A statistically-based viscoelastic model for glass-forming polymers during cure

Abstract

Polymeric materials often exhibit complex viscoelastic behaviors during cure, which fundamentally arise from the dynamic processes of polymer network constituents in the rubbery and glass-forming state. However, these molecular mechanisms have not been fully integrated into the development of continuum model of cure-related viscoelasticity. By integrating statistical mechanics and mode coupling theory (MCT), this study develops a novel constitutive model for characterizing the cure-dependent viscoelastic behavior of glass-forming polymers. The proposed model treats the polymer network as a composite system consisting of two distinct dynamical components: (1) frozen Kuhn monomers underlying dynamics governed by MCT in the glass-forming state, and (2) entangled polymer chains following reptation dynamics in the rubbery state. The cure effects on these dynamics are considered by solving the MCT dynamic equations, which enables the derivation of a cure-related constitutive framework. The stress constitutive equation is derived from the statistical description of these dynamic processes. The model predictions are validated by comparing with the experimental data of four typical resins. The comparisons between theoretical predictions and experimental data are quite satisfactory. Furthermore, the physical insights of the stress relaxation behaviors in glassy and rubbery states are elaborated, together with a discussion of modeling the glass transition effects on the relaxation behaviors.