Voltammetric Measurement of Intermicellar Interaction Parameters

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Voltammetric Measurement of Intermicellar Interaction Parameters; Correlation with Predicted Interaction Energies Ian D. Charlton and Andrew P. Doherty*,† Chemistry Department, Bedson Building, University of Newcastle, Newcastle upon Tyne, United Kingdom, NE1 7RU Received November 17, 1998. In Final Form: April 15, 1999 We have used the rotating disk electrode (RDE) to measure micellar long-time self-diffusion coefficients (Ds) and intermicellar interaction parameters (kd) for cetyltrimethylammonium chloride (CTAC) micelles as a function of KCl concentration. Ds values were found to be a function of surfactant concentration and the observed behavior conformed to the linear interaction theory up to 1.00 mol dm-3 KCl. The electrolyte concentration dependence on Ds exhibited three regions of behavior. With increasing KCl concentration, Ds initially increased because of increasing Coulombic screening and then decreased linearly because of a linear spherical expansion of the micelles resulting from the increasing aggregation number, Nagg. Finally, Ds decreased precipitously because of the micellar structural transition from spherical to rod-shaped particles and associated electrolyte-dependent micellar elongation. Intermicellar interaction parameters were also found to be a function of electrolyte concentration and exhibited two distinct regions of behavior. At high electrolyte concentration (>1.00 mol dm-3 KCl), kd reflected the strong interaction between growing rodlike particles while, over the electrolyte concentration range 0.00-1.00 mol dm-3 KCl, interaction parameters correlated with the calculated Coulombic interparticle interaction energy.

Introduction As well as being excellent models for suspended nanoscale supramolecular particles1 and membrane mimetic systems,2 the behavior of micellar systems is of significant technical importance.3 For these reasons, considerable experimental4 and theoretical5 effort has been expended to understand the phenomenological basis of micellar behavior on the microscopic level. It is well-known that such mesoscale systems exhibit structural evolution, for example, particle shape changes6 and particle growth.7 Such behavior is controlled by variables including surfactant concentration, electrolyte concentration, and type and temperature.6,7 A major area of technical importance is the behavior of such systems under flowing conditions.8 It is well-accepted9 that intermicellar interaction processes play a major role in defining the rheological properties of such solutions; therefore, measurement of interaction is vital in understanding the phenomena governing the flow properties of such systems. Intermicellar interaction is directly accessible from the micellar diffusion coefficient (self-diffusion and mutual diffusion) measurements.10 The usual techniques employed are light scattering,11 quasi-elastic light scattering,12 neutron scattering,13 moving boundary techniques,14 * To whom correspondence should be addressed. Fax: +00 44 191 2226929. E-mail: [email protected]. † Present address: School of Chemistry, Queen’s University of Belfast, Belfast, BT9 5AG, Northern Ireland. (1) Ahlstrom, P.; Berendsen, H. J. C. J. Phys. Chem. 1993, 97, 1369113702. (2) Fendler, J. H. Membrane Mimetic Chemistry; Wiley-Interscience: New York, 1982; pp 4-47. (3) Zana, R.; Talmon, Y. Nature 1993, 362, 228-230. (4) Moulik, S. P. Curr. Sci. 1996, 71, 68-376. (5) Slusarczyk, C.; Wlochowicz, A. Polimery 1997, 42, 532-537. (6) Wang, S. Q. J. Phys. Chem. 1990, 94, 8381-8384. (7) Candau, S. J.; Hirsch, E.; Zana, R.; Adam, M. J. Colloid Interface Sci. 1988, 122, 430-440. (8) Hu, Y.; Wang, S. Q.; Jamieson, A. M. J. Rheol. 1994, 37, 531-536. (9) Wang, S. Q. Colloid Polym. Sci. 1992, 270, 1130-1134. (10) Dickinson, E. Annu. Rep. Prog. Chem. 1983, (C), 3-37.

and tracer diffusion,15 all of which (with the exception of tracer diffusion which gives self-diffusion) yield mutual diffusion coefficients (Dm). Recently, the use of simple electrochemical techniques to study micellar systems has been introduced16-18 where the mobility of micellarimmobilized electroactive probes is determined and from which the micellar long-time self-diffusion coefficient can be obtained. Such diffusion coefficient data are usually analyzed using the linear interaction theory with eq 110 to obtain kd, the intermicellar interaction parameter:

Ds ) D0s [1 - kd(Cs - cmc)]

