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Dynamics of AOT and AOT/Nonionic Cosurfactant Microemulsions. An Iodine-Laser Temperature Jump Study Luı´s M. M. Naza´rio,† Joa˜o P. S. G. Crespo,† Josef F. Holzwarth,‡ and T. Alan Hatton*,§ Departamento de Quı´mica, Faculdade Cieˆ ncias e Tecnologia, Universidade Nova de Lisboa, 2825 Monte de Caparica, Portugal, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany, and Chemical Engineering Department, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 Received December 23, 1999. In Final Form: April 4, 2000 The iodine-laser temperature jump (ILTJ) technique was used to probe the interfacial and intermicellar dynamics of water-in-isooctane microemulsions stabilized by AOT both in the presence and in the absence of a cosurfactant such as an aliphatic chained alcohol (hexanol or decanol) or poly(oxyethylene) alkyl ether (C10E4 or C10E8). These cosurfactants have been shown to induce changes in the interfacial rigidity; the former increase it, and the latter decrease it. Two relaxation times were observed, one in the microsecond range and another, previously undetected, in the millisecond range. The relaxation times obtained in the microsecond range were higher for CiEj-containing microemulsions and lower for decanol-containing ones. This is consistent with the effect of the cosurfactants on interfacial rigidity, as this relaxation is inversely proportional to the bending modulus, κ. The value of κ ) 0.3 kT determined for AOT reversed micelles (Wo ) 55) is in agreement with those found in the literature. The relaxation time in the millisecond range was only obtained above a certain water content and temperature, and its value depended on water content, interfacial composition, and reversed micelle concentration. This relaxation time is discussed in terms of different processes that dominate at different temperatures. At lower temperatures processes relating to the dynamics of the interface are observed, and as temperature is increased reversed micelle coalescence dominates, eventually leading to percolation. The fact that two relaxation times, which are related to interfacial dynamics and to reversed micelle interactions, respectively, can be detected without the need for added electrolyte, probes, or intramicellar reactions is indicative of the potential of ILTJ in the study of these complex systems.
Introduction Nanometer-scale water droplets can often be stabilized in organic solvents by surfactant monolayers adsorbed at the oil-water interfaces. The resulting systems are normally known as (swollen) reversed micellar solutions or water-in-oil microemulsions. These complex systems have attracted a great deal of attention over the past two decades because of their potential applications in such diverse fields as biocatalysis, bioseparations,1 cosmetics, nanoparticle synthesis,2 and oil recovery.3 In some cases the interaction dynamics in these reversed micellar systems can have important ramifications with regard to their ability to function as desired in practical applications, and this has led to a number of studies on microemusion dynamics. Such investigations have focused on a wide range of time scales, covering the internal motions of the various components making up the microemulsion, the dynamics of the reversed micellar interface itself, and intermicellar processes such as clustering and coalescence. The various techniques used to study these systems indicate clearly that reversed micelles are highly dynamicaggregates that collide, coalesce, and then break apart again. * To whom correspondence should be addressed. † Universidade Nova de Lisboa. ‡ Fritz-Haber-Institut de Max-Planck-Gesellschaft. § Massachusetts Institute of Technology. (1) Hatton, T. A. In Surfactant-Based Processes; Scamehorn, J. F., Harwell, J. H., Eds.; Marcel Dekker: New York, 1989. (2) Robinson, B. H., Khan-Lodhi, A. N., Towey, T. In Structure and Reactivity in Reversed Micelles; Pileni, M. P., Ed.; Elsevier: New York, 1989. (3) Neogi, P. In Microemulsions: Structure and Dynamics; S. E., F., P., B., Eds.; CRC Press: Boca Raton, FL, 1987.
