Modelling Volume Relaxation Of Amorphous Polymers: Modification Of The Equation For The Relaxation Time In The KAHR Model

An expression for the relaxation time, τ, which applies both in the liquid and in the glassy state, is proposed and coupled with the kinetic equation for the volume relaxation of the KAHR (Kovacs, Aklonis, Hutchinson, and Ramos) phenomenological theory. The expression for τ reproduces the WLF (Williams, Landel, and Ferry) behaviour above the glass transition temperature, contains the thermodynamic scaling proposed by Casalini and Roland, gives finite values of the equilibrium relaxation time for any value of temperature and pressure, and is assembled in way that the relationship between the logarithmic relaxation time and the internal order parameter is strongly nonlinear even when the system is very close to the equilibrium. The resulting model contains ten parameters, and five of these are treated as fitting parameters. With one set of model parameters, the model is able to describe quantitatively the isobaric specific volume response on cooling at various rates and as a function of pressure, the overshoot response on heating after cooling at different rates, the pressure dependence of Tg, the asymmetry of response that characterizes volume relaxation after temperature up and down jumps, and the tau-effective paradox and associated expansion gap. The model also reasonably predicts the overshoot response observed after the two-step memory experiment