Effects of Solvent on Polymer Chain Dimensions: A Born-Green-Yvon Integral Equation Study

TL;DR

This study uses a Born-Green-Yvon integral equation approach to analyze how solvent properties influence the size and shape of polymer chains in a hard sphere solvent, providing insights into polymer-solvent interactions.

Contribution

It introduces a novel application of the BGY integral equation with a two-site solvation potential to model polymer dimensions in various solvent conditions.

Findings

Polymer dimensions decrease with increasing solvent density.

Maximum polymer compression occurs when solvent diameter is 2-3 times the monomer size.

Scaling exponents relate polymer size to chain length and solvent density.

Abstract

The equilibrium properties of a tangent-hard-sphere polymer chain in a hard sphere monomer solvent are studied using a Born-Green-Yvon integral equation in conjunction with a two-site solvation potential. The solvation potential is constructed using low density results for a hard-sphere trimer in a hard sphere solvent. The BGY equation has been solved for polymers of lengths up to 100 for a range of solvent densities and solvent diameters. The theory accurately describes the compression of the average polymer dimensions with increasing solvent density. The theory also accurately describes the variation in this compression as a function of the solvent diameter, predicting a maximum effect when the solvent diameter is two to three times larger than the polymer site diameter. Scaling exponents relating the polymer dimensions to chain length and solvent density are also obtained.