Langmuir 1994, IO, 680-684
680
Can Micelles Mediate a Mass Transfer between Oil Droplets?? Alexey S. Kabalnovj Institute of Food Substances, Russian Academy of Sciences, ulitsa Vavilova 28, Moscow, Russia Received June 7,1993. In Final Form: November 18,199P The effect of sodium dodecyl sulfate concentrationon the rate of Ostwald ripening in undecane-in-water emulsions was studied. Varying the surfactant concentration from 0.03 to 1M virtually did not affect the Ostwald ripening rate, despite a considerable increase in solubilization. The observed rates were close to the estimate based only on the molecular solubility. To explain this behavior, it was argued that (i) SDS micelles cannot absorb the oil directly from the emulsion droplets and the stage of a molecular diffusion through the medium is a necessary step and (ii) the micelles are not in a local equilibrium with the oil-in-water molecular solution, presumably because the rate of the oil monomer exchange between the aqueous solution and the micellar interior is quite low.
Introduction The phenomena of diffusion in surfactant and colloidal systems, in particular, emulsions, are attracting considerable interest. Among the mass transfer processes in emulsions, one may mention (i) mass transfer in emulsion mixtures, which is driven by the difference in the droplet compositions,and (ii)the Ostwald ripening process, which is driven by the increment of capillary pressures between the droplets of different sizes (Figure 1). The first process is of interest for food emulsions' and emulsion and suspension polymerization;2one should worry about the second one when dealing with submicrometer emulsions, such as intravenous nutrition, intravenous drug delivery, and fluorocarbon emulsions for local oxygentransport (see, e.g., ref 3). This paper mainly concerns the Ostwald ripening mechanism; its results are however applicable to other mass transfer processes. The theory of the Ostwald ripening process is well developed.a At the steady-state stage of the process, the kinetics becomes independent of the initial particle size distribution and is characterized by (i) linear growth of the cubed average particle radius 6 with time and (ii) the scaling behavior of the particle size distribution function: the distribution function of the ratio a / &tends with time to a time-invariant attractor. I discuss below only the kinetics of the average particle size growth. According to refs 4-6, the growth rate can be written as follows:
where t~ is the interfacial tension, Vmis the molar volume t Partially presented at the 12th ECIC, Lund, Sweden, 1992, and at the Symposium on Diffusion and Mass Transfer in Colloidal
Systems, Chicago, IL,1993.
*
Temporary address: Physical Chemistry I, Chemical Center, Lund University, S-22100 Lund, Sweden. Abstract published in Advance ACS Abstracts, February 15, 1994. (1) Mdlements, D.J.; Dungan, S. R.; German, J. B.; Kinsela,J. E. @
Food Hydrocolloids 1992,6,415. ( 2 ) Ugelstad, J.; Mork, P. C.; Kaggerud, K. H.; Ellingsen, T.; Berge, A. Adv. Colloid Interface Sci. 1980,13,101. (3) Kabalnov, A. S.; Shchukin, E. D. Adv. Colloid Interface Sci. 1992, 38,69. (4) Lifshits,I. M.; Slezov, V. V. Zh. Exp. Teor. Fiz. 1958,35,479. (5) Wagner, C. Z. Electrochem. 1961,35, 581. (6)For a review of a recent development, see: Voorhees, P. J. Stat. Phys. 1985,38,231.
0743-7463/94/2410-0680$04.50/0
0
0
b
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Figure 1. Mass transfer in emulsions. (Left)Ostwald ripening; Ac = c@(2aVm/RT)(l/a-l/A). (Right)Mass transferinemulsion mixtures. Emulsions of two mutually soluble liquids are mixed. Liquids are assumed to form an ideal solution in each other, and one of them is assumed to have a zero solubility in the medium; AC = C@(Xa - XA). Here Xa and X A are molar fractions of the nondiffusing component in droplets a and A, respectively.
