Free energy binary surfactant systems

From thermodynamics, the lowering of surface free energy due to surfactant adsorption is given by the Gibbs adsorption equation for a binary, isothermal system containing excess electrolyte ... 

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... 

While the amphiphile/surfactant ratio is progressively increased from the surfactant-water binary system, as a consequence of the decrease in spontaneous curvature one-dimensional micellar growth occurs that may, then, be considered as a tendency of the system to nrmiiriize the excess free energy by reducing the number of endcaps, where the hydrophUic surfactant situates (see Figure 12.1), in spite of the counteracting entropy factor. 

Another way to study a surfactant—oil-water ternary system is to study the case of OW binaries at different amounts of surfactant, so that only binary diagrams are involved. This would produce a series of two-dimensional diagrams that indicate the variation of the free energy G of a water-oil mixture at increasing surfactant content (see Fig. 3). 

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