Negative Energetic Elasticity in Gels: Insights from a Lattice Polymer Chain*

The recent observation of negative energetic elasticity in polymer gels challenges the traditional notion that the elastic moduli of rubberlike materials primarily arise from entropic elasticity. To understand the microscopic origin of this phenomenon, we examined the n-step interacting self-avoiding walk (ISAW) on a cubic lattice [Phys. Rev. Lett. 130, 148101 (2023)]. This model represents a single polymer chain—a subchain in a polymer gel network. Our theoretical investigations, based on exact enumerations up to n=20, reveal the emergence of negative energetic elasticity. The underpinning of this behavior is the attractive interaction between polymer and solvent. This model reproduces the temperature-dependent behavior of negative energetic elasticity observed in polymer gel experiments, suggesting that single-chain analysis can elucidate the properties intrinsic to polymer gel's negative energetic elasticity. Through these insights, our work offers a comprehensive understanding of polymer gel mechanics.