- Email: [email protected]
Ostwald Ripening in Sodium Dodecyl Sulfate-Stabilized Decane-in-Water Emulsions
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
181, 225–231 (1996)
0374
Ostwald Ripening in Sodium Dodecyl Sulfate-Stabilized Decane-in-Water Emulsions JAYAPRAK ASH SOMA
AND
KYRIAKOS D. PAPADOPOULOS 1
Department of Chemical Engineering, Tulane University, Louisiana 70118 Received October 18, 1995; accepted January 17, 1996
The kinetics of Ostwald ripening of decane-in-water emulsions stabilized by the anionic surfactant sodium dodecyl sulfate (SDS) was studied by means of photon correlation spectroscopy. The experimental rates of Ostwald ripening were compared with those predicted by Lifshitz–Slezov–Wagner (LSW) theory and were found to be higher at all surfactant concentrations. Below the critical micelle concentration (CMC), the experimentally determined rates were found to decrease with an increase in SDS concentration, in agreement with the theory. Above the CMC, the ripening rates were found to increase with an increase in micellar concentration. The increase in the rates is attributed to the enhancement of mass transfer between droplets by micelles, which is not accounted for by LSW theory. The volume fraction of the dispersed phase was found not to affect the rates in the low concentration range (0–0.002) used in this study. q 1996 Academic Press, Inc. Key Words: Ostwald ripening; emulsions; sodium dodecyl sulfate; micelles.
INTRODUCTION
Ostwald ripening is the process by which larger particles in a dispersion grow in size at the expense of smaller particles due to the difference in the chemical potential between particles of different radii (1). It is a direct consequence of the Kelvin effect (2) which relates the vapor pressure above a spherical surface to its radius. When applied to the equilibrium solubility of a particle in solution (1), the Kelvin equation shows that the solubility of a particle rises sharply as its radius tends to zero. Thus in a polydispersed suspension, the smaller particles tend to dissolve and reprecipitate onto larger particles, thereby resulting in an increase in average particle size with time. Ostwald ripening assumes importance only for systems with small particle sizes and a significant solubility in the continuous phase. It has been experimentally observed in aerosols (3), solid dispersions (4), vesicles (5), and emulsions (6–14). Phase transformation processes that proceed by nucleation and growth or by spino1
To whom correspondence should be addressed.
dal decomposition are also usually accomplished by the initial growth of the particles by Ostwald ripening when the initial size of the particles is larger than the critical dimension (15). Several investigators have studied Ostwald ripening in emulsions, and it is now recognized as one of the major mechanisms of instability of emulsions (9). In hydrocarbonin-water emulsions, high-molecular-weight hydrocarbon emulsions were found to be more stable than low-molecularweight hydrocarbon emulsions due to their lower solubility in water (6). In fluorocarbon-in-water emulsions, the rate of coarsening was found to depend substantially on the nature of the fluorocarbon (9, 10). The role of micelles in Ostwald ripening of emulsions is not clearly understood (9) and has been a subject of many recent studies (11–13). The presence of micelles is expected to show a large effect on the rate of Ostwald ripening due to the increase in solubility of the oil phase in the presence of micelles; however, such a drastic effect has not been observed experimentally. Kabalnov (11) found no systematic dependence of rates on surfactant concentration above the critical micelle concentration (CMC) from his studies of Ostwald ripening of undecane emulsions stabilized by sodium dodecyl sulfate (SDS). On the contrary, Taylor (13) found the rate to increase with an increase in surfactant concentration above the CMC. Nevertheless, the increase in rate was much smaller than the expected increase of several orders of magnitude. In view of the conflicting reports in the literature, the role of micelles in Ostwald ripening is further investigated in the present study, in relation to micellar dynamics and facilitated transport. THEORY
Though Ostwald ripening has been studied since the year 1900 (16), it was not until much later that a comprehensive theory was developed by Lifshitz and Slyozov (17) and Wagner (18). They proposed a theory on the kinetics of precipitation from supersaturated solid solutions (which is now known as the LSW theory) based on the following assumptions (9): (1) Mass transport is due to molecular
225
AID
JCIS 4235
/
6g11$$$401
06-03-96 01:25:50
0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
coida
AP: Colloid
226
SOMA AND PAPADOPOULOS
diffusion in the continuous phase. (2) The dispersed phase particles are spherical and fixed in space. (3) There is no interaction between neighboring particles; i.e., the particles are separated by distances much larger than the diameter of the particles. (4) The concentration of the molecularly dissolved dispersed phase material in the continuous phase is constant except adjacent to the particle boundaries; i.e., inhomogeneities in the concentration distribution in space caused by diffusion are negligible. According to LSW theory, the rate of Ostwald ripening ( v ) can be represented by
vÅ
da 3 8DC eqVmg Å , dt 9RT
[1]
where a is the number average radius of the particles, D is the diffusion coefficient of the dissolved dispersed phase in the continuous phase, C eq is the aqueous solubility of the dispersed phase reduced to its density, Vm is the molar volume of the dispersed phase material, g is the interfacial tension between the dispersed and the continuous phases, R is the universal gas constant, and T is the absolute temperature. LSW theory is valid only for low dispersed phase volume fractions as it does not take into account the influence of volume fraction of the dispersed phase. Moreover, the effects of the adsorbed surfactant layer and the micellar solubility of the dispersed phase on the mass transfer process are also not considered by the theory. Despite its limitations, it has been successful in explaining the experimental data to a reasonable accuracy (8, 13). In the recent past, considerable effort has gone into improving basic LSW theory to allow for finite volume fractions and other factors affecting the ripening kinetics (19). Ludwig et al. (20) have recently shown that the gap between experimental and theoretical results can be significantly diminished by considering the influence of stochastic effects on ripening. Simulation studies of Ostwald ripening (21) also indicate that thermal and convective contributions can significantly enhance the growth rate without affecting the fundamental nature of the process. MATERIALS AND METHODS
Materials Decane ( ú99% pure), n-hexadecane ( ú99% pure), and SDS (98% pure) were obtained from Aldrich Chemical Company, USA. All chemicals were used as received without any further purification. The water used in the preparation of emulsions was purified by passing it through an Epure water purification system (Barnstead) and had a resistivity of 18.1 MV-cm.