Almost all aspects of the dynamics and thermodynamics of microemulsions are affected by the flexibility of the reversed micellar interface. These include the partitioning of amphiphilic solutes to the interface, interfacial fluctuations caused by system perturbations, and intermicellar exchange of components through reversed micellereversed micelle coalescence and dissociation processes. Several attempts have been made to measure the bending flexibility or rigidity of the reversed micelle interface in terms of the bending modulus, κ, which is defined by Helfrich4 as the energy required to bend a unit area of surface by a unit amount of curvature. Among the techniques used to obtain the bending modulus are size polydispersity (SANS),5 electrically induced birefringence,6 time-resolved fluorescence,7 electron spin-echo,8 titration microcalorimetry,9 and iodine-laser temperature jump (ILTJ).10,11 The reported values of κ for AOT-based microemulsions range from 0.2 to 5 kT depending on the technique employed. Cosurfactants can affect the interfacial flexibility of (4) Helfrich, W. Z. Naturforsch. 1973, C28, 693. (5) Kotlarchyk, M.; Stephens, R. B.; Huang, J. S. J. Phys. Chem. 1988, 92, 1533-1538. (6) Linden, E.; Bedeaux, D.; Hilfiker, R.; Eicke, H. F. Ber. Bunsenges. Phys. Chem. 1991, 95, 876-880. (7) Almgren, M.; Johansson, R.; Eriksson, J. C. J. Phys. Chem. 1993, 97, 8590-8594. (8) Huang, J. S.; Milner, S. T.; Farago, B.; Richter, D. Phys. Rev. Lett. 1987, 59, 2600-2603. (9) Nazario, L. M. M.; Hatton, T. A.; Crespo, J. P. S. G. Manuscript In preparation. (10) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Langmuir 1993, 9, 2045-2052. (11) Petit, C.; Holzwarth, J. F.; Pileni, M. P. Langmuir 1995, 11, 2405-2409.
10.1021/la991674u CCC: $19.00 © 2000 American Chemical Society Published on Web 06/10/2000
Dynamics of AOT and AOT/Cosurfactant Microemulsions
Figure 1. Location of cosurfactants in an AOT interface and their impact on the preferred curvature of the microemulsion droplets.
reversed micelles. We have worked with two nonionic cosurfactant systems, alcohols and alkyl polyoxyethylenes, to demonstrate that they have very different effects on the apparent hydrodynamic radii of AOT reversed micelles as obtained by dynamic light scattering, and on the percolation threshold temperature.12 The locations of these two cosurfactants in AOT reversed micelles are illustrated schematically in Figure 1. The alcohols are localized within the tail region of the AOT surfactant interface, and favor a higher curvature of this interface toward the water pool, making the interfacial film more rigid. As a consequence the onset of percolation is delayed relative to that observed for the AOT-only system. The CiEj surfactants, on the other hand, have their polar headgroups within the water pools, and tend to produce more flexible films as they try to curve the interface away from the water pool. In this case, the percolation begins at lower temperatures than for the AOT reversed micelles. The bending modulus and intermicellar interactions and coalescence processes should reflect these trends; the purpose of this study is to investigate these phenomena using noninvasive ILTJ experiments. The iodine-laser temperature jump method is a chemical relaxation technique that imposes a reversible perturbation on the interface. It allows the identification and determination of the relaxation of the microemulsion to a new equilibrium state following a small but rapid increase in temperature. This technique was developed by Holzwarth and co-workers13-16 and uses an iodine laser with photon emission in the near-IR (1315 nm). Radiation of this wavelength is absorbed by the O-H overtone vibrations of the water molecules and gives rise to a rapid temperature increase in aqueous solutions (T-jump pulses as short as 200 ps are possible). In contrast to other temperature jump techniques in which highly concentrated electrolytes or dye molecules have to be used, the ILTJ method needs only the water molecules to absorb the applied energy. Our very sensitive detection system can allow a time resolution of about 2 µs and has the capability of following the complete time range between 2 µs and 1 s. The longer time limit is imposed by the backcooling of the thermostated samples to the original temperature of the solution prior to the temperature jump. Alexandridis et al.10,17 have used the ILTJ method to study AOT microemulsion interfacial dynamics, and (12) Nazario, L. M. M.; Hatton, T. A.; Crespo, J. P. S. G. Langmuir 1996, 12, 6326-6335. (13) Holzwarth, J. F.; Schmidt, A.; Wolff, H.; Volk, R. J. Phys. Chem. 1977, 81, 2300. (14) Holzwarth, J. F. In Techniques and Applications of Fast Reactions in Solution; Gettins, W. J., Wyn-Jones, E., Eds.; D. Reidel: Dordrecht, The Netherlands, 1979; p 47. (15) Holzwarth, J. F., Eck, V., Genz, A., Bayley, A. M., Dale, R. E., Eds.; 1985; p 351. (16) Genz, A.; Holzwarth, J. F. Eur. Biophys. J. 1986, 13, 323. (17) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. J. Mol. Liq. 1997, 72, 55-68.
