature.10 We will show that voltammetrically measured reverse micellar Ds values not only exhibit behavior characteristic of the linear interaction theory40 normally found in aqueous phase micellar systems but also tail-group mediated attractive interaction, depletion forces, and adhesive sticky interactions are observed. Since there is a great need for techniques to study complex processes in microheterogeneous media, will also discuss the potential of microelectrode voltammetry for studying dynamic behavior such as interaction and exchange processes in such systems. Experimental Section AOT Reverse Micellar Solution Preparation. The reverse micellar systems were prepared by the phase transfer approach.41 The electroactive probe (K3Fe(CN)6; BDH, AnalaR) was dissolved in the H2O phase prior to mixing with the AOT/ isooctane (Aldrich) phase. After mixing, sonication (typically 10-15 min) resulted in transparent stable reverse micellar solutions. AOT was obtained from BDH (98%) and was used as received, and the water was distilled, deionized (Millipore), and sparged with N2 prior to solution preparation. No extraneous electrolyte was added to the organic phase. All solutions were prepared analytically and used freshly. Voltammetric and Rheological Measurements. A twoelectrode arrangement was used (Sycopel AEW2 potentiostat) in conjunction with a Faraday cage. The working electrode was a carbon microelectrode (r ) 5.2 µm as determined electrochemically using ferricyanide (diffusion coefficient ) 7.6 × 10-6 cm2 s-1 in aqueous 1.0 mol dm-3 KCl solution at 298 K) obtained from BAS which was polished with 0.015 µm alumina on glass prior to use. The pseudo reference electrode was a silver wire (Goodfellows) coated with the redox polymer [Os(bipy)2(PVP)10Cl]Cl;42 the coating did not participate in developing the reference electrode potential but acted to prevent passivating adsorption of AOT on the Ag surface (as evident by SEM and EDAXS measurements) and therefore provided a stable reference potential of -0.125 V vs Ag/AgClsat.25 All currentpotential measurements were carried out at 5.0 mV s-1 at 298.0 ( 0.1 K. All potentials are quoted with respect to the Ag/AgClsat reference electrode, and all measurements were repeated at least three times. Explicit details of the measurement procedure may be found elsewhere.25 Viscosity measurements were made using a calibrated digital Brookfield DVI cone and plate viscometer at 298.0 ( 0.1 K with distilled-deionized water as the reference. Results and Discussion Preamble. The basic tenet of the approach is that voltammetric measurement of self-diffusion of electroactive probes immobilized within electroinactive micelles gives a direct measure of micelle diffusion from which structural details and information concerning interaction processes may be discerned.40 The correct choice of electroactive probe in such systems is crucial because uncertainties associated with probe distribution (or the electrolytic product) between the phases may lead to difficulties in interpreting the voltammetric data.4,37 To avoid such uncertainties, the electroactive probe must be soluble in the aqueous pseudophase while being completely insoluble in the continuous phase. Under this condition, iLim measurements

Self-Diffusion Coefficient Measurements

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Figure 1. Current-potential curves for the reduction of (a) 1.403, (b) 1.831, (c) 2.545, and (d) 3.131 × 10-3 mol dm-3 Fe(CN)63- in AOT reverse micelles at 5 mV s-1 with φ ) 0.084 and W ) 10.

reflect micellar diffusion only. We use ferricyanide here because both redox forms are chemically stable and highly soluble in the aqueous pseudophase while completely insoluble in the isooctane phase.43 In addition, this probe exhibits simple facile reversible electrochemistry at moderate potentials; therefore, no electrokinetic limitations complicate interpretation of the voltammetric data. The presence of extraneous material in reverse micelles may lead to structural changes or perturbation of intermicellar interaction,4,44 therefore, the effect of the electroactive probe must be considered carefully. However, ferricyanide has been used as a fluorescence quencher in AOT reverse micellar systems, and it has been shown that the concentrations (i.e., [ferricyanide]/[micelle]) used here do not affect Nagg or the extent of polydispersity,43,44 therefore we may use this probe with confidence. Electrochemistry of Fe(CN)63- within AOT Reverse Micelles. The electrochemistry of various probes in microemulsions has been reported frequently;4,45 however, to the best of our knowledge, the system studied here is the first reported example of voltammetry in a reverse micellar system.25 The electrochemical reduction of the probe within the AOT reverse micelles was effected at three different surfactant concentrations (i.e., 0.15, 0.20, and 0.25 mol dm-3) in isooctane with 1.50, 2.00, and 2.50 mol dm-3 H2O, respectively. It is usual to express the solution composition in terms of micellar volume fraction (φmic) as given by the expression of Cassin12 in eq 3