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
Emulsion Preparation The emulsions were prepared by first mixing the oil phase in aqueous surfactant solutions in a high-speed rotor/stator mixer (Silverson) to form a coarse emulsion. These were further homogenized by passing them through a microfluidizer (Model 110T, Microfluidics Corp.) for 2 to 4 passes at 6500 psi (22, 23), which produced nearly monodispersed emulsions in the size range of 200 nm. In the first set of experiments, separate emulsions were prepared at varying SDS concentrations (ranging from 1 1 10 04 to 5 1 10 02 M), at a fixed oil volume fraction, f, of 2 1 10 03 . These emulsions will be referred to as ‘‘undiluted’’ emulsions as they were used for studying the ripening rates without any dilution. In another set of experiments, a stock emulsion of decane ( f Å 2 1 10 03 ) in 5 1 10 02 M SDS was prepared using the above procedure. This was then diluted to various surfactant concentrations by adding the required amount of water. These emulsions were then used immediately for ripening studies. The volume fraction of the oil was not maintained constant in these experiments. These emulsions will be referred to as ‘‘diluted’’ emulsions. The maximum volume fraction of the oil phase used in these experiments was 2 1 10 03 and the minimum average particle diameter of the emulsions was around 200 nm. As˚ 2 for an SDS molecule (24), the suming an area of 50 A amount of surfactant required for saturation coverage of all the oil drops is around 2 1 10 04 M. The surfactant concentrations used in this study were all above the concentration required for saturation coverage, except for the low surfactant concentration of 1 1 10 04 M. The low volume fraction of the oil used coupled with the saturation coverage of SDS at the oil/water interface ensured that the emulsions were stable against coalescence within the time frame of the experiments. Size Distribution Measurements Drop-size analysis of the emulsions was performed by photon correlation spectroscopy using a Coulter Sub-Micron Particle Analyzer (Model N4MD, Coulter Electronics). The analysis was performed at a scattering angle of 907, and the correlation data were processed using the cumulants method (8, 25). The initial average diameter of the droplets was 200 nm and their growth rate was followed until they reached an average diameter of 300 nm. This size range has been chosen as the Rayleigh–Debye approximation is applicable, thus avoiding any abnormal scattering effects arising from the form of the scattering functions for droplet diameters above 300 nm (11). Due to the low volume fraction of the dispersed phase used in the experiments, no further dilution was required to perform the size analysis. This allowed for the sequential particle size measurements directly in the spectrometer cuvette at close intervals of 2–3 min for the
coida
AP: Colloid
227
OSTWALD RIPENING
FIG. 1. Plot of normalized cube of z-average diameter as a function of time at different concentrations of SDS below the CMC.
experimental duration of 1–2 h. The run time for each measurement was fixed at 120 s, which was sufficient to give reproducible results. To avoid any creaming of the emulsions, the spectrometer cuvette was frequently inverted during the particle size analysis. The polydispersivity of the emulsion, defined (26) as the ratio of variance to squared mean value of the decay time constant of the correlation function, t, was less than 0.2 for all emulsions and remained so during the kinetic experiments, suggesting a narrow distribution of the emulsion droplets.
solubility in water than decane and thus a lower rate of Ostwald ripening. No change in size distribution was observed in those emulsions within the time frame of the ripening experiments conducted in this study ( Ç2 h). Table 1 shows the theoretical ( vt ) , experimental ( ve ) , and relative ( vr , defined as the ratio of experimental to theoretical rate ) ripening rates at various surfactant concentrations. Theoretical rates were calculated from Eq. [1] , using an aqueous solubility of 5.1 1 10 05 kg m03 ( 27 ) , a diffusion coefficient of 6.79 1 10 010 m2 s 01 ( 13 ) , and a density of 0.75 g cm03 ( 13 ) for decane. Interfacial tensions at the decane – water interface as a function of SDS concentration were obtained from Rehfeld ( 24 ) . Experimental Ostwald ripening rates were obtained from the slopes of lines from Figs. 1 and 2 by dividing by a factor 0 of 8 1 ( 1.14 ) 3 and multiplying it by ( d inst ) 3 . The factor 3 of 8 1 ( 1.14 ) was used to convert the experimentally obtained z-average diameter to number-average radius ( 8, 13 ) . Variations in the rates between repeat runs were found to have an upper bound of 10%. The CMC of SDS is 8.2 1 10 03 M (24). Below this concentration, the interfacial tension at the decane–water interface decreases with increasing surfactant concentration. Similarly, Ostwald ripening rate is seen to decrease with an increase in surfactant concentration (Fig. 1), in accordance with Eq. [1], which predicts the rate to decrease with a decrease in the interfacial tension. Below the CMC, the experimental rates are higher than the theoretical rates by a factor of 2 to 4 (Table 1). Similar results have been observed by previous investigators where the experimentally observed rates were higher than the theoretical rates by a factor of 2
RESULTS AND DISCUSSION
Ostwald Ripening Rates According to LSW theory, the cube of number-average radius should vary linearly with time (Eq. [1]). Figures 1 and 2 show the plots of normalized cube of z-average diameter (dinst /d 0inst ) as a function of time at various surfactant concentrations for the ‘‘undiluted’’ emulsions. Due to the slight variation in the initial average diameter of the emulsion droplets prepared at different surfactant concentrations, the z-average diameter of the droplets, dinst , has been normalized by dividing with the initial z-average diameter, d 0inst , in these plots to facilitate a comparison among different runs. As can be seen from Figs. 1 and 2, the plots at different surfactant concentrations are linear within experimental error, suggesting the applicability of LSW theory to emulsions. To verify that the observed variations in size with time were not due to coalescence, similar experiments were repeated with n-hexadecane as the oil phase, which has a much lower
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
FIG. 2. Plot of normalized cube of z-average diameter as a function of time at different concentrations of SDS above the CMC.
coida
AP: Colloid
228
SOMA AND PAPADOPOULOS
TABLE 1 Comparison of the Experimentally Observed Ostwald Ripening Rates with the Theoretical Rates at Different Surfactant Concentrations ‘‘Undiluted’’ emulsions Concentration of SDS (M)
1.0 5.0 1.0 5.0 1.0 2.5 5.0
0.0 1 1004 1 1004 1 1003 1 1003 1 1002 1 1002 1 1002
Theoretical rate, vt (m3 s01) 1.62 1.59 1.35 1.17 5.41 2.82 2.82 2.82
1 1 1 1 1 1 1 1
10025 10025 10025 10025 10026 10026 10026 10026
Experimental rate, ve (m3 s01) 2.50 4.62 4.17 3.68 2.13 2.06 2.87 3.64
1 1 1 1 1 1 1 1
Relative rate, vr Å ve / vt
10024 10025 10025 10025 10025 10025 10025 10025
to 3 (8, 12, 13). This is attributed to the Brownian motion of the particles (8), which LSW theory does not take into account. The experimental rate in the absence of any surfactant was found to be much higher than the theoretical rate ( Ç15 times), suggesting that coalescence was also playing a significant role in nonstabilized emulsions. Above the CMC, the rates were found to increase with an increase in the concentration of SDS (Fig. 2). The rates increased from 2.06 1 10 025 m3 s 01 at 1 1 10 02 M SDS to 3.64 1 10 025 at 5 1 10 02 M SDS for ‘‘undiluted’’ emulsions (Table 1 and Fig. 3). Similar results were obtained by Taylor (13), who found the rate to increase from 0.61 1 10 025 m3 s 01 at 7.8 1 10 03 M SDS to 1.8 1 10 025 m3 s 01 at 7 1 10 02 M SDS at a decane volume fraction of 7 1 10 03 . This is in contrast to the results obtained by Kabalnov (11), who
‘‘Diluted’’ emulsions Experimental rate, ve (m3 s01)
15.43 2.91 3.09 3.15 3.94 7.31 10.18 12.91
2.80 2.56 2.30 1.61 1.59 2.38
— 1 10025 1 10025 1 10025 1 10025 1 10025 1 10025 —
Relative rate, vr Å ve / vt — 1.76 1.90 1.97 2.98 5.64 8.40 —
did not find any difference in the rates above the CMC. LSW theory does not predict any increase in rates above the CMC, as it does not take into consideration the presence of micelles; however, the results obtained in this study clearly indicate that the presence of micelles affects the Ostwald ripening rate, though only to a small extent. The rate of ripening of the emulsions as a function of SDS concentration is illustrated in Fig. 3 for both ‘‘undiluted’’ and ‘‘diluted’’ emulsions. The ‘‘diluted’’ emulsions had lower rates than the ‘‘undiluted’’ emulsions both below and above the CMC, though the variation was larger below the CMC. This effect was found to be reproducible and is not an artifact of experimental error. It should be noted that the volume fraction of the oil was not maintained constant in the ‘‘diluted’’ emulsions. To see if this had an effect on the rates, experiments were performed at two different volume fractions which are described below. Effect of Volume Fraction
FIG. 3. Ostwald ripening rates as a function of surfactant concentration.
