Langmuir 1996, 12, 6351-6353
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Microemulsions, Macroemulsions, and the Bancroft Rule Eli Ruckenstein Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260 Received August 30, 1996. In Final Form: October 11, 1996X In most cases, in both micro- and macroemulsions, the phase in which the surfactant is most soluble constitutes the continuous phase. There are, however, violations to this Bancroft rule, and the goal of the paper is to delineate the conditions of validity of the rule. For microemulsions two ratios are significant from this point of view. One of them, R1, compares the interactions in the bulk between surfactant and oil to those between surfactant and water; the other, R2, compares the interactions between the hydrocarbon chains of the surfactant in the interfacial layer and oil to those between the head groups of the surfactant molecules in the interfacial layer and water. Ratio R1 indicates the preferred phase, while ratio R2 indicates the preferred curvature. When both ratios are smaller or larger than unity, the Bancroft rule is obeyed. When one of them is smaller and the other larger than unity, the Bancroft rule is violated. The violations observed by Binks regarding the phase behavior of the ternary mixture C12E5 (a nonionic surfactant of the polyoxyethylene glycol ether type)/water/heptane can be thus explained. For macroemulsions, three regimes are identified. At low surfactant concentrations, the type of emulsion is controlled by the mixing process, at sufficiently high concentrations by the mass transfer (case in which the Bancroft rule is obeyed), and at even higher concentrations by hole nucleation in black films. The violations of the Bancroft rule noted by Binks are in the mixing controlled regime.
Even though microemulsions are thermodynamically stable and macroemulsions have only kinetic stability, it appears that, in most cases and for both kinds of emulsions, the phase which contains most of the surfactant becomes the continuous phase. In 1913 Bancroft1,2 formulated the rule that in an emulsion “a hydrophile colloid will tend to make water the dispersing phase while a hydrophobe colloid will tend to make water the dispersed phase”, which can be considered almost equivalent to the preceding formulation. Winsor3 found that in ternary surfactant, oil, and water phase diagrams there are three types of systems, I, II, and III, and that the preceding rule is valid at thermodynamic equilibrium as well. In Winsor’s type I systems, an oil in water (O/W) microemulsion coexists with excess oil and the surfactant is mostly present in the water phase, while in Winsor’s type II systems a water in oil (W/O) microemulsion coexists with excess water, and the surfactant is mostly present in the oil phase. In both types of systems, almost spherical globules are dispersed in the continuous phase. In type III systems, a microemulsion coexists with both excess phases, the surfactant is distributed between the two phases, and one can no longer identify dispersed and continuous phases. Thermodynamics4-6 can explain the phase behavior of microemulsions and can also provide an explanation for the change in the structure of the microemulsion at the transition between either I and III or II and III systems. There are, however, some violations of the above rule, for both macroemulsions and microemulsions. Smith and Lim7 investigated the morphologies and inversions of emulsions formed by pairs of conjugate liquids in the system C4H9OC2H4OH/n-C10H22/aqueous NaCl solution as a function of phase volume fraction. They observed that the emulsions obeyed the Ostwald8 stereometric hard sphere model and violated the Bancroft rule, since they X Abstract published in Advance ACS Abstracts, December 15, 1996.
(1) Bancroft, W. D. J. Phys. Chem. 1913, 17, 501. (2) Bancroft, W. D. J. Phys. Chem. 1915, 19, 275. (3) Winsor, P. A. Chem. Rev. 1968, 68, 1. (4) Ruckenstein, E. Chem. Phys. Lett. 1983, 98, 573. (5) Ruckenstein, E. Fluid Phase Equilibria 1985, 20, 189. (6) Ruckenstein, E. In Progress in Microemulsions; Martelluci, S., Chester, A. N., Eds.; Plenum Press: New York, 1989; p 3. (7) Smith, D. H.; Lim, K. H. J. Phys. Chem. 1990, 94, 3746.
