Effect of Chain Polydispersity on the Elasticity of Disordered Polymer Networks

Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology industrial processes. In order elucidate how these properties are controlled by the physical details of network (\textit{e.g.} chain-length end-to-end distributions), we generate disordered phantom with crosslinker concentrations $C$ initial density $\rho_{\rm init}$ evaluate elastic properties. We find that shear modulus computed at same strand concentration for $C$, which determines number chains distribution, depends strongly on preparation protocol network, here init}$. rationalise this dependence employing a generic stress-strain relation does not rely specific form distance distribution. is non-monotonic function elastically-active strands, behaviour has purely entropic origin. Our results show if short abundant, as it always case networks, knowledge exact chain conformation distribution essential predicting correctly Finally, apply our theoretical approach published experimental data, qualitatively confirming interpretations.