Monte Carlo investigations of dense copolymer systems, 1. Pivot algorithm and pair distribution function

Abstract

ABA triblock copolymers (the solvent being a 0-solvent for B and an athermal one for A) as well as their constituent homopolymers were investigated by means of Monte Carlo simulations in a 5-choice cubic lattice. The polymer concentration (represented by the fraction o of sites occupied by the polymer) varied from 0 (isolated chain) to 0.80. An investigation of the usefulness of the pivot algorithm in dense systems resulted in reasonable acceptance fractions up to a volume fraction of 0.12 (athermal chain and ABA copolymer) and 0.05 (0-chain). For larger volume fractions only the chain-ends remain mobile. The overlap concentration of the polymers defined by several quantities was approximately 0.07 (athermal chain), 0.12 (0-chain) and 0.09 (ABA copolymer). At a polymer fraction of 0.32, the chains had the same number of inter- and intramolecular contacts on average. At higher concentrations, the behaviour of the chains was primarily determined by intermolecular interactions. Contrary to isolated pairs, the pair distribution function g(r) of two athermal chains in a (cubic) box exceeded unity at intermediate distances because of the influence of the finite size of the box. The larger the size of the box, the smaller the (positive) deviation was. In the limit of r → 0 the pair distribution function g(r) - being smaller than unity - increased with increasing concentration while the maximum at intermediate distances simultaneously decreased. Ultimately, at the highest concentration, the pair distribution function resembled that of isolated 0-chains. The concentration dependence of the 0-pair distribution function itself, however, is negligible. At low concentrations the pair distribution function of the ABA triblock copolymer behaved like that of an athermal chain (up to o 0.40) where characteristic oscillations around 1 developed. This might be taken as indicative of the formation of a lamellar phase.