A model of heterogeneous undercooled liquid and glass accounting for temperature-dependent nonexponentiality and enthalpy fluctuation.

Dynamic heterogeneity is a fundamental characteristic of glasses and undercooled liquids. The heterogeneous nature causes some of the key features of systems' dynamics such as the temperature dependence of nonexponentiality and spatial enthalpy fluctuations. Commonly used phenomenological models such as Tool-Narayanaswamy-Moynihan (TNM) and Kovacs-Aklonis-Hutchinson-Ramos fail to fully capture this phenomenon. Here we propose a model that can predict the temperature-dependent nonexponential behavior observed in glass-forming liquids and glasses by fitting standard differential scanning calorimetry curves. This model extends the TNM framework of structural relaxation by introducing a distribution of equilibrium fictive temperature (Tfe) that accounts for heterogeneity in the undercooled liquid. This distribution is then frozen at the glass transition to account for the heterogeneous nature of the glass dynamics. The nonexponentiality parameter βKWW is obtained as a function of temperature by fitting the Kohlrauch-Williams-Watts (KWW) equation to the calculated relaxation function for various organic and inorganic undercooled liquids and glasses. The calculated temperature dependent βKWW shows good agreement with the experimental ones. We successfully model the relaxation dynamics far from equilibrium for two silicate systems that the TNM model fails to describe, confirming that temperature dependent nonexponentiality is necessary to fully describe these dynamics. The model also simulates the fluctuation of fictive temperature δTf during isothermal annealing with good qualitative agreement with the evolution of enthalpy fluctuation reported in the literature. We find that the evolution of enthalpy fluctuation during isothermal annealing heavily depends on the cooling rate, a dependence that was not previously emphasized.