Closure to the PRISM equation derived from nonlinear response theory

JP Donley, JOURNAL OF CHEMICAL PHYSICS, 161, 124902 (2024).

DOI: 10.1063/5.0226882

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model 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, T-c, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for T-c 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 T-c about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for T-c of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

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