φmic )

( )( ) VH2O VO

1+

21 W

(3)

where VH20 is the volume of water used in the solution of total volume VO; therefore, the solutions used here contained reverse micellar volume fractions of 0.084, 0.112, and 0.140. The probe concentration was varied between [probe]/[micelle] ) 0.5-1.5 as calculated from the expression [AOT]/Nagg ) [micelles] using the previously reported Nagg value of 75 for AOT in isooctane at W ) 10.10,46 Current-potential profiles for the reduction of micelleimmobilized Fe(CN)63- at a micellar volume fraction of 0.084 and with four different probe concentrations are shown in Figure 1a-d. The traces exhibit sigmoidal-shaped limiting currentvoltage behavior as expected for a diffusion-controlled redox process at a microelectrode,38 Similar profiles were obtained

Figure 2. Composite Nernstian plot for the Fe(CN)64/3- redox couple in various AOT reverse micelle solutions.

for all solution compositions examined. These profiles represent diffusion of the electroactive species (i.e., ferricyanide) to the microelectrode surface,38 and because the probe is entirely immobilized within the reverse micelle structure, the curves represent the steady-state diffusion of the micelles. The steadystate nature of the iLim measurement is important as it reflects micellar self-diffusion over long time-scales where sticky interaction may possibly be observed. It should be noted that the sloping baseline is due to residual uncompensated solution resistance (iR), which is not surprising given the low conductivity of AOT-isooctane reverse micellar media, i.e., 20-100 nS cm-1.18 It is usual to analyze such i-V behavior in terms of electrochemical reversibility using Nernstian plots of E - E0 vs log10 i/(iLim) - i, where E0 is the Fe(CN)63/4- formal potential (E0 ≈ E1/2 (the half-wave potential) ) 0.140 V vs Ag/AgClsat) and i is the current at any point along the i - E wave. A nernst plot of composite i - E data obtained from various solutions is shown in Figure 2. The average value of the Nernstian slopes found here is ≈ 0.060 V × 10-1, which is close to that expected for a simple reversible electroactive probe such as ferricyanide.48 These results demonstrate that it is possible to carry out respectable voltammetric measurements in reverse micellar systems, and, significantly, the ability to obtain well-defined reversible electrochemical responses facilitates the measurement of Ds which, in turn, introduces the possibility to probe reverse micellar structure and observe micellar structural evolution.35-37,40,45 It is known that AOT micelle immobilized material may be found in various loci within the micelle, and it is the unique properties of such loci that give rise to the usefulness of such structures in many catalytic applications.49,50 Usually, micelleimmobilized material may reside at the charged internal surface, in the aqueous pseudophase, or with sophisticated probes, straddling the interface.51 Ferricyanide was found not to exhibit UV/visible spectral differences (λmax ) 420 nm) compared to that obtained in bulk 1.0 mol dm-3 KCl electrolyte solution, therefore the probe is located in the aqueous environment as expected.43 However, the microenvironment (i.e., the outer and inner solvation sphere) of simple electroactive probes strongly influences electron-transfer dynamics, and therefore E1/2 values, so voltammetry may give useful information about the probe’s microenvironment.52 From plots such as those in Figure 2 we can obtain E1/2 values for the Fe(CN)64/3- couple in the reverse micelles. In all cases, E1/2 ) 0.140 ( 0.002 V vs Ag/AgClsat

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TABLE 1: Ds Values as a Function of Micellar Volume Fraction and Fe(CN)63- Concentration K3Fe(CN)6] (× 10-3 mol dm-3)

Ds (× 10-7 cm2 s-1) (at varying φmic)

