Correlations in polymer blends: simulations, perturbation theory, and coarse-grained theory.

Abstract

A thermodynamic perturbation theory of symmetric polymer blends is developed that properly accounts for the correlation in the spatial arrangement of monomers. By expanding the free energy of mixing in powers of a small parameter α which controls the incompatibility of two monomer species, we show that the perturbation theory has the form of the original Flory-Huggins theory, to first order in α. However, the lattice coordination number in the original theory is replaced by an effective coordination number. A random walk model for the effective coordination number is found to describe Monte Carlo simulation data very well. We also propose a way to estimate Flory-Huggins χ parameter by extrapolating the perturbation theory to the limit of a hypothetical system of infinitely long chains. The first order perturbation theory yields an accurate estimation of χ to first order in α. Going to second order, however, turns out to be more involved and an unambiguous determination of the coefficient of α2 term is not possible at the moment. Lastly, we test the predictions of a renormalized one-loop theory of fluctuations using two coarse-grained models of symmetric polymer blends at the critical composition. It is found that the theory accurately describes the correlation effect for relatively small values of χN. In addition, the universality assumption of coarse-grained models is examined and we find results that are supportive of it.