On the Scaling of the Critical Solution Temperature of Binary Polymer Blends with Chain Length

Abstract

Monte Carlo simulations have been performed to examine the scaling with chain length of the upper critical solution temperature (Tc) of binary, symmetric blends of polymers. Critical parameters were obtained by histogram reweighting analysis of semigrand canonical ensemble simulations near the critical temperature. For several continuum space polymeric models, it is found that Tc/ε scales approximately as either ρc(A + B N) or ρcN/(B-1 + A/ ), where N is chain length, ρc is the density at Tc, ε is a chemical mismatch parameter, and A and B are constants that depend on the specific characteristics of the model. Constant A provides a measure of the correction to the Flory−Huggins' prediction Tc ∼ N. The effect of such correction term becomes unimportant for large N, ε, and temperature. Excellent agreement is found, however, with the mean-field prediction that χE ∼ 2/N (for all systems studied), where χE is a continuum space, enthalpic “chi” parameter which takes into account the variations of local structure of the fluid for different chain lengths at the critical point.