Theoretical Model of Polymer Network Chain Formation under Strain

In this article, the polymer network chain formation through cross-linking and scission under n strain stages is studied based on the thermal fluctuation principle. The aim is to clarify the effects of chemical reactions, especially the network chain cross-linking, dangling chain cross-linking, cross-link scission, and network chain scission, on the free energy of network chain to generalize the classical two-network model. In our model, the free energy change for a chain formation is associated with the reaction sequences, except network chain cross-linking or cross-link scission reactions under the same strain stage. A new constitutive expression for network chain formed under two strain stages is derived according to affine deformation theory in which independent network hypothesis and stress-transfer function are not required. Comparison between our model and previous experimental data about recovered stretch ratio of γ-irradiated silicone elastomer validates that our model can give more precise result than previous two-network model.