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Langmuir 1998, 14, 5402-5411
Kinetics of Swelling of Oil-in-Water Emulsions B. P. Binks, J. H. Clint, P. D. I. Fletcher,* and S. Rippon Surfactant Science Group, Department of Chemistry, University of Hull, Hull HU6 7RX, U.K.
S. D. Lubetkin and P. J. Mulqueen Dow AgroSciences, Letcombe Laboratory, Letcombe Regis, Wantage, Oxon OX12 9JT, U.K. Received May 5, 1998. In Final Form: July 6, 1998 We have investigated the kinetics of swelling of squalane-in-water emulsion drops by the addition of decane-in-water emulsion drops. Squalane is sufficiently insoluble in the aqueous continuous phase that it cannot transfer between oil drops. Decane is able to transfer between drops and swells the squalane drops. The mixed emulsions were stabilized by the nonionic surfactant n-dodecyl octaoxyethylene glycol ether (C12E8) and were stable with respect to drop coalescence. We have made a systematic series of experiments in which the swelling rates were determined as functions of the initial drop radii, volume fractions, and oil compositions of both types of emulsions. Using a theoretical model originally developed by Ugelstad et al., the entire data set was successfully fitted with a single adjustable parameter equal to the product of the solubility of decane (C∞) and its diffusion coefficient in the aqueous continuous phase (D). The measured value of C∞D was consistent with a mechanism of decane transport in which micelles of C12E8 act as carriers facilitating decane transport between emulsion drops. Also in agreement with this mechanism, it was observed that increasing the aqueous phase concentration of C12E8 increased the swelling rate. Ostwald ripening rates of the decane-in-water emulsions gave values of C∞D consistent with those derived from swelling experiments.
Introduction Oil-in-water (o/w) emulsions consist of a thermodynamically unstable dispersion of micrometer-sized oil drops in water coated by a monolayer of adsorbed surfactant. One of the instability mechanisms of emulsions is Ostwald ripening (OR), which is the process whereby the higher Laplace pressure inside small emulsion drops drives the transfer of dispersed oil from small to large drops. The speed of OR depends primarily on the solubility of the dispersed oil in the aqueous continuous phase.1-13 Oils that are slightly water soluble (termed “mobile” oils here) can transfer between droplets at significant rates and thus show OR. OR is negligibly slow for oils of sufficiently low aqueous phase solubility and these oils are termed “immobile”. As shown by Higuchi and Misra,14 OR can be prevented by the addition of a small quantity of an immobile oil to drops of a mobile oil when drop composition differences oppose OR. Mass transfer between drops in emulsion mixtures can be driven * To whom correspondence should be addressed. (1) Lifshitz, I. M.; Slezov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (Original article published in Zh. Exp. Teor. Fiz. 1958, 35, 479.). (2) Wagner, C. Z. Electrochem. 1961, 35, 581. (3) Voorhees, P. W. J. Stat. Phys. 1985, 38, 231. (4) Kabalnov, A. S.; Aprosin, Yu. D.; Pavlova-Verevkina, O. B.; Pertzov, A. V. Shchukin, E. D. Colloid J. USSR 1986, 48, 20. (5) Enomoto, Y.; Tokuyama, M.; Kawasaki, K. Acta Metall. 1986, 34, 2119. (6) Kabalnov, A. S.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1987, 118, 590. (7) Kabalnov, A. S.; Makarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (8) Kabalnov, A. S.; Makarov, K. N.; Shchukin, E. D. Colloids Surf. 1992, 62, 101. (9) Kabalnov, A. S. Langmuir 1994, 10, 680. (10) Taylor, P.; Ottewill, R. H. Colloids Surf. A 1994, 88, 303. (11) Taylor, P.; Ottewill, R. H. Prog. Colloid Polym. Sci. 1994, 97, 199. (12) Taylor, P. Colloids Surf. A 1995, 99, 175. (13) Soma, J.; Papadopoulos, K. D. J. Colloid Interface Sci. 1996, 181, 225. (14) Higuchi, W. I.; Misra, J. J. Pharm. Sci. 1962, 51, 459.
Figure 1. Swelling of a “template” emulsion of immobile oil by the addition of a mobile oil. The initial “template” emulsion of immobile oil (1) is diluted with aqueous continuous phase, and a volume of mobile oil is added (2). Low-energy mixing produces an initial mixed emulsion of large drops of mobile oil plus the small drops of immobile oil (3). Virtually complete transfer of the mobile oil produces swollen drops of mixed oil (4). Under these conditions the final radius of the drops of mobile oil is vanishingly small and these are not shown.
by drop composition differences.15-23 A review of mass transport (and other phenomena) in emulsions can be found in ref 24. This paper concerns the kinetics of an emulsion drop swelling process, shown schematically in Figure 1, which consists of the following steps. We prepare an o/w (15) Hallworth, G. W.; Carless, J. E. J. Pharm. Pharmac. 1972, 24, Suppl. 71P. (16) Buscall, R.; Davis, S. S.; Potts, D. C. Colloid Polym. Sci. 1979, 257, 636. (17) Davis, S. S.; Round, H. P.; Purewal, T. S. J. Colloid Interface Sci. 1981, 80, 508. (18) Pertsov, A. V.; Kabalnov, A. S.; Shchukin, E. D. Kolloidn. Zh. 1984, 46, 1172. (19) Kabalnov, A. S.; Pertzov, A. V.; Aprosin, Yu. D.; Shchukin, E. D. Colloid J. USSR 1985, 47, 898. (20) Kabalnov, A. S.; Shchukin, E. D.; Pertsov, A. V. Colloids Surf. 1987, 24, 19. (21) Kabalnov, A. S.; Shchukin, E. D. Adv. Colloid Interface Sci. 1992, 38, 69. (22) Weers, J. G.; Arlauskas, R. A. Langmuir 1995, 11, 474. (23) Taisne, L.; Walstra, P.; Cabane, B. J. Colloid Interface Sci. 1996, 184, 378.
