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Rate of Water Uptake by Water-in-Oil Microemulsions in Relation with the Properties of the Amphiphilic Film† Ce´line Caillet, Marc Hebrant, and Christian Tondre* Laboratoire d’Etude des Syste` mes Organiques et Colloı¨daux (LESOC), Unite´ Associe´ e au CNRS No. 406, Universite´ Henri Poincare´ sNancy I, Institut Nance´ ien de Chimie Mole´ culaire, B.P. No. 239, 54506 Vandoeuvre les Nancy Cedex, France Received December 15, 1997. In Final Form: April 27, 1998 We examine in this work the possible correlations between the rate of water solubilization in inverse microemulsion systems (AOT/n-decane/H2O, with different additives) and the fluidity or rigidity of the droplet amphiphilic film. Conductivity measurements are used to characterize the existence (or absence) of droplet percolation. The stopped-flow technique with turbidity detection has allowed us to perform fast injection of small amounts of water and to follow the kinetics of water uptake. A careful control of the flow rate was found necessary to obtain relevant data. A stirred-cell with variable stirring rates was also used for additional measurements. Different additives known for their effect on the droplet behavior (either favoring or retarding droplet coalescence) were considered in this study: NaCl (0-0.3 M); POEG (with molecular weights 2000 and 10000); n-alkanols (from 1-butanol to 1-decanol). The turbidity changes with time were best fitted with biexponential functions, where the fast process characterized by a firstorder rate constant k1 (s-1) was assumed to control the collisions between the dispersed water droplets and the water-in-oil microemulsion droplets. The significance of this rate constant is analyzed, taking into account the part played by the distance from the phase boundary. The results demonstrate a systematic tendency for k1 to be larger for the percolating systems compared to the nonpercolating ones. The possible relation of k1 with the amphiphilic film rigidity is discussed.
Introduction In surfactant-based organized systems such as emulsions, microemulsions, reverse micelles, etc., the properties of the amphiphilic film play an important part in controlling the structure and stability of the systems.1 For this reason the understanding of the behavior of the interfacial film separating the hydrophobic and hydrophilic regions is of importance in the description of diverse processes including droplet coalescence, phase transition phenomena, solute transport, and reactivity control, for instance. To be extremely simple it is clear that a fluid amphiphilic film will favor coalescence processes whereas a rigid film will prevent such processes to some extent. A significant amount of work2-13 has been dedicated to characterizing one of the essential parameters, the elastic constant K, which has the dimensions of an energy and describes the † Part of the results reported in this paper were presented at the 71st Colloid and Surface Science Symposium of the American Chemical Society, Newark, Delaware, June 29th to July 2nd 1997.
(1) Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Proceedings of the International School of Physics “Enrico Fermi”; Degiorgio, V., Corti, M., Eds.; North-Holland Physics Publishers: Elsevier, 1985. (2) Helfrich, W. Z. Naturforsch. C 1973, 28, 693. (3) De Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982, 86, 2294. (4) Kellay, H.; Binks, B. P.; Hendrikx, Y.; Lee, L. T.; Meunier, J. Adv. Colloid Interface Sci. 1994, 49, 85. (5) Binks, B. P.; Kellay, H.; Meunier, J. Europhys. Lett. 1991, 16, 53. (6) Binks, B. P.; Kellay, H.; Meunier, J. Thin Solid Films 1992, 210/ 211, 118. (7) Meunier, J.; Jerome, B. In Surfactants in Solution; Mittal, K. L., Ed.; Plenum Press: New York, 1989; Vol. 9, p 463. (8) Lee, L. T.; Langevin, D.; Strey, R. Physica A 1990, 168, 210. (9) Bassereau, P.; Appell, J.; Marignan, J. J. Phys. II 1992, 2, 1257. (10) Freyssingeas, E.; Roux, D.; Nallet, F. J. Phys.: Condens. Matter 1996, 8, 2801. (11) Linden, E. v. d.; Bedeaux, D.; Hilfiker, R.; Eicke, H.-F. Ber. Bunsenges. Phys. Chem. 1991, 95, 876. (12) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Langmuir 1993, 9, 2045. (13) Petit, C.; Holzwarth, J. F.; Pileni, M. P. Langmuir 1995, 11, 2405.
