Quantum-mechanical model of viscous flow near the glass transition

Abstract A model of viscous flow is proposed in which the normal local vibrations of the kinetic units responsible for the process are treated as one-dimensional quantum harmonic oscillators, and the elementary act consists of the transition of kinetic units to a new equilibrium state upon reaching a critical value of the reaction coordinate during thermal motion. The glass transition process is considered as the freezing-out of a particular frequency of local vibrations. The obtained temperature dependence of viscosity qualitatively agrees with experimental data over a wide temperature range and can be described by a semi-empirical one- or two-parameter function that takes into account the law of corresponding states for a specific class of glasses. Quantitative discrepancies between the empirical parameters and generally accepted estimates characterise the role of structural changes during the glass transition. Within the proposed model, the possibility of a cooperative nature of the elementary act of viscous flow during glass transition is discussed as an analogy to a chain reaction.