S0743-7463(96)00849-9 CCC: $12.00
inverted when the volume fraction of the dispersed phase became about 0.6. It is clear that in those experiments, the mixing process, hence the hydrodynamics, plays the dominant role and that the surface active agent employed plays a secondary role. Ross and Kornbrekke,9 mixing two immiscible conjugate solutions of benzene-ethanolwater, noted that, for any given volume ratio of the two liquids, only a probability of obtaining one type of emulsion rather than the other can be determined. It is important to emphasize that in both cases relatively weak surface active agents were employed, and hydrodynamics was most likely responsible for the outcome. In contrast, Binks10 investigated a system containing a nonionic surfactant of the polyoxyethylene glycol ether type, namely C12E5, which is a stronger surface active agent than those employed in the preceding references. Heptane was the oil, and a 0.01 M aqueous NaCl solution was the water phase. Binks was interested both in the phase behavior and in the morphology of the macroemulsion obtained by mixing the microemulsion with the excess phase. Regarding the phase behavior, he observed, as expected, an O/W microemulsion in equilibrium with excess oil at low temperatures (T < 30 °C), a W/O microemulsion in equilibrium with excess water at high temperatures (T > 30 °C), and a middle phase microemulsion coexisting with both excess phases at intermediate temperatures (T = 30 °C). However, the Bancroft rule was violated at low temperatures, since the continuous phase was water and most of the surfactant present in the bulk phases was distributed in the oil phase. Regarding the macroemulsions, Binks noted that, for surfactant concentrations greater than the critical microemulsion concentration at which a microemulsion forms, the macroemulsion type is that of the corresponding microemulsion and that the Bancroft rule holds. However, for surfactant concentrations small compared to the critical microemulsion concentration, the emulsions formed were of the O/W type and the Bancroft rule was violated, since the higher concentration of surfactant was in the oil phase, hence in the dispersed and not the continuous phase. It (8) Ostwald, W. Kolloid Z. 1910, 6, 103; 1910, 7, 64. (9) Ross, S.; Kornbrekke, R. E. J. Colloid Interface Sci. 1981, 81, 58. (10) Binks, B. P. Langmuir 1993, 9, 25.
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is clear that the Bancroft rule does not have general validity, either in the case of microemulsions or in the case of emulsions. In the comments which follow we will try to delineate the conditions of validity of the above rule. A Two R Ratios Approach to Phase Behavior The most simple way to examine the phase behavior from a qualitative point of view is to employ Winsor’s R ratio, which compares the surfactant oil interactions to those between surfactant and water. We suggest here two such ratios, whose comparison can indicate when the Bancroft rule is valid. One of them is
R1 ) Aso/Asw where Aso is a measure of surfactant-oil interactions and Asw is a measure of the surfactant-water interactions for the surfactant molecules present in the bulk phases. It is obvious that if R1 < 1 the water phase is preferred by the surfactant and that if R1 > 1 the oil phase is the preferred one. The second ratio R2 determines the morphology of the dispersion and is obtained on the basis of an approximate expression for the free energy of formation of a microemulsion. The considerations which follow are similar to those made by Bancroft regarding macroemulsions (to which they cannot be applied for reasons discussed later in the paper) and by Winsor3 to microemulsions. The packing of the surfactant molecules at the surface of the globules is expected to affect in a major way the free energy of the system; consequently, the interfacial free energy Fint of the “surface” of the globule should play an important role. The globules being small (∼10 nm), the thickness of the surfactant layer cannot be neglected compared to the radius of the globules and the interfacial free energy of a globule can be considered given by the expression
Fint ) Ahwγhw + Acoγco where Ahw and Aco are the surface areas of the globule between the head groups of the surfactant and water, and between the hydrocarbon chains and oil, respectively, γhw and γco are the corresponding surface tensions, which because of the smallness of the globules are curvature dependent. At low temperatures, the interactions between the polar head groups and water are expected to be strong, and hence, γhw can be smaller than γco. In this case, Fint is smaller when the head groups are located on the external, larger area and an O/W microemulsion coexisting with excess oil will be formed. The curvature of the globules is positive in this case. By increasing the temperature, the interactions between the head groups and water decrease, because of dehydration, in intensity, but as long as γhw < γco, the system will be of type I. At sufficiently high temperatures, γhw > γco and a microemulsion of type II will be generated. In this case the curvature of the globules is negative. Finally, at moderate temperatures, γhw = γco, both kinds of dispersions become equally probable and a type III system will be formed. The interactions between the hydrocarbon chains of the surfactant molecules of the interfacial layer and oil and those between the head groups of the surfactant molecules of the interfacial layer and water determine the kind of microemulsion. Their ratio, denoted R2, can be considered to vary in the same direction as γhw/γco. The interactions in the bulk phases between surfactant molecules, oil, and water determine the distribution of the surfactant mol-