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
LSW theory is valid only for dilute solutions as it assumes no interaction between neighboring particles. At higher concentrations, the rate of ripening has been shown to be dependent on the volume fraction of the dispersed phase due to the interaction between diffusion spheres of neighboring particles (28). To account for this effect, previous investigations by Kabalnov (8), which were conducted at a volume fraction of 0.1, relied on a correction factor for the calculation of the ripening rates. The experiments carried out here had a maximum dispersed phase volume fraction of 2 1 10 03 and can be considered to be sufficiently dilute for LSW theory to be applicable. Yet to ascertain the independence of volume fraction at low dispersed phase content in the presence or absence of micelles, experiments were conducted to at two different volume fractions of 1 1 10 03 and 2 1 10 03 . Figure 4 shows the cube of z-average diameter, dinst , as a function of time for the two different volume fractions at SDS concentration
coida
AP: Colloid
229
OSTWALD RIPENING
experiments that when a large dilution is made in micellar solutions, i.e., from above the CMC to below, a minimum of 3 h was required for the solution to attain equilibrium. A similar time-dependent equilibration process is expected to occur when an emulsion is diluted in water. In the present study, it was observed that when the ‘‘undiluted’’ emulsions were diluted in water, the average drop size decreased initially due to solubilization, the decrease being higher for larger dilutions. In the absence of Ostwald ripening, the average drop size is expected to decrease further until solubilization equilibrium is attained. In the presence of Ostwald ripening, however, the competing effect of solubilization would have the effect of lowering the ripening rates. Thus, the competition between solubilization equilibrium and Ostwald ripening may be responsible for the small decrease in the observed ripening rates on dilution (Fig. 3). Effect of Micelles
FIG. 4. Plot of cube of z-average diameter versus time for two different volume fractions at an SDS concentration of 1 1 10 03 M (below CMC).
below the CMC (1 1 10 03 M). As can be seen from the plot, within experimental error, all the data points fall on a straight line, indicating the negligible effect of volume fraction on the ripening rates at low dispersed phase volume fractions. The ripening rates in the presence of micelles at two different volume fractions are shown in Fig. 5. As was the case in the absence of micelles, no significant effect of volume fraction is seen. Similar nondependence of rates on volume fraction within the range 10 05 to 10 03 was also observed by Kabalnov (8). Taylor (13) also found no significant difference in the rates obtained at a volume fraction close to zero from those obtained at higher volume fractions ( Ç0.3). Thus, the difference in rates of ripening for ‘‘undiluted’’ and ‘‘diluted’’ emulsions is not due to the variation in volume fraction.
Micelles have long been known to facilitate transport in liquid–liquid extractions (31). That such a facilitated transfer can also occur between emulsion droplets is evident from the study of McClements and Dungan (32), who have shown that oil can be exchanged between droplets stabilized by a nonionic surfactant, even though the droplet size remains unchanged. Solubilization and transport of oil by surfactant micelles were considered to be the major mechanism for the exchange of oil. Lee and Tadros (33) also observed that mass transfer through Ostwald ripening was enhanced in the presence of micelles. They postulated that in the presence of micelles, increased solubilization of the oil molecules
Effect of Dilution In the ‘‘undiluted’’ emulsions, due to the high shear rates used in their preparation, the micelles can be considered to reach equilibrium with the bulk phase and the oil droplets with respect to solubilization. When these emulsions are diluted, however, the micelles and the oil drops are no longer in equilibrium with the bulk phase and now have to attain a new equilibrium state. The equilibration process is not instantaneous and is rather a time-dependent process. In fact, it was observed that the process of equilibration of the droplets when contacted with micellar solutions is rather slow and takes at least several hours (11). Such a period is also required for micellar solutions to attain equilibrium (29, 30). Becher and Clifton (30) found through light scattering
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
FIG. 5. Plot of cube of z-average diameter versus time for two different volume fractions at an SDS concentration of 5 1 10 02 M (above CMC).
coida
AP: Colloid
230
SOMA AND PAPADOPOULOS
within the aqueous phase enhances their transport by diffusion as a result of the increase in concentration gradient between the oil droplets and the continuous medium. Similarly, from the results presented here and from those of Taylor (13), it is apparent that the presence of micelles affects the rate of mass transfer between droplets, though the exact mechanism of the transfer process is not known. Kabalnov (11) considered three mechanisms by which micelles can mediate mass transfer between oil droplets: (1) Micelles take up oil directly from the oil droplets and exchange it with other droplets through Brownian motion and fusion–fission processes. (2) Micelles are in a local equilibrium with the continuous medium and they can take up oil only from the continuous medium and not directly from the droplets. (3) Micelles are not in a local equilibrium with the dissolved oil and cannot solubilize the oil fast enough so as to affect the rate. The first mechanism was ruled out on the basis that the electrostatic repulsion between the oil droplets and the micelles will obstruct any collisional encounters, thus preventing any direct exchange of oil between the droplets and the micelles. Also, such a mechanism would show a linear increase in rate with micellar concentration due to an increase in the number of collisions, which was not observed in that study (11). The second mechanism was discounted on the basis that it is equivalent to replacing the aqueous solubility of the oil in the LSW equation with the micellar solubility, suggesting at least a 1000-fold increase in rates in the presence of micelles, which has not been observed experimentally. It was thus suggested that the third mechanism holds; i.e., micelles are not in equilibrium with the surrounding medium as they move fast and equilibrate themselves quite slowly. This observation was based on the fact that the equilibration time of the micelle with the surrounding solution is of the order of 0.1 s (assuming a diffusion controlled mechanism), whereas the average residence time of the micelle near the drop is of the order of 0.001 s. Thus it was concluded (11) that micelles do not play any role in mediating mass transfer between droplets. In lieu of the experimental evidence for the transfer of oil between droplets in the presence of micelles (13, 32), a mechanism other than diffusion-controlled kinetics might be responsible for mass transfer. A simple diffusion-controlled mechanism was also unable to explain the results obtained by Carroll (34) on the kinetics of solubilization of nonpolar oils by micelles. It was observed (34) that the solubilization mechanism of insoluble oils must involve the adsorption– desorption of micelles at the oil/water interface, rather than the diffusion of the oil molecules into the micelles through the aqueous phase. The rate-determining step was found to be the adsorption process of the micelle at the interface. Better fit with the experimental data was observed when dissociation of the micelle prior to adsorption was taken into account, indicating that micellar dynamics play a significant