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attributed relaxation times in the microsecond range to the disturbance and reorganization of the surfactant interface caused by the temperature jump. The current paper extends this earlier investigation to probe cosurfactant effects on the interfacial relaxation processes in perturbed microemulsion systems. In addition, we also report relaxation times in the submillisecond range that have not been observed before in pure AOT microemulsions, and relate them to reversed micelle coalescence and eventually to percolation processes. In both cases the ILTJ method has proved to be a powerful tool for the determination of dynamic properties of the reversed micellar systems. Materials and Methods Materials. All reagents were better than 99% pure and used as received. Sodium dioctylsulfosuccinate (AOT) was purchased from Sigma and isooctane from Merck. The alcohols used were hexanol (Hex) from Fluka and decanol (Dec) from Aldrich. The alkyl polyoxyethylene surfactants, purchased from Nikkol, were C10E4 (lot no. 0005) and C10E8 (lot no. 1008). Filtered Milli-QPlus water was used in the preparation of all solutions and microemulsions. Methods. Microemulsions. The microemulsions were prepared using the injection method, i.e., to 5 mL of the organic solution (AOT with or without cosurfactant in isooctane) was added the necessary amount of water to obtain the desired Wo (water to surfactant molar ratio). The resulting solution was vortexed for about 60 s and placed in a water bath overnight at 25 °C. Iodine-Laser Temperature Jump Experiments. Two different laser arrangements and detection systems were used; simplified schematics of each of the setups are shown in Figure 2. A more detailed description of the ILTJ apparatus can be found in the literature.13-16 Laser Detection (Figure 2a). An iodine laser emitting at 1315 nm carrying pulse energies of 0.5-0.8 J, produced in about 1 µs, was used. The temperature rise caused by the laser pulse was about 0.5-1 °C. The change in light scattering intensity (turbidity) in the sample was followed using an INNOVA-100K3 krypton ion CW laser (Coherent, Palo Alto, CA). The beam of the detection laser was at 90° to the incident iodine laser and had a detection wavelength of 407 nm. The signal from the photomultiplier (RCA1P28 for absorption measurements) was fed into the amplifier circuit of a Tektronix 7904 oscilloscope equipped with a 7A22 amplifier of 1 MHz bandwidth and a 7B92A timebase. The analogue signal from the oscilloscope was connected to two Tektronix 390AD transient digitizers which were used in the dual-timebase mode for digitizing and recording the relaxation signals in four time windows of 2048 channels each. The digitizers were linked through an IEEE bus to a HP Vectra computer where, after the signals were sampled and averaged, relaxation times and their corresponding amplitudes could be extracted. About 1 mL of the microemulsion was placed in a Tefloncapped quartz cuvette which was then placed in the temperaturecontrolled sample holder of the ILTJ detection chamber and allowed to equilibrate at the set temperature. The temperature was controlled to within 0.1 °C by a Haake F3C water bath and ranged between 10 and 40 °C. The microemulsions were single phased and optically transparent in all the experiments. The recording of the forward scattering started 5 µs before the iodine laser pulse and covered the time range up to 2 ms; longer relaxations were not detected. Nine relaxation signals were averaged for each experiment, resulting in a signal-to-noise ratio of 103. Lamp Detection (Figure 2b). In this arrangement, an iodine laser was also used but the detection light source was a 200 W Xe/Hg arc lamp focused with the aid of quartz lenses, a water filter, a UG11 UV filter, and a cutoff 360 nm filter so that the desired wavelength range between 360 and 380 nm was selected. The light beam was opposite and coaxial to the iodine laser, and a fluorescence photomultiplier (EMI 9659QB) fitted with a UG11 and a filter cutoff 360 nm filter detected the relaxation signal at 90°. The signal was displayed on a 7904 Tektronix oscilloscope
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Figure 3. Relaxation traces for AOT microemulsions subjected to temperature perturbations by the iodine-laser pulses: (a) laser detection and (b) lamp detection systems.
Figure 2. Schematics of the iodine-laser temperature jump experimental arrangements: (a) laser detection and (b) lamp detection. equipped with a 7A22 amplifier and sent to a Biomation 8100 transient recorder in the dual-timebase mode for digitizing and recording the signal in 2048 channels. The digitizer was connected to a HP9845B computer (Hewlett-Packard, Loveland, CO) where the signals were sampled and averaged, before the relaxation fitting was done. The placement and equilibration of the sample were as described above. The lower limit of detection in this setup was ca. 5-10 µs due to light flashes produced in the sample during the iodine laser pulse; these very short light flashes can be detected by a highly sensitive fluorescence photomultiplier but not in the setup of Figure 2a. Nine relaxation signals were averaged for each experiment to achieve a signal-to-noise ratio of 103.16 Data Analysis. In both cases the averaged and sampled signals were adequately fitted to a single-exponential curve of the form
I ) (I0 - I∞)e-t/τ + I∞
(1)
where IO and I∞ are the intensities at times zero and infinity, respectively, and τ is the relaxation time.
