The effective chi parameter in polarizable polymeric systems: One-loop perturbation theory and field-theoretic simulations

We derive the effective Flory-Huggins parameter in polarizable polymeric systems, within a recently introduced polarizable field theory framework. The incorporation of bead polarizabilities in the model self-consistently embeds dielectric response, as well as van der Waals interactions. The latter generate a χ parameter (denoted χ ̃) between any two species with polarizability contrast. Using one-loop perturbation theory, we compute corrections to the structure factor S(k) and the dielectric function εˆ(k) for a polarizable binary homopolymer blend in the one-phase region of the phase diagram. The electrostatic corrections to S(k) can be entirely accounted for by a renormalization of the excluded volume parameter B into three van der Waals-corrected parameters BAA, BAB, and BBB, which then determine χ ̃. The one-loop theory not only enables the quantitative prediction of χ ̃ but also provides useful insight into the dependence of χ ̃ on the electrostatic environment (for example, its sensitivity to electrostatic screening). The unapproximated polarizable field theory is amenable to direct simulation via complex Langevin sampling, which we employ here to test the validity of the one-loop results. From simulations of S(k) and εˆ(k) for a system of polarizable homopolymers, we find that the one- loop theory is best suited to high concentrations, where it performs very well. Finally, we measure χ ̃ N in simulations of a polarizable diblock copolymer melt and obtain excellent agreement with the one- loop theory. These constitute the first fully fluctuating simulations conducted within the polarizable field theory framework.

Douglas J. Grzetic, Kris T. Delaney and Glenn H. Fredrickson
Journal of Chemical Physics
Volume: 148
Number: 204903
Pages: 1-18
Date: May, 2018
ICB Affiliated Authors: Glenn H Fredrickson