S0743-7463(98)00522-8 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/27/1998
Kinetics of Swelling of Oil-in-Water Emulsions
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emulsion containing small droplets of a pure immobile oil component. A second, mobile (i.e., slightly water soluble) oil (chosen to be completely miscible with the immobile oil) is added with simple stirring together with an additional volume of the aqueous continuous phase. In favorable cases, the second, mobile oil is transferred entirely into the original drops of immobile oil with no change in the number of drops. The driving force for the process arises from the tendency of the two oil components to mix together in the drops. The final drop radius may be precisely controlled by changing the volume ratio of immobile and mobile oils. For an emulsion containing a volume of immobile oil Vimm to which a volume of mobile oil Vmob is added, the final mean drop radius (rf) is related to the initial value (ri) according to
() rf ri
3
)
Vimm + Vmob Vimm
(1)
This type of process using mainly polymer latex particles as the immobile, swellable particles was first described by Ugelstad et al.25-28 The related process of transfer of a mobile oil to emulsion drops of an immobile oil has been described qualitatively.29-31 The swelling of “template” emulsions of an immobile oil to provide a low-energy route for the formation of emulsions of precisely controlled mean size has been developed recently for applications in the formulation of emulsion products.32 We note here that although the mean size can be precisely controlled by variation of the volume of mobile added (eq 1), the process does not allow control of droplet polydispersity or the shape of the drop size distribution functions. In this paper we describe a theoretical model for the kinetics of the emulsion swelling process. The model is tested against a systematic series of experimental swelling rate measurements for emulsions stabilized by a nonionic surfactant. Conclusions concerning the oil transfer mechanism in this system and its relation to the process of Ostwald ripening are discussed. Theory To model the equilibrium and kinetic features of the emulsion swelling process, we consider a system containing low volume fractions of two types of emulsion drop, one originating from the “template” emulsion of immobile oil (type 1) and one from the drops of mobile oil (type 2). For most of the experiments described here, type 1 drops of initially pure immobile oil are mixed with type 2 drops of pure mobile oil. During the swelling process, the mole fraction of mobile oil in the type 1 drops increases and the radius of the type 2 drops decreases. In addition, we also describe experiments in which both type of drops initially contain different mole fractions of both oils. Both droplet populations are assumed initially to be monodisperse, (24) Binks, B. P. R. Soc. Chem. Annu. Rep., Section C 1996, 92, 97. (25) Ugelstad, J. Makromol. Chem. 1978, 179, 815. (26) Ugelstad, J.; Herder Kaggurud, K.; Hansen, F. K.; Berge, A. Makromol. Chem. 1979, 180, 737. (27) Ugelstad, J.; Mork, P. C.; Herder Kaggurud, K.; Ellingsen, T.; Berge, A. Adv. Colloid Interface Sci. 1980, 13, 101. (28) Ugelstad, J.; Mork, P. C.; Berge, A.; Ellingsen, T.; Khan, A. A. In Emulsion Polymerisation, Piirma, I., Ed.; Academic Press: New York, 1982; p 383. (29) Pertsov, A. V.; Kabalnov, A. S.; Kumacheva, E. E.; Amelina, E. A. Kolloid Zh. (Engl. Transl.) 1988, 50, 543. (30) Kumacheva, E. E.; Amelina, E. A.; Pertsov, A. V.; Shchukin, E. D. Kolloid Zh. (Engl. Transl.) 1989, 51, 1059. (31) Kumacheva, E. E.; Amelina, E. A.; Parfenova, A. M. Kolloid Zh. (Engl. Transl.) 1990, 52, 318. (32) Lubetkin, S. D.; Mulqueen, P. J.; Banks, G.; Fowles, A. U.K. Patent Appl. 1995, 9319129.4.
nonflocculating, and noncoalescing. Type 1 drops have radius r1 and contain a mole fraction of mobile oil (with respect to the total oil content of the drop) of X1. The parameters for type 2 drops are indicated by subscript 2. Equilibrium Considerations. We first consider the (pseudo)equilibrium state for two drops, one of type 1 and one of type 2. The chemical potential, µ, of the mobile oil in a drop is a function of both the mole fraction, X, and drop radius, r according to
µ(X,r) ) µo + RT ln X +
2γVm r
(2)
where γ is the oil-water tension and Vm is the molar volume of the mobile oil. µ° is the standard chemical potential and corresponds to pure mobile oil in bulk, i.e., X ) 1 and r ) ∞. Equation 2 assumes that the mixtures of immobile and mobile oil behave ideally for all X. Activity coefficient corrections could be incorporated but are neglected here as the mixtures of mobile and immobile oils used here (decane and squalane) show only minor deviations from ideal behavior.33 For two drops 1 and 2, radii r1 and r2 and mobile oil fraction X1 and X2 respectively, equilibrium is reached when the chemical potential of the mobile oil is equal in the two drops.
