Thermodynamics of Microemulsions

FIGURE 4.28 The Gibbs free energy of formation of microemulsions AG, shown as a function of droplet radii R under various conditions. The curves A and B show that negative values of AG can be obtained (i.e., that microemulsions can form spontaneously). The actual radius is corresponding to a minimum AG. The curve C shows kinetic stability and D is unstable. Reprinted from Ruckenstein and Chi (1975) with permission. 

Miller and Neogi (1980) and Mukheijee et al. (1983) analyzed the case of a microemulsion in equilibrium with excess dispersed phase (e.g., an oil-in-water microemulsion in eqnilibrinm with excess oil) using concepts based on Hill s ([1963] 1992) thermodynamics of small systems and expUdtly including bending effects. Their equations for equilibrium are given by 

It is also possible, as indicated previously, for a microemulsion containing spherical droplets to separate into a more concentrated microemulsion and excess continuous phase (e.g., an oil-in-water microemulsion in equilibrium with excess water), provided that attractive interaction among the droplets is sufficiently large. In other words, a microemulsion can have a limited capability to solubilize its continuous phase as well as its dispersed phase. Interfadal tension between the phases should be very low since both are continuous in the same component. Such a phase separation is similar to that which takes place at the cloud point of nonionic surfactants discussed previously. A simple theory of how it could occur for microemulsions was proposed by Miller et al. (1977). If excess continuous phase separates in this way and, at the same time, there is more dispersed phase present than can be solubilized, the microemulsion can coexist with both oil and water phases. While this situation of three-phase coexistence involving a microemulsion containing droplets probably exists for some compositions in some systems, in most situations the microemulsion in a three-phase region is bicon-tinuous. The above discussion emphasizes the early theoretical work on microemulsions with droplets, but numerous other developments have been reported since then. 

Several theories of surfactant phase are available. Following Scriven (1976), this phase is assumed to be bicontinuous in oil and water, and the interface is assumed to have zero mean curvature, hence the pressure difference between oil and water is zero. Talmon and Prager (1978, 1982) divided up the medium into random polyhedra. The flat walls ensure no pressure difference between oil and water. They placed oil and water randomly into the polyhedra so that both oil and water were continuous when sufficient amounts of both phases were present. As in the earlier models of oil-in-water microemulsions, this randomness gave rise to an increased entropy which overcame the increased surface energy to yield a negative free energy of formation, reached only when the interfadal tension is ultralow. Such structures can form spontaneously. This random structure is characterized by a length scale. This led Jouffrey et al. (1982) to postulate that 

These theories also take into aecount the energy to deform the interfaee at a constant area. It is frequently expressed as (Safran, 1994) 

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See also in sourсe #XX -- [ ]

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