of the substance of the dispersed phase, a is the numberaverage radius, c q is the dimensionless solubility of the bulk dispersed phase in the medium, mL/mL (reduced to the density of the solute), D is the diffusivity of the dispersed phase substance in the medium, w will be referred to as the rate of Ostwald ripening, R is the universal gas constant, and T is the absolute temperature. The coefficient ~ ( 4reflects ) the dependence of the Ostwald ripening rate on the volume fraction of the particles 4 (see ref 6). This parameter takes on the values from 1(4 0)to 2.5 (4 = 0.3). When the kinetics of the process is far from being steady-state, eq 1is valid as an estimate. The usual way to control the emulsion stability is to vary the nature and concentration of the surfactant. One can argue about several ways in which a surfactant may affect the Ostwald ripening rate: (i) Surfactants usually change the interfacial tension, which enters into eq 1.(ii) The interfacial layers formed by the surfactant at the interface may impose an additional diffusional resistance on the mass transfer. If the resistance is larger than that of the bulk medium, one can expect a crossover from the cubic to quadratic growth of the average particle size; in this case, the rate of the process is controlled by the surfactant layer ~ e r m e a b i l i t y .(iii) ~ ~ If ~ the surfactant has a low solubility in the medium (comparable to that of the dispersed oil), a peculiar coupling between the surfactant and oil diffusion may occur and the Ostwald ripening rate may be controlled by the diffusion of surfactant. (iv) If a surfactant forms micelles in the medium, they may mediate the transport among the emulsion droplets (Figure
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(7) Kahlweit, M. In Physical Chemistry; Eyring, H., Henderson, D., Jost, W., Eds.; Academic Press: New York, 1970; Vol. 10.
0 1994 American Chemical Society
Langmuir, Vol. 10, No. 3, 1994 681
Mass Transfer between Oil Droplets 0 0 0
I
o
o
O
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e -
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Figure 2. Micellar mediation of mass transfer among emulsion droplets.
2). This paper is mainly concerned with this mechanism; let me consider it here in more detail. It is well known that micelles present a much better surrounding for an oil solubilizate than the aqueous medium and the partition coefficients of hydrocarbons between a micelle and water are usually quite high. This particularly holds for highmolecular-weight hydrocarbons (n-CgH20 to n'C16H34) whose water solubilities are on the order of ceq= lW7-1011 mL/mLSl0 whereas the usual amount of oil solubilizate per micelle (in volume fractions) c z varies from -0.01 to 1(ref ll),the partition coefficient at the saturation point being 'I = c:/cq = 106-1011. The micellar diffusivity is usually fairly high Dm = 10-6-10-7 cm2/s.12 Therefore, the micelles diffuse around the oil droplets with large oil pools inside, and one can expect them to mediate the oil mass transfer. One can argue about several possible mechanisms of how this can be accomplished (A) Micelles take up the oil directly from the bulk droplets of the solubilizate and exchange it with other droplets and micelles as a result of Brownian collisions and fusionfission processes. (B) Micelles do not show an appreciable fusion-fission rate and cannot take up the solubilizate directly from the bulk phase; they absorb it from the molecular solution in water. Solubilizate exchange between the medium and the micelles is fast, and the micelles are in a local equilibrium with the medium. (C) This mechanism is the same as (B), but the rate of the oil monomer exchange between the micelles and the medium is low; the micelles are not in a local equilibrium with the medium. If mechanism A is valid, then the micellar contribution to the rate of mass transfer should be proportional to the number of droplet-micelle collisions. I shall not consider this mechanism in detail; let me point out only that the rate of this process should increase with the number of micelles per unit volume. If mechanism B is dominant, then the rate of Ostwald ripening should increase by a factor of r, with respect to the micelle-free state:
-
Here 6s is the volume fraction of micelles in the solution; x q = #sCmq is the net oil solubility in the micelles per unit volume of micellar solution, reduced to the density of the solute, which is called below the micellar solubility (the derivation of eq 1 will be presented in the Results and ~
~~
(8) Water solubilities of C11-Cl~hydrocarbons can be approximated in homologous series using the experimental solubilitydata availablefor C d l o hydrocarbons.gJ0 (9) McAuliffe, C. J. Phys. Chem. 1966, 70, 1267. (10) McAuliffe, C. Science 1969,163, 478. (11) Chaiko,M. A.; Nagarajan, R.; Ruckenstein,E. J. Colloid Interface Sci. 1984, 99, 168. (12) Lindman,B.; Siiderman,0.;Stilbs, P. In Surfactants in Solution; Mittal, K. L., Ed.; Plenum Press: New York, 1989; p 1.