RT ln X1 +
2γVm 2γVm ) RT ln X2 + r1 r2
(3)
Equation 3 gives the ratio of radii and X values required for transfer of oil between the drops to cease. This occurs when the Laplace pressure driving force (driving transfer from small to big drops) is balanced by the driving force arising from the oil composition difference between the drops. Note that eq 3 is valid only for situations in which r1 and r2 remain greater than zero as the equilibrium situation is approached. It becomes invalid in the case, for example, when complete adsorption of the mobile oil occurs, causing r2 to approach zero. At complete adsorption of the mobile oil, it is expected that the radius of type 2 emulsion drops eventually shrinks to give thermodynamically stable micelles or microemulsion droplets. The real mixed emulsion system contains number concentrations N1 and N2 of the two drop types. Since it is assumed that no drop coalescence occurs, N1 and N2 do not change with time or the extent of mobile oil transfer (except when complete transfer of the mobile occurs, in which case N2 drops discontinuously to zero). The ratio of volume fractions of the two drop types (φ1 and φ2) is
()
φ 2 N 2 r2 ) φ 1 N 1 r1
3
(4)
Combining eqs 3 and 4 gives the condition for oil transfer equilibrium when complete transfer of the mobile oil does not occur.
{
() }
X2 φ2 N2 r2RT ) ln +1 φ1 N1 2γVm X1
3
(5)
For the process illustrated in Figure 1, the small “template” emulsion drops generally consist initially of pure immobile oil, i.e., X1 ) 0, to which pure mobile drops (X2 ) 1) are (33) Activity coefficients for decane in squalane vary from approximately 0.8 at low mole fraction of decane to unity for pure decane. These values were estimated by extrapolation from data given in Ashworth, A. J.; Everett, D. H. Faraday Soc. Trans. 1960, 56, 1609.
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added. Under these conditions, complete transfer of the mobile oil is expected to occur. In practice, it has been observed experimentally that the volume of mobile oil absorbed by the template emulsion can easily exceed several hundred times the volume of the immobile oil.32 We note here that, if all the added mobile oil is not absorbed, then the final emulsion radius of the swollen template drops is less than that predicted by eq 1. An important conclusion from eq 5 is that the chemical potential difference due to the concentration gradient is commonly much larger than that due to the Laplace pressure difference. For the purpose of this discussion, we have taken γ to be independent of the composition of the mixed oil within the two drop types. This is generally not the case, and more complex equations incorporating the variation of γ with X may be derived. However, this modification does not substantially affect the conclusions reached here. Swelling Rates in Mixed Emulsions. The model assumes the swelling proceeds by a diffusion-controlled transport of the mobile oil through the continuous phase with no energy barriers to the entrance or exit of the mobile oil to or from the emulsion drops. The derivation follows the work of Higuchi and Misra14 and Ugelstad et al.25-28 The rate of transport of the mobile oil from the surface of a sphere of radius r is
dV ) 4πDr(Cs - Co) dt
(6)
where D is the diffusion coefficient of the mobile oil, Cs is the concentration of the mobile oil at the drop surface, and Co is the concentration a long distance from the surface. The surface concentration Cs is equal to the solubility C∞ (for an infinite sized drop containing pure oil) multiplied by an exponential term to account for the different chemical potential of the oil in the drop under consideration.
Cs ) C∞ exp
∆µ (RT )
(7)
where ∆µ is the free energy of transfer of the mobile oil from the bulk pure mobile oil (the standard state) to the drop at mole fraction activity X and radius r.
∆µ ) µ(X,r) - µ0 ) RT ln X +
2γVm r
(8)
We consider the transport of the mobile oil from type 2 emulsion (with drops of radius r2, number concentration N2, and mobile oil fraction X2) to a template emulsion (type 1 with r1, N1, and X1). Let V1 and V2 be the volume fractions of mobile oil in type 1 and type 2 drops, respectively. At steady state, mass balance requires
dV1 dV2 + )0 dt dt
(9)
Denoting A1 ) N1r1, A2 ) N2r2, M1 ) exp(∆µ1/RT), and M2 ) exp(∆µ2/RT), the rate balance for a mixed emulsion containing N1 and N2 number concentrations of type 1 and type 2 drops is
A1[C∞M1 - Co] ) -A2[C∞M2 - Co]
(10)
Rearranging eq 10, we obtain the steady-state value of Co as
Co )
A1C∞M1 + A2C∞M2 A2 + A 1
(11)
Combining eqs 11 and 6 and changing the sign so that a flux of mobile oil to type 1 drops is denoted as positive yield the final differential rate equation
[ ( )
( )]
∆µ2 ∆µ1 dV1 4πDA1A2C∞ exp - exp ) dt A2 + A 1 RT RT
(12)
The rate equation can be expressed in terms of the drop radii by noting the following relationships.
