Cell dynamical system approach to block copolymers

Abstract

A cell-dynamical-system (CDS) model of the microphase separation of block copolymers is described in detail. The model suggests a partial-differential-equation (PDE) model that allows us to find a close relation between the block copolymer and spinodal decomposition problems. A detailed numerical study of the CDS model is given, which indicates that hydrodynamic effects are crucial for very late time-ordering processes. The strong segregation regime is studied analytically with the aid of an exactly solvable PDE model, which is suggested by the universality supported by the CDS simulations. The results obtained show that dimensional analysis gives the correct exponent for the block copolymer lamellar thickness.