Results and Discussion Iodine-laser temperature jump experiments were performed on AOT water-in-oil microemulsion systems formulated both with and without nonionic cosurfactants that are known to affect the reversed micelle interfacial properties in different ways. Long-chain alcohols increase the interfacial rigidity, while poly(oxyethylene) alkyl ethers (CiEj) have the opposite effect. The differences in the interfacial properties of these three microemulsion
systems are also reflected in the microemulsion dynamic properties, as shown in this section. The two different iodine lasers with different detection schemes having complementary time domain sensitivities described above were employed to capture the system relaxation dynamics in response to the temperature jump perturbation from equilibrium. Representative relaxation traces obtained using the two detection systems are shown in Figure 3. The trace shown in Figure 3a is typical of the results obtained using the laser detection optics of Figure 2a, and is consistent with the behavior observed by Alexandridis et al.10 for the pure AOT system. Only one relaxation, in the microsecond region, is observed over the observation period. The trace shown in Figure 3b was obtained with the lamp detection setup of Figure 2b, and shows the two timebases followed during each run. The faster timebase ranges from 0 to 50 µs, while the slower timebase is from 0.05 to 10 ms. The sharp peak of about 10 µs width at the beginning of the trace is caused by the light flash during the iodine laser pulse (this is longer than the 2 µs pulse obtained with the first laser system), and masks any relaxation processes that may occur in this time range. A relaxation in the submillisecond to millisecond range is clearly evident. That this relaxation was not observed with the laser system of Figure 2a is due to the much smaller sensitivity of the photomultiplier used in that setup, and to instabilities in the krypton laser in the time range of milliseconds or longer that overshadowed any weak relaxation processes. From these results, it is clear that there are two observable relaxation processes separated by 2 orders of magnitude in time. These two times clearly represent different dynamic processes occurring within the system, and are discussed separately in what follows. First Relaxation Time. The first relaxation signal is that reported by Alexandridis et al.10 and Petit et al.11 and is attributed to the dynamics of the interfacial relaxation processes as the volume expansion and oscillation of the reversed micelles to their new equilibrium size are balanced by the viscous forces due to the induced fluid motion. The relaxation time for this process can be related to the bending modulus of the AOT interface using the formulation developed by Eicke and co-workers for bire-
Dynamics of AOT and AOT/Cosurfactant Microemulsions
Figure 4. First relaxation time, τ1, as a function of temperature for AOT, C10E4/AOT ) 0.2, and Dec/AOT ) 0.2 surfactant systems (Wo ) 55, [AOT] ) 0.1 M).
fringent microemulsions:18
E(2l3 + 3l2 - 5) + (2l3 + 3l2 + 4) τ1 ) ηiRw3β (2) 1 l(l2 - 1)(l + 2) Kβl(l + 1) 8πσ2
[
]
where ηi is the viscosity of isooctane, Rw is the radius of the water pool, β ) (kBT)-1, kB is Boltzmann’s constant, T is the absolute temperature, E ) ηw/ηi (ηw is the viscosity of water), l is equal to 2 (only the ellipsoidal shape fluctuations are relevant), σ is the polydispersity, and κ is the bending modulus. Milner and Safran19 replaced the term (8πσ2)-1 with 2κβ[3 - 2(Rw/Rs)], with Rs being the natural radius of curvature, to show that τ1 ≈ ηiRw3/κ. The relaxation time is thus inversely proportional to the bending modulus; with increasing bending modulus, the shape fluctuations of the interface are smaller, and the relaxations are more rapid. The relaxation times for AOT, Dec/AOT ) 0.2 and C10E4/ AOT ) 0.2, with the same water content and surfactant concentration ([AOT] ) 0.1 M), are shown as functions of temperature in Figure 4. The values for the relaxation times are between 3 and 10 µs, consistent with the results reported by Alexandridis et al.10 and Petit et al.11 for AOT/ isooctane microemulsions. Owing to the low scattering intensities, and the need for deconvolution of the scattering signal from the light flash associated with the iodine laser, there is a reasonably large error of 20-30% associated with these results. Nevertheless, trends in the data can be discerned with respect to interfacial compositions and temperature. The decanol-containing microemulsion shows a more rapid relaxation to its new equilibrium state than does the C10E4/AOT reversed micellar system, with the time constants for the AOT reversed micelles being intermediate between those for the two different cosurfactant systems. Since the bending modulus is directly proportional to the relaxation rate, or inversely related to the time constant, these results indicate that the C10E4/ AOT interface has a lower bending energy and lower interfacial rigidity than the pure AOT system, which in turn has a lower bending modulus and more flexible interface than the alcohol-containing microemulsions. This conclusion is in accord with our earlier results obtained using dynamic light scattering and electrical conductivity methods to probe the structures of these microemulsion systems,12 and can be interpreted to be a consequence of the different solubilization sites for the two different types of cosurfactant, as shown in Figure 1. Temperature also affects the flexibility of the interface, with the interfacial flexibility increasing as temperature increases, as inferred from the temperature-dependent (18) Eicke, H. F.; Sheperd, J. C. W.; Steinemann, A. J. Colloid Interface Sci. 1976, 56, 168. (19) Milner, S. T.; Safran, S. A. Phys. Rev. A 1987, 36, 4371-4379.