1.403 1.831 2.545 3.131 1.762 3.171 4.368 1.880 3.192 4.140 5.072

4.75 (0.084) 4.71 (0.084) 4.64 (0.084) 4.52 (0.084) 4.39 (0.112) 4.30 (0.112) 4.21 (0.112) 4.10 (0.140) 4.08 (0.140) 4.03 (0.140) 4.03 (0.140)

and was invariant with solution composition, i.e., micellar volume fraction and probe concentration. This values compares with 0.180 V vs Ag/AgClsat obtained in bulk electrolyte (1.0 mol dm-3 KCl), which suggests that the microenvironment in which the redox species exists (i.e., its solvation sphere) is different from bulk water containing simple electrolyte. At W ) 10, some water is likely to be unbound;10,12,53 however, at low W values (i.e., W e 10) it is known that the water is highly polarized,54 resulting in increased basicity of the water pseudophase.55 Also, it is likely that electrostatic repulsion will result in Fe(CN)64/3- residing in a basic locus away from the anionic surface.49 Since the E1/2 for Fe(CN)64/3- is pH dependent E0 in 0.01 mol dm-3 NaOH ) 0.46 V vs SHE and 0.69 V vs SHE in 1.0 mol dm-3 H2SO456 with a slope of -0.019 V pH-1. The negative shift in E1/2 of 0.040 V from neutral conditions in bulk solution to the basic conditions of the reverse micellar interior is expected and suggests that the apparent pH of the aqueous pseudophase in which the probe is located is ≈ 9. Several reports have suggested that the apparent pH (determined spectrophotometrically) in AOT reverse micelles is 9 at W ) 1.554 and 10 at W ) 1.55 It is recognized that due to the heterogeneity of the aqueous core,55 pH has a less precise meaning than usual, i.e., it will be dependent on the probe’s location within the micellar structure and W. It is clear that for ferricyanide, a significant shift in E1/2 occurs indicating strong interaction with highly polarized water.54,55 Reverse Micellar Self-Diffusion Coefficients and Depletion Forces. Inserting limiting current values into eq 2 yields Ds values at each micellar volume fraction at various probe concentrations; these are given in Table 1. These results are also plotted in Figure 3a-c, where a number of interesting features are immediately obvious. First, Ds values are inversely dependent on micellar volume fraction which is in agreement with known behavior of interacting micellar systems.40 This behavior reflects increasing intermicellar interactions (e.g., repulsive, attractive, hydrodynamic, etc.) associated with increasing number density of interacting particles in solution.40 The second striking feature is the Ds dependence on probeconcentration where addition of probe results in diminution in micellar mobility, superficially suggesting significant micellar growth behavior. It should be noted that since the probe molecule is totally insoluble in the continuous phase, the effect of probe partitioning influencing diffusion coefficients as experienced in other systems4 does not occur. A number of reports detailing the effect of added material within AOT reverse micelles have appeared, in particular, the effect of simple electrolytes27,57,58 and macromolecules such as polymers44 and proteins.59 Several possibilities must be considered to explain this probe-induced behavior. First, attenuation of the micellar size; second, and related to average micellar size, polydispersity, and finally, attenuation of intermicellar interactions.

Figure 3. Plots of Ds vs [Fe(CN)64/3-] at volume fractions of (a) 0.084, (b) 0.112 and (c) 0.140.