rigidity of the interfacial film2 (the reciprocal of K being sometimes used to characterize the film flexibility3). The rigidity constant K, or bending modulus, has been defined as twice the amount of energy required to bend a unit area of surface by a unit amount of curvature.2 Its determination has been attempted through different experimental approaches, which call for sophisticated equipment, leading to values not always in agreement.4 In a majority of cases, the experiments were dealing with surfactant monolayers at macroscopic oil/water interfaces.4-8 The rigidity parameter controls in that case the “persistence length” of the layer, which has been shown3 to increase exponentially with K. Ellipsometry and surface light scattering have been the main techniques used for the measurements, demonstrating the effect of parameters such as the chain length of normal alkanes5,6 or the salinity of water.7 The case of amphiphilic monolayers coating microemulsion droplets has been less investigated because essentially indirect methods have to be conceived in order to gain some information on the film rigidity. One approach of this problem was carried out using the dynamic Kerr effect:11 the relaxation of the electrically induced birefringence is related to the rate of change of the shape of the monolayer. The interpretation is nevertheless complicated by the facts that (i) the surface area may change during the relaxation process, due to rapid exchange of surfactant molecules, and (ii) the assumed polydispersity is of primary importance in the calculations. The interfacial dynamics of water-in-oil (w/o) microemulsion droplets was also investigated in a completely different manner using the iodine laser temperature-jump (ILTJ) technique with light scattering detection.12,13 The relaxations observed in the ILTJ experiments were attributed to the perturbation and reorganization of the interfacial film after the temperature rise in the water
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pools. The characteristic time for the droplet shape relaxation was shown to be inversely proportional to the bending rigidity of the surfactant layer surrounding the nanodroplet. The addition of salt to the aqueous water pools resulted in a slight decrease of the bending modulus measured in that way.12 On the other hand, there has been quite a large number of investigations in which the dynamic properties of the amphiphilic film have been correlated with the resistance to coalescence. This has been probed for instance by looking at the exchange of materials contained in microemulsion droplets when they collide.14-18 The droplet percolation detected from measurements of the electrical conductivity has been shown to be correlated with a threshold value of the exchange rate constant, determined by the time-resolved fluorescence quenching method, which characterizes the transfer of a fluorescent probe from one droplet to another.14-17 Similar techniques have been used to demonstrate that the resistance to coalescence of different surfactant monolayers scales with the bending elasticity constants measured independently for planar monolayers by ellipsometry.18 Interestingly, a similar correlation was also established between the rigidity constant and the emulsion water resolution rate observed in macroemulsions of the same surfactants. Although the preceding results as a whole have brought a lot of information concerning the properties of the amphiphilic films and their related consequences in different applied aspects, there seems to remain some controverted questions as we will see below. As was pointed out before,19 the determination of the rigidity constants is by no means a simple task and the literature shows that different methods often lead to different results. In addition it is not clear if the values measured on planar monolayers can also be applied to the strongly curved interfaces of microemulsion droplets made of the same surfactants. Our main concern in this work came from the observation that there seems to be a strong disagreement on the effect of salt on the rigidity of the amphiphilic film. On one hand, there are several reports indicating either no dependence20 or even a decrease of the rigidity constant when the salinity increases,7,12 and the latter case has been observed both for planar interfaces in Winsor systems7 and for w/o microemulsion droplets.12 If the film becomes more fluid, as suggested here, we would expect that the resistance to coalescence becomes weaker. On the other hand, a completely opposite salt effect has been described by Hou and Shah,21 which was confirmed by several other investigators.22,23 Indeed, these authors have analyzed the limiting solubilization capacity of water in water-in-oil microemulsions as depending on the relative values of a critical radius Rc, above which the droplet interactions lead to phase separation, or of a radius of spontaneous curvature Ro. At low salt concentrations the maximum solubilization is controlled by Rc and the (14) Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1989, 93, 10. (15) Lang, J.; Lalem, N.; Zana, R. J. Phys. Chem. 1991, 95, 9533. (16) Lang, J.; Lalem, N.; Zana, R. J. Phys. Chem. 1992, 96, 4667. (17) Lang, J.; Lalem, N.; Zana, R. Colloids Surf. 1992, 68, 199. (18) Fletcher, P. D. I.; Horsup, D. I. J. Chem. Soc., Faraday Trans. 1992, 88, 855. (19) Gradzielski, M.; Langevin, D.; Farago, B. Phys. Rev. E 1996, 53, 3900. (20) Binks, B. P.; Meunier, J.; Abillon, O.; Langevin, D. Langmuir 1989, 5, 415. (21) Hou, M.-J.; Shah, D. O. Langmuir 1987, 3, 1086. (22) Garcia-Rio, L.; Leis, J. R.; Mejuto, J. C.; Pena, M. E. Langmuir 1994, 10, 1676. (23) Derouiche, A.; Tondre, C. J. Dispersion Sci. Technol. 1991, 12, 517.