4 dV1 ) πN1 dr13 3
and
dr13 ) 3r13 dr1
and
dV1 ) -dV2 (13)
[ ( )
( )]
DN2r2C∞ ∆µ2 ∆µ1 dr1 ) exp - exp dt RT RT r1(N1r1 + N2r2)
(14)
Equation 14 for dr1/dt is numerically integrated and combined with various mass balance relationships (i.e., using the fact that N1, N2 and the total volumes of mobile and immobile oils are constant) to obtain the time evolution of all the parameters of the mixed swelling emulsion (i.e., r1, r2, X1, X2, φ1, and φ2). The calculations were made using a VISUAL BASIC program within EXCEL. The input parameters are the initial compositions and drop sizes for the mixed emulsion together with measured values for the tension, temperature, and molar volumes of the mobile and immobile oils. Again, the tension is assumed independent of X. This approximation, which greatly simplifies the analysis, is valid since the sensitivity of the chemical potential of the mobile oil with respect to γ is very much smaller than the effect of X (as noted previously). The model contains only a single unknown fitting parameter equal to the product C∞D. In this paper we describe a test of this model against a systematic series of experimental data in which the initial values of r1, r2, φ1, φ2, X1, and X2 were varied for mixed emulsions containing squalane as the immobile oil, decane as the mobile oil, and n-dodecyl octaoxyethylene glycol ether (C12E8) as the stabilizing surfactant. If the model works correctly, a single value of the (unknown) parameter C∞D should correctly account for the rate variation with the initial parameters of the mixed emulsions. As will be discussed later, the same value of C∞D should also account for the rate of OR in emulsions of pure mobile oil. Experimental Section Water was purified by reverse osmosis and further treated by passage through a Milli-Q reagent water system. The oils squalane (Aldrich, 99%) and n-decane (Aldrich, 99%) and the nonionic surfactant C12E8 (a chromatographically pure sample from Nikkol) were used without further treatment. Squalane-in-water (type 1) emulsions were prepared by initially blending squalane into a concentrated aqueous surfactant solution followed by high shear mixing with an Ultra Turrax homogenizer (Janke & Kunkel, T25 head) operating at 24 000 rpm. Emulsification was continued until the desired drop size was achieved (typically 3-4 min). The composition of the type 1 emulsion was 15 wt % C12E8, 40 wt % squalane, and 45 wt % water. Decane-in-water (type 2) emulsions were made similarly except that the homogenization was done using a low shear Silverson mixer (model L4R) operating at its lowest mixing speed.
Kinetics of Swelling of Oil-in-Water Emulsions
Figure 2. Emulsion diameter volume weighted distribution plots (right-hand ordinates) for the stock type 1 (squalane) and 2 (decane) emulsions before mixing. The solid curves shows the cumulative volume distributions (left-hand ordinates). One minute of homogenization was generally sufficient to produce the desired drop size. The composition of the type 2 emulsion was 1 wt % C12E8, 40 wt % decane, and 59 wt % water. Mixed emulsion samples of the desired compositions were made by mixing the required volumes of the stock emulsions of types 1 and 2 together with volumes of water and aqueous surfactant solution. For all swelling and OR experiments, the emulsion samples were held in an orbital shaker operating at a few rpm to prevent creaming of the emulsions during the experiment. The size distributions of the emulsion samples were obtained using a Malvern Mastersizer MS20 instrument, which allowed resolution of drop diameters in the range 0.1-100 µm. For the sizing experiments, a few drops of the emulsion were diluted (with stirring and low power ultrasonic dispersion) into a large volume of water. It was checked that dilution into either pure water or an aqueous solution containing C12E8 at a concentration equal to the critical micelle concentration gave identical results. Each size distribution measurement took less than 1 min. For the analysis of the Mastersizer data, the “model independent” analysis mode was used in which no assumptions concerning the nature of the drop size distribution are made. The extent of oil solubilization in the aqueous surfactant solutions was measured by titration of oil into a surfactant solution. The solubilization limit was detected visually from the onset of a permanent turbidity of the dispersion. All measurements were made at ambient temperature of 20 ( 2 °C.
Results and Discussion Figure 2 shows the (volume weighted) drop diameter distributions for typical type 1 and 2 emulsions before mixing. The squalane emulsions (type 1) showed no change in the size distribution over a period of weeks, indicating the absence of coalescence and OR. The type 2 decane emulsions showed slow growth over a period of 10-20 days, which was ascribed to OR (see later). The type 2 emulsions showed no separation of free oil over a period of weeks, and it was assumed that drop coalescence
Langmuir, Vol. 14, No. 19, 1998 5405
does not occur. The initial drop size distributions of Figure 2 are single peaked but show a significant degree of polydispersity. This point is important when comparing the kinetic data with the theoretical model in which the initial drop distributions were assumed to be monodisperse. An example of the evolution of a mixed emulsion system with time after mixing is shown in Figure 3. The solid curve in each figure shows the cumulative volume fraction of the different drop sizes. With increasing time, r1 increases and r2 decreases. The radii r1 and r2 were taken to be equal to the volume weighted mean values from the measured bimodal distributions. The volume fraction of total oil in the type 1 drops (φ1) increases, whereas that for the type 2 (φ2) decreases. Although there is a degree of overlap in the distributions of types 1 and 2 drops, the cumulative volume distribution curves show an intermediate plateau region that allows the individual values of φ1 and φ2 to be obtained with reasonable precision. The time evolution of the volume fraction ratio φ1/(φ1 + φ2) and the radii r1 and r2 are plotted in Figure 4. The solid curves are calculated using the model described earlier with a value of C∞D equal to 4 × 10-14 m2 s-1 (note here that C∞ is expressed as a volume fraction and is thus unitless). The