Solvent-Induced Negative Energetic Elasticity in a Lattice Polymer Chain

TL;DR

This paper models a polymer chain in solvent to explain negative energetic elasticity observed in polymer gels, revealing that solvent interactions can locally stiffen the chain and influence overall elasticity.

Contribution

It provides a theoretical explanation for negative energetic elasticity in polymer gels based on a lattice model and exact enumeration, linking microscopic interactions to macroscopic properties.

Findings

Negative energetic elasticity arises from attractive polymer-solvent interactions.

The model reproduces the temperature dependence observed experimentally.

Local chain stiffening explains the negative energetic elasticity phenomenon.

Abstract

The negative internal energetic contribution to the elastic modulus (negative energetic elasticity) has been recently observed in polymer gels. This finding challenges the conventional notion that the elastic moduli of rubberlike materials are determined mainly by entropic elasticity. However, the microscopic origin of negative energetic elasticity has not yet been clarified. Here, we consider the $n$-step interacting self-avoiding walk on a cubic lattice as a model of a single polymer chain (a subchain of a network in a polymer gel) in a solvent. We theoretically demonstrate the emergence of negative energetic elasticity based on an exact enumeration up to $n=20$ and analytic expressions for arbitrary $n$ in special cases. Furthermore, we demonstrate that the negative energetic elasticity of this model originates from the attractive polymer--solvent interaction, which locally stiffens the chain and conversely softens the stiffness of the entire chain. This model qualitatively reproduces the temperature dependence of negative energetic elasticity observed in the polymer-gel experiments, indicating that the analysis of a single chain can explain the properties of negative energetic elasticity in polymer gels.