Glassy polymers' strain-hardening moduli scale with their statistical-segment volumes

TL;DR

This study uses molecular dynamics simulations to challenge existing theories on glassy-polymer strain hardening, proposing a new scaling law that relates the strain-hardening modulus to the statistical segment volume, applicable to both flexible and semiflexible polymers.

Contribution

It introduces a new scaling theory linking strain-hardening moduli to Kuhn length, segment length, and binding energy, improving understanding of polymer glass mechanics.

Findings

Existing theory fails for semiflexible polymers with small entanglement lengths.

The new scaling law accurately predicts $G_R$ across a wide range of polymer flexibilities.

The theory aligns well with simulation data for various polymer types.

Abstract

Using molecular dynamics simulations, we show that a widely-accepted theoretical prediction for glassy-polymeric strain hardening moduli ($G_R \propto \rho_e$, where $\rho_e$ is the entanglement density) fails badly for semiflexible polymers with $N_e \lesssim 4C_\infty$. By postulating that the length, energy and strain scales controlling $G_R$ are the Kuhn length $\ell_K$ and statistical segment length $b = \sqrt{\ell_0 \ell_K}$ (where $\ell_0$ is the backbone bond length), the intermonomer binding energy $u_0$, and the incremental elastic strain $S_{\rm c}$ required to activate Kuhn-segment-scale plastic rearrangements, we develop a scaling theory predicting that $G_R = S_{\rm c}(u_0/\ell_0^3) b^3$ in the athermal limit. This prediction agrees quantitatively (semi-quantitatively) with simulated $G_R$ values for both flexible and semiflexible polymer glasses subjected to athermal uniaxial-stress extension (constant-volume simple shear), over a range of $\ell_K/\ell_0$ that is wider than that spanned by real systems.