The influence of finite extensibility of the chains on the orientation behaviour of a polymer network

Abstract

The chains of a deformed polymer network can only be extended up to their contour lengthL. In this work, it is assumed that the chain vector initially undergoes an affine deformation, and then subsequently a pseudo-affine rod orientation as soon as it is fully extended. The density distribution of the chain vectors$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r}$ forr<L is approximated by an affinely deforming Gaussian distribution. We calculate the proportion of fully extended chains, their orientation distribution, the Hermans' orientation factor of the segments for both the fully extended and the partially extended chains, and the strain birefringence for this phantom network model. We take into account that the lack of further extension of the fully extended chains results in an excess strain in the partially extended network chains. This leads to non-affine orientation behaviour, and relates the finite extensibility of the chains to the finite elasticity of the network.