The mean field to Ising crossover in the critical behavior of polymer mixtures : a finite size scaling analysis of Monte Carlo simulations

Publisher Website
Google Scholar
Abstract
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths NA=NB=N) are analyzed near the critical temperature Tc(N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number zeff≈14 or zeff≈5, respectively, at a volume fraction φ=0.5 of occupied lattice sites, and chain lengths in the range 8≤N ≤512. A linear relation between N and Tc(N) is established, Tc(N)=AN+B, where the correction term B is positive for zeff≈14 but negative for zeff≈5. The critical behavior of the models is analyzed via finite size scaling techniques, paying attention to the crossover from three-dimensional Ising-like behavior to mean-field behavior, using a formulation based on the Ginzburg criterion. It is shown that the location of the crossover does not depend on zeff, consistent with the expected entropic origin of the mean-field behavior for long chains. However, despite large numerical efforts only a crude estimation of the crossover scaling function of the order parameter (describing the coexistence curve of the blends) and of the singular chain length dependence of the associated critical amplitude is possible. These results are discussed in the context of pertinent theories and related experiments

This publication has 0 references indexed in Scilit: