Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener–Volterra approach and extended Tool–Narayanaswamy–Moynihan models

Abstract

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener–Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool–Narayanaswamy–Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole–Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole–Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener–Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.