D3scussion). For a decane emulsion in the presence of 0.1 M SDS,D J D I0.01 (ref 12) and xq/cW = lo5 (refs 11and 13); therefore, at least a 1000-fold increase in the rate of Ostwald ripening in the presence of micelles can be expected. From the previous paragraphs, one may expect the surfactant effects on Ostwald ripening kinetics to be very broad in nature. In experiment, one finds them however rather limited, and, in most cases, reasonably explained only by the interfacial tension e f f e ~ t .Thus, ~ emulsions of fluorocarbons in water show virtually the same Ostwald ripening rates when stabilized by Pluronics of different molecular weight and composition,14J5sodium dodecyl sulfate,16 and Tween 8017 (an appreciable effect on the rate occurs however when Pluronics cause a flocculation of the emulsion dropletsl4J5). The effect of micelles on the Ostwald ripening rate was studied in more detail in our previous paper.l3 We found that Ostwald ripening in decane emulsionsstabilized by 0.1 M SDSbelow the Krafft point (i.e., in the absence of micelles) and that above it differ by a factor of 3, which is considerably lower than the estimate by eq 2 (-1000). The absolute rates for emulsions of c9-c16 hydrocarbons in water, stabilized by 0.1 M SDS at 25 "C are rather close to the estimate based only on the molecular solubility, the experimental rates being higher by a factor of -2.5. Again, a much higher factor would be expected. The (1.5-fold excess can be, in principle, attributed to the micellar-mediated transport. It is difficult to explain, however, why it turns out to be constant for all the homologous series, despite the fact that the xq/cq ratio increases with the molecular weight. From these data, one concludes that the effect of micelles on the Ostwald ripening is unexpectedly low. In contrast to those findings, in a very recent study,' an enhancement of mass transfer between the hexadecane and octadecane droplets in the presence of Tween-20 was found, although the experimental data were not analyzed quantitatively. The objective of this paper is to study in more detail the effect of surfactant micelles on the kinetics of Ostwald ripening. In my opinion, the crucial experiment to check which mechanism (A, B, or C) holds is to vary the concentration of micelles in the system. If the Ostwald ripening rate is independent of the micellar concentration, one can rule out mechanisms A and B (at least for the given oil-surfactant system). We have chosen n-CllH24SDS-H20 system for these studies; the surfactant concentration in this system was varied from 0.01 to 1 M. This choice was made for several reasons: (i) SDS forms micelles within this concentration (ii) above the cmc point of SDS (0.0082 M), the undecane vs water interfacial tension is virtually constant and the monolayer properties are the same, which allows one to keep the relevant effects constant. The hydrocarbon was chosen because of the convenient time scale of the kinetic experiment (the increase in the average diameter from -0.1 to 0.2 pm takes ca. 5 h). The paper is organized as follows. After the Experimental Section,the experimental . results are discussed and possible hypotheses accounting (13) Kabalnov, A. S.;Makarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (14) Amelina, E. A.; Kumacheva, E. E.; Pertsov, A. V.; Shchukin, E. D. Kolloidn. Zh. 1990,52, 216. (15) Kumacheva, E. E.;Amelina,E. A.; Parfenova,A. M. Kolloidn.Zh. 1990,52, 368. (16) Kabalnov, A. S.;Makarov, K. N.; Shcherbakova, 0.V. J. Fluorine Chem.1990,50,271. (17) Kabalnov, A. S. Thesis, Moscow State University, 1985. (18) Fontell, IG. Mol. Cryst. Liq. Cryst. 1981, 63, 59. (19) Kbkichef, P.; Gabrielle-Madelmont,C.; Ollivon, M. J. Colloid Interface Sci. 1989,131,112. (20) KBkichef, P. J. Colloid Interface Sci. 1989,131,133.
Kabalnou
682 Langmuir, Vol. 10, No. 3, 1994 for the data obtained are presented. Whenever possible, comparisons with existing theories and experimental data on the solubilization mechanism and kinetics are made.