value of the tension used was that for the decanewater interface with C12E8 (1.1 mN m-1) and was obtained by interpolation of measured values for a range of CnEm surfactants with different alkanes from ref 34. To test the approximation that γ is independent of X, the simulation was run with different γ values. Using γ values from 0.5 to 5 mN m-1 made no significant difference to the calculated rates, in agreement with the conclusion noted earlier that the ∆µ values in eq 14 are dominated by the terms in X. There is a significant difference between the experimental data and the theoretical curves, which is ascribed mainly to the finite polydispersity of the emulsion samples. Of the three parameters for which the time dependence was obtained (the volume fraction ratio φ1/ (φ1 + φ2), r1 and r2), the volume fraction ratio was obtained with the best precision and r2 with the worst. For this reason, the “best fit” value of C∞D was chosen so that the time taken to reach a value of φ1/(φ1 + φ2) halfway between the initial and final values is coincident for the theoretical and experimental plots. This time is denoted as t1/2. As will be seen later, t1/2 increases with increasing r2, i.e., small type 2 drops cause faster swelling than large type 2 drops. Because of this, the finite polydispersity of the type 2 drops is expected to cause the experimental rate to be faster than predicted at short times (when the small type 2 drops are consumed) and slower than predicted at long times (when only the larger type 2 drops remain). This effect is seen in Figure 4. The polydispersity (together with the volume weighting of the drop size distributions) is the probable reason the experimental values of r2 are larger than theoretically predicted. The finite polydispersity of the emulsion samples imposes a limit to the accuracy with which C∞D can be estimated from the swelling experiments. This accuracy is of the order of (50%. The variation of t1/2 with the initial values of r1, r2, X1, X2, φ1, and φ2 are shown in Figures 5-10. For each plot, all remaining initial parameters were kept constant at the values given in the figure legends. The solid lines in each case correspond to the calculated variation using a single value of C∞D of 3 × 10-14 m2 s-1, obtained by a global fit to the entire data set. This best, global fit value of C∞D is slightly different from the value (C∞D ) 4 × 10-14 m2 s-1) obtained from the fit to the single data set of Figure 4. The variation in values of C∞D for the
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Figure 3. Emulsion diameter volume weighted distribution plots (right-hand ordinates) for a mixed emulsion system at different times after mixing. The initial conditions were r1 ) 0.39 µm, r2 ) 8.6 µm, φ1 ) 0.01, φ2 ) 0.07, X1 ) 0, and X2 ) 1, and the C12E8 concentration was 2.5 wt %. The solid curves show the cumulative volume distributions (left-hand ordinates). The plot labeled t ) ∞ corresponds to complete absorption of the mobile oil and was recorded after 24 h.
individual data sets gave a standard deviation in C∞D of (1.6 × 10-14 m2 s-1 around the mean value. The measured values of t1/2 increase slightly for both r1 and r2 (Figures 5 and 6), whereas the theory for monodisperse emulsions predicts the value to be independent of r1 and an increase with r2. Adding mobile oil to the template emulsion (i.e., increasing X1) has little effect on t1/2 until X1 is greater than approximately 0.8 (Figure 7). At higher X1 values, the rate drops to zero (t1/2 approaches infinity) corresponding to the system approaching an equilibrium position, as predicted by eq 5. Adding squalane to the type 2 drops (i.e., decreasing X2 from 1, Figure 8) again causes an equilibrium position corresponding to less than complete swelling to be reached. Under these conditions, the difference between the initial and final values of φ1/ (φ1 + φ2) is small and therefore difficult to determine with reasonable precision. For this reason we have chosen to plot the time taken for φ1/(φ1 + φ2) to reach 90% of its final value (t0.9). Adding squalane to the type 2 drops decreases the time required for 90% swelling even though the driving force for swelling is decreased. This is because the amount of decane to be transferred to achieve 90% of the final equilibrium value is decreasing with squalane addition. The variation of both t0.9 and the measured final, equi-
librium values of r1 with X2 (shown in Figure 8) are in reasonable agreement with theory. It can be seen that the addition of a relatively small amount of immobile oil to the type 2 drops is sufficient to prevent complete swelling. The effects of varying the initial volume fractions of the types 1 and 2 drops are shown in Figures 9 and 10. Increasing φ1 increases the rate, whereas increasing φ2 slows the rate since, in this case, a larger volume of decane must be absorbed into the template emulsion drops. Viewing the entire data set together with the theoretical plots, it can be seen that a single value of C∞D of 3 × 10-14 m2 s-1 accounts reasonably well for the variation in t1/2 values for all the different initial drop sizes and compositions of the mixed emulsions. We now attempt to interpret the value of C∞D obtained as described above in terms of possible mechanisms for the transfer of decane between emulsion drops. The model for the swelling process assumes that oil transport occurs between isolated droplets and is a diffusion-controlled process with no energy barriers to transport across the oil-water interfaces of the droplets. If these conditions are not fulfilled then the value of C∞D obtained in the swelling experiments must be regarded as an apparent or effective value. Before discussing possible oil transfer
Kinetics of Swelling of Oil-in-Water Emulsions
Langmuir, Vol. 14, No. 19, 1998 5407
Figure 6. Variation of t1/2 with initial value of r2. The fixed initial emulsion parameters were r1 ) 0.39 µm, φ1 ) 0.01, φ2 ) 0.07, X1 ) 0, X2 ) 1, and C12E8 concentration ) 2.5 wt %. The solid line is calculated with C∞D equal to 3 × 10-14 m2 s-1.
Figure 4. Plots of φ1/(φ1 + φ2) (upper plot), r1 (middle plot), and r2 (lower plot) versus time after mixing. The initial conditions were the same as for Figure 3. The solid lines show the calculated variation using a value of the product C∞D equal to 4 × 10-14 m2 s-1.
