Mechanics of Elastomers Based on Polymer Chain Length Statistics

Polymer chain length statistics as it results from the polymerization process has long been known in chemistry but has not so far been applied to mechanics of elastomers. In the present contribution, this chain length statistics is incorporated into a full network model. The free energy of such a network results from the integral of single chain energies over the unit sphere. The so derived multi-scale model is able to describe not only the elastic behavior but also inelastic effects peculiar to filled rubbers. These are, in particular, the Mullins effect, permanent set and strain induced anisotropy. Special attention is focused to modelling of rubbers reinforced by carbon nanotubes. The carbon nanotubes introduce additional cross-linking into the network and by this means influence the probability density function of chain lengths. Model predictions demonstrate good agreement with experimental data.