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interfacial film is fluid, highly deformable, and droplet percolation occurs. At high salt concentration the droplets behave like hard spheres, and the conductivity percolation no longer takes place (excess water constitutes then a second phase when the droplet radius reaches the value of Ro). This difference in the interpretation of the salt effect is puzzling, as already pointed out by Alexandridis et al.,12 and more experiments appear necessary to rationalize all the previous observations. We have considered in this work a new approach to this problem by attempting to correlate the rate of dissolution of small amounts of water in AOT reversed micelles with the properties of the amphiphilic film, as evidenced by the conductivity behavior (percolating or not percolating, which is expected to qualify the ability to coalesce or, on the contrary, the resistance to coalescence). The idea was that if we are far enough from the phase boundary, the rate of water uptake, after a fast injection of a small volume, should depend on the rigidity of the amphiphilic layer of the water-in-oil microemulsion droplets. This means that the incorporation should be faster when the droplets are coated with a highly deformable film than when they behave like hard spheres. The results are expected to also depend on other parameters, such as the initial state of dispersion of the injected water or the proximity of the phase limit. Provided that these parameters are well controlled, the analysis of the effect of different additives known to affect the physical properties of the film may furnish interesting information. In relation with what was said before, we considered the effect of salt addition as being of special interest, but we have also looked at the effect of adding hydrophilic polymers of different molecular weight (poly(ethylene oxide)s)24-26 or cosurfactant having different chain lengths.21,27 All the systems investigated were characterized by conductivity measurements, and the rate of water uptake was measured by the stopped-flow technique with turbidity detection. To our knowledge only two preceding publications have been concerned with the rate of water dissolution accompanying fast injection in microemulsion systems28,29 (this ignores the experiments reporting slow incorporation through diffusion across macroscopic liquid-liquid interfaces30-32). The first paper has mainly investigated the rates of dissolution of n-alkanes in oil-in-water microemulsions of water/sodium dodecyl sulfate/1-pentanol/n-dodecane, which were interpreted in terms of a dissolution process involving diffusion-controlled collisions between oil droplets and microemulsion droplets.28 The rate of water uptake by water-in-oil microemulsions of the same systems turned out to be too fast to be measured with the stopped-flow apparatus used for the experiments. The second paper reported the rate of formation of water pools in the system isooctane/water/AOT, after injection of water in the sample cuvette of a spectrophotometer.29 The time course of the turbidity decay curve was found to be bimodal, and the effects of adding salts, buffer, and proteins were investigated. The values and variations of (24) Suarez, M.-J.; Levy, H.; Lang, J. J. Phys. Chem. 1993, 97, 9808. (25) Suarez, M.-J.; Lang, J. J. Phys. Chem. 1995, 99, 4626. (26) Meier, W. Langmuir 1996, 12, 1188. (27) Nazario, L. M.; Hatton, T. A.; Crespo, P. S. G. Langmuir 1996, 12, 6326. (28) Tondre, C.; Zana, R. J. Dispersion Sci. Technol. 1980, 1, 179. (29) Battistel, E.; Luisi, P. L. J. Colloid Interface Sci. 1989, 128, 7. (30) Hebrant, M.; Mettelin, P.; Tondre, C.; Joly, J. P.; Larpent, C.; Chasseray, X. Colloids Surf., A 1993, 75, 257. (31) Nitsch, W.; Plucinski, P.; Ehrlenspiel, J. J. Phys. Chem. B 1997, 101, 4024. (32) Adachi, M.; Shioi, A.; Harada, M. Langmuir 1997, 13, 4280.
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the kinetic rate constants measured in the two papers are extremely different due in part to the injection methods used. The stopped-flow equipment used in the present work was especially adapted to the proposed experiments since it has allowed us to control important parameters such as the rate of injection or the state of dispersion of water. Experimental Part Chemicals. Aerosol OT (sodium bis(2-ethylhexyl) sulfosuccinate) was purchased from Sigma and used without further purification. Decane (purum quality) was from Fluka and sodium chloride (analytical grade) from Prolabo (France). The series of 1-alkanols from butanol to heptanol (puriss quality) and 1-nonanol (purum) were obtained from Fluka; 1-decanol was from Prolabo. The hydrosoluble polymers poly(ethylene glycol) had the following origins: POEG 2000 (Aldrich) and POEG 10 000 (Hoechst). Deionized doubly distilled water was used throughout. Techniques. Determination of the Phase Limit of the Microemulsion Domain. The maximum solubilization of aqueous solutions (eventually containing different concentrations of salt or POEG) in AOT/decane binary systems (w/w ratio ) 25/75) was determined by titration in a thermostated container (25 °C). Details on the procedure can be found in ref 23. Note that, as recently reported,33 the maximum solubilization capacity measured with the titration method is different from that obtained when using the contact method. When 1-alkanols were present as cosurfactants, they were introduced in decane with AOT, the molar ratio [1-alkanol]/[AOT] being equal to 0.5. This value was adopted by reference to previous works.21 It corresponds