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
role in the transfer of oil between micelles and oil droplets. A similar mechanism has been proposed by Chan et al. (35) for the solubilization of solid fatty acids by anionics, based on studies of the rate of removal of tagged acid from a rotating disk. Micelles are characterized by two relaxation times, t1 and t2 (36). t1 refers to the rapid transfer of monomer molecules to and from the micelle, and t2 relates to the time scale of total breakup and reformation of the micelle. The demicellization process is postulated to occur by the stepwise removal of the monomers from the micelles rather than a single-step dissociation of the micelle (37). t2 differs from t1 by as much as two to three orders of magnitude and usually varies in a large range, from fractions of milliseconds to minutes depending on the nature and concentration of the surfactant (36). For SDS micelles, t2 is around 1.8 1 10 03 s (37) at the CMC with no significant change until the concentration reaches 5 1 10 02 M (38). Ward and Quigley (39) have shown that the average time intervals between solubilization events at the oil/water interface exhibit a time scale similar to that of the dynamic micellar processes. The average time between successful micellar dissociations that lead to monomer adsorption at the oil/ water interface with resulting desorption of mixed oil and surfactant was found to be about 1 1 10 03 s for SDS micelles. This shows good coherence with the slow relaxation time for SDS micelles which is around 1.8 1 10 03 s (37, 38). Incidentally, the average residence time of a micelle near an oil drop in the emulsion is also of the order of 1 1 10 03 s (11). It is thus probable that the micelles can transfer mass from oil droplets into the bulk phase through the micellar breakdown and solubilization mechanism. Recent molecular dynamic simulation studies (40) indicate that such collective desorption of surfactant and oil molecules from the oil droplets is one of the major mechanisms for the solubilization of oil droplets in micellar solutions. In summary, exchange of oil can be accomplished through the following steps: micellar dissociation, monomer adsorption at the oil/ water interface, micelle formation and solubilization at the interface, desorption of the swollen micelle, diffusion of the micelle into the bulk phase followed by the breakdown of micelles. This process increases the effective concentration of the oil in the bulk phase, which has the effect of increased ripening rates. The higher the concentration of micelles, the higher is the rate of mass transfer and thus a proportional increase in Ostwald ripening with micellar concentration. Another possible mechanism for the increased ripening rates in the presence of micelles can be through depletion flocculation. Aronson (41, 42) has found that the presence of surfactants at a critical concentration above their CMC causes the oil-in-water emulsions to flocculate rapidly. This flocculation process was suggested to be induced by the exclusion of the surfactant micelles between approaching droplets. Binks et al. (43) also found that oil-in-water emul-
coida
AP: Colloid
231
OSTWALD RIPENING
sions stabilized by a nonionic surfactant had a maximum stability at the CMC. Above the CMC, the main destabilization mechanism was shown to be depletion flocculation. In terms of Ostwald ripening, depletion flocculation has an effect similar to that of increased volume fraction, as the diffusion fields of the neighboring droplets start interacting with each other. Emulsions with droplet sizes less than about 200 nm, however, are less sensitive to micelle depletion than emulsions with larger droplets (42). Therefore, such a mechanism might be unlikely here due to the smaller size of the droplets and low concentration of micelles used in this study. ACKNOWLEDGMENTS Financial support for this research from the NIEHS (Grant 5-P42ES05946-02) and the NSF (Grant EHR-9108765) is gratefully acknowledged.
REFERENCES 1. Hunter, R. J., ‘‘Foundations of Colloid Science,’’ Vol. 2. Oxford Univ. Press, New York, 1986. 2. Thomson, W. (Lord Kelvin), Proc. R. Soc. Edinburgh 7, 63 (1871). 3. LaMer, V. K., and Gruen, R., Trans. Faraday Soc. 48, 411 (1952). 4. Davies, C. K. L., Nash, P., and Stevens, R. N., Acta. Metall. 28, 179 (1980). 5. Madani, H., and Kaler, E. W., Langmuir 6, 125 (1990). 6. Davis, S. S., Round, H. P., and Purewal, T. S., J. Colloid Interface Sci. 80, 508 (1981). 7. Kabalnov, A. S., Pertzov, A. V., and Shchukin, E. D., J. Colloid Interface Sci. 118, 590 (1987). 8. Kabalnov, A. S., Makarov, K. N., Pertzov, A. V., and Shchukin, E. D., J. Colloid Interface Sci. 138, 98 (1990). 9. Kabalnov, A. S., and Shchukin, E. D., Adv. Colloid Interface Sci. 38, 69 (1992). 10. Trevino, L., Sole-Violan, L., Daumar, P., Devallez, B., Postel, M., and Riess, J. G., New. J. Chem. 17, 275 (1993). 11. Kabalnov, A. S., Langmuir 10, 680 (1994). 12. Taylor, P., and Ottewill, R. H., Colloids Surf. 88, 303 (1994).
AID
JCIS 4235
/
6g11$$$403
06-03-96 01:25:50
13. Taylor, P., Colloids Surf. 99, 175 (1995). 14. Weers, J. G., and Arlauskas, R. A., Langmuir 11, 474 (1995). 15. Pan, M. X., Chen, X. S., Sun, J. R., and Zhao, D. Q., Microgravity Q., 3, 209 (1993). 16. Ostwald, W., Z. Phys. Chem. (Leipzig) 34, 295 (1900). 17. Lifshitz, I. M., and Slyozov, V. V., J. Phys. Chem. Solids 19, 35 (1961). 18. Wagner, C., Z. Electrochem. 65, 581 (1961). 19. Jayanth, C. S., and Nash, P., J. Mater. Sci. 24, 3041 (1989). 20. Ludwig, F. P., Schmelzer, J., and Bartels, J., J. Mater. Sci. 29, 4852 (1994). 21. Parbhakar, K., Lewandowski, L., and Dao, L. H., J. Colloid Interface Sci. 174, 142 (1995). 22. Sengupta, T., and Papadopoulos, K. D., J. Colloid Interface Sci. 163, 234 (1994). 23. Soma, J., and Papadopoulos, K. D., Colloids Surf. 101, 51 (1995). 24. Rehfeld, S. J., J. Phys. Chem. 71, 738 (1967). 25. Koppel, D. E., Chem. Phys. 57, 4814 (1972). 26. Davies, R., Graham, D. E., and Vincent, B., J. Colloid Interface Sci. 126, 616 (1988). 27. McAuliffe, C. A., Science 163, 478 (1969). 28. Enomoto, Y., Tokuyama, M., and Kawasaki, K., Acta. Metall. 34, 2119 (1986). 29. Nash, T., J. Colloid Interface Sci. 14, 59 (1959). 30. Becher, P., and Clifton, N. K., J. Colloid Interface Sci. 14, 519 (1959). 31. Otsuki, J., and Seno, M., J. Phys. Chem. 95, 5234 (1991). 32. McClements, D. J., and Dungan, S. R., J. Phys. Chem. 97, 7304 (1993). 33. Lee, G. W. J., and Tadros, Th. F., Colloids Surf. 5, 117 (1982). 34. Carroll, B. J., J. Colloid Interface Sci. 79, 126 (1981). 35. Chan, A. F., Evans, D. F., and Cussler, E. L., AIChE J. 22, 1006 (1976). 36. Langevin, D., Annu. Rev. Phys. Chem. 43, 341 (1992). 37. Annianson, E. A. G., and Wall, S. N., J. Phys. Chem. 78, 1024 (1974). 38. Oh, S. G., Klein, S. P., and Shah, D. O., AIChE J. 38, 149 (1992). 39. Ward, A. J. I., and Quigley, K., J. Dispersion Sci. Technol. 11, 143 (1990). 40. Karaboni, S., van Os, N. M., Esselink, K., and Hilbers, P. A. J., Langmuir 9, 1175 (1993). 41. Aronson, M. P., Langmuir 5, 494 (1989). 42. Aronson, M. P., Colloids Surf. 58, 195 (1991). 43. Binks, B. P., Fletcher, P. D. I., and Horsup, D. I., Colloids Surf. 61, 291 (1991).
