Commensurability and finite size effects in lattice simulations of diblock copolymers

Abstract

Lattice Monte Carlo (MC) simulations provide an efficient method for exploring the structure and phase behavior of block polymer melts. However, the results of such simulations may differ from the equilibrium behavior of a hypothetical infinite system as a consequence of the finite size of the simulation box. Standard finite-size scaling techniques cannot be employed to remove the effects of a small system size due to incommensurability between the ordered structure domain spacing and the periodicity of the simulation box. This work describes a systematic approach to estimating the equilibrium domain spacing in lattice MC simulations of symmetric diblock copolymers, and thereby minimize the effects of incommensurability. Results for simulations with commensurate simulation boxes, which are designed to be commensurate with the preferred lattice periodicity but contain different numbers of unit cells, show that once the effects of incommensurability are removed, the effects of finite size alone are relatively small.