Monte Carlo simulations of polymeric materials reveal that critical temperatures in symmetric mixtures follow a linear relation, crossover phenomena from Ising to mean field critical behavior are observed, and pretransitional stretching of chains occurs in block copolymers.

Abstract

Polymeric materials present a major challenge to computer simulation, since they exhibit structure on many different length scales (bond length, 1 A; coil size, 102 A; correlation length in mixtures, 103 A). For a study of collective phenomena, such as unmixing of polymer mixtures and mesophase formation in block copolymers, coarse-grained simplified lattice models hence are used. It is shown that in symmetric polymer mixtures (chain lengths NA = NB = N) the critical temperature follows a simple linear relation, TC(N) = aN + b. The onset of crossover phenomena from Ising to mean field critical behavior is observed, but even for N = 512 chains do not behave fully mean-field-like. Asymmetric mixtures also are considered and the corresponding predictions of Flory-Huggins theory are tested. In block copolymers a pretransitional stretching of the chains is found for both symmetric and asymmetric concentrations and analysed in detail. A density reduction in the interfaces between A and B blocks is found in the ordered phase.