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Figure 5. Second relaxation time as a function of temperature for AOT reversed micelles at different water contents ([AOT] ) 0.1 M).
behavior of the hydrodynamic radii of AOT reversed micelles. The results of Figure 4 suggest an increasing interfacial flexibility with increasing temperature, supporting the conclusions reached in earlier studies. The bending modulus can be estimated from the time constants using eq 2. For an AOT reversed micellar system with Wo ) 55 having a polydispersity of 15% (estimated from light scattering data), we estimate a bending energy of 0.3 kT, which is in agreement with the values reported previously using a range of different methods.5-8,10,11 Precise estimates of the bending energy are difficult to make using this approach, however, both because of the large uncertainties in the values of τ1 itself and because κ is sensitive to the polydispersity; a polydispersity of 12% would yield a κ of 0.47 kT, for instance. We have attributed this first relaxation process to shape fluctuations as the reversed micelles approach their new equilibrium state following the temperature jump perturbation. Other causes, such as changes in the shape or size of the reversed micelles due to reversed micelle coalescence can be ruled out as they would lead to a concentration-dependent relaxation rate. Alexandridis et al.10 pointed out that their relaxation rates did not depend on the reversed micelle concentration, and the present results obtained at lower reversed micelle concentrations are also in the same range as those reported previously, corroborating the interpretation that this relaxation is due to the dynamics of the interface. Second Relaxation Time. The relaxation events observed with the lamp detection setup (Figure 2b) were about 2 orders of magnitude slower than those observed with the laser detection system, and were only observed above a certain water content and temperature, which depended on the system studied. Figure 5 shows the temperature dependence of the relaxation time for AOT reversed micelles with different water contents. These curves are typical of all the results obtained. No relaxation signals were observed for reversed micelles having W0 lower than 45, and the temperature at which observable changes in the relaxation time could be discerned (the onset temperature) appeared to be independent of W0. At the higher W0 values, the relaxation time constant increased very rapidly over a short temperature span immediately above the onset temperature, and then decreased more slowly with increasing temperature. The effect of surfactant concentration on the relaxation time constant τ2 is shown as a function of temperature in Figure 6. The onset temperature again appears to be insensitive to the reversed micelle solution parameters for Wo > 45. In contrast to the first relaxation process, however, the second relaxation time constant is strongly concentration dependent, suggesting that reversed micelle-reversed micelle interactions such as clustering and/ or coalescence must play a role in the relaxation process.
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Figure 6. Effect of the AOT concentration on the second relaxation (Wo ) 55).
concentrations are too low to be able to detect temperatureinduced changes in these concentrations. For sticky collisions of C12E5 oil-laden microemulsion droplets in water, Fletcher et al.21 reported dissociation constants from 80 to 240 s-1. At the higher temperatures the rate constants increase nonlinearly with reversed micelle concentration, indicating that other factors may come into play during the relaxation processes at these temperatures. This is probably a result of multiple coalescence or clustering processes leading to larger transient reversed micelles or clusters than obtained by simple binary collisions, and thus to increased polydispersity. In the limit of smaller reversed micelle concentrations, however, only binary coalescence or clustering should be dominant, and thus Eq 3 should be valid as [M] f 0. This is clearly the case for the results at 25 °C shown in Figure 7, from which reasonably reliable estimates of the two rate constants k2 and k-2 can be extracted; less reliable but still valid estimates of these parameters at 27.5 °C can also be obtained from the limiting behavior of the results at this temperature. A general procedure to obtain the parameters in a consistent manner was used, which entailed the fitting of the data to an exponential function of the form
1/τ2 ) A exp(B[M]) Figure 7. Reciprocal relaxation time dependency on reversed micelle concentration (Wo ) 55).