Ruckenstein
ecules between water and oil. When the latter interactions are in the same direction as the former, hence if both ratios are smaller or larger than unity, Bancroft’s rule is obeyed; it is, however, violated when one is larger and the other one smaller than unity. In Binks’ experiments, water is the continuous phase at low temperatures even though most of the surfactant is present in the oil phase because γhw < γco (R2 < 1), while Aso > Asw (R1 > 1). In most cases, the Bancroft rule holds probably because R1 = R2. The violation occurs for this particular surfactant probably because of the high sensitivity of the properties of this class of surfactants to the number of E groups. Some experimental data11 regarding the interfacial tension at the isooctane-water interface for a somewhat different class of surfactants, namely, p,t-octylphenoxyethoxyethanols with ethylene oxide chain lengths between 1 and 10, illustrate this point. Indeed, the interfacial tension is about 0.5 dyn/cm for a number of E groups between 1 and 6 and becomes 4 for a number of E groups of 10. Macroemulsions and Bancroft’s Rule The Bancroft rule was formulated for emulsions, and Bancroft brought a thermodynamic argument in its favor. He concluded that “liquid A will form drops in the emulsion when liquid B lowers the surface tension of the surfactant layer more than does liquid A”. Hildebrand12 commented, in a forgotten short paper, that the thermodynamic explanation based on the lower surface tension provided by the preferred curvature cannot be applied to macroemulsions because the curvature does not affect the surface tension of the large droplets involved (>1 µm). In addition, he noted that because of the kinetic stability of macroemulsions, kinetics should explain the Bancroft rule. He provided such an explanation, which was completed with more details, qualitatively, by Davis.13 The first quantitative formulation, due to Lee and Hodgson,14 was later developed in a number of papers summarized by Zapryanov et al.15 The qualitative presentation which follows is largely borrowed from the Lee and Hodgson paper, our final goal being to explain the violations of the Bancroft rule noted by Binks. Emulsions are prepared by applying a shear which generates oil fingers in water and water fingers in oil at the interfaces of which molecules of surfactant are adsorbed. These fingers break up, generating locally O/W and W/O emulsions. The surface concentration of surfactant is unequally distributed, being larger on the older areas of the droplet than on the newer areas just formed. As a result, the surface tension is lower on the former than on the latter areas, and a surface tension gradient is generated. In order to decrease the surface free energy, the areas with low surface tension have the tendency to expand and those with higher surface tension to contract, and a Marangoni motion is generated from the areas of lower to those of higher surface tension. This motion opposes the drainage of the liquid between two neighboring droplets formed by the breaking of a finger and which approach one another. If the strength of the Marangoni motion is high enough, it will delay the coalescence of the droplets. In addition, for distances between the approaching surfaces below about 102 nm, the van der Waals interactions accelerate and the repulsive interactions (11) Crook, E. H.; Fordyce, D. B.; Trebbi, G. F. J. Phys. Chem. 1963, 67, 1987. (12) Hildebrand, J. H. J. Phys. Chem. 1941, 45, 1303. (13) Davies, J. T. Proc. Int. Cong. Surf. Activity, 2nd 1957, 417. (14) Lee, J. C.; Hodgson, T. D. Chem. Eng. Sci. 1968, 23, 1375. (15) Zapryanov, Z.; Malhotra, A. K.; Aderangi, N.; Wasan, D. T. Int. J. Multiphase Flow 1983, 9, 105.
The Bancroft Rule
hinder the drainage. Of course, the Marangoni motion is important only if the surface concentration gradient is large enough and is not annihilated too rapidly. If most of the surfactant is present in the oil phase and the concentration of surfactant is large enough, the rate of diffusion in the oil droplets to the fresh surfaces just formed will be high and the surface tension gradient will be annihilated rapidly; the coalescence of the approaching oil droplets will be then rapid. The water droplets generated contain in the considered case a small amount of surfactant and the rate of mass transfer from the continuous oil phase to the surface of the droplets is low because the amount of surfactant in the small space between the droplets is small and is depleted rapidly, and the additional surfactant molecules have to diffuse a long distance from the bulk to the space between the two droplets. When a large fraction of surfactant is present on the surface of globules of a W/O microemulsion, the diffusion is even slower because only the single surfactant molecules or small clusters of such molecules which must first dissociate from the globules can diffuse in the small space between droplets. As a result, the coalescence of the water droplets is slow. There are additional effects which are relevant, such as the surface viscosity, the surface diffusion, and the instability of the thin film between the droplets to thermal and mechanical perturbations of its surfaces. The