(1)

where Ds represents the measured micellar self-diffusion coefficient, D0s is the self-diffusion coefficient in the absence of interaction (i.e., at the cmc where Ds ) D0s ), Cs is the surfactant concentration, and cmc is the critical micellar concentration. A detailed discussion of selfdiffusion and mutual diffusion coefficients may be found elsewhere.10 A useful micellar system for the examination of interparticle interaction is obtained from the cationic surfactant CTAC. Above the cmc (e 1.57 × 10-3 mol dm-3, depending on the electrolyte concentration19), this surfactant forms cationic spherical micelles which remain spherical up to (11) Prochazka, K.; Limpouchova, Z.; Tuzar, Z. Chem. Listy 1994, 88, 569-579. (12) Phillies, C. D. J. J. Colloid Interface Sci. 1989, 119, 518-523. (13) Cummins, P. G.; Staples, E.; Hayter, J. B.; Penfold J. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2773-2786. (14) Leaist, D. G. J. Solution Chem. 1991, 20, 189-197. (15) Tominaga, T.; Nishinaka, N. J. Chem. Soc., Faraday Trans. 1993, 89, 3459-3464. (16) Georges, J.; Desmettre, S. Electrochim. Acta 1984, 29, 521525. (17) Mandal, A. B.; Nair, B. U. J. Phys. Chem. 1991, 95, 9008-9013. (18) Doherty, A. P.; Christensen, P. A.; Scott, K. Chem. Commun. 1996, 1531-1532. (19) Johnson, S. B.; Drummond, C. J.; Scales, P. J.; Nishimura, S. Colloids Surf. A 1995, 103, 195-206.

10.1021/la981606s CCC: $18.00 © 1999 American Chemical Society Published on Web 06/23/1999

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relatively high electrolyte (NaCl) concentrations20 and several reports detailing interaction measurements in this system (and in CTABr solutions) have appeared.21,22 Also, CTAC is known to solubilize ferrocene predominately in the micellar interior23 which facilitates the use of this simple and reversible electroactive probe for voltammetric measurement of the micellar self-diffusion coefficient. Significantly, the rheological properties of CTAC in KCl solutions are well-established and it is known that they behave as newtonian fluids.24 In this contribution, we present comprehensive voltammetrically measured micellar self-diffusion coefficients and intermicellar interaction parameters for CTAC micelles as a function of surfactant and KCl concentrations. We will explicate the changing self-diffusion coefficient behavior as a function of KCl concentration and show that kd values obtained at low electrolyte concentrations correlate with calculated Coulombic interaction energies, suggesting the dominance of electrostatic interaction in this region, while at high electrolyte concentrations the interaction parameter increases dramatically, suggesting transition from spherical to rodlike particles and associated micellar growth behavior. Experimental Section All voltammetric measurements were carried out using a microprocessor-driven Sycopel AEW-2 potentiostat and an Oxford rotating disk electrode (RDE) system using a potential sweep rate of 5 mV s-1. The RDE technique was employed as this gives steady-state diffusional limiting currents (iLim) which may be measured with high accuracy and precision. The working electrode was polished (with 0.015-µm alumina as a aqueous slurry), 0.7-cm diameter glassy carbon shrouded in epoxy (Sycopel), the reference electrode was the saturated Ag/AgCl electrode (S. H. Scientific), and the counter electrode was flamed platinum gauze (Aldrich). The electrochemical system was calibrated using a 2.00 × 10-3 mol dm-3 aqueous solution of potassium ferricyanide of known diffusion coefficient (7.6 × 10-6 cm2 s-1). Each micellar self-diffusion coefficient measurement was made at least three times with separate fresh solutions. Typically, electrode rotation rates from 2 to 12 Hz were used, although linear Levich plots (vide infra) were obtained from 0.2 Hz up to at least 20 Hz, indicating the absence of flow-induced structural changes under measurement conditions.16,18 All measurements were made with large sample volumes (≈500 cm3) under thermostatic control at 293 ( 0.1 K using a continuous N2 blanket. Solution viscosity measurements were made using a calibrated digital Brookfield LVDV1 cone and plate viscometer at 293 ( 0.1 K. All CTAC/KCl (Aldrich) solutions were prepared quantitatively using N2-purged deionized water (Millipore). Ferrocene (Fc; Aldrich) was added to the solutions such that, on average, at least 1 ferrocene molecule occupied each micelle, that is, 3 g [ferrocene]/[micelles] g 1. This is achieved using previously reported aggregation numbers (Nagg which are between 100 and 200 depending on electrolyte concentration) for CTAC in the presence of KCl19 using the following expression: [micelles] ) [Cs - cmc]/Nagg. This is an important requirement as we have found that the measured micellar self-diffusion coefficient is a function of the fraction of micellar particles containing ferrocene up to, on average, 1 ferrocene molecule per micelle; this stochastic behavior will be the subject of a separate report.25 No detectable changes in Ds were observed from 1 ferrocene up to 3 ferrocene (20) Ikeda, S. Colloid Polym. Sci. 1991, 269, 49-61. (21) Dorshow, R. B.; Bunton, C. A.; Nicoli, D. F. J. Phys. Chem. 1983, 87, 1409-1416. (22) Nicoli, D. F.; Dorshow, R. B. In Proceedings of the International School of Physics, Italian Physical Society, Course 90; North-Holland Physics Publishers: Amsterdam, 1985; pp 429-447. (23) Mandal, A. B. Langmuir 1993, 9, 1932-1933. (24) Clausen, T. M.; Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. J. Phys. Chem. 1992, 96, 474-484. (25) Charlton, I. D.; Doherty, A. P. Anal. Chem., in press.