to a weight percent of alcohol in the initial mixture varying from 2.04 to 4.26 from butanol to decanol, with a correlative correction of the AOT and decane content. In the cases of octanol, nonanol, and decanol the previously described procedure23 could not be applied and the phase limit could only be obtained after checking the number of phases in a series of test tubes maintained several days at the right temperature. The variable wo measures the molar ratio [H2O]/[AOT] as is usual. Conductivity Measurements. Two different apparatuses have been used for the conductivity measurements: a Wayne Kerr B 331 autobalance precision bridge (ω ) 104 rad/s) equipped with a microelectrode Tacussel CM 05.55 G and a Meterlab CDM 210 (Radiometer/CTB Choffel Electronique) equipped with a XE100 microelectrode. The cell constants were determined with standard KCl solutions. The conductivity was recorded during the titration by the aqueous solutions. Stopped-Flow Kinetics. The rates of water solubilization (with the exception of a few data obtained with a stirred cell) were determined using the stopped-flow technique with turbidity detection. The apparatus was a Biologic SFM-3 stopped-flow (Biologic S.A., France), which allows fast mixing of solutions in variable ratios. It is totally computer-controlled (Tandon PC ASL/486-110) and uses the Bio-Kine software. In the present experiments 25 µL of water was mixed with 500 µL of a reverse microemulsion. To ensure the best possible dispersion, the two solutions were mixed in a first mixer and then passed through a second mixer separated from the first one by a short delay line. The rate of injection was varied from 3 to 7 mL/s, showing a better reproducibility with 7 mL/s, that is, a total injection time of 75 ms. The volume of the spectrophotometric cell (TC 110) being 23 µL, this means that the contents of the cell were renewed a large number of times during the injection time. Since 25 µL represents the smallest volume that can be accurately delivered, this was the only way to obtain a 1/20 mixing ratio. The turbidity change was recorded at 500 nm, and the data analysis was performed with the Bio-Kine software by fitting the curves with mono- or biexponential functions. All the experiments were run at 25 °C. Stirred-Cell Experiments. A few experiments were carried out in a stirred cell with controlled agitation. A part of the device had been described in a previous publication.34 The same light source as that of the SFM-3 stopped-flow apparatus was used, (33) Rabie, H. R.; Helou, D.; Weber, M. E.; Vera, J. H. J. Colloid Interface Sci. 1997, 189, 208.
Figure 1. Maximum water solubilization capacity per AOT molecule versus NaCl concentration (b) (left scale): wo ) [H2O]/ [AOT]; Rc and Ro indicate the phase boundaries respectively controlled by the droplet critical radius and spontaneous radius of curvature.21 Conductivity (S‚cm-1) measured near the phase limit (+) (right scale). Initial AOT/decane ) 25/75 (wt/wt); T ) 25 °C; woi and wof represent the initial and final water content in a typical stopped-flow experiment. and the detection of the turbidity change was recorded with the aid of a high-speed diode array spectrophotometer (TIDAS/ Biologic) connected to the stirred cell through a light guide. The multiwavelength kinetic signal (200-600 nm) was analyzed with the Kinspec software. The microemulsion volume initially introduced in the stirred cell was 1.5 mL, and a Hamilton Microlab M diluter was used for the injection of 75 µL of aqueous solution, keeping thus the same mixing ratio as in the stopped-flow experiments. Karl Fischer Titration. The amount of water injected in the stopped-flow experiments and the amount of water present in the AOT samples were checked with a Karl Fischer Automat E 547 (Metrohm Herisau). The preprogrammed amount of injected water was found to be accurate within the limits of (1%. The AOT samples were found to contain 1.85 ( 0.4% of water. This amount was considered low enough to be neglected when calculating the compositions of the microemulsions.
Results and Discussion Effect of Salt Addition. A ternary phase diagram for the AOT/n-decane/water system, in the absence of salt, has been reported by Assih et al.,35 demonstrating a complex phase behavior when the limits of the reverse microemulsion domain are passed by adding excess water: a liquid crystalline phase forms, which can coexist with the L2 phase. When enough salt is present, this no longer happens and excess water forms a separate phase (Winsor II system).23 These two different behaviors are associated respectively with the ascending and descending branches of the water solubilization curve shown in Figure 1.21,23 The reason for the existence of a maximum of solubilization for a particular salt concentration, which has been briefly recalled in the Introduction, is discussed in detail in ref 21. We have shown on the same figure the conductivity values measured close to the phase limit. These values correspond to the end points of the conductivity curves represented in Figure 2. The high values measured in the low salt situation are related to a percolating behavior, which no longer occurs in the high salt situation (see Figure 2). The conductivity drop (3-4 orders of magnitude) had been previously shown to be nicely correlated with the solubilization maximum.23 (34) Tondre, C.; Robert, A.; Burger, C. J. Dispersion Sci. Technol. 1986, 7, 581. (35) Assih, P.; Delord, P.; Larche, F. C. In Surfactants in Solution; Mittal, K. L., Lindman, B. Eds.; Plenum Press: New York, 1982; Vol. 3, p 1821.
