Micelle formation in statistical copolymers

Abstract

Formation of microdomain structures in concentrated systems of irregular (stochastic) copolymers with weak composition asymmetry (epsilon>>1) is considered theoretically. The study is focused on the weak segregation regime for infinitely long copolymer chains near the disorder-to-order transition. It is shown that the transition occurs below the spinodal (at chi(0)< chi*) and that it results in the formation of micelles rather than in a superposition pattern of a few harmonic composition waves. The micelle size is inversely proportional to Delta(chi=chi)-(chi0). For small Delta(chi) the micelles are like large nearly uniform droplets with "reflected" composition, -epsilon. As Delta(chi) increases the micelle composition profile develops oscillations. A first-order transition from spherical-wave micelles to micelles with internal bcc structure is predicted at chi/chi*-1 proportional to epsilon(2). Interaction of micelles is also considered. It is shown that micelles always tend to form a fcc superlattice. The micellization in the weak segregation regime is controlled by the so-called nonlocal free energy. The classical fourth order (in composition parameter A) approximation for this energy is significantly generalized in the regime of low volume fraction of micelles. It is shown that the nonlocal energy strongly (exponentially) increases with A near and above a certain critical value A approximately equal to A*.