Figure 1. (Main) current-potential curves for the oxidation of 1. 563 × 10-3 mol dm-3 ferrocene immobilized in 0.1563 mol dm-3 CTAC with 0.10 mol dm-3 KCl supporting electrolyte at various electrode rotation rates; (insert) nernstian plot for the Fc/Fc+ couple measured at 12 Hz under the same conditions. molecules per micelle, indicating that incorporation of the probe molecules does not perturb the micellar structure detectably. All solutions were prepared and used freshly.

Results and Discussion Determination of Micellar Ds. Figure 1(main) shows current-potential curves, at various electrode rotation rates (ω), for the one-electron oxidation of 1.563 × 10-3 mol dm-3 ferrocene (eq 2) in a solution containing 0.1563 mol dm-3 CTAC with 0.10 mol dm-3 KCl as the supporting electrolyte.

Fc h Fc+ + e-

(2)

For all combinations of CTAC/KCl concentrations examined, such curves were similarly sigmoidally shaped with well-defined limiting currents and exhibited typical 59 ( 2 mV decade-1 nernstian slopes (Figure 1 (insert)), indicating the simple reversible electrochemistry of the electroactive probe in the micellar media as expected.17 In addition, all limiting current data produced linear plots of iLim versus ω1/2 with intercepts at the origin. Figure 2a-c shows such plots for 0.1563, 0.0938, and 0.0313 mol dm-3 CTAC with 1.563 × 10-3, 9.38 × 10-4, and 3.13 × 10-4 mol dm-3 ferrocene, respectively, and at a KCl concentration of 0.10 mol dm-3. Such behavior is indicative of a simple diffusional controlled reversible redox process.26 As the limiting current represents the steady-state longtime self-diffusion of micelles to the electrode surface (vide infra), these results reflect the “average” mobility of the micellar particles, therefore reflecting the average of both the micellar size and extent of interparticle interaction. It must be remembered that individual micellar sizes will be distributed about a mean value;27 however, CTAC solutions are known to have narrow particle size distribu(26) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980; pp 283-298. (27) Mukerjee, P. J. Phys. Chem. 1972, 76, 565-570.

Measurement of Intermicellar Parameters

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Figure 2. Levich plots for the oxidation of (a) 1.563 × 10-3, (b) 9.38 × 10-4, and (c) 3.13 × 10-4 mol dm-3 ferrocene immobilized in 0.1563, 0.0938, and 0.0313 mol dm-3 CTAC, respectively, with 0.10 mol dm-3 KCl supporting electrolyte throughout.

Figure 3. Plots of Ds vs KCl concentration at (a) 0.1563, (b) 0.0938, and (c) 0.0313 mol dm-3 CTAC.

tion ranges28 and it is usual to consider such solutions as monodispersed systems,28,29 although this assumption has been questioned recently.29 The micellar self-diffusion coefficient may be obtained from limiting current data such as that plotted in Figure 2 by using the Levich relation in 3:21

iLim ) 1.554nFADs2/3ν-1/6ω1/2c∞

(3)

