Effect of chain length distribution on mechanical behavior of polymeric networks

TL;DR

This paper develops a simple theoretical model to understand how the distribution of chain lengths in polymer networks influences their mechanical strength and failure behavior.

Contribution

It introduces a novel theory incorporating strand length distribution into rubber mechanics, extending beyond classical uniform-length assumptions.

Findings

Longer strands enhance mechanical strength.

Short strands break at small deformations, affecting load transfer.

Polydispersity influences the onset of bulk failure.

Abstract

The effect of network chain distribution on mechanical behavior of elastomers is one of the long standing problems in rubber mechanics. The classical theory of rubber elasticity is built upon the assumption of entropic elasticity of networks whose constitutive strands are of uniform length. The kinetic theories for vulcanization, computer simulations, and indirect experimental measurements all indicate that the microstructure of vulcanizates is made of polymer strands with a random distribution of length. The polydispersity in strand length is expected to control the mechanical strength of rubber as the overloaded short strands break at small deformations and transfer the load to the longer strands. The purpose of this contribution is to present a simple theory of rubber mechanics which takes into account the length distribution of strands and its effect on the onset of bulk failure.