Theory of Micellar Stability in Isotropic and Nematic Phases

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Abstract
In this paper we present the basic ideas underlying the statistical thermodynamic theory of micellized solutions of soap in water. First we outline briefly the low concentration limit in which the micellar aggregates are essentially isolated from one another. Here the preferred shapes and sizes are determined by a delicate interplay between single-micelle free nergies and solution entropies of mixing. Then we focus on higher concentration situations in which inter-aggregate forces become important. In isotropic suspensions of rod-like micelles, for example, it can be shown that the effect of excluded volume interactions between micelles is to enhance their length-to-width ratio. As the “rods” become longer and more concentrated they are eventually forced to align. Unlike in ordinary colloidal suspensions (lyotropics) and thermotropic systems, however, the aggregates reorganize themselves internally as they undergo the isotropic–nematic transition. We show in particular that the rods “grow” longer in the aligned phase. At still higher concentrations the coupling between growth and orientational ordering becomes so strong that finite aggregates can “explod” into the hexagonal phase. We conclude with a discussion of the effects of cosurfactant on micellar size and phase stability.