Phenomenological theory of equilibrium thermodynamic properties and phase separation of micellar solutions

Abstract

A detailed description and generalization of a recently developed theory, which provides analytic representations of the distribution of micellar species and the equilibrium thermodynamic properties of amphiphile–water solutions that exhibit phase separation and critical phenomena, is presented. We propose a form for the structure of the Gibbs free energy which accurately describes the essential physical factors responsible for micellization and phase separation. These are: the free-energy advantage associated with the formation of individual micellar species,the entropy of mixing of the extended micelles and the water molecules, and the free energy of interaction between each member of the micellar size distribution. By applying to this Gibbs free energy the conditions of multiple chemical equilibrium and thermodynamic stability, all the relevant statistical and thermodynamic equilibrium properties of the micellar solution can be calculated. These properties include the location of the critical concentration and temperature, the shape of the coexistence curve and the spinodal line, the micellar size distribution, and the osmotic compressibility. The proposed Gibbs free energy provides an excellent description of a wide range of experimental findings in two quite different micellar solutions. The first is constituted of the zwitterionic amphiphile dioctanoyl phosphatidylcholine (C8-lecithin) and water, which exhibits an upper consolute point. The second is constituted of the nonionic amphiphile n-dodecyl hexaoxyethylene glycol monoether (C12E6) and water, which exhibits a lower consolute point. In addition, we use our theoretical approach to analyze a model of amphiphile–water solutions containing monodisperse micelles in equilibrium with monomeric amphiphiles. We also implement our theoretical framework with a Flory–Huggins type model of the Gibbs free energy and compare its predictions with experimental findings in the C12E6 and water micellar system.