Closure to the PRISM equation derived from nonlinear response theory

TL;DR

This paper derives a new closure for the PRISM equation using nonlinear response theory, improving predictions of critical temperatures in polymer blends and enhancing understanding of polymer liquid properties.

Contribution

It introduces a molecular generalization of the MSA closure for PRISM, connecting nonlinear response theory with polymer liquid modeling.

Findings

Predicts unmixing critical temperature scaling linearly with molecular weight.

Shows the new closure's Tc predictions are closer to experimental values than previous models.

Highlights the importance of specific ingredients in theories for polymer equilibrium properties.

Abstract

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model (PRISM) equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation, and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to model properly the equilibrium properties of a polymeric liquid at both short and long lengthscales.