A molecular-derived constitutive model of viscoelasticity based on chain statistical mechanics of polymers during cure

Polymers exhibit complex mechanical behaviors during curing process, ranging from viscous liquids to elastic solids, which are linked to the dynamic processes of the highly flexible polymer chains. However, these physical insights have not been fully integrated into the development of continuum model of viscoelasticity. Based on chain statistical mechanics, a molecular-derived constitutive model is developed to provide molecular picture that underlies the viscoelasticity of soft polymers during cure. The polymer network is assumed to comprise the entangled chain and crosslinked strands. At first, the stress evolution of a single entangled chain is derived from its dynamic process based on polymer dynamics. Then the effect of curing reaction on the dynamic process is analyzed by statistically describing the evolution of the network structure during cure. Finally, the stress constitutive equation of the whole network is derived based on the affine deformation assumption. The underlying molecular meanings of viscoelastic measurements such as the temperature shift factor, the cure shift factor and the relaxation spectrum, are demonstrated by the proposed model. Further, the connection between viscoelastic measurements and molecular dynamics as well as the physical foundation of the constitutive form is discussed.