An existence of universality in the dynamics of two types of glass-forming liquids -- fragile liquids and strong liquids

Abstract

By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. The numerical solutions are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a static structure factor for a whole system. It is confirmed based on four different simulation results that the supercooled state consists of two substates, a weakly supercooled state in which the nonlinear parameter $μ$ in the memory function increases as $D$ decreases and a deeply supercooled state in which $μ$ becomes constant up to the glass transition. Here $μ$ is shown to be constant in a liquid state, while it is shown to grow rapidly in a glass state. The value of $μ$ in each state is shown to be uniquely determined by $D$ and also to depend on a type of liquids. Hence there exists such a universality that there is only one solution for different liquids of a same type at a given value of $D$. This may be consistent with the fact that strong liquids are structurally quite different from fragile liquids. Thus, it is emphasized that such a universality must be helpful to predict $q_m$ from experimental data.