where n is the number of electrons (n ) 1), F is the Faraday constant, A is the electrode area, ν is the solution kinematic viscosity, ω is the electrode rotation rate (Hz), and c∞ is the concentration of the electroactive probe immobilized within the micelle. The voltammetrically measured micellar self-diffusion coefficients, as a function of KCl concentration, for various CTAC concentrations are shown in Figure 3. It is immediately evident that Ds is a function of both CTAC and KCl concentrations; such behavior is well-known in micellar systems.30 Considering that the diffusion coefficient for ferrocene in water is 10.5 × 10-6 cm2 s-1,23 it is clear that the values reported here are typically over an order of magnitude smaller than those expected for a molecular solution phase species, thus indicating that they reflect micellar self-diffusion and not simple free ferrocene diffusion.16-18 The results have been corrected for the finite aqueous solubility of ferrocene (1.0 × 10-5 mol dm-3) as previously described.23 Effect of CTAC Concentration on Ds. The effect of the surfactant concentration on micellar diffusion coefficients is usually analyzed with reference to the linear interaction theory using eq 1.10 Plots of Ds vs Cs for several KCl concentrations are shown in Figure 4 (for simplicity, Cs is used rather than Cs - cmc since cmc is much smaller than Cs;19 this procedure does not affect D0s or kd values). Such plots are linear (r g 0.9996) for KCl and CTAC (28) Healy, T. W.; Drummond, C. J.; Grieser, F.; Murray, B. S. Langmuir 1990, 6, 506-508. (29) Reekmans, S.; Bernik, D.; Gehlen, M.; Van Stam, J.; Van der Auweraer, M.; Deschryver, F. C. Langmuir 1993, 9, 2289-2296. (30) Dorshow, R. B.; Bunton, C. A.; Nicoli, D. F. J. Phys. Chem. 1983, 87, 1409-1416.

Figure 4. Plots of Ds vs CTAC concentration at (a) 0.00, (b) 0.10, (c) 0.40, and (d) 1.00 mol dm-3 KCl.

concentrations up to 1.00 and 0.1563 mol dm-3, respectively. It is apparent that the CTAC/KCl system adheres to the linear interaction theory up to these surfactant/ electrolyte concentrations, and we therefore can conclude that the micellar particles retain their structural integrity; that is, they remain spherical up to 1.00 mol dm-3 KCl. This observation is reasonable as it has been shown by dynamic light scattering that CTAC micelles remain spherical up to 1.18 mol dm-3 NaCl.20 With the knowledge that the micellar particles remain spherical31 and that Nagg does not change appreciably with increasing CTAC concentration at constant KCl concentration,31 these results also indicate that gross changes in Ds, as a function of increasing CTAC concentration, are a result of increased interparticle interaction over this electrolyte concentration range, as expected.20 (31) Malliaris, A.; Lang, J.; Zana, R. J. Chem. Soc., Faraday Trans. 1986, 82, 109-118.

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Table 1. Micellar Solution Viscosities as a Function of KCl Concentration [CTAC] (mol dm-3) 0.0313

0.0938

0.1563

[KCl] (mol dm-3)

η (×10-2 g cm-1 s-1)

η (×10-2 g cm-1 s-1)

η (×10-2 g cm-1 s-1)

0.00 0.01 0.02 0.05 0.08 0.10 0.20 0.40 0.80 1.00 1.20 1.40 1.60

1.097 1.050 1.032 1.027 1.027 1.027 1.027 1.027 1.027 1.027 1.027 1.027 1.047

1.278 1.199 1.167 1.131 1.118 1.113 1.100 1.091 1.081 1.089 1.118 1.192 1.344

1.500 1.408 1.360 1.295 1.267 1.256 1.229 1.210 1.190 1.245 1.394 1.736 2.376

At KCl concentrations g1.20 mol dm-3, distinct deviation from the linear interaction theory is observed with a decrease of r for the Ds-[CTAC] relationship from 0.9996 to 0.9960 over the narrow KCl concentration range 1.001.60 mol dm-3. For quaternary ammonium surfactant systems, a sphere-to-rodlike transition and extensive micellar elongation are expected at high electrolyte concentration6,7 because of decreased headgroup repulsion, resulting in attractive-driven growth.21 The breakdown of the linear interaction theory observed here may therefore be interpreted in terms of electrolyte-dependent micellar structural evolution, that is, the transition from spherical to rodlike micellar structures.6 This is confirmed by an increase in solution viscosity (shown in Table 1) in the region >1.20 mol dm-3 KCl as well as the dramatic decrease in Ds, especially at high surfactant concentrations (cf. Figure 3a, vide infra). In summary, these results show two types of Ds behavior with respect to CTAC concentration. At electrolyte concentrations corresponding to the known transition to rodlike micellar structures in the system, CTAC concentration dependence deviates from the linear interaction theory while at low KCl concentrations adherence to the theory is evident. It is also clear that variation in the KCl concentration influences the structure of the micellar assemblies and their interaction. Effect of KCl Concentration. In Figure 3, three distinct regions of behavior with respect to KCl concentration may be discerned. At low electrolyte concentrations (σ

