6533b7d5fe1ef96bd126459e

RESEARCH PRODUCT

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

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Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths N A =N B =N) are analyzed near the critical temperature T c (N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number z eff ≃ 14 or z eff ≃ 5, respectively, at a volume fraction O= 0.5 of occupied lattice sites, and chain lengths in the range 8≤ N≤ 512. A linear relation between N and T c (N) is established, T c (N)= AN+B, where the correction term B is positive for z eff = 14 but negative for z eff = 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 z eff , consistent with the expected entropic origin of the mean-field behavior for long chains.