Relaxation mode coupling and universality in stress-strain cycles of networks including the glass transition region

Abstract

The temperature and strain rate dependence of stress-strain cycles of poly(methyl methacrylate) (PMMA) networks are investigated. The van der Waals theory of polymer networks describes the quasi-static stress-strain behaviour. Time-dependent effects during deformation are treated within the framework of irreversible thermodynamics. The Gibbs function of the network is extended by an appropriate set of hidden variables. The orthogonal relaxation modes of the Onsager type, represented by these hidden variables, couple in an isotropic and scalar manner with the network (relaxation mode coupling model). The time dependence of the nominal force is characterized by a relaxation time distribution that is independent of strain and of the deformation mode. In the thermodynamic limit the strain-energy of the network is the fundamental state of reference even at large strains. In the rubbery region the Williams-Landel-Ferry (WLF) equation describes thermorheological simple behaviour. In the glass transition region, the WLF-shift procedure fails when the mean relaxation time becomes large (WLF boundary). A specific, but universal modification of the WLF-shift procedure due to the strain-induced process of polymer segments changing place is observed and results in a unique frequency-temperature relationship (elastic and rheological simple behaviour).