Figure 5. Variation of t1/2 with the initial value of r1. The fixed initial emulsion parameters were r2 ) 8.6 µm, φ1 ) 0.01, φ2 ) 0.07, X1 ) 0, X2 ) 1, and C12E8 concentration ) 2.5 wt %. The solid line is calculated with C∞D equal to 3 × 10-14 m2 s-1.
mechanisms, it is relevant to note the following features of the emulsion system used in this study. Results have been presented in Figures 5-10 for systems containing a total concentration of C12E8 in the overall mixed emulsions of 2.5 wt %. The total quantity
Figure 7. Variation of t1/2 with the initial value of X1. The fixed initial emulsion parameters were r1 ) 0.44 µm, r2 ) 8.7 µm, φ1 ) 0.01, φ2 ) 0.07, X2 ) 1, and C12E8 concentration ) 2.5 wt %. The solid line is calculated with C∞D equal to 3 × 10-14 m2 s-1.
of C12E8 in the emulsion is present as monomer in the water, monomer in the oil, adsorbed monolayers coating the emulsion drops, and micellar or microemulsion aggregates in the aqueous continuous phase. For the decane/ water/C12E8 system, the phase inversion temperature is estimated (using an empirical equation given in ref 35 to be approximately 70 °C. Hence, at the experimental temperature used here (20 °C), surfactant aggregates of C12E8 are expected to be located exclusively in the aqueous phase. For an emulsion system with r1 ) 2 µm, r2 ) 2 µm, φ1 ) 0.01, and φ2 ) 0.07, surfactant monomer is present in the aqueous and oil phases at concentrations equal to the critical aggregation concentrations in water and decane (approximately 1 × 10-4 M in water36 and 1 × 10-3 M in decane37). Thus, the monomer concentrations account for approximately 0.01 wt % of the total surfactant present in the emulsions. Using a value of the area occupied per (34) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; MacNab, J. R. Langmuir, 1995, 11, 2515. (35) Ravey, J. C.; Stebe, M. J. Colloids Surf. A, 1994, 84, 11. (36) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, 1993. (37) Shinoda, K.; Fukuda, M.; Carlsson, A. Langmuir 1990, 6, 334.
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Figure 10. Variation of t1/2 with the initial value of φ2. The fixed initial emulsion parameters were r1 ) 0.39 µm, r2 ) 8.7 µm, φ1 ) 0.01, X1 ) 0, X2 ) 1, and C12E8 concentration ) 2.5 wt %. The solid line is calculated with C∞D equal to 3 × 10-14 m2 s-1.
Figure 8. Variation of t0.9 with the initial value of X2 (upper plot). The fixed initial emulsion parameters were r1 ) 0.39 µm, r2 ) 10.5 µm, φ1 ) 0.01, φ2 ) 0.07, X1 ) 0, and C12E8 concentration ) 2.5 wt %. The lower plot shows the final equilibrium values of r1 versus X2. The solid lines are calculated with C∞D equal to 3 × 10-14 m2 s-1.
Figure 9. Variation of t1/2 with the initial value of φ1. The fixed initial emulsion parameters were r1 ) 0.39 µm, r2 ) 8.6 µm, φ2 ) 0.07, X1 ) 0, X2 ) 1, and C12E8 concentration ) 2.5 wt %. The solid line is calculated with C∞D equal to 3 × 10-14 m2 s-1.
C12E8 at the oil-water surface of 0.5 nm2, the concentration present as adsorbed monolayers coating the droplets is estimated to be approximately 0.02 wt %. Thus, for the surfactant concentrations used in this work, the major fraction of the total C12E8 is present as surfactant
Figure 11. Maximum extent of solubilization of decane in aqueous solutions of C12E8 as a function of surfactant concentration.
aggregates in the aqueous continuous phase which have the possibility of solubilizing decane and hence act as “carriers” for the oil transport. Experimental results for the maximum solubilization of decane in aqueous solutions of C12E8 are shown in Figure 11. The extent of solubilization is proportional to the surfactant concentration with 0.06 mol of decane solubilized per mole of aggregated surfactant. The solubilization of squalane by C12E8 is negligible. The theoretical model used for the swelling process assumes that oil transfer occurs between isolated droplets. Two possible processes may invalidate this assumption. First, creaming of the less dense oil drops produces a close packed drop system. As described in the Experimental Section, this process was prevented in the swelling experiments by continuous agitation of the emulsions using an orbital shaker. Second, for the uncharged oil drops used here, van der Waals’ forces may act to flocculate the drops. Additionally, the presence of high concentrations of nanometer-sized surfactant aggregates in the continuous phase may promote flocculation by an attractive, depletion interaction between the emulsion drops.38,39 Microscopic observation of the emulsions used here showed (38) Aronson, M. P. Langmuir 1989, 5, 494.