coida
AP: Colloid
181, 225–231 (1996)
0374
Ostwald Ripening in Sodium Dodecyl Sulfate-Stabilized Decane-in-Water Emulsions JAYAPRAK ASH SOMA
AND
KYRIAKOS D. PAPADOPOULOS 1
Department of Chemical Engineering, Tulane University, Louisiana 70118 Received October 18, 1995; accepted January 17, 1996
The kinetics of Ostwald ripening of decane-in-water emulsions stabilized by the anionic surfactant sodium dodecyl sulfate (SDS) was studied by means of photon correlation spectroscopy. The experimental rates of Ostwald ripening were compared with those predicted by Lifshitz–Slezov–Wagner (LSW) theory and were found to be higher at all surfactant concentrations. Below the critical micelle concentration (CMC), the experimentally determined rates were found to decrease with an increase in SDS concentration, in agreement with the theory. Above the CMC, the ripening rates were found to increase with an increase in micellar concentration. The increase in the rates is attributed to the enhancement of mass transfer between droplets by micelles, which is not accounted for by LSW theory. The volume fraction of the dispersed phase was found not to affect the rates in the low concentration range (0–0.002) used in this study. q 1996 Academic Press, Inc. Key Words: Ostwald ripening; emulsions; sodium dodecyl sulfate; micelles.
INTRODUCTION
Ostwald ripening is the process by which larger particles in a dispersion grow in size at the expense of smaller particles due to the difference in the chemical potential between particles of different radii (1). It is a direct consequence of the Kelvin effect (2) which relates the vapor pressure above a spherical surface to its radius. When applied to the equilibrium solubility of a particle in solution (1), the Kelvin equation shows that the solubility of a particle rises sharply as its radius tends to zero. Thus in a polydispersed suspension, the smaller particles tend to dissolve and reprecipitate onto larger particles, thereby resulting in an increase in average particle size with time. Ostwald ripening assumes importance only for systems with small particle sizes and a significant solubility in the continuous phase. It has been experimentally observed in aerosols (3), solid dispersions (4), vesicles (5), and emulsions (6–14). Phase transformation processes that proceed by nucleation and growth or by spino1
To whom correspondence should be addressed.
dal decomposition are also usually accomplished by the initial growth of the particles by Ostwald ripening when the initial size of the particles is larger than the critical dimension (15). Several investigators have studied Ostwald ripening in emulsions, and it is now recognized as one of the major mechanisms of instability of emulsions (9). In hydrocarbonin-water emulsions, high-molecular-weight hydrocarbon emulsions were found to be more stable than low-molecularweight hydrocarbon emulsions due to their lower solubility in water (6). In fluorocarbon-in-water emulsions, the rate of coarsening was found to depend substantially on the nature of the fluorocarbon (9, 10). The role of micelles in Ostwald ripening of emulsions is not clearly understood (9) and has been a subject of many recent studies (11–13). The presence of micelles is expected to show a large effect on the rate of Ostwald ripening due to the increase in solubility of the oil phase in the presence of micelles; however, such a drastic effect has not been observed experimentally. Kabalnov (11) found no systematic dependence of rates on surfactant concentration above the critical micelle concentration (CMC) from his studies of Ostwald ripening of undecane emulsions stabilized by sodium dodecyl sulfate (SDS). On the contrary, Taylor (13) found the rate to increase with an increase in surfactant concentration above the CMC. Nevertheless, the increase in rate was much smaller than the expected increase of several orders of magnitude. In view of the conflicting reports in the literature, the role of micelles in Ostwald ripening is further investigated in the present study, in relation to micellar dynamics and facilitated transport. THEORY
Though Ostwald ripening has been studied since the year 1900 (16), it was not until much later that a comprehensive theory was developed by Lifshitz and Slyozov (17) and Wagner (18). They proposed a theory on the kinetics of precipitation from supersaturated solid solutions (which is now known as the LSW theory) based on the following assumptions (9): (1) Mass transport is due to molecular
225
AID
JCIS 4235
/
6g11$$$401
06-03-96 01:25:50
0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
coida
AP: Colloid
226
SOMA AND PAPADOPOULOS
diffusion in the continuous phase. (2) The dispersed phase particles are spherical and fixed in space. (3) There is no interaction between neighboring particles; i.e., the particles are separated by distances much larger than the diameter of the particles. (4) The concentration of the molecularly dissolved dispersed phase material in the continuous phase is constant except adjacent to the particle boundaries; i.e., inhomogeneities in the concentration distribution in space caused by diffusion are negligible. According to LSW theory, the rate of Ostwald ripening ( v ) can be represented by
vÅ
da 3 8DC eqVmg Å , dt 9RT
[1]
where a is the number average radius of the particles, D is the diffusion coefficient of the dissolved dispersed phase in the continuous phase, C eq is the aqueous solubility of the dispersed phase reduced to its density, Vm is the molar volume of the dispersed phase material, g is the interfacial tension between the dispersed and the continuous phases, R is the universal gas constant, and T is the absolute temperature. LSW theory is valid only for low dispersed phase volume fractions as it does not take into account the influence of volume fraction of the dispersed phase. Moreover, the effects of the adsorbed surfactant layer and the micellar solubility of the dispersed phase on the mass transfer process are also not considered by the theory. Despite its limitations, it has been successful in explaining the experimental data to a reasonable accuracy (8, 13). In the recent past, considerable effort has gone into improving basic LSW theory to allow for finite volume fractions and other factors affecting the ripening kinetics (19). Ludwig et al. (20) have recently shown that the gap between experimental and theoretical results can be significantly diminished by considering the influence of stochastic effects on ripening. Simulation studies of Ostwald ripening (21) also indicate that thermal and convective contributions can significantly enhance the growth rate without affecting the fundamental nature of the process. MATERIALS AND METHODS
Materials Decane ( ú99% pure), n-hexadecane ( ú99% pure), and SDS (98% pure) were obtained from Aldrich Chemical Company, USA. All chemicals were used as received without any further purification. The water used in the preparation of emulsions was purified by passing it through an Epure water purification system (Barnstead) and had a resistivity of 18.1 MV-cm.
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
Emulsion Preparation The emulsions were prepared by first mixing the oil phase in aqueous surfactant solutions in a high-speed rotor/stator mixer (Silverson) to form a coarse emulsion. These were further homogenized by passing them through a microfluidizer (Model 110T, Microfluidics Corp.) for 2 to 4 passes at 6500 psi (22, 23), which produced nearly monodispersed emulsions in the size range of 200 nm. In the first set of experiments, separate emulsions were prepared at varying SDS concentrations (ranging from 1 1 10 04 to 5 1 10 02 M), at a fixed oil volume fraction, f, of 2 1 10 03 . These emulsions will be referred to as ‘‘undiluted’’ emulsions as they were used for studying the ripening rates without any dilution. In another set of experiments, a stock emulsion of decane ( f Å 2 1 10 03 ) in 5 1 10 02 M SDS was prepared using the above procedure. This was then diluted to various surfactant concentrations by adding the required amount of water. These emulsions were then used immediately for ripening studies. The volume fraction of the oil was not maintained constant in these experiments. These emulsions will be referred to as ‘‘diluted’’ emulsions. The maximum volume fraction of the oil phase used in these experiments was 2 1 10 03 and the minimum average particle diameter of the emulsions was around 200 nm. As˚ 2 for an SDS molecule (24), the suming an area of 50 A amount of surfactant required for saturation coverage of all the oil drops is around 2 1 10 04 M. The surfactant concentrations used in this study were all above the concentration required for saturation coverage, except for the low surfactant concentration of 1 1 10 04 M. The low volume fraction of the oil used coupled with the saturation coverage of SDS at the oil/water interface ensured that the emulsions were stable against coalescence within the time frame of the experiments. Size Distribution Measurements Drop-size analysis of the emulsions was performed by photon correlation spectroscopy using a Coulter Sub-Micron Particle Analyzer (Model N4MD, Coulter Electronics). The analysis was performed at a scattering angle of 907, and the correlation data were processed using the cumulants method (8, 25). The initial average diameter of the droplets was 200 nm and their growth rate was followed until they reached an average diameter of 300 nm. This size range has been chosen as the Rayleigh–Debye approximation is applicable, thus avoiding any abnormal scattering effects arising from the form of the scattering functions for droplet diameters above 300 nm (11). Due to the low volume fraction of the dispersed phase used in the experiments, no further dilution was required to perform the size analysis. This allowed for the sequential particle size measurements directly in the spectrometer cuvette at close intervals of 2–3 min for the
coida
AP: Colloid
227
OSTWALD RIPENING
FIG. 1. Plot of normalized cube of z-average diameter as a function of time at different concentrations of SDS below the CMC.