(4)

where r is the micellar center-to-center distance,  is the dielectric constant of the medium (H2O), 0 is the permittivity of free space, κ is the Debye-Hu¨ckle inverse screening length as determined by the ionic strength of the solution, and σ ) 2R0h, where R0h is the micellar hydrodynamic radius. R0h is obtained from D0s , which is found by extrapolation of the plots of Ds versus Cs to the cmc10 and using the Stokes-Einstein relation (5):

D0s )

kT 6πη0R0h

(5)

where kT has its usual meaning. The value for r is calculated from the micellar volume fraction (φ) (obtained from a knowledge of R0h and the micellar aggregation numbers32 using relations (6) and (7),

r ) 2R0h + l

(6)

l3 ) [8π/21/3]φ(R0h)3

(7)

where

A plot of U(r) versus kd is shown in Figure 6a for KCl concentrations up to 1.00 mol dm-3; a smooth curve is drawn through the points for clarity. It is immediately evident that the intermicellar interaction parameter is a direct function of the Coulombic interaction potential, thus indicating the Coulombic nature of the interaction controlling the micellar self-diffusion behavior over this range of electrolyte concentrations, that is, 0.00-1.00 mol dm-3 KCl. At low electrolyte concentration (at the extreme right(40) Wang, S. Q. Macromolecules 1992, 25, 1153-1156. (41) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109-118.

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particles grow such that their mean separation decreases and hence they interact more strongly.

Figure 6. Plots of (a) U(r) (real) vs kd (real) and (b) U(r)(apparent) vs kd (apparent).

hand side of the curve), the interaction parameter tends toward a constant value of 2.5 mol-1 dm-3 as the Coulombic interaction energy tends toward infinity; this behavior represents significant unscreened Coulombic interaction between neighboring micellar particles. This observation is not surprising given the magnitude of the micellar surface potential at low electrolyte concentration.19 With increasing electrolyte concentration (moving toward the left of Figure 6a), the interaction parameter decreases monotonically as the Coulombic interaction energy approaches zero; such behavior represents the journey from Coulombic repulsion toward total screening of the electrostatic interaction and the concurrent increase in the contribution of van der Waals attractive forces. However, increasing the KCl concentration beyond 1.00 mol dm-3 does not result in negative kd values as might be expected;37 rather, kd values remain positive and increase in magnitude (as shown in Figure 6b). Although values for U(r) above 1.00 mol dm-3 KCl are only apparent values (because the particles are no longer spherical), they approach the limit U(r) f 0 and are therefore negligible; so the behavior in Figure 6b suggests significant excluded volume intermicellar interaction associated with the growing rodlike particles.40 Effectively, the micellar

Conclusions In this study we have observed, electrochemically, that CTAC micellar self-diffusion coefficients are functions of both surfactant and KCl concentration and that the intermicellar interaction parameter is a function of KCl concentration. It was shown that, up to 1.00 mol dm-3 KCl, CTAC micellar self-diffusion behaved according to the simple linear interaction theory. At higher electrolyte concentrations, the linear interaction theory breaks down because of the sphere-to-rodlike micellar structural transition which is accompanied by electrolyte-dependent micellar elongation. Three regions of behavior in Ds were observed with increasing KCl concentration which resulted from (1) increased electrostatic screening, (2) linear spherical micellar growth, and (3) sphere-to-rod structural transition and micellar elongational growth. The interaction parameter has been shown to exhibit two regions of behavior. Up to 1.00 mol dm-3, kd is a direct function of the calculated Coulombic interaction potential. At KCl concentrations g1.20 mol dm-3, kd values increased because of the increased interparticle interaction between the growing micellar structures. Although electrochemical techniques have been previously used to study self-diffusion in micellar systems,42 this work is the first exhaustive (i.e., to collectively consider effect of electrolyte, surfactant, interparticle interaction, and micellar structural transitions) electrochemical investigation of diffusion and interaction processes in such systems. The rotating disk electrode allows simple steady-state diffusion coefficient measurements to yield unambiguous measurement of the average micellar self-diffusion coefficients and consequently interaction parameters to give insight into the structural behavior of such systems. As structural evolution in microheterogeneous systems appears to be an area of increasing interest,43 these results suggest that electrochemical tools may provide a powerful, yet simple, means of observing such transitions in real time. Acknowledgment. A.P.D. would like to thank The Royal Society for a University Fellowship while I.D.C. would like to thank the EPSRC for a Ph.D. Studentship. LA981606S (42) Rusling, J. F. In Electroanalytical Chemistry, A: Series of Advances; Bard, A. J., Ed.; Dekker: New York, 1994; Vol. 18, pp 1-87. (43) O’Connor, A. J.; Hatton, T. A.; Bose, A. Langmuir 1997, 13, 6931-6940.