Spatial-Temporal Oscillations of the Order Parameter in Confined Diblock Copolymer Mixtures

Abstract

The mathematical model describing the evolution of the order parameter in confined polymer melts is under consideration. The corresponding equation is derived from a special energy functional introduced by Fredrickson and Binder to describe the behavior of polymer chains in block copolymer melts. This equation is modified to take into account the "memory" of correlated blends. The resulting hyperbolic partial differential equation is of order six in space variable. The Puri–Binder dynamical boundary conditions with "feedback" describe processes of cyclic surface crystallization and melting. Two types of polymer mixtures (ideal and non-ideal) are studied. In the case of the ideal mixture, the attractor of the boundary problem consists of asymptotically periodic piecewise constant functions with finite or infinite number of discontinuities per period (spatial-temporal structures of relaxation or turbulent type). In the non-ideal case, the attractor contains quasi-periodic functions or it is so-called strange chaotic or strange non-chaotic. The bifurcation diagram is constructed.