experimental duration of 1–2 h. The run time for each measurement was fixed at 120 s, which was sufficient to give reproducible results. To avoid any creaming of the emulsions, the spectrometer cuvette was frequently inverted during the particle size analysis. The polydispersivity of the emulsion, defined (26) as the ratio of variance to squared mean value of the decay time constant of the correlation function, t, was less than 0.2 for all emulsions and remained so during the kinetic experiments, suggesting a narrow distribution of the emulsion droplets.
solubility in water than decane and thus a lower rate of Ostwald ripening. No change in size distribution was observed in those emulsions within the time frame of the ripening experiments conducted in this study ( Ç2 h). Table 1 shows the theoretical ( vt ) , experimental ( ve ) , and relative ( vr , defined as the ratio of experimental to theoretical rate ) ripening rates at various surfactant concentrations. Theoretical rates were calculated from Eq. [1] , using an aqueous solubility of 5.1 1 10 05 kg m03 ( 27 ) , a diffusion coefficient of 6.79 1 10 010 m2 s 01 ( 13 ) , and a density of 0.75 g cm03 ( 13 ) for decane. Interfacial tensions at the decane – water interface as a function of SDS concentration were obtained from Rehfeld ( 24 ) . Experimental Ostwald ripening rates were obtained from the slopes of lines from Figs. 1 and 2 by dividing by a factor 0 of 8 1 ( 1.14 ) 3 and multiplying it by ( d inst ) 3 . The factor 3 of 8 1 ( 1.14 ) was used to convert the experimentally obtained z-average diameter to number-average radius ( 8, 13 ) . Variations in the rates between repeat runs were found to have an upper bound of 10%. The CMC of SDS is 8.2 1 10 03 M (24). Below this concentration, the interfacial tension at the decane–water interface decreases with increasing surfactant concentration. Similarly, Ostwald ripening rate is seen to decrease with an increase in surfactant concentration (Fig. 1), in accordance with Eq. [1], which predicts the rate to decrease with a decrease in the interfacial tension. Below the CMC, the experimental rates are higher than the theoretical rates by a factor of 2 to 4 (Table 1). Similar results have been observed by previous investigators where the experimentally observed rates were higher than the theoretical rates by a factor of 2
RESULTS AND DISCUSSION
Ostwald Ripening Rates According to LSW theory, the cube of number-average radius should vary linearly with time (Eq. [1]). Figures 1 and 2 show the plots of normalized cube of z-average diameter (dinst /d 0inst ) as a function of time at various surfactant concentrations for the ‘‘undiluted’’ emulsions. Due to the slight variation in the initial average diameter of the emulsion droplets prepared at different surfactant concentrations, the z-average diameter of the droplets, dinst , has been normalized by dividing with the initial z-average diameter, d 0inst , in these plots to facilitate a comparison among different runs. As can be seen from Figs. 1 and 2, the plots at different surfactant concentrations are linear within experimental error, suggesting the applicability of LSW theory to emulsions. To verify that the observed variations in size with time were not due to coalescence, similar experiments were repeated with n-hexadecane as the oil phase, which has a much lower
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
FIG. 2. Plot of normalized cube of z-average diameter as a function of time at different concentrations of SDS above the CMC.
coida
AP: Colloid
228
SOMA AND PAPADOPOULOS
TABLE 1 Comparison of the Experimentally Observed Ostwald Ripening Rates with the Theoretical Rates at Different Surfactant Concentrations ‘‘Undiluted’’ emulsions Concentration of SDS (M)
1.0 5.0 1.0 5.0 1.0 2.5 5.0
0.0 1 1004 1 1004 1 1003 1 1003 1 1002 1 1002 1 1002
Theoretical rate, vt (m3 s01) 1.62 1.59 1.35 1.17 5.41 2.82 2.82 2.82
1 1 1 1 1 1 1 1
10025 10025 10025 10025 10026 10026 10026 10026
Experimental rate, ve (m3 s01) 2.50 4.62 4.17 3.68 2.13 2.06 2.87 3.64
1 1 1 1 1 1 1 1
Relative rate, vr Å ve / vt
10024 10025 10025 10025 10025 10025 10025 10025
to 3 (8, 12, 13). This is attributed to the Brownian motion of the particles (8), which LSW theory does not take into account. The experimental rate in the absence of any surfactant was found to be much higher than the theoretical rate ( Ç15 times), suggesting that coalescence was also playing a significant role in nonstabilized emulsions. Above the CMC, the rates were found to increase with an increase in the concentration of SDS (Fig. 2). The rates increased from 2.06 1 10 025 m3 s 01 at 1 1 10 02 M SDS to 3.64 1 10 025 at 5 1 10 02 M SDS for ‘‘undiluted’’ emulsions (Table 1 and Fig. 3). Similar results were obtained by Taylor (13), who found the rate to increase from 0.61 1 10 025 m3 s 01 at 7.8 1 10 03 M SDS to 1.8 1 10 025 m3 s 01 at 7 1 10 02 M SDS at a decane volume fraction of 7 1 10 03 . This is in contrast to the results obtained by Kabalnov (11), who
‘‘Diluted’’ emulsions Experimental rate, ve (m3 s01)
15.43 2.91 3.09 3.15 3.94 7.31 10.18 12.91
2.80 2.56 2.30 1.61 1.59 2.38
— 1 10025 1 10025 1 10025 1 10025 1 10025 1 10025 —
Relative rate, vr Å ve / vt — 1.76 1.90 1.97 2.98 5.64 8.40 —
did not find any difference in the rates above the CMC. LSW theory does not predict any increase in rates above the CMC, as it does not take into consideration the presence of micelles; however, the results obtained in this study clearly indicate that the presence of micelles affects the Ostwald ripening rate, though only to a small extent. The rate of ripening of the emulsions as a function of SDS concentration is illustrated in Fig. 3 for both ‘‘undiluted’’ and ‘‘diluted’’ emulsions. The ‘‘diluted’’ emulsions had lower rates than the ‘‘undiluted’’ emulsions both below and above the CMC, though the variation was larger below the CMC. This effect was found to be reproducible and is not an artifact of experimental error. It should be noted that the volume fraction of the oil was not maintained constant in the ‘‘diluted’’ emulsions. To see if this had an effect on the rates, experiments were performed at two different volume fractions which are described below. Effect of Volume Fraction
FIG. 3. Ostwald ripening rates as a function of surfactant concentration.