If this process were a simple second-order process depending only on binary reversed micelle-reversed micelle coalescence and breakup processes, then the relaxation rate constant 1/τ2 would depend linearly on the reversed micelle concentration, [M], according to the relationship
1/τ2 ) 4k2[M] + k-2
(4)
to obtain the two regression parameters A and B. The association and dissociation constants were then estimated using
lim 1/τ2 ) lim A exp(B[M]) ) A(1 + B[M] + ...) )
[M]f0
[M]f0
4k2[M] + k-2 (5)
where k2 and k-2 are the association (coalescence) and dissociation (decoalescence) rate constants, respectively. The relaxation rate constant is plotted in Figure 7 as a function of reversed micelle concentration for three different temperatures. At the lowest temperature, 17.5 °C, the rate constant depends linearly on the reversed micelle concentration, as predicted by eq 3 for a secondorder encounter between reversed micelles. The rate constant value of k2 ) 3.1 × 106 (Ms)-1 extracted from these data by linear regression compares well with the coalescence rates reported by Fletcher et al.20 for this system. At this temperature, the dissociation rate constant k-2 has a value of approximately 2000 s-1, suggesting that the average lifetime of a dimer must be on the order of 0.5 ms. Such values have not been reported before in the literature, as all previous studies on reversed micellar coalescence processes have been based on irreversible chemical reactions between probe molecules distributed over the reversed micellar population, and were able to detect only the coalescence events, and not the breakup of the transient dimers. Fletcher et al.20 suggested that the dimer lifetime may be on the order of 25 µs, but this was by supposition only, and was not based on any direct empirical evidence. Nevertheless, this may be a reasonable estimate for the low-Wo reversed micelles, which are much further away from the phase separation boundary than are the systems used in the present study. Indeed, our failure to detect the second relaxation times at low Wo values and at low temperatures could be because the dimer
to yield k2 ) AB/4 and k-2 ) A, respectively. The association rate constants extracted from the data in this way are shown in Figure 8a, and are consistent in magnitude with results determined by Fletcher et al.20 at lower Wo values using chemical probes, although a smaller temperature dependence is indicated. The Arrhenius plot in Figure 8b provides an estimate of 24 kJ/mol for the activation enthalpy for fusion, which is lower by a factor of approximately 4 than would be anticipated on the basis of an extrapolation of Fletcher’s data. Titration microcalorimetry results for the heats of solubilization of water by AOT reversed micellar solutions indicate, however, that the energetics of the system change in nature at a Wo of approximately 35.9 The solubilization energy per mole of water is strongly endothermic at low Wo and becomes increasingly less so as the size of the reversed micelles increases; above a Wo of about 35 the solubilization energy is essentially constant at about 10 J/mol of water. The differences in behavior are more striking when the solubilization energy is plotted as dE/dWo vs Wo , as a clear break in the slope of this curve is observed at a Wo of 35. We have attributed this to the change in the packing of the AOT around the spherical micelles; below the Wo of 35, the tail region is still solvated by the oil phase, so there is significant desolvation of the tail regions as the curvature decreases (Wo increases). Above a Wo of 35, the tails are essentially well-packed and desolvated already, and increasing size (decreasing curvature) results in more solvation of the headgroup region by water. Clearly, such factors will also play a role in the clustering and coalescence processes depending on the sizes of the
(20) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1987, 83, 985-1006.
(21) Fletcher, P. D. I.; Holzwarth, J. F. J. Phys. Chem. 1991, 95, 2550-2555.
(3)
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Figure 9. The relaxation rate constant and apparent hydrodynamic radius increase dramatically as the percolation threshold indicated by the electrical conductivity is approached (Wo ) 55, [AOT] ) 0.1 M).