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Figure 2. Conductivity titrations performed in the monophasic region of Figure 1 at different NaCl concentrations (the titration end points correspond to the phase limit): logarithm of κ (S‚cm-1) versus wo.
The rate of water solubilization was measured at different salt concentrations starting with an initial value of wo, noted woi, and ending with a final value wof. This corresponds to displacements along vertical paths in Figure 1 and the curves of Figure 2 were measured along these same paths. The symbol ∆wo was used to represent the gap between woi (at the point of injection) and the limiting value (wolimit), corresponding to the phase limit at the same salt concentration. To optimize the conditions of the stopped-flow experiments, we had to make the best possible choice for the rate of injection. This was necessary for several reasons: (i) there is a compromise to find for the state of water dispersion: with a slow rate the dispersion is poor and the experiments in such conditions have shown that the turbidity change with time is similar for the percolating and for the nonpercolating systems; on the other hand, with a too high rate the change of absorbance may become too fast to be correctly analyzed with the stopped-flow technique; (ii) the shearing produced by the flow of injected liquids may induce the formation of transient liquid crystals;36 (iii) in the low salt condition, a locally high concentration of water may be responsible for the formation of liquid crystalline domains, which will obviously alter the kinetics of water solubilization by the droplets. Parts a and b of Figure 3 illustrate points i and points ii plus iii, respectively. In Figure 3a we have represented the effect of the flow rate on the observed absorbance change with time, and in Figure 3b we have plotted the evolution with time of the birefringence, which is associated with liquid crystal formation. This birefringence signal (in arbitrary units) was simply obtained by looking at the evolution of the transmitted light when crossed polarizers were placed on both sides of the stopped-flow observation cuvette. What we truly observed is the (36) Hall, A. C.; Tekle, E.; Schelly, Z. A. Langmuir 1989, 5, 1263.
Figure 3. Effect of the injection rate in stopped-flow experiments (25 µL of water solution rapidly mixed with 500 µL of microemulsion): total flow rate 3, 3.5, 4.2, 5.3, and 7 mL/s; (a) absorbance signal (turbidity); (b) birefringence signal (arbitrary units). The nonzero baseline is simply due to the residual light passing through the crossed polarizers. It is in no way related to the existence of liquid crystals at equilibrium.
superposition of the turbidity and birefringence signals. If we compare the two sets of curves and the time scales involved, it is clear that for the slower injection rates, liquid crystal formation will affect the course of the kinetics, and in fact it turned out that this was a cause of bad reproducibility. Considering that the disturbances due to liquid crystal formation, no longer occur with a flow rate of 7 mL/s (see Figure 3b), we have adopted these experimental conditions for all the following experiments. In Figure 4, we have collected some of the kinetic curves obtained at different salt concentrations for the solubilization of water in w/o microemulsions with woi ) 24.7, ending with a final value wof ) 32.1. Important variations of the signal amplitude are observed depending on the salt concentration. Note that a small amplitude means that a large part of the solubilization process was already taking place during the mixing time. All these curves have been nicely fitted with biexponential functions of the form
A ) Ao + A1e-k1t + A2e-k2t which is in agreement with the work of Battistel and Luisi.29 A is the turbidity; Ao is the residual absorbance at infinite time; A1 and A2 are the relaxation amplitudes corresponding to the two kinetic processes characterized by the apparent first-order rate constants k1 and k2. We recall that these rate constants have no absolute significance, since they depend on the flow rate. Only the
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Figure 4. Absorbance (turbidity) change with time at different NaCl concentrations. Flow rate 7 mL/s. woinit ) 24.7; wofinal ) 32.1. The dashed lines are the best theoretical fits with a biexponential function.