Kinetics of Swelling of Oil-in-Water Emulsions
the presence of weakly bound floccs which could be redispersed by gentle shaking. Emulsion drop flocculation complicates the interpretation of the apparent value of C∞D since the close proximity of emulsion drops in floccs might be expected to increase the oil transfer rate. With this background in mind, we discuss possible mechanisms for the oil transfer together with estimates of the values of C∞D expected in the different cases. (a) Oil Transport between Isolated Drops by Molecular Diffusion with No Energy Barriers. In this case, the value of C∞D should equal the product of C∞ and D for molecular decane in water. The aqueous solubility of decane in water expressed as a volume fraction is 7 × 10-8 40 and the diffusion coefficient of decane in water (estimated using the Hayduk-Laudie equation41) is 6 × 10-10 m2 s-1. Therefore, the parameter C∞D for molecular transport of decane is 4 × 10-17 m2 s-1, much smaller than the measured apparent value obtained from emulsion swelling experiments (C∞D ) 3 × 10-14 m2 s-1 for systems containing 2.5 wt % C12E8). We conclude that molecular transport of decane is not the dominant oil transport mechanism in the present systems. (b) Oil Transport between Isolated Drops by Molecular Diffusion with Finite Energy Barriers. If there is an activation energy barrier to the process of a decane molecule crossing the surfactant monolayer covered drop interfaces, the emulsion swelling rate should be slower than predicted by the model with a value of C∞D ) 4 × 10-17 m2 s-1. Since the measured rate is faster, invoking an energy barrier to molecular transport does not give a reasonable explanation of the results. (c) Oil Transport between Isolated Drops by Micellar “Carriers” with No Energy Barrier. In this mechanism, the micelles present in the continuous phase are postulated to act as carriers of the oil between emulsion droplets. It is assumed there is no energy barrier to the process of a micelle fusing with the surface of an emulsion drop and “budding off” to then diffuse to and fuse with another drop. In this case, C∞ should be equal to the oil solubility in the aqueous micellar solution and D should be the diffusion coefficient of an oil swollen micelle. As shown in Figure 11, 1 mol of micellized C12E8 solubilizes 0.06 mol of decane. For an emulsion containing 2.5 wt % C12E8, this gives a value of 5.5 × 10-4 for C∞. The value of D for swollen micelles containing 0.062 mol of decane/ C12E8 was taken to be the same as that measured for C12E7 micelles containing the same molar ratio of decane42 (D ) 7.0 × 10-11 m2 s-1). Therefore C∞D for unhindered micellar transport is approximately 4 × 10-14 m2 s-1 for 2.5 wt % C12E8. Hence, the measured swelling rate is consistent with the mechanism of micellar transport. Since the decane solubility in the continuous phase of the emulsions rises linearly with increasing C12E8 concentration (Figure 11), the apparent value of C∞D determined from emulsion swelling experiments should increase linearly with surfactant concentration. To test this, we determined C∞D for a series of emulsions with C12E8 concentrations ranging from 0.44 to 15 wt %. The results are compared with theoretical values for unhindered micellar transport in Figure 12. The measured values of C∞D rise approximately linearly (with the magnitude correctly predicted by the theoretical line) at low C12E8 concentrations but fall below the predicted values at higher (39) Aronson, M. P. in Emulsions. A Fundamental and Practical Approach, Sjoblom, J., Ed.; Kluwer Academic Publishers: Amsterdam, 1992; p 75. (40) McAuliffe, C. Science 1969, 163, 478. (41) Hayduk, W.; Laudie, H. AIChE J. 1974, 20, 611. (42) Morris, J. S. Ph.D. Thesis, University of Hull, 1995.
Langmuir, Vol. 14, No. 19, 1998 5409
Figure 12. Derived values of C∞D as a function of the aqueous phase concentration of C12E8. Open circles refer to OR experiments and filled circles refer to emulsion swelling experiments. The solid line shows the values predicted for the micellar transport mechanism assuming a constant value of D. The dashed line is calculated assuming that D varies with surfactant concentration according to eq 15.
concentrations. A plausible explanation for the deviation may be that the micellar diffusion through the aqueous continuous phase becomes increasingly hindered at the higher surfactant concentrations. For hard sphere particles, the long time self-diffusion coefficient (D) varies with particle volume fraction (φmicelles in this context) according to43
D ) D0(1-2.1φmicelles)
(15)
where Do is the particle diffusion coefficient in water containing no micelles. As shown in ref 44, the selfdiffusion coefficient of oil swollen micelles of C12E5 decreases with increasing φmicelles in reasonable agreement with eq 15. The dashed line in Figure 12 shows that incorporating the variation of D with increasing surfactant concentration (eq 15) gives a reasonable description of the experimental data. (d) Oil Transport between Isolated Drops by Micellar “Carriers” with Finite Energy Barrier. If the process of micelle fusion/separation with the emulsion drop surfaces has a finite energy barrier, then the rate is expected to be slower than for mechanism (c) above. Hence, the presence of an energy barrier would give a rate slower than that observed experimentally. In the context of this discussion, it is relevant to note that OR rates of o/w emulsions increase only slightly with the addition of micelles of the anionic surfactant sodium dodecyl sulfate SDS.7,12,13 Unlike C12E8 micelles, aggregates of SDS appear to be ineffective in increasing oil transport, possibly due to the presence of an energy barrier for the fusion/fission process of the SDS micelles with the emulsion drop surfaces. Oil exchange rates between emulsion droplets stabilized by the nonionic surfactant polyoxyethylene sorbitan monolaurate increase linearly with the concentration of added surfactant, indicating these micelles are effective in promoting oil transfer.45 These comparisons suggest that electrostatic repulsion may play a role in determining the magnitude of the energy (43) See, for example: Russel, W. B.; Saville, D. A.; Schowalter, W. L. In Colloidal Dispersions; Cambridge University Press: Cambridge, U.K., 1989; p 448. (44) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389. (45) McClements, D. J.; Dungan, S. R. J. Phys. Chem. 1993, 97, 7304.
5410 Langmuir, Vol. 14, No. 19, 1998
Binks et al.
