Molecular dynamics study on the viscosity of glass-forming systems near and below the glass transition temperature

Temperature-dependent viscosity is critical to decipher two profound questions in condensed matter physics, namely the glass transition and the relaxation of amorphous solids. However, direct measurement of viscosity over a large temperature range is extremely difficult. Here, using classical molecular dynamics (MD) simulations, we report a novel method to calculate the equilibrium viscosity of supercooled liquid both above and below the glass transition temperature (T_g) and to estimate the nonequilibrium viscosity of glass down to room temperature. Based on the shoving model, we derived an analytical formula showing that the shear viscosity in logarithmic scale changes linearly with the shear-induced variation in shear modulus or potential energy of the glass-forming system. The shear viscosity as a function of steady-state potential energy of liquid under different shear strain rates can be directly calculated in MD simulations; together with its equilibrium potential energy, one can extrapolate the zero-strain-rate equilibrium viscosity. We verified the proposed model by reliably calculating equilibrium viscosity near T_g of four glass-forming systems (Kob–Andersen system, silica, Cu_45.5Zr_45.5Al₉, and silicon) with different fragilities. Furthermore, our model can estimate the nonequilibrium viscosity of glass below T_g; the upper-bound nonequilibrium viscosity of amorphous silica and silicon at room temperature are calculated to be ~10³² and 10²⁵ Pa·s, respectively.