This [probe]/[micelle] ratio used here is higher that usually used; however, a series of reports have detailed probe and quencher concentrations in this range.43,44 Since the molecular volume of the simple redox complex is small (≈ 0.5 nm3) compared to the known dimensions of the reverse micelles at W ) 1015,23 (≈ 14 nm3), physical attenuation of the micellar size is highly unlikely. It is also known that addition of electrolyte to reverse micellar systems leads to a reduction in surfactant headgroup electrostatic repulsion58 which, in turn, leads to an increase surfactant curvature parameter58,60 which favors smaller micelles. Also, added electrolyte may lead to a reduction in aggregation number.43 From these considerations, smaller micelles would be expected from the addition of the probe. However, it is believed that the AOT system is “forced to keep a structure similar to that holding in the absence of additive because of geometrical constraints”,58 therefore, little effect on micellar radii should occur with the addition of ferricyanide.58 Valeur61 has also shown that little change in reverse micellar size is observed with the addition of up to 0.4 mol dm-3 salt. Only one report62 has suggested that reverse micelles increase in size with added electrolyte, which would suggest a decrease in surfactant curvature, contrary to the natural tendency of AOT upon addition of salt.58 Finally, Lang et al.43,44 have used ferricyanide as a fluorescence quencher in AOT studies and have reported that its presence does not perturb Nagg values or the extent of polydispersity (AOT reverse micellar systems are usually considered to be effectively monodispersed)63 significantly over the same [ferricyanide]/[micelle] ratio used here. From these considerations, we can rule out both an increase in average micellar size and varying polydispersity as causing the diminution of Ds with increasing probe concentration. That voltammetrically determined Ds values are found to decrease significantly with increasing ferricyanide concentration is an important observation. Given that polydispersity and Nagg changes may effectively be discounted, attenuation of intermicellar interaction therefore seems the most likely explanation for the observed behavior. This hypothesis is in keeping with many reports30,41,64-67 which suggest that addition of small amounts of electrolyte results in reorganization of the surfactant

Self-Diffusion Coefficient Measurements headgroups which, in turn, influences the orientation and packing of the micellar tail groups, ultimately resulting in attenuation of intermicellar interaction. Because the Ds values are an inverse function of probe concentration, which suggests increased attractive interaction,57 it appears likely that the observations made here reflect probe-induced reorganization of the micellar tail groups to an orientation which favors attractive interparticle interactions, i.e., tail group entanglement.30 From electrostatic considerations, the Fe(CN)63- species is unlikely to be sufficiently close to the SO3- headgroups to effect significant changes in headgroup organization and therefore attenuate the tail group configuration. Also, it has been shown that the anion type of added electrolyte does not perturb reverse micellar structure, whereas the cation exerts significant influence.68 Since the ferricyanide counterion is K+, equilibrium exchange with Na+ at the internal micellar interface is highly likely to occur, considering that ca. 30% of the sulfonate groups are dissociated within the reverse micelle.69 The effect of foreign counterions may be dramatic; for example, it has been shown that exchange of Na+ for Li+ results in drastic structural changes, i.e., the formation of multiwalled vesicles from simple reverse micellar structures.68 This behavior has been interpreted in terms of enhanced headgroup area due to a larger degree of Li+ counterion hydration. Also, it has been shown58 that the effect of cations on the percolation temperature (Tp) in AOT systems is a function of counterion ionic radii, with smaller cations being more intimately related with the headgroups, which reduces the headgroup surface area. Notwithstanding, the effects of Na+ and K+ were similar,58 therefore it seems unlikely that simple ion exchange would result in the significant attractive interaction attenuation observed here. However, since the added K3Fe(CN)6 is anhydrous, the degree of hydration of the surfactant headgroups, and hence headgroup surface area, is likely to be attenuated significantly with increasing ferricyanide concentration. Variation in the headgroup surface area leads to variation in the molecular packing arrangement58 (i.e., curvature) of the surfactant at the water/oil interface, therefore it is reasonable to argue that a similar effect is observed here with the addition of anhydrous potassium ferricyanide. By whichever mechanism, the results suggest that addition of the probe results in tail group reconfiguration, which ultimately results in attenuation of attractive micellar interactions. A perplexing aspect of the curves in Figure 3 is the different slope behavior, i.e., -0.129, -0.069, and -0.025 cm2 s-1 mol-1 dm3, respectively. The solution compositions are identical with the exception of the number density of micellar particles, therefore, the relative effect of adding probe should be, intuitively, identical. The variation of slopes demonstrates that the attenuation of the attractive intermicellar interaction is a direct function of micellar volume fraction. That the plots are separated with different intercepts (vide infra) also demonstrates that the probe-induced effect is superimposed on the normal Ds dependence on micellar volume fraction.40 The microscopic origin of the attractive forces in such systems is still unclear,66 although mutual interpenetration of surfactant tails has been proposed.30,67 It has been shown that the sticky parameter (i.e., attractive interactions) determined for AOT in isooctane systems decreases with increasing micellar volume fraction,70,71 although the phenomenological basis of this is not well understood.12 However, recently, a model of AOT systems has been proposed where the sticky parameter is a logarithmic function of micellar volume fraction so that the decrease in interdroplet attractions with increasing volume fraction, as observed by SAXS, could be accounted for.12,70,71 The model considered the existence of

