CRITICAL-BEHAVIOR AND CROSSOVER SCALING IN SYMMETRICAL POLYMER MIXTURES - A MONTE-CARLO INVESTIGATION

Symmetrical polymer A-polymer B mixtures (chain length N(A) = N(B) = N) are simulated by Monte Carlo methods, using the bond fluctuation model on simple cubic lattices, for N = 16 to N = 256 at a volume fraction of occupied lattice sites phi = 0.5 (which corresponds to a dense melt). Applying recently developed efficient simulation techniques (grand-canonical sampling of the mixture thermodynamics is combined with multiple histogram data evaluation and finite size scaling techniques), very precise estimates of critical temperatures, phase diagrams, composition-dependent effective Flory-Huggins parameters, and, last but not least, critical exponents and amplitudes are obtained. The data provide clear evidence for a linear dependence of the critical temperature on chain length, k(B)T(c)/epsilon almost-equal-to 2.15N + 1.35, and thus disagree with the integral equation theory prediction (T(c) is-proportional-to square-root N) of Schweizer and Curro. Consistent with the work of Sariban and Binder, however, it is concluded that the naive application of Flory-Huggins theory would overestimate strongly the proportionality constant relating T(c) with N. For the first time, clear evidence for a crossover from Ising-like critical behavior (dominating at small N) to mean-field critical behavior (which emerges in the limit N - infinity) is seen in simulations, consistent with the Ginzburg criterion for polymer mixtures.