comparison of the rate constants obtained in identical experimental conditions is meaningful. The above expression is taking into account at least 95% of the absorbance change. The remaining few percent, observed in some cases, corresponded to a very small and very slow drift of the absorbance signal, which was ignored in the data treatment. The amplitude of the fast process A1 was much larger than that of the slow process A2 as long as the salt concentration was below or very close to the solubilization maximum. After that maximum, A2 became larger than A1 and it kept increasing with larger salt concentrations. The two steps can be interpreted29 as corresponding to (i) an initial rapid uptake of water with formation of a random size nonequilibrium microemulsion and (ii) a slower readjustment leading to the final thermodynamically stable droplet size. With this interpretation we assume that the most significant parameter to evaluate the properties of the microemulsion amphiphilic film when it is encountering a water droplet is k1. We thus expect that the more fluid the amphiphilic film is, the faster the incorporation of the injected water will be. It is interesting to notice that molecular dynamics simulations have been performed to understand the mechanism of oil solubilization in surfactant solutions,37 a case symmetrical to the situation investigated in the present paper. The mechanisms identified by these authors include the exchange of oil molecules between the oil droplet and the micelles during collision and the collective desorption of surfactants and oil molecules from the oil droplet surface. It should also be emphasized that in our case the water incorporation can by no means be obtained when keeping constant the number of reverse micelles. In fact, a simple calculation, based on the wellestablished relation between wo and the radius of the water core of the microemulsion droplet ra (ra(nm) ) 0.175wo),38 shows that (assuming that the surface area occupied by the AOT polar heads does not change) a 30% increase in the water core radius means a number of droplets divided by 1.7. This is roughly what we expect in our experiments when wo changes from 24.7 to 32.1 between the initial and final state (see above). The effect of approaching the phase limit on the water solubilization rate is shown in Figure 5 for two different concentrations of salt, one below and one above the (37) Karaborni, S.; Van Os, N. M.; Esseling, K.; Hilbers, P. A. J. Langmuir 1993, 9, 1175. (38) Fletcher, P. D. I. Chem. Phys. Lett. 1987, 141, 357.
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Figure 5. Effect of approaching the phase limit. Variation of the rate constants k1 (full symbols) and k2 (open symbols) versus final value of wo: NaCl, 0.02 M (b, O); NaCl, 0.08 M (2, 4).
Figure 6. First-order rate constant k1 (s-1) versus ∆wo (∆wo ) wolimit - woinjection) at varying NaCl concentrations. The horizontal dashed line indicates the approximate limit of validity of the stopped-flow measurements.
solubilization maximum. The results tend to demonstrate that the differences in k1 for the percolating (0.02 M NaCl) and nonpercolating (0.08 M NaCl) systems are vanishing when the phase boundary is approached. The decrease of the observed rate constant is in line with previous experiments reporting on the solubilization of oil in oilin-water microemulsions.28 This means that the distance of the final composition with respect to the phase limit must necessarily be taken into account when investigating the part played by the properties of the amphiphilic film in the solubilization process. For this reason we have plotted in Figure 6 the values of k1 versus ∆wo (see definition in the first paragraph of Results and Discussion) at varying NaCl concentrations. When k1 is larger than 750 s-1, the results have to be considered with caution because we reach here the limit of validity of the stoppedflow apparatus. Within this restriction, we can easily distinguish two curves in Figures 6: an upper curve corresponding to the percolating systems and a lower one corresponding to the nonpercolating systems. The difference in the properties of the amphiphilic film is thus clearly evidenced when we get rid of the problems posed by the phase limit. A confirmation of the preceding observation was obtained from solubilization rate measurements performed with a stirred cell. The first-order rate constants measured for different stirring rates are shown in Figure 7 for the
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Figure 7. Stirred cell experiments: first-order rate constant k (s-1) versus stirring rate: NaCl, 0.02 M (b); NaCl, 0.08 M (2) woinit ) 32.1; wofinal ) 39.8.
Figure 9. Conductivity titrations performed in the monophasic regions of Figure 8 at different POEG concentrations: POEG 2000, 5% (b), 10% (9), 15% ([); POEG 10000, 5% (2). The arrows indicate the limits of the miscibility gap for POEG 2000 15% (VV) and for POEG 10000 5% (vv).
Figure 8. Maximum water solubilization capacity per AOT molecule versus POEG 2000 concentration. wo ) [H2O]/[AOT]. T ) 25 °C. The dashed area indicates approximately the miscibility gap.
two salt concentrations 0.02 and 0.08 M. These concentrations have been chosen because the water saturation limits, wolimit, are pratically the same in both cases. The initial situation corresponded to woi ) 32.1 and the final one to wof ) 39.8. The rate of incorporation is significantly faster for the percolating system compared to the nonpercolating one, and it increases in both cases with the stirring rate. However this increase is by a factor of about 6 in the former case and only by a factor less than 3 in the latter case, when the stirring rate varies from 300 to 1000 rpm. Effect of Polymer Addition. The effect of solubilizing POEG in the water pools is known to produce a decrease of the interdroplet attractive interactions (at least when the polymer chains are smaller than the water droplets).24-26 The water solubilization limit in AOT/ decane (25/75, w/w) is shown in Figure 8 as a function of the percent of POEG 2000 solubilized in the titrating water. The solubilization capacity increases, and the variation of wo is qualitatively similar to the ascending branch of the curve shown in Figure 1. Note that between 15% and 20% of added POEG in the aqueous phase there is a miscibility gap, which was already mentioned in previous works.24 With POEG 10000 this miscibility gap is already present at 5%. Unfortunately it does not seem that by simply adding POEG one can make the microemulsion droplets behave like hard spheres. Indeed, the conductivity titration curves (Figure 9) demonstrate a percolation behavior whatever the amount of added POEG
Figure 10. First-order rate constants k1 (b) and k2 (O) versus POEG 2000 concentration. (woinit ) 35).