Experimental Section Emulsions were prepared from chromatographically-pure undecane and doubly distilled water. Sodium dodecyl sulfate was synthesized from chromatngraphically-pure dodecanol and was then thoroughly purified according to ref 21; its surface pressure isotherm and cmc value (0.0082M)coincided with the ones known in the literature.= Undecane-in-water emulsions (10 vol %) were prepared ultrasonically using a W-375 sonicator-cell disrupter (Heat Systems-Ultrasonics). Particle size analysiswas carried out with a Coulter N4 photon correlation spectrometer (Coultronics)at the angle 0 = 90° using the cumulant method. The kinetics of the growth of the experimentalaveragediameter d, was studied from -0.1 to 0.2 pm. The details of the experimentaltechnique are described elsewhere.ls The particle size range was chosen because of the simplicity of the light scattering data processing, Le., the applicability of the Rayleigh-Debye approximati~n.~~ The experimental average diameter vs time data were straightened on a cubic scale. The theoretical Ostwald ripening rate was calculated with eq 1, as described in detail in ref 13. The undecane-in-water diffusion coefficient D = 5.4 X 10-8 cmz s-1 was estimated with the Hayduk-Laudie equation.u The water solubility of undecane c q = 2.0 X 10-8 was estimated by extrapolating the chromatographically-determinedsolubilities of C&lo hydrocarbons.eJ0 u = 9.3 dyn cm-l (ref 22) and y(4) = 1.76 (ref 6 ) were used. The ratio of the experimental average diameter to the number-average value &.Jd = 1.17 was assumed.= The relative polydispersity, as determined by the cumulant method, usuallyamountedto -0.2. The solubilization of undecane in SDS solutionswas evaluated as follows. A 20 vol % emulsion of undecane in a SDS solution of appropriate concentration was left overnight, after which its particle size amounted to -0.3 pm. Then, different volumes of the emulsion were added to a series of SDS solutionsof the same concentration. Below the saturation point, the sharp rise in the turbidity of the solutions was followed by the gradual decay of their turbidity to almost the initial value. The sharp onset of the emulsion turbidity which did not extinguishovernightwas regarded as the saturation point of the micelleswith the solubilizate. In general,the process of equilibration was rather slow and took at least several hours, which hampered the measurements. The data obtained should be regarded as estimates (the error limits amounting to -50%). The absence of coalescence was controlled by ultracentrifugation studies similar to the ones described in ref 13. All the experiments were conducted at 20 O C . Results and Discussion Figure 3 shows that d h t vs t plots adequately straighten on a cubic scale at all the SDS concentrations, except for C, = 0.01 M. The Ostwald ripening rates found fall cm3s-1 (Table 1).They and 5.6 X between 3.9 X show no systematic dependence on the surfactant concentration, and are quite close to the rate calculated on the basis of the molecular solubility (2.2 x cm3 s-l). The number of micelles per unit volume in these emulsions can be evaluated after taking into account the surfactant depletion due to adsorption a t the oil-water interface. From the SDS area per molecule (50 A2),22the volume fraction of oil (equal to O,l), and the average particle size in the emulsions studied d h t = 10+200 nm, one concludes that the depletion equals 0.03-0.015 M a t the complete coverage of the interface. Taking into account that the critical micelle concentration (cmc) of SDS is equal to (21) Dreger, E.E.;Keim, G. I.; Miles, G. D.;Sheldovski, L.; Ross, J. Ind. Eng. Chem. 1944,36,610. (22) Rehfeld, S. J. J. Phya. Chem. 1967, 71, 738. (23) Kabalnov, A. S. Kolloidn. Zh. 1991,53, 850. (24) Hayduk, W.; Laudie, H. AIChE J. 1974,20,611.
0
a0 -
.
V
0
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01 a
0
v
V
v o
o
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SDS
- 0.3 M SDS
V - 0.1 M SDS
v - 0033 M SDS a
0
- 0.01 M SDS
I
I
2
4
6 t,hours
Figure 3. dkt3 vs t plots of undecane-in-water emulsions at different SDS concentrations. Table 1. Ostwald Ripening Rates and Solubilization Values at Different SDS Concentrations at 20 OC Ostwald ripening rate, w
SDS concn, M 0.033 0.1 0.3 1.0 a
x 1020, cm* 6-1
expt
theo@
3.9 5.6 5.3 3.9
2.2
solubilizatnof undecane in SDS soh, x q x I@, mL/mL 0.6 2.5 15 60
Molecular solubility-basedestimate.