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Figure 4. Plot of D′s vs micellar volume fraction.

solvent-mediated depletion forces (the tendency of hard-sphere solvent molecules to “push” microheterogeneous particles together) that vary with volume fraction and effectively decrease attractive intermicellar interaction with increasing micellar volume fraction.12 It should be noted that solvent-mediated depletion forces are distinct from microheterogeneous particle (e.g., polymers) mediated depletion, although the effect is the same. Because there is an apparent decrease in the probe-induced attractive interaction effect at higher volume fractions, it seems reasonable to suggest that the origin of the observed behavior here is decreased solvent mediated depletion forces at higher volume fractions. Volume fraction dependent depletion forces12 arise from the entropic tendency to control the motion of microheterogeneous particles.72,73 Such forces have been harnessed recently for the controlled self-organization of colloidal systems at surfaces73-76 and are currently of great fundamental and technological interest. The results presented here indicate that such forces may be studied quantitatively using microelectrode voltammetry, although such forces only become evident with changes in attractive interactions. Linear Interaction Theory, Micellar Size, and Sticky Intermicellar Interactions. It is evident that extrapolation of the plots in Figure 3 to infinite dilution yields self-diffusion coefficients in the absence of probe-induced interaction changes, D′s. This value may be considered the “raw” micellar longtime self-diffusion coefficient and is seen to decrease with increasing surfactant concentration behavior commonly encountered in normal micellar systems and represents the net effect of interaction processes attenuating the micellar self-diffusion coefficient.40 It is usual to analyze D′s behavior using the linear interaction theory with the following expression:40

D′s ) D0s [1 + kdφmic]

(4)

where D0s is the long-time self-diffusion coefficient in the absence of intermicellar interaction (i.e., as φmic f 0) and kd is the intermicellar interaction parameter. Figure 4 shows a plot of D′s vs φmic where it can be seen that the linear interaction theory is adhered to and yields a value for kd of -2.33. Values of kd from 0 (slightly attractive) to -12.4 (highly attractive) for a series of cationic reverse micelles have been reported.74 Since AOT micelles interact strongly, the value obtained here is somewhat lower than can be expected. However, it was shown for the water/chlorobenzene/alkyl(phenylalkyl)dimethylammo-

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nium chloride (W ) 10, 20) reverse micellar systems that two regions of behavior exist depending on volume fraction.72 At low volume fraction (φ < 0.06), large slopes reflecting strong attractive interaction were observed, whereas at higher volume fractions low slopes were evident attributable to the formation of micellar aggregates mediated by sticky interactions. Unfortunately, due to the difficulty in obtaining acceptable voltammetric responses at low volume fractions, we did not pursue this region; however, our data is consistent with the previous findings and therefore reflect sticky interactions. It is evident that application of the linear interaction theory at high volume fraction will not yield correct hydrodynamic radii; however, it is informative to apply the theory as this leads to an empirical quantification of the effect of sticky interactions. Extrapolation of the plot yields D0s ) 6.13 ( 0.07 × 10-7 cm-2 s-1, which is almost an order of magnitude greater than simple ferricyanide diffusion in aqueous media, indicating the diffusion of the large micellar particle. The micellar hydrodynamic radius R0h may subsequently be obtained using the Stokes-Einstein relation in eq 5

D0s )

kBT 6πη0R0h

(5)