qualitative image remains mostly unchanged, and we will not discuss them here. Of course, for long time stability the repulsive interactions among the globules play a major role. Consequently, when the oil phase contains most of the surfactant, the emulsion will be of the W/O type, while when the water phase contains most of the surfactant, the emulsion will be of the O/W type. When one of the phases is a microemulsion, the total amount of surfactant present in the microemulsion is the source of diffusing surfactant molecules. The preceding conclusion is just the Bancroft rule. It needs, however, a moderating amendment. It is valid for sufficiently high but not too high surfactant concentrations. At low surfactant concentrations, the surface concentration gradient is too low to generate a sufficiently strong Marangoni flow. At too high concentrations, a black film may be generated and the rupture of such a film, via a nucleation mechanism,16-21 may be the rate-determining step of the coalescence process. Let us now consider the cases noted by Binks10 as violations to Bancroft’s rule and to show that the violations are due to the too low concentrations of surfactant and that the behavior of the system is controlled in that case by the mixing (hydrodynamic process). In those cases, most of the surfactant is present in the oil phase, but water is the continuous phase of the macroemulsion (and the continuous phase is not an O/W microemulsion). In addition, the surfactant concentration is low and the macroemulsions are very unstable. If the adsorptiondesorption process is rate determining and the adsorbability from oil is smaller than that from the water phase, the O/W emulsion may be more stable, as long as the (16) deVries, A. J. Recl. Trav. Chim. Pays-Bas 1958, 77, 383; 1958, 77, 441. (17) Kashchiev, D.; Exerowa, D. J. Colloid Interface Sci. 1980, 77, 51. (18) Kashchiev, D. Colloid Polym. Sci. 1987, 265, 436. (19) Muler, H. J.; Balinov, B.; Exerowa, D. Colloid Polym. Sci. 1988, 266, 921. (20) Exerowa, D.; Kashchiev, D.; Platikanov, D. Adv. Colloid Interface Sci. 1992, 40, 201. (21) Kabalnov, A.; Wennerstrom, H. Langmuir 1996, 12, 276.
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Marangoni motion is effective, than the W/O emulsion. This mechanism is unlikely because the adsorption equilibrium for surfactants is achieved rapidly. Can a nucleation mechanism16-21 explain the violation found by Binks? Most unlikely, because relatively large concentrations of surfactant are needed to generate a black film and the formation of such a film implies a relatively high stability. The amount of surfactant employed by Binks in the experiments that violated Bancroft’s rule was small, and the emulsions were very unstable. The most convincing argument is provided by Figure 3 of Binks’ paper, in which he plots the electrical conductivity of the macroemulsion against temperature for various initial concentrations of surfactant, between 0 and 84 mM, in the oil phase. The curve for zero surfactant concentration in that figure shows relatively high conductivities that increase with temperature, hence that the macroemulsion in the absence of surfactant was of the O/W kind without any inversion to the W/O type. Obviously, in that case the macroemulsion type was controlled by the mixing process; it is, therefore, most likely that mixing determined the outcome for surfactant concentrations in the range 0-16 mM for which the curves of the figure show an increase in conductivity with temperature. In the range 28-84 mM, the emulsions inverted from O/W to W/O at 30 °C and the Bancroft rule was obeyed. There is an intermediate behavior for the concentrations of 20 and 23 mM. The experiments from refs 7, 9, and 10 suggest the existence of three regimes. At low surfactant concentrations or when less powerful surface active agents are employed, the macroemulsion type is determined by mixing and the Bancroft rule should not be obeyed. At surfactant concentrations high enough for the Marangoni flow to be effective, the outcome is determined by the Bancroft rule. Finally, at even higher surfactant concentrations at which black films can be generated, the outcome is determined by the nucleation of holes in the bilayer films. Conclusion Regarding microemulsions, the comparison of two ratios determines if the Bancroft rule is valid or not. One ratio compares the interactions in the bulk phases between surfactant and oil to those between surfactant and water. The other one compares the interactions between the hydrocarbon chains of the surfactant molecules of the interfacial layer and oil to those between the head groups of the surfactant molecules of the interfacial layer and water. When both are smaller or larger than unity, Bancroft’s rule is obeyed. Some violations to the above rules have been observed in recent experiments carried out by Binks.10 Using the two ratios, those experimental observations could be explained. Regarding macroemulsions, three regimes were identified, a mixing controlled regime at low surfactant concentrations, a mass transfer controlled regime at sufficiently high surfactant concentrations, and, finally, a hole rupture mediated bilayer regime at even higher surfactant concentrations. The Bancroft rule is valid only for the mass transfer controlled regime. It was shown that the violations observed by Binks in macroemulsions to Bancroft’s rule were in the mixing controlled regime for which the rule is not valid. LA960849M