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
LSW theory is valid only for dilute solutions as it assumes no interaction between neighboring particles. At higher concentrations, the rate of ripening has been shown to be dependent on the volume fraction of the dispersed phase due to the interaction between diffusion spheres of neighboring particles (28). To account for this effect, previous investigations by Kabalnov (8), which were conducted at a volume fraction of 0.1, relied on a correction factor for the calculation of the ripening rates. The experiments carried out here had a maximum dispersed phase volume fraction of 2 1 10 03 and can be considered to be sufficiently dilute for LSW theory to be applicable. Yet to ascertain the independence of volume fraction at low dispersed phase content in the presence or absence of micelles, experiments were conducted to at two different volume fractions of 1 1 10 03 and 2 1 10 03 . Figure 4 shows the cube of z-average diameter, dinst , as a function of time for the two different volume fractions at SDS concentration
coida
AP: Colloid
229
OSTWALD RIPENING
experiments that when a large dilution is made in micellar solutions, i.e., from above the CMC to below, a minimum of 3 h was required for the solution to attain equilibrium. A similar time-dependent equilibration process is expected to occur when an emulsion is diluted in water. In the present study, it was observed that when the ‘‘undiluted’’ emulsions were diluted in water, the average drop size decreased initially due to solubilization, the decrease being higher for larger dilutions. In the absence of Ostwald ripening, the average drop size is expected to decrease further until solubilization equilibrium is attained. In the presence of Ostwald ripening, however, the competing effect of solubilization would have the effect of lowering the ripening rates. Thus, the competition between solubilization equilibrium and Ostwald ripening may be responsible for the small decrease in the observed ripening rates on dilution (Fig. 3). Effect of Micelles
FIG. 4. Plot of cube of z-average diameter versus time for two different volume fractions at an SDS concentration of 1 1 10 03 M (below CMC).
below the CMC (1 1 10 03 M). As can be seen from the plot, within experimental error, all the data points fall on a straight line, indicating the negligible effect of volume fraction on the ripening rates at low dispersed phase volume fractions. The ripening rates in the presence of micelles at two different volume fractions are shown in Fig. 5. As was the case in the absence of micelles, no significant effect of volume fraction is seen. Similar nondependence of rates on volume fraction within the range 10 05 to 10 03 was also observed by Kabalnov (8). Taylor (13) also found no significant difference in the rates obtained at a volume fraction close to zero from those obtained at higher volume fractions ( Ç0.3). Thus, the difference in rates of ripening for ‘‘undiluted’’ and ‘‘diluted’’ emulsions is not due to the variation in volume fraction.
Micelles have long been known to facilitate transport in liquid–liquid extractions (31). That such a facilitated transfer can also occur between emulsion droplets is evident from the study of McClements and Dungan (32), who have shown that oil can be exchanged between droplets stabilized by a nonionic surfactant, even though the droplet size remains unchanged. Solubilization and transport of oil by surfactant micelles were considered to be the major mechanism for the exchange of oil. Lee and Tadros (33) also observed that mass transfer through Ostwald ripening was enhanced in the presence of micelles. They postulated that in the presence of micelles, increased solubilization of the oil molecules
Effect of Dilution In the ‘‘undiluted’’ emulsions, due to the high shear rates used in their preparation, the micelles can be considered to reach equilibrium with the bulk phase and the oil droplets with respect to solubilization. When these emulsions are diluted, however, the micelles and the oil drops are no longer in equilibrium with the bulk phase and now have to attain a new equilibrium state. The equilibration process is not instantaneous and is rather a time-dependent process. In fact, it was observed that the process of equilibration of the droplets when contacted with micellar solutions is rather slow and takes at least several hours (11). Such a period is also required for micellar solutions to attain equilibrium (29, 30). Becher and Clifton (30) found through light scattering
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
FIG. 5. Plot of cube of z-average diameter versus time for two different volume fractions at an SDS concentration of 5 1 10 02 M (above CMC).
coida
AP: Colloid
230
SOMA AND PAPADOPOULOS
within the aqueous phase enhances their transport by diffusion as a result of the increase in concentration gradient between the oil droplets and the continuous medium. Similarly, from the results presented here and from those of Taylor (13), it is apparent that the presence of micelles affects the rate of mass transfer between droplets, though the exact mechanism of the transfer process is not known. Kabalnov (11) considered three mechanisms by which micelles can mediate mass transfer between oil droplets: (1) Micelles take up oil directly from the oil droplets and exchange it with other droplets through Brownian motion and fusion–fission processes. (2) Micelles are in a local equilibrium with the continuous medium and they can take up oil only from the continuous medium and not directly from the droplets. (3) Micelles are not in a local equilibrium with the dissolved oil and cannot solubilize the oil fast enough so as to affect the rate. The first mechanism was ruled out on the basis that the electrostatic repulsion between the oil droplets and the micelles will obstruct any collisional encounters, thus preventing any direct exchange of oil between the droplets and the micelles. Also, such a mechanism would show a linear increase in rate with micellar concentration due to an increase in the number of collisions, which was not observed in that study (11). The second mechanism was discounted on the basis that it is equivalent to replacing the aqueous solubility of the oil in the LSW equation with the micellar solubility, suggesting at least a 1000-fold increase in rates in the presence of micelles, which has not been observed experimentally. It was thus suggested that the third mechanism holds; i.e., micelles are not in equilibrium with the surrounding medium as they move fast and equilibrate themselves quite slowly. This observation was based on the fact that the equilibration time of the micelle with the surrounding solution is of the order of 0.1 s (assuming a diffusion controlled mechanism), whereas the average residence time of the micelle near the drop is of the order of 0.001 s. Thus it was concluded (11) that micelles do not play any role in mediating mass transfer between droplets. In lieu of the experimental evidence for the transfer of oil between droplets in the presence of micelles (13, 32), a mechanism other than diffusion-controlled kinetics might be responsible for mass transfer. A simple diffusion-controlled mechanism was also unable to explain the results obtained by Carroll (34) on the kinetics of solubilization of nonpolar oils by micelles. It was observed (34) that the solubilization mechanism of insoluble oils must involve the adsorption– desorption of micelles at the oil/water interface, rather than the diffusion of the oil molecules into the micelles through the aqueous phase. The rate-determining step was found to be the adsorption process of the micelle at the interface. Better fit with the experimental data was observed when dissociation of the micelle prior to adsorption was taken into account, indicating that micellar dynamics play a significant
