Variational model for micelle structure

Abstract

A free energy variational principle is proposed for the study of aggregation structures in amphiphile solutions. For nonionic amphiphiles the postulated free energy functional depends on the scalar concentration fields for solvophilic head groups (H) and solvophobic tail groups (T); it has a form appropriate for a binary mixture of head-group chains and tail-group chains supplemented by a term that enforces chemical bond connection between pairs of those chains. Numerical solutions to the Euler equations for the variational principle are presented for molecules with formal constitution (H)10 (T)10, under conditions of spherical aggregate symmetry. These solutions include globular micelles, hollow vesicles, and a type of point defect in a smectic A lamellar system.