Figure 8. Association and dissociation rate constants for the AOT/isooctane system: (a) comparison of the results of Fletcher et al.20 (open symbols) with the present results (closed symbols), (b) Arrhenius plots for the association and dissociation rate constants, and (c) temperature dependency of the equilibrium constant for the coalescence/decoalescence processes.
participating reversed micelles, and thus different activation enthalpies might be anticipated depending on the Wo range under investigation. The dissociation rate constants in Figure 8b are consistent with an activation enthalpy of about -70 kJ/ mol, indicating that dissociation is an enthalpically driven process. The equilibrium constant K in Figure 8c shows an increasing tendency for dimerization as the temperature increases. The rapid increase in coalescence rate as temperature increases is indicative of the approach to percolation and ultimately phase separation. In Figure 9 we show the electrical conductivity, the apparent hydrodynamic radius, and the relaxation rate constant as functions of temperature. The point at which the conductivity begins to rise sharply has been attributed to prepercolation clustering, and is known as the critical clustering temperature. Clearly, both the apparent hydrodynamic radius and the relaxation rate constant increase rapidly as the percolation threshold (indicated by the vertical dashed line) is approached. Small-angle neutron scattering results indicate that the droplets are essentially constant in size over the entire temperature range shown here.9 At the
same time, interparticle interactions, as reflected through the interparticle structure factor, S(q), appear to be small below the threshold temperature, and are strong only once the temperature threshold has been crossed; statistically relevant nonzero values for the Ornstein-Zernicke parameters were obtained only for temperatures above the percolation threshold. Note that S(q) ≈ 1 as observed below the threshold temperature does not necessarily indicate an absence of interparticle interactions, as the effect of attractive interactions can, in principle, be compensated for by a hard core repulsion potential for the particles. It is unlikely, however, that the rapid rise in the relaxation rate constant and apparent hydrodynamic size shown in Figure 7 is due to clustering phenomena for which there is a direct repulsive compensation factor in the S(q). We conclude, therefore, that this rise is due to increased reversed micellar shape fluctuations through multiple collisions and coalescence with surrounding reversed micelles with the attendant increase in polydispersity, rather than to strong reversed micelle clustering, which is observable only above the threshold temperature. These conclusions give added weight to our earlier thermodynamic analysis22 of clustering phenomena, which were treated in much the same way as surfactant micellization processes, with the critical clustering temperature being analogous to the critical micellization temperature used for surfactant systems; in this model, clustering was assumed to occur appreciably only above the percolation temperature. Cosurfactant Effects. The effect of interfacial composition on the relaxation time τ2 is illustrated in Figure 10 where the results for each of the systems AOT, Dec/ AOT ) 0.2, and C10E4/AOT ) 0.2 are shown as functions of temperature for two different water uptake numbers Wo. The presence of the cosurfactant does not alter the general characteristics of the relaxation processessthe relaxation times pass through a maximum (assumed for the C10E4 case) and then decrease with increasing temperature and with decreasing Wosalthough it does affect the position of the curve on the plot. For the C10E4 cosurfactant the curves are displaced to lower temperatures relative to those of AOT, and the temperature at which the (assumed) maximum occurs is lower than the lowest temperature probed in this study. The effect of adding decanol to the AOT reversed micelle system is to delay the onset of measurable relaxation times to higher (22) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. J. Phys. Chem. 1995, 99, 8222-8232.
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Figure 10. The effect of cosurfactants on the relaxation time constant for AOT reversed micelles. Polyoxyethylenated surfactants, C10E4/AOT ) 0.2 and Dec/AOT ) 0.2, and two different water contents. Open symbols are for Wo ) 50, and closed symbols are for Wo ) 55.
Figure 11. Relaxation time as a function of temperature for Dec/AOT ) 0.2 and Hex/AOT ) 0.2 (Wo ) 55, [AOT] ) 0.1 M).
temperatures. The trends are consistent with the known effects that these cosurfactants have on the critical clustering temperature and percolation threshold of AOT microemulsions. Indeed, the temperature dependencies of the percolation curves, relaxation rate constant, and hydrodynamic radii for the cosurfactant systems show the same overall relative behavior as observed in Figure 9 for the AOT system without cosurfactants. The effects of alcohol chain length on the relaxation dynamics are summarized in Figure 11 for hexanol and decanol cosurfactants. The shorter chained hexanol is known to have less of an effect on the interfacial rigidity of AOT reversed micelles than decanol, and this is reflected in the approximately 5 °C displacement of the hexanol curve to lower temperatures relative to the decanol results shown in this figure. In the above discussions, we have not accounted for the possible effect of temperature on the partitioning of the cosurfactants between the AOT interfacial region and the bulk solvent phase. Clearly, changes in the interfacial composition will affect the bending properties of the interface, and hence reversed micelle-reversed micelle interactions. It is difficult to anticipate precisely the magnitude of this effect, but it can be expected that at the higher temperatures the alcohols will partition more to the bulk solvent and the results should approach those of the simple AOT system in the absence of cosurfactants. This is not evident from the results presented in Figure 10, and in our earlier light-scattering and percolation studies, in which stable microemulsions were obtained in the presence of the cosurfactants at much higher temperatures than are possible without the cosurfactants. Conclusions The iodine laser temperature jump technique has been used to study the dynamics of AOT reversed micelles with and without cosurfactants present. Two different
Naza´ rio et al.