AID
JCIS 4235
/
6g11$$$402
06-03-96 01:25:50
role in the transfer of oil between micelles and oil droplets. A similar mechanism has been proposed by Chan et al. (35) for the solubilization of solid fatty acids by anionics, based on studies of the rate of removal of tagged acid from a rotating disk. Micelles are characterized by two relaxation times, t1 and t2 (36). t1 refers to the rapid transfer of monomer molecules to and from the micelle, and t2 relates to the time scale of total breakup and reformation of the micelle. The demicellization process is postulated to occur by the stepwise removal of the monomers from the micelles rather than a single-step dissociation of the micelle (37). t2 differs from t1 by as much as two to three orders of magnitude and usually varies in a large range, from fractions of milliseconds to minutes depending on the nature and concentration of the surfactant (36). For SDS micelles, t2 is around 1.8 1 10 03 s (37) at the CMC with no significant change until the concentration reaches 5 1 10 02 M (38). Ward and Quigley (39) have shown that the average time intervals between solubilization events at the oil/water interface exhibit a time scale similar to that of the dynamic micellar processes. The average time between successful micellar dissociations that lead to monomer adsorption at the oil/ water interface with resulting desorption of mixed oil and surfactant was found to be about 1 1 10 03 s for SDS micelles. This shows good coherence with the slow relaxation time for SDS micelles which is around 1.8 1 10 03 s (37, 38). Incidentally, the average residence time of a micelle near an oil drop in the emulsion is also of the order of 1 1 10 03 s (11). It is thus probable that the micelles can transfer mass from oil droplets into the bulk phase through the micellar breakdown and solubilization mechanism. Recent molecular dynamic simulation studies (40) indicate that such collective desorption of surfactant and oil molecules from the oil droplets is one of the major mechanisms for the solubilization of oil droplets in micellar solutions. In summary, exchange of oil can be accomplished through the following steps: micellar dissociation, monomer adsorption at the oil/ water interface, micelle formation and solubilization at the interface, desorption of the swollen micelle, diffusion of the micelle into the bulk phase followed by the breakdown of micelles. This process increases the effective concentration of the oil in the bulk phase, which has the effect of increased ripening rates. The higher the concentration of micelles, the higher is the rate of mass transfer and thus a proportional increase in Ostwald ripening with micellar concentration. Another possible mechanism for the increased ripening rates in the presence of micelles can be through depletion flocculation. Aronson (41, 42) has found that the presence of surfactants at a critical concentration above their CMC causes the oil-in-water emulsions to flocculate rapidly. This flocculation process was suggested to be induced by the exclusion of the surfactant micelles between approaching droplets. Binks et al. (43) also found that oil-in-water emul-
coida
AP: Colloid
231
OSTWALD RIPENING
sions stabilized by a nonionic surfactant had a maximum stability at the CMC. Above the CMC, the main destabilization mechanism was shown to be depletion flocculation. In terms of Ostwald ripening, depletion flocculation has an effect similar to that of increased volume fraction, as the diffusion fields of the neighboring droplets start interacting with each other. Emulsions with droplet sizes less than about 200 nm, however, are less sensitive to micelle depletion than emulsions with larger droplets (42). Therefore, such a mechanism might be unlikely here due to the smaller size of the droplets and low concentration of micelles used in this study. ACKNOWLEDGMENTS Financial support for this research from the NIEHS (Grant 5-P42ES05946-02) and the NSF (Grant EHR-9108765) is gratefully acknowledged.
REFERENCES 1. Hunter, R. J., ‘‘Foundations of Colloid Science,’’ Vol. 2. Oxford Univ. Press, New York, 1986. 2. Thomson, W. (Lord Kelvin), Proc. R. Soc. Edinburgh 7, 63 (1871). 3. LaMer, V. K., and Gruen, R., Trans. Faraday Soc. 48, 411 (1952). 4. Davies, C. K. L., Nash, P., and Stevens, R. N., Acta. Metall. 28, 179 (1980). 5. Madani, H., and Kaler, E. W., Langmuir 6, 125 (1990). 6. Davis, S. S., Round, H. P., and Purewal, T. S., J. Colloid Interface Sci. 80, 508 (1981). 7. Kabalnov, A. S., Pertzov, A. V., and Shchukin, E. D., J. Colloid Interface Sci. 118, 590 (1987). 8. Kabalnov, A. S., Makarov, K. N., Pertzov, A. V., and Shchukin, E. D., J. Colloid Interface Sci. 138, 98 (1990). 9. Kabalnov, A. S., and Shchukin, E. D., Adv. Colloid Interface Sci. 38, 69 (1992). 10. Trevino, L., Sole-Violan, L., Daumar, P., Devallez, B., Postel, M., and Riess, J. G., New. J. Chem. 17, 275 (1993). 11. Kabalnov, A. S., Langmuir 10, 680 (1994). 12. Taylor, P., and Ottewill, R. H., Colloids Surf. 88, 303 (1994).
AID
JCIS 4235
/
6g11$$$403
06-03-96 01:25:50
13. Taylor, P., Colloids Surf. 99, 175 (1995). 14. Weers, J. G., and Arlauskas, R. A., Langmuir 11, 474 (1995). 15. Pan, M. X., Chen, X. S., Sun, J. R., and Zhao, D. Q., Microgravity Q., 3, 209 (1993). 16. Ostwald, W., Z. Phys. Chem. (Leipzig) 34, 295 (1900). 17. Lifshitz, I. M., and Slyozov, V. V., J. Phys. Chem. Solids 19, 35 (1961). 18. Wagner, C., Z. Electrochem. 65, 581 (1961). 19. Jayanth, C. S., and Nash, P., J. Mater. Sci. 24, 3041 (1989). 20. Ludwig, F. P., Schmelzer, J., and Bartels, J., J. Mater. Sci. 29, 4852 (1994). 21. Parbhakar, K., Lewandowski, L., and Dao, L. H., J. Colloid Interface Sci. 174, 142 (1995). 22. Sengupta, T., and Papadopoulos, K. D., J. Colloid Interface Sci. 163, 234 (1994). 23. Soma, J., and Papadopoulos, K. D., Colloids Surf. 101, 51 (1995). 24. Rehfeld, S. J., J. Phys. Chem. 71, 738 (1967). 25. Koppel, D. E., Chem. Phys. 57, 4814 (1972). 26. Davies, R., Graham, D. E., and Vincent, B., J. Colloid Interface Sci. 126, 616 (1988). 27. McAuliffe, C. A., Science 163, 478 (1969). 28. Enomoto, Y., Tokuyama, M., and Kawasaki, K., Acta. Metall. 34, 2119 (1986). 29. Nash, T., J. Colloid Interface Sci. 14, 59 (1959). 30. Becher, P., and Clifton, N. K., J. Colloid Interface Sci. 14, 519 (1959). 31. Otsuki, J., and Seno, M., J. Phys. Chem. 95, 5234 (1991). 32. McClements, D. J., and Dungan, S. R., J. Phys. Chem. 97, 7304 (1993). 33. Lee, G. W. J., and Tadros, Th. F., Colloids Surf. 5, 117 (1982). 34. Carroll, B. J., J. Colloid Interface Sci. 79, 126 (1981). 35. Chan, A. F., Evans, D. F., and Cussler, E. L., AIChE J. 22, 1006 (1976). 36. Langevin, D., Annu. Rev. Phys. Chem. 43, 341 (1992). 37. Annianson, E. A. G., and Wall, S. N., J. Phys. Chem. 78, 1024 (1974). 38. Oh, S. G., Klein, S. P., and Shah, D. O., AIChE J. 38, 149 (1992). 39. Ward, A. J. I., and Quigley, K., J. Dispersion Sci. Technol. 11, 143 (1990). 40. Karaboni, S., van Os, N. M., Esselink, K., and Hilbers, P. A. J., Langmuir 9, 1175 (1993). 41. Aronson, M. P., Langmuir 5, 494 (1989). 42. Aronson, M. P., Colloids Surf. 58, 195 (1991). 43. Binks, B. P., Fletcher, P. D. I., and Horsup, D. I., Colloids Surf. 61, 291 (1991).
coida
AP: Colloid