0.082M, one concludes that the SDS concentration safely remains above the cmc after SDS adsorption if the initial concentration is higher than 0.0382 M. This holds for all the samples except for the one with the lowest surfactant concentration (0.01 M); a t 0.033 M, the micelles could be absent at the very beginning of the kinetic experiment, but they should appear at the end. At Cs = 0.01 M, the monolayer is not covered completely and one may expect the interfacial tension of this sample to be higher than that for the other samples. Moreover, this value may decrease as the average particle size in the emulsion increases with time and the total interfacial area decreases. This presumably explains the observed nonlinearity of the d h t vs t plot at Cs = 0.01 M (remember, the Ostwald ripening rate is proportional to a; see eq 1). Obviously, this effect on the interfacial tension is negligible for other samples, whose surfactant concentrations are above the cmc after the surfactant depletion is taken into account. If one assumes the size and form of SDS micelles are independent of the SDS concentration, one may expect more than a 10-foldincrease in the number of micelles per unit volume from Cs = 0.1 M to Cs = 1 M. The experimentallydetermined micellar solubilities x q are shown in Table 1. The increase in x q with SDS concentration is steeper than linear: a 30-fold increase in the surfactant concentration leads to a 100-fold increase in solubilization; this is in qualitative agreement with the theory of solubilization of hydrocarbons by ionic surfacThe enhancement factors expected on the basis of eq 2 are at least 103-104 a t SDS concentrations of 0.1-1 M; the experimental value is -2.5. (A) The first conclusion is that the rate of Ostwald ripening does not depend on the concentration of micelles in the system. In my opinion, it rules out mechanism A; (25) Aamodt, M.; Landren, M.; Jbnseon, B. J.Phys. Chem. 1992,96, 945. (26) Landgen, M.; Aamodt, M.; Jbnsson, B. J. Phya. Chem. 1992,96, 950.
Mass Transfer between Oil Droplets Le., the micelles and bulk phase do not show an appreciable rate of oil exchange due to Brownian collisions. One can argue about electrostatic repulsion between the oil droplets and micelles that prevent such an event from occurring. This conclusion, from the first glance, disagrees with experimental results and their interpretation due to Carroll et al.2731 The authors found very high rates of solubilization of nonpolar oils by nonionic surfactants near the cloud point temperature; the rates were too high to be attributed to the molecular diffusion mechanism. To explain this, the authors assumed that "empty" spherical micelles of nonionic surfactant dissociate into monomers and adsorb at the oil-water interface, and then newmicelles with solubilizate are formed due to the oil-water interface instability. To reconcile our data with these findings, let us point out the following: (i) It is not clear whether the high solubilization rates found by these authors are a general phenomenon or mainly limited to the case of solubilization by nonionic surfactants near the cloud point and very far from saturation. For instance, in ref 32,the kinetics of solubilizationof hexadecane by ionic surfactants in the presence of nonionics was investigated. The authors were not able to detect any measurable rate of solubilization without additivies of the nonionic surfactant to the system. Recently Miller et al.33 examined the solubilization kinetics of nonpolar oils by ionic surfactants by using the spinning disk method. They found that the rates of solubilization show a correlation with the water solubility of the oils, in agreement with the molecular diffusion mechanism. (ii) As far as the interpretation27is concerned, modeling the nonionic surfactant solution in the vicinity of oil droplets as a disperison of spherical micelles in water could be an oversimplification (in this part, my interpretation is close to the one due to Miller and Raney.% Nonionic surfactants show an appreciable solubility in oil, the partition coefficient between water and oil being in favor of the oil. The first elementary act could be a dissolution of the surfactant in the oil droplet followed by the bicontinuous intermediate phase formation between the oil droplet and water. Formation of such a phase ensures avery high mass transport rate; it is however strongly temperature-dependent and usually occurs near to the cloud point. I believe therefore that the very high solubilization rate found in refs 27-31 and a strong temperature dependence of that rate may be related to the "intermediate phase" formation,%and is not therefore of a general nature, but rather limited to the case of solubilizationby nonionic Surfactants near the cloud point. (B) The second conclusion is that SDS micelles are not in a local equilibrium with the surrounding water solution, since the enhancement factor r is much lower than one could expect on the basis of eq 2. To illustrate this, I start with derivation of eq 2; then assuming that a micelle adsorbs oil via the molecular diffusion mechanism, I evaluate the time necessary for a micelle to be equilibrated and compare it with the time of the micellar random walk (27) Carroll, B. J. J. Colloid Interface Sci. 1981, 79, 126. (28) Carroll, B. J.; O'Rourke, B. G. C.; Ward, A. J. I. J . Pharm. Pharmacol. 1982,34,287. (29) Carroll, B. J.; Doyle, P. D. J. Phurm. Pharmacol. 1988,40, 229. (30) Donegan, A. C.;Ward, A. J. I. J. Pharm. Pharmacol. 1987,39,45. (31) O'Rourke, B. G. C.; Ward, A. J. I.; Carroll, B. J. J. Pharm. Pharmacol. 1987,39,885. (32) Bolsman, T. A. B. M.; Veltmaat, F. T. G.; van Os,N. M. J. Am. Oil Chem. Soc. 1988,65, 280.