detection arrangements allowed for determination of relaxation times in the microsecond (τ1) and millisecond (τ2) time ranges, respectively. This latter relaxation time had not been observed in previous studies using temperature jump techniques for probing AOT microemulsion systems. The relaxations in the microsecond range are inversely proportional to the bending energy of the reversed micellar interface, and indicate the CiEj-containing reversed micelle has a smaller bending energy and an alcohol-containing microemulsion droplet a larger bending energy than the pure AOT reversed micelle. This conclusion is consistent with the solubilization site proposed for these systems and its consequent effect on the interfacial rigidity. The value obtained for this relaxation time agrees with values reported in the literature. The second relaxation time τ2 was observed only above a certain water content and temperature. The general trend for τ2 with temperature is a rapid increase from its onset (although this increase could not always be observed over the temperature range investigated), and as temperature is further increased, the relaxation time decreases. The onset temperature appears to be independent of both water content and surfactant concentration for the pure AOT system. A pronounced effect of the interfacial composition is observed, however. In the CiEj-containing system, this relaxation appears at lower temperatures while the addition of an alcohol has the opposite effect. This relaxation time is also changed if the reversed micelle concentration is changed; the lower the concentration the higher the value of τ2. The dependence of τ2 on reversed micelle concentration is indicative of a second-order process such as reversed micellar clustering and/or coalescence. This relation to reversed micellar coalescence processes is substantiated by the close agreement between the values of published coalescence rate constants and estimates of these constants from the dependence of the reciprocal relaxation time on reversed micelle concentration. However, the observation that often the relaxation time passes through a maximum with increasing temperature indicates that more than one process is involved. It could be that at lower temperatures phenomena relating to the dynamics of the interface are dominant (the onset temperature is concentration independent), and as temperature is increased, reversed micellar coalescence and aggregation become more important, eventually dominating the relaxation processes as increasing cooperativity leads to percolation. For the first time, a direct measurement has been made of the dissociation constant for the dimer formed when two reversed micelles coalesce. We find that dimer lifetimes for Wo ) 55 are on the order of 0.5-1 ms, and that the relative dimer concentration is about an order of magnitude smaller than the reversed micelle concentration. The dimer lifetimes may be much shorter and hence the dimer population much smaller at the lower temperatures and lower water contents such that temperatureinduced changes in dimer concentration cannot be detected. Closer to the percolation threshold temperature, the strong concentration dependence of 1/τ2 on reversed micelle concentration indicates a more complex process is occurring than the simple coalescence/dissociation of two reversed micelles. This is to be the subject of further studies. The observation that two relaxation times can be measured using the ILTJ technique to provide estimates of the interfacial bending modulus and the reversed micellar coalescence and dissociation rate constants
Dynamics of AOT and AOT/Cosurfactant Microemulsions
shows the potential of this technique for the study of the dynamics of reversed micellar systems. Both relaxation times were determined without the need for added electrolytes or dyes and without recourse to intermicellar reactions which can themselves induce changes in the system that they are supposed to study, and can lead to some ambiguity in the interpretation of the results.23 This method is limited, however, to those regions of the phase (23) Bommarius, A. S.; Holzwarth, J. F.; Wang, D. I. C.; Hatton, T. A. J. Phys. Chem. 1990, 94, 7232-7239.
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diagram where dimer lifetimes and concentration perturbations are sufficiently large that detectable signals are obtainable. Acknowledgment. L.M.M.N. acknowledges the FritzHaber Institut der Max-Planck Gesellschaft, the Junta Nacional Investigaca˜o Cientı´fica e Te´cnica for grant PraxisXXI/BD/5428/95, and the INVOTAN commission for the NATO fellowship 8/96. LA991674U
