Linear elasticity of polymer gels in terms of negative energy elasticity

TL;DR

This paper reviews the linear elasticity of polymer gels, highlighting the significant negative energy contribution and proposing a unified formula to reconcile experimental results, challenging traditional entropy-based models.

Contribution

It introduces a unified formula for polymer gel elasticity and discusses the negative energy contribution, advancing understanding beyond classical rubber elasticity theories.

Findings

Negative energy elasticity can significantly affect shear modulus.

A unified formula can reconcile diverse experimental results.

Fundamental unresolved problems remain in the field.

Abstract

We recently found that the energy contribution to the linear elasticity of polymer gels in the as-prepared state can be a significant negative value; the shear modulus is not proportional to the absolute temperature [Y. Yoshikawa et al., Phys. Rev. X 11, 011045 (2021) (arXiv:1912.13191)]. Our finding challenges the conventional notion that the polymer-gel elasticity is mainly determined by the entropy contribution. Existing molecular models of classical rubber elasticity theories, including the affine, phantom, and junction affine network models, cannot be used to estimate the structural parameters of polymer gels. In this focus review, we summarize the experimental studies on the linear elasticity of polymer gels in the as-prepared state using tetra-arm poly(ethylene glycol) (PEG) hydrogels with a homogenous polymer network. We also provide a unified formula for the linear elasticity of polymer gels with various network topologies and densities. Using the unified formula, we reconcile the past experimental results that seemed to be inconsistent with each other. Finally, we mention that there are still fundamental unresolved problems involving the linear elasticity of polymer gels.