Use of the Fixman–Alben distribution function in the analysis of non-Gaussian rubber-like elasticity

A probability distribution of the end-to-end distance of a polymer chain obtained by Fixman and Alben and recommended particularly for short chains is employed here in the calculation of stress–strain isotherms for a polymer network in elongation. The specific systems investigated are bimodal elastomeric networks containing a large enough number of very short chains to give markedly non-Gaussian behavior. The general shape of the experimental isotherms and its dependence on the relative numbers of very short and long chains are satisfactorily reproduced by the calculated results.