Universal Scaling of Macroscopic Softening and Microscopic Scission in Phantom Chain Networks

TL;DR

This paper reveals that fracture behavior in phantom-chain polymer networks can be described by two universal master curves for macroscopic softening and microscopic scission, with a new scaling relationship linking strength, modulus, and concentration.

Contribution

It introduces a universal framework decoupling macroscopic and microscopic damage in polymer networks, supported by an analytical model and a novel scaling law.

Findings

Fracture behavior is governed by two universal master curves.

An analytical expression captures nonlinear microscopic damage growth.

A new scaling law relates broken strength, shear modulus, and concentration.

Abstract

This study demonstrates that the apparent complexity of fracture in phantom-chain polymer networks is fully decoupled into two universal master curves: (i) macroscopic softening governed by the absolute stretch, and (ii) microscopic scission governed solely by the relative stretch. Using the previously proposed network mechanics model, an analytical expression has been derived to quantitatively capture the nonlinear growth of microscopic damage. Combining the softening exponent with polymer-solution scaling yields a simple novel relationship, $\sigma_{nb} / G \propto (c / c^* )^{(-1/3)}$, where $\sigma_{nb}$ is the nominal broken strength, $G$ is the initial shear modulus, $c$ is the prepolymer concentration, and $c^*$ is its overlapping threshold.