Equilibrium Statistics of Weakly Slip-Linked Gaussian Polymer Chains

TL;DR

This paper analyzes the equilibrium properties of weakly slip-linked Gaussian polymer chains, revealing how slip-links influence free energy, pressure, and aggregation behavior, with implications for modeling polymer systems.

Contribution

It introduces a calculation of free energy and pressure for slip-linked chains, highlighting differences from ideal chains and the role of repulsive potentials.

Findings

Pressure decreases in slip-linked systems compared to ideal chains

Slip-linked chains tend to form aggregated, compact structures

Repulsive potentials can counteract artificial pressure decreases

Abstract

We calculate the free energy and the pressure of a weakly slip-linked Gaussian polymer chains. We show that the equilibrium statistics of a slip-linked system is different from one of the corresponding ideal chain system without any constraints by slip-links. It is shown that the pressure of a slip-linked system decreases compared with the ideal system, which implies that slip-linked chains spontaneously form aggregated cluster like compact structures. These are qualitatively consistent with previous theoretical analyses or multi chain simulations. We also show that repulsive potentials between chains, which have been phenomenologically utilized in simulations, can cancel the artificial pressure decrease.