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

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, ${\sigma }_{nb}\mathrm{/}G\propto (c\mathrm{/}{c}^{\ast }{)}^{(-1\mathrm{/}3)}$, where ${\sigma }_{nb}$ is the nominal broken strength, $G$ is the initial shear modulus, $c$ is the prepolymer concentration, and $c^{\ast }$ is its overlapping threshold.