Critical properties of the Flory–Huggins lattice model of polymer mixtures

Abstract

Monte Carlo simulations are presented for a model of a symmetrical polymer mixture on the simple cubic lattice, modeling both polymers A, B by self-avoiding walks of NA=NB=N steps. If a pair of nearest-neighbor sites is taken by monomers of the same species, an energy ε is won. In the Monte Carlo algorithm local motions of the chains are considered (allowing for 20% vacancies to ensure enough chain mobility) as well as transformations of A chains into B chains and vice versa, since the simulation applies the grand-canonical ensemble where the chemical potential difference rather than the volume fraction is fixed. The phase diagram, the excess specific heat, and the structure factor in the long-wavelength limit are obtained for N=4, 8, 16, and 32 using finite L×L×L lattices with L ranging from 8 to 20. Analyzing these results with finite size scaling techniques, both critical exponents and critical amplitudes are estimated. Although the exponents are consistent with those of the three-dimensional Ising model, the variation of critical amplitudes with N is much closer to mean-field predictions. In contrast to qualitative expectations (‘‘Ginzburg criterion’’), the crossover scaling region from Ising to mean-field behavior has not yet been reached. Implications for experimental work are briefly discussed.