Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness

TL;DR

This study unifies the understanding of negative energetic elasticity in lattice polymers by showing that both self-repulsion and bending stiffness mechanisms produce negative energetic contributions, with implications for internal-energy scaling behaviors.

Contribution

It demonstrates that self-repulsion and bending stiffness mechanisms both lead to negative energetic elasticity, unifying two previously separate explanations and analyzing their effects on energy scaling.

Findings

Energetic contribution to stiffness is negative across all parameters.

Entropic contribution remains positive regardless of parameters.

Bending stiffness disrupts the energy scaling observed in the self-repulsion limit.

Abstract

We study a single lattice polymer chain under a fixed end-to-end distance, incorporating both Domb--Joyce (DJ) soft-core self-repulsion between polymer segments and a local bending-energy cost. By decomposing the stiffness into energetic and entropic contributions, we survey the parameter space defined by the self-repulsion strength and bending-energy cost. We find that the energetic contribution to stiffness is negative across the entire explored range, whereas the entropic contribution remains positive. These results unify two previously independent mechanisms of negative energetic elasticity -- solvent-induced self-repulsion and bending stiffness -- and demonstrate that either mechanism alone, as well as their combination, produces the same sign. Beyond this sign-level unification, we analyze the internal-energy scaling and show that, in the absence of the bending-energy term, the DJ (self-repulsion) limit exhibits a robust $(n-r)^{7/4}/n$ scaling collapse. In contrast, the introduction of finite bending stiffness progressively disrupts this scaling, providing an internal-energy-based diagnostic to distinguish between contributions from self-repulsion and bending stiffness.