barrier to micelle-mediated oil transfer. The rates of solubilization of oil emulsion drops into added micelles have been investigated.46 However, no clear conclusions concerning the solubilization mechanism could be drawn owing to complications in the interpretation of the results arising from the fact that solubilization and OR occurred concurrently. Studies of the rates of fusion/fission of w/o microemulsion drops with either planar oil-water interfaces47,48 or microemulsion drops49,50 have shown that the barriers to these processes may be high but depend on the nature of the surfactant. For the case of fusion/fission of w/o microemulsion drops stabilized by nonionic surfactants, the magnitudes of the energy barriers have been correlated with the monolayer bending elastic constants.50 With this background in mind, we are currently extending the present emulsion drop swelling study to include a range of surfactants of different structures and charge types. (e) Oil Transport across Thin Emulsion Films between Flocculated Drops. So far, we have assumed mechanisms whereby oil is transported between separated drops. In fact, the emulsion system investigated here appears to show weak flocculation where the drops adhere in clusters with thin emulsion films separating them. It seems reasonable to suppose that oil transport within a flocculated emulsion may well be faster than for separated drops resulting in high values of the measured C∞D. At present, it is rather difficult to judge whether flocculation of the drops is a significant factor in the emulsion swelling rates obtained here. The close agreement between the measured C∞D and that calculated for the micellar transport mechanism suggests that it is not necessary to invoke effects associated with flocculation to explain the data. However, the agreement may be fortuitous. For example, it would be possible, in principle, for the micellar transport to be slowed by an energy barrier to interfacial fusion/fission with this slowing effect offset by flocculation effects. We note here that flocculation induced by micelle addition has been observed previously to increase the rate of OR.51,52 In this final section we compare emulsion swelling rates with those for OR in emulsions containing only the mobile oil (decane). The rate of OR for a low volume fraction of isolated emulsion drops is:1-3
drj3 8γC∞DVmf(φ) ) dt 9RT
(16)
where rj is the mean drop radius and f(φ) is a function of volume fraction which approaches unity for low φ. A value of unity was assumed here. Equation 16 predicts that the effective value of C∞D may be obtained from a linear plot of rj3 versus time. Figure 13 shows an illustrative plot of decane-in-water emulsions containing 2.5 wt % C12E8. It can be seen that the initial region is approximately linear but that the drop sizes eventually reach a plateau value or even decrease at longer times. The (46) Weiss, J.; Coupland, J. N.; McClements, D. J. J. Phys. Chem. 1996, 100, 1066. (47) Albery, W. J.; Choudhery, R. A.; Atay, N. Z.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2407. (48) Nitsch, W.; Plucinski, P.; Ehrlenspiel, J. J. Phys. Chem. B 1997, 101, 4024. (49) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1987, 83, 185. (50) Fletcher, P. D. I.; Horsup, D. I. J. Chem. Soc., Faraday Trans. 1992, 88, 855. (51) Kumacheva, E. E.; Amelina, E. A.; Popov, V. I. Kolloid Zh. (Engl. Transl.) 1989, 51, 1057. (52) Amelina, E. A.; Kumacheva, E. E.; Pertsov, A. V.; Shchukin, E. D. Kolloid Zh. (Engl. Transl.) 1990, 52, 185.
Figure 13. Ostwald ripening plot for decane-in-water emulsion with φ ) 0.01 and C12E8 concentration ) 2.5 wt %. The solid line shows the initial linear slope used to estimate C∞D.
origin of this effect is uncertain but may be due to comminution of larger drops associated with the orbital shaking used to prevent creaming. The initial slopes of the plots were used to obtain values of C∞D for different concentrations of C12E8, as shown in Figure 12. Although the OR results must be regarded as approximate, they are in reasonable agreement with the values obtained from swelling experiments. Conclusions 1. The model for the swelling kinetics (eq 14) provides a satisfactory explanation for the measured swelling rates for emulsions with different initial drop radii, volume fractions, and oil phase compositions. Deviations between theory and experiment are probably due to the finite polydispersity of the emulsions studied here. 2. The measured value of C∞D is consistent with a mechanism of oil transport in which micellar aggregates of C12E8 act as carriers for decane between emulsion drops. There appears to be no energy barrier for the micellemediated oil transfer process. Consistent with this mechanism, the swelling rates increase with increasing aqueous phase concentration of C12E8. 3. Ostwald ripening rates for the decane-in-water emulsions yield values of C∞D that are consistent with those derived from swelling experiments. Acknowledgment. We are grateful to Dow AgroSciences for financial support. We thank Mr. C. Collier of the University of Hull for making some of the OR measurements. List of Symbols C∞ Co Cs D Do f(φ) N1
solubility (given as a volume fraction) of the mobile oil in the continuous phase of the emulsion concentration of the mobile oil far from the drop surface concentration of the mobile oil at the drop surface diffusion coefficient of the mobile oil in the continuous phase diffusion coefficient in the limit of zero volume fraction function describing drop volume fraction dependence of the OR rate number concentration of type 1 droplets
Kinetics of Swelling of Oil-in-Water Emulsions N2 rj r R r1 r2 rf ri t T t1/2 V V1 V2 Vimm Vm
number concentration of type 2 droplets mean emulsion drop radius emulsion drop radius gas constant radius of type 1 droplets radius of type 2 droplets final drop radius after swelling initial drop radius before swelling time absolute temperature time for the volume fraction ratio φ1/(φ1 + φ2) to reach halfway between its initial and final value emulsion drop volume volume fraction of mobile oil present in type 1 emulsion drops volume fraction of mobile oil present in type 2 emulsion drops total volume of the immobile oil in the emulsion molar volume of the mobile oil
Langmuir, Vol. 14, No. 19, 1998 5411 Vmob X X1 X2 ∆µ φ1 φ2 φmicelle γ µ(X,r) µ°
total volume of the mobile oil in the emulsion mole fraction of mobile oil in the mixed oil drops mole fraction of mobile oil in type 1 droplets with respect to the total oil content of type 1 droplets mole fraction of mobile oil in type 2 droplets with respect to the total oil content of type 2 droplets free energy of transfer of the mobile oil from the pure bulk liquid to an emulsion drop volume fraction of type 1 droplets in the total emulsion volume fraction of type 2 droplets in the total emulsion volume fraction of micelles in the aqueous phase oil-water interfacial tension chemical potential of the mobile oil (function of X and r) standard chemical potential of the mobile oil for the pure bulk liquid LA980522G
