Physics of the iso-structural viscosity

This paper examines both experimental data and theoretical understanding of iso-structural viscosity in fragile glass forming liquids. Available experimental data in wide variety of systems are reviewed to establish generic features of iso-structural viscosity and quantitative values of some pertinent parameters are tabulated. These generic features are used to test the validities of existing phenomenological models of iso-structural viscosity. It is concluded that the existing models have significant limitations. For example, the Adam–Gibbs model fails to explain the observed inequality in several systems of iso-structural and equilibrium pre-exponential factors. The main contribution of this paper is a new model of iso-structural viscosity based on continuous time random walk through meta-basins in the potential energy landscape of a system. There are two main ingredients of this model: trap model of continuous time random walk through the meta-basins (MB) and a percolation energy level as the transition state that determines the average escape rate out of a MB. The model is solved for the Gaussian MB landscape that is considered a model for fragile liquids. Analytical expression is derived for the temperature dependences of iso-structural viscosity. It is shown that the model is in qualitative agreement with all generic features of iso-structural viscosity. The expression for the iso-structural viscosity contains three fitting parameters (an attempt frequency, the energy of the transition state, and the shape of the landscape) and reduces, in equilibrium, to the one proposed by Heuer and Saksaenggwijit in 2008. Additional support for the model is provided by analyzing the previously published low temperature viscosity data of Fontana and Plummer in eight silicate melts. The model predicts that, in general, iso-structural viscosity is non-Arrhenius and the deviation from the Arrhenius behavior increases with increase in the fragility of the system.