where kBT has its usual meaning and η0 ) (4.9 × 10-3 g cm-1 s-1). The reverse micellar R0h is therefore 7.5 ( 0.02 nm. The expected micellar radius predicted by eq 1 is 3.25 nm, which agrees with published values between 3.1 and 3.8 nm determined experimentally.1,9,22-24 Significantly, the value obtained here is more than a factor of 2 greater than expected from literature values and appears to reflect the effect of sticky interactions.22-24 A number of possible electrochemical explanations for the apparent overestimation of R0h may also be considered, including hindered diffusion due to migration, iR effects, or slow electron-transfer kinetics. However, as the responses are Nernstian and as we measure a diffusion-controlled limiting current, these may be discounted. In addition, the possibility of probeinduced structural changes being responsible for an actual increase in micellar size may also be ignored. It has been demonstrated previously74 for short chain length surfactants using QELS, that, at the limit of zero volume fraction, predicted reverse micellar sizes are comparable with experimental values. However, disparity between experimental and predicted values was observer for long-chain surfactants. “Coiling” of the tail group was postulated to result in an erroneous prediction of micellar radii, and consequently the evident nonagreement of values.74 Obviously, such an effect is not accountable here as the micellar size can be predicted with accuracy. Given that the effect of probe and micellar volume fraction may be eliminated by extrapolation to infinite dilution, the enhanced R0h value (in the absence of micellar growth) suggests that the value is an apparent value only and reflects additional intermicellar interactions that suppress self-diffusion, i.e., sticky, interactions.57 This is reasonable because the effect of aggregate formation due to sticky interactions has been shown to affect self-diffusion coefficients, therefore extrapolation using high volume fraction data will lead to erroneously high values for the micellar dimensions.72 Considering the second-order rate constant for micellar collisions kc ≈ 1010 mol-1 dm3 s-1 and the long time scales under which self-diffusion coefficients are measured here (i.e., steady-state reached in seconds), adhesive encounters are expected to result in a decrease in D0s and ultimately an apparent increase in R0h. Also, such behavior is not observed

with voltammetric measurements of normal cationic or neutral micellar self-diffusion35-37,45 in aqueous solution, where it is known that sticky adhesive encounters are not observed. That microelectrode voltammetry overestimates the value of R0h superficially suggests a limitation of this technique for the study of intermicellar interaction and structure. However, an important feature of voltammetry is the vast range of time scales over which measurements can be obtained, i.e., nanoseconds to seconds. Obviously, decreasing the measurement time scale (e.g., using fast cyclic voltammetry or chronoamperometry) will also decrease the time-dependent effect of sticky interactions. In this way, it will be possible to probe micellar self-diffusion on time scales where sticky interactions are negligible or, by extrapolation to the time f 0 limit, to obtain reliable R0h values as well as information concerning attractive interactions, sticky interactions, and depletion forces. Also, the construction of low current/low noise potentiostatic circuitry will allow measurements at very low volume fractions and low probe loadings for such measurements. We are currently pursuing this avenue. Conclusions This study is the first voltammetric structural investigation of true reverse micellar systems, and it has been shown that attractive interaction, depletion forces, and adhesive interaction may be observed simultaneously and easily using the unsophisticated and inexpensive microelectrode technique. This is a significant observation because the complex behavior of multiple interaction processes may be delineated and analyzed in terms of interaction parameters without the need for elaborate fitting of experimental data. In addition, the simplicity and rapidity of the technique means that significant experimental work directed at understanding structural evolution and interaction in such systems can be carried out easily. That electrochemistry can be achieved in such hostile media is not too surprising,38 but the unexpected electrochemical reversibility is useful since electrochemical studies may be effected in diffusing membrane mimetic species using electroactive probes. Such probes may be designed to locate the redox active site within the aqueous core, at the charged internal surface or at the external micellar surface. Such probes will facilitate studies of electron-transfer processes in various microenvironments analogous to biological membrane systems. Coupling electroactivity with photoactivity (e.g., fluorescence) and pH sensitivity may also result in methodologies capable of probing the heterogeneity of the aqueous pseudophase of reverse micellar systems with respect to apparent pH, microviscosity, and rigidity using two radically different but complimentary techniques. In summary, steady-state microelectrode voltammetry has been shown to be a simple and useful tool for studying various interaction processes in reverse micellar systems. In addition, the use of voltammetric techniques over a range of time-scales (or sensitivity) is likely to yield both information on timedependent interaction processes and micellar structural parameters. The fact that voltammetry is precise, inexpensive, and rapid suggests this tool may become important in the study of reverse micellar systems, in particular the time-dependent evolution of supramolecular structure and interaction processes. Acknowledgment. A.P.D. thanks The Royal Society for a University Fellowship and I.D.C. thanks the EPSRC for a studentship. References and Notes (1) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J. Chem. Soc., Faraday Trans. 1979, 75, 132-139.

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