How to Distinguish Nonexponentiality and Nonlinearity in Isothermal Structural Relaxation of Glass-Forming Materials

The nonexponentiality and nonlinearity are two essential features of the structural relaxation in any glass-forming material, which seem to be inextricably bound together by the material time. It is shown that the temperature down-jump and up-jump experiments of the same magnitude ΔT = T₀ - T to the same temperature T provide a clue for their separation. The isothermal structural relaxation can be quantified using the stabilization period on the logarithmic time scale log(t_m/t₀). It is described as the sum of the nonexponentiality term 1.181/ß and the nonlinearity term (σ/2.303)ΔT for the temperature down-jump, and as their difference for the temperature up-jump. The material parameter σ = -(∂lnτ/∂T_f)_i quantifies variation of the relaxation time with structural changes at the inflection point of the relaxation curve and is formulated for the most widely used phenomenological models. The asymmetry of approach to equilibrium after the temperature down-jump and up-jump was first described by Kovacs in 1963. A detailed analysis of this asymmetry is provided, and a simple method for the estimation of the parameters characterizing the nonexponentiality (ß) and nonlinearity (σ) is proposed. The applicability of this method is tested using previously reported isothermal experimental data as well as calculated data for aging of polymers and other glass-forming materials. This concept illuminates differences in structural relaxation kinetics in a simple and consistent way that can be useful in the design of novel materials and the evaluation of their physical aging treatment.