(a similar curve not represented in the figure has been obtained with 20% of POEG 2000). We can thus consider in this case that the amphiphilic film coating the droplets becomes slightly less interacting when adding the hydrosoluble polymer. The rate solubilization curves after injection of polymer-containing water were again best fitted with biexponential functions. The values of k1 and k2 are plotted in Figure 10. The amplitude of the turbidity change associated with the fastest step was always much larger than that of the slow step: the ratio A1/A2 increased from 3.7 ((0.5) to 8.9 ((0.8) when the POEG 2000 concentration changed from 5 to 15%, but the overall amplitude decreased as the dissolution process became faster. As in the case of salt addition, we assume that we have a competition between the effect of the film rigidity and the effect of the excess solubilization capacity (distance of the phase limit). The second effect is obviously
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Caillet et al.
Figure 11. Maximum water solubilization capacity per AOT molecule versus alcohol chain length with [1-alkanol]/[AOT] ) 0.5: this work at 25 °C (b); from Hou and Shah21 at room temperature (+). Data points for the present work for octanol, nonanol, and decanol could not be obtained by simple titration (see text).
predominant here since the variation of k1 (Figure 10) is roughly paralleling the variation of wolimit (Figure 8). The high values of k1 are consistent with a percolating system, and for comparable ∆wo taken in the percolating domain, the rate of solubilization appears to be faster for the polymer-containing water than that for the salt-containing water. Effect of Alcohol Addition (Cosurfactant). The addition of cosurfactant is another way to change the properties of the amphiphilic film.21,27 Figure 11 shows the variation of the water solubilization limit with the alkyl chain length of linear alcohols added to the system. Similar results had been previously reported by Hou and Shah21 who did their experiments at room temperature. Since the knowledge of the phase limit at the same temperature as that used in the kinetic experiments is very important here, we have measured the water solubilization capacity at 25 °C. It can be seen in Figure 11 that the results are quite close to those determined by the preceding authors, who have also explained how the cosurfactant changes the droplet interactions.21 This modification of the properties of the amphiphilic film is illustrated in Figure 12. For the short chain alcohols from butanol to hexanol the droplets show a percolation behavior, but their interactions for a same value of wo are less and less pronounced. For the alcohols with chain lengths from C8 to C10, the droplets behave like hard spheres and we do not observe any conductivity percolation. However addition of excess water does not lead in these cases to Winsor II systems. The case of heptanol, which corresponds to the maximum solubilization capacity, appears as an intermediary one since only a small rise in conductivity is observed before the titration endpoint is attained. Note that the transition from percolating to nonpercolating systems occurs when the chain length of the alcohol becomes similar to that of the surfactant. The results of the stopped-flow kinetics of water solubilization in the presence of all the series of 1-alkanol are collected in Figure 13, for the cases where woi was 25 and wof 32.6. From the biexponential analysis of the change of turbidity with time we have obtained k1 values with the following characteristics: very large k1 for the short chain alcohols (638, 972, and 851 s-1 for butanol, pentanol, and hexanol, respectively, recalling that the accuracy of the determinations becomes questionable when the rate constant is higher than about 750 s-1); very
Figure 12. Conductivity titrations performed in the monophasic region of Figure 11 varying the alcohol chain length: 1-butanol (b); 1-pentanol (9); 1-hexanol ([); 1-heptanol (2); 1-octanol (O); 1-nonanol (0); 1-decanol (4). [1-alkanol]/[AOT] ) 0.5.
Figure 13. Change of absorbance (turbidity) with time for water solubilization in alcohol-containing microemulsions. The dashed lines are the best theoretical fits with biexponential functions. woinit ) 25; wofinal ) 32.6.
small k1 comparatively to the above situation for the alcohols with chain lengths from C8 to C10 (5.6, 1.65, and 1.04 s-1 for octanol, nonanol, and decanol, respectively); intermediate k1 for the case of heptanol (134 s-1). Not forgetting that the distance to the phase limit is changing with the nature of the alcohol, we nevertheless observe that the change of k1 is considerably more important than what would be expected from a simple effect of this phase limit if one refers to the results of Figure 5. The rate of water dissolution is thus clearly affected in this case by the fluidity of the amphiphilic film. The amplitude of the turbidity change associated with the first-order rate constant k1 was again always larger than that of the slow process: A1 was at least 2.3 times larger than A2 (in the case of octanol) and could be up to more than 20 times larger (in the case of pentanol and hexanol).
Water Uptake by W/O Microemulsions
Figure 14. Recapitulation of measured k1 (s-1) values versus ∆wo, the difference between wolimit and woinjection. The diagonal dashed line separates the percolating systems (upper part of the figure) and the nonpercolating systems (lower part).