(33) Miller, D. D., Paper presented at the Symposium on Diffusion and Mass Transfer in Colloidal Systems, Chicago, IL. (34) Miller, C. A.; h e y , K. H. Colloids Surf. A: Physicochem. Eng. Aspects 1993, 74, 169-215.
Langmuir, Vol. 10, No.3, 1994 683 in the concentration decay profile around the emulsion droplets. The conclusion is that micelles solubilize too slow and diffuse too fast to react on the local concentration environment. To prove eq 2,let me start with the problem of dissolution of a spherical particle in an infinite micellefree medium, which underlies the Ostwald ripening theory at the infinite dilution limit. In a steady state, the mass flow per unit time, J , g s-l, and the continuity equation are as follows:
J = -4rpDx2(dc/dx)
(3)
dJ/dx = 0
(4)
Here x is the distance from the center of the particle and is the oil density (remember, the concentration c and, below, cm and x are reduced to the oil density and are dimensionless). Integration of these equations leads to the following equations for the concentration profile around a spherical droplet and for the flow J (Figure 5):
p
c ( x ) - c(-) = ( a / x ) [ c y a )- c(m)l
(5)
J = -4rpDa[cq(a) - ~ ( m ) ]
(6)
Here a is the particle radius, cW(a) is the equilibrium concentration at the particle interface, and c(=) is the concentration at infinity. Now, the micelles are added to the system. Since I assume a local equilibrium between the micelles and the surrounding solution, the concentrations of solubilizate in and outside the micelle are interrelated by the partition coefficient I' throughout all the concentration profile:
For simplicity, I assume r and Dm to be independent of the amount of solubilizate per micelle, and suppose that the micelles are allowed to diffuse in the solution without any constraints, i.e., 4s = const throughout the solution volume. Then, in a steady state, the mass flow with the micelles and the continuity equations are as follows: J, = -4rpDmx2(dx/dx)
d(J
+ J,)/dx
=0
(9)
(10)
Solving eqs 3 and 8-10 yields the same concentration profile of the molecular solution as in the absence of micelles (eq 5 ) and the overall mass flow, which is increased by the factor
and one comes to eq 2. Since eq 2 gives strongly overestimated values of the rates, something is wrong in the underlying assumptions. Let me analyze it in more detail. (i) I assume that the partition coefficient r is not dependent on the amount of solubilizate per micelle. However, according to the theory of solubilization of hydrocarbons by ionic surfactants,26t26r increases with the amount of solubilizate per micelle; see Figure 4. Nevertheless, for eq 2 to be valid, it is sufficient to assume
684 Langmuir,
VoZ. 10, No. 3, 1994
KabaZnov I I
I I I
Figure 5. Schematicoil monomerconcentration profile around
emulsion droplets (eq 5).
