Microemulsions curvature energy

Davis [799] summarized the concepts about HLB, PIT, and Windsor s ternary phase diagrams for the case of microemulsions and reported topological ordered models connected with the Helfrich membrane bending energy. Because the curvature of surfactant lamellas plays a major role in determining the patterns of phase behavior in microemulsions, it is important to reveal how the optimal microemulsion state is affected by the surface forces determining the curvature energy... 

As been shown above, it is possible to prepare a hard-sphere microemulsion up to a rather high volume fraction [curvature energy model which predicts spheres at the solubility limit with a size dictated primarily by the spontaneous curvature. It appears also that we can understand the intriguing kinetic properties of the droplets, when quenched into the supersaturated state, within the curvature-energy approach. 

Surfactants form semiflexible elastic films at interfaces. In general, the Gibbs free energy of a surfactant film depends on its curvature. Here we are not talking about the indirect effect of the Laplace pressure but a real mechanical effect. In fact, the interfacial tension of most microemulsions is very small so that the Laplace pressure is low. Since the curvature plays such an important role, it is useful to introduce two parameters, the principal curvatures... 

Qualitatively the thermodynamics of microemulsions is well understood as the interplay between a small interfacial free energy and a small entropy of mixing. However, because of these contributions being small, other small effects, such as the influence of curvature on the interfacial tension and the influence of fluctuations, become important, and quantitative understanding still leaves a lot to be desired. 

In Sec. II we discuss the mechanism by which the interfacial tension may become ultralow. After that, in Sec. Ill we mention curvature effects of the oil/water interface. Subsequently, a number of models for thermodynamic calculations are described (Sec. IV). In Secs. V-VII we discuss droplet-type microemulsions in some detail. Section Vdescribes a thermodynamic formalism that incorporates the interfacial free energy (as influenced by the curvature) and the free energy of mixing of droplets and continuous medium and ultimately leads to equations for the size distribution of microemulsion droplets. This size distribution is important because measurable properties can be calculated... 

A theoretical basis for different shapes of microemulsions (even for small W/O or O/W volume fractions) has been established on the basis of the relationship between shape and interfacial curvature [350,351]. It is reasonable to expect that the relevant properties of the surfactant film are represented by a bending elasticity with a spontaneous curvature, Co (as was demonstrated for binary systems). If the elastic modulii k, ksT, the fluctuations in curvature of the film are very small, and the entropy associated with them can be neglected. The actual morphology is the result of the competition between the tendency to minimize the bending free energy (which prefers spheres of optimal radius of curvature, = l/c ) and the necessity to use up all of the water, oil, and surfactant... 

The most lucid way of conceptually and quantitatively understanding the rich structural variation and structural transitions of microemulsions is to use the framework of the flexible surface model (35). The basic assumption in this model is to describe a surfactant monolayer or bilayer as a mathematical surface dividing space into two or more separate regions. With each configuration of the surface one associates a curvature (free) energy G. obtained as a surface integration of a local curvature free-energy density... 

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