We have collected in Figure 14 most of the values measured for k1, for the different kinds of systems investigated in this work, as a function of ∆wo (i.e., the difference between wolimit and woinit.). The percolating (full circles) and nonpercolating (open circles) systems have been distinguished in this figure by reference to their conductivity behavior. It is noteworthy that all the percolating systems are situated above a diagonal line separating the figure into two parts, whereas all the nonpercolating systems are situated below this line. The coalescing properties of the surfactant layer coating the microemulsion droplets, and consequently the film rigidity, are thus clearly influencing the rate of water solubilization. Physical Interpretation of the Observed Rates of Water Dissolution. The preceding part of this paper has shown how complicated is the interpretation of the rate parameters characterizing the different systems. By reference to a previous work28 we expected the observed rate constant k1 to be that of a diffusion-controlled collisional process between the water droplets and the microemulsion droplets when there is no resistance to coalescence:
k1 ) kd[M] where kd is the second-order diffusion-controlled rate constant and [M] the concentration of microemulsion droplets. An ideal situation would have been to be able to demonstrate that, when the film becomes less fluid, the observed rate constant has to be corrected by a factor taking into account the collision efficiency. In that case, an inverse proportionality of this factor with the rigidity constant would have appeared reasonable. In fact the analysis of the rate values that was proposed for the water/ sodium dodecyl sulfate/pentanol/n-dodecane systems28 does not seem to hold here. Indeed, if one considers that the AOT reverse micelles behave as globally uncharged entities (the counterions being confined in the water pool) the application of the Smoluchowski equation39 for the two encountering species leads to observed rate constants that are in any case larger than those experimentally
Langmuir, Vol. 14, No. 16, 1998 4385
measured. This is one of the reasons why, in the present stage of our investigations, we are not in a favorable situation to try to quantify the rigidity constant from the kinetic measurements. The part played by the phase limit (which is controlled by the thermodynamics) is another complicating factor, which is acting against the natural effect of the film fluidity. We have already mentioned the relation between the aqueous core radius and wo: the radius of the particle, R, increases when wo increases and this is expected to be associated with an increase of the film fluidity. Parallely the Laplace pressure given, for spherical particles, by 2γ/R (where γ is the interfacial tension)40 should decrease, which means that the solubilization should be easier, whereas the opposite is observed. On the other side, when R increases, we expect the number of collisions to be decreased, since the number of particles is reduced. The solubilization rates that were measured when adding POEG 2000 were surprisingly high, since on the other hand the polymer is retarding the onset of the conductivity percolation. Two different explanations can be proposed: (i) due to the association of AOT molecules with POEG it may well be that when an effective collision with a water droplet occurs, a large piece of the microemulsion surfactant film is transferred to the water microphase in a collective manner, which would obviously increase the rate of dissolution; (ii) the presence of polymer molecules confined inside the droplets may be responsible for an increase of the osmotic pressure, which in turn will favor the penetration of water. Such a process would be driven by the gradient of chemical potential between the free water solution and its confined counterpart, not forgetting that the simple hydration of the ethylene oxide (EO) units of the polymer requires about 2 to 2.5 water molecules per EO units.41 To conclude this paper let us say that to the question “is the rate of water solubilization (a macroscopic phenomenon taking place on a time scale of a few seconds or sometimes less) influenced in some way by the rigidity of the amphiphilic film coating the water-in-oil microemulsion droplets (a microscopic property associated with droplet shape fluctuations on the microsecond time scale12)?”, the answer is very likely yes. Note that there are other examples where a process occurring on a microscopic scale influences a macroscopic property. For instance the lifetime of micelles has been shown to be correlated with foam stability.42,43 However the effect of the film rigidity on water dissolution rates is associated with other parameters from which a discrimination is far from being easy. This was demonstrated in our study of the salt effect in which a distinction between the percolating and the nonpercolating systems was only possible after taking into account the part played by the distance of the system from the phase boundary. LA971374H (39) Amdur, I.; Hammes, G. G. In Chemical Kinetics, Principles and Selected Topics; McGraw-Hill Book Co.: New York, 1966; p 61. (40) Mukerjee, P. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Publ. Corp.: New York, 1979; Vol. 1, pp 153-174. (41) Tondre, C.; Xenakis, A.; Robert, A.; Serratrice, G. In Surfactants in Solution; Mittal, K. L., Bothorel, P., Eds.; Plenum Publ. Corp.: New York, 1986; Vol. 6, pp 1345-1355. (42) Oh, S. G.; Shah, D. O. J. Dispersion Sci. Technol. 1994, 15, 297. (43) Patist, A.; Chhabra, V.; Pagidipati, R.; Shah, R.; Shah, D. O. Langmuir 1997, 13, 432.