cc Figure 4. Schematic plot of cmvs c. The concave form of the
plot followsfrom the theoretical model%under the assumption of the logarithmic dependence of the oil chemical potential on the oil monomer concentration in water. that the Cm and c are linearly related with each other within the c range from c-(a) to c(a): cm(x)- c: = flc(x) - c-1
(12)
In the case of Ostwald ripening, the relative difference between cq(a)and c( a)is quite small (-0.01 at the average particle size, -100 nm). I‘ therefore has the meaning of the Cm vs c derivative at the saturation point c = cy and, in this sense, is constant. Let me emphasize that r > I? = c : / P , see Figure 4, which makes the factor r in eq 2 even larger. (ii) The micelles are assumed to diffuse freely in solution. However, for ionic surfactants, the micelles and the oil surface must exhibit electrostatic repulsions. This leads to formation of a “prohibited zone” around the oil droplets which the micelles cannot enter. The transport inside this zone can be accomplished only by the molecular diffusion mechanism, and the overall rate may be controlled by this process.33 This idea can explain why the Ostwald ripening is lower than the estimate with eq 2. However,in this case,the average particle size should show a quadratic scaling with time, whereas our experimental data are better fitted by a cubic scaling. I believe therefore that this factor can be important but is not determining. (iii)The micellesare assumed to be in a local equilibrium with the medium. If one models a micelle as a sphere with a radius X and the diffusionof the solubilizateto the micelle is assumed to follow the Fick law, the time necessary for a micelle to be equilibrated wiih the surrounding solution should be 0: the order of 71 = I’X2/D. Again, the partition coefficient r has the meaning of the Cm vs c derivative c = cq. I estimate it as a ratio of equilibrium solubilitesfor undecane, r = c:/cw = O.l/lW. Assuming X =,30 A and D = 103cm2 s-1, one obtains 71 = 0.1 s. Since I’ > I’, the actual 71is longer. This time is comparable to the reported lifetime of aromatic hydrocarbon molecules in SDS micelles (lV-lC3 if one takes into account the difference in the water solubilitiesof those hydrocarbons and undecane. The concentrationprofile of the molecular solution in water around the oil droplet obeys eq 5;it is a hyperbola with the decay length equal to the radius of
the particle a. At x > 2a, the concentration profile rapidly levels off. For a micelle to be an effective mediator, it should enhance the transport at x < 2a. The time during which a micelle stays there has the order 7 2 = a2/Dm. Assuming a = 100 nm and Dm = 10-6 cm2 s-1, one obtains 7 2 = 0.001 s. Obviously, 71 > 72; this means that micelles are not in a local equilibrium with the medium, because they move fast and equilibrate themselves quite slow. I emphasize that the micelles and the aqueous solution are in equilibrium “on average”: the spatially averaged values of hydrocarbon concentration in water and in micelles are interrelated by eq 7. However, the concentration profiles c ( x ) and cm(x) in the vicinity of oil droplets ( x < 2a) do not obey eq 7. Namely, the oil monomer concentration profile is described by eq 5 and shows a -1/x decay, whereas the cm(x) concentration is virtually constant. This means that the actual enhancement factor will be substantially reduced, which may be a reason for such a small effect of micelles on the mass transfer rate.
Conclusions The Ostwald ripening rate shows a very slight dependence on the SDS concentration within the surfactant concentration range from 0.033 to 1M. A 30-fold rise in the SDS content, and 100-foldincrease in solubilization, leads to negligible changes in the Ostwald ripening rate. These findings agree with the previous studies of Ostwald ripening kinetic^.^^^^^ They differ from the findings of McClements et al.,l who have shown that the mass transfer between the hexadecane and octadecane droplets can be intensified in the presence of Tween-20; this can be attributed to a different behavior of ionic and nonionic surfactants in this type of experiment. For instance, one cannot rule out the possibility of the fusion-fission processes among nonionic micelles and emulsion droplets, since there is no electrostatic reuplsion among them. In my opinion, the experimental results of this paper prove that (i) SDS micelles cannot absorb the oil directly from the bulk phase and the stage of molecular diffusion is a necessary step and (ii) micelles are not in local equilibrium (with respect to the oil chemical potential) with the surrounding oil droplets. It is unclear however whether these results are of a general nature, and the studies with other surfactants are necessary.
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s35936),
(35) Almgren, M.; Grieser, F.; Thomas,K. J. Am. Chem. SOC.1979, 101,279-291. (36) Almgren, M.; Alsins, J. Prog. Colloid Polym. Sci. 1987,74,55-63.
Acknowledgment. This work has been partially conducted in the Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia. I appreciate discussions with David Miller, Ulf Olsson, Brendan Carroll, Olle Soderman, and Krister Fontell. I am thankful to Hakan Wennerstrom and Bengt Jonsson for their comments on this paper.
