Dynamical singularities near the liquid-glass transition: Theory and molecular dynamics study

Abstract

This review article discusses recent developments in the study of the dynamical property of supercooled liquids close to the liquid-glass transition, in particular the dynamical singularity accompanied by the transition. The glass transition is a dynamical transition in the sense that when a liquid is rapidly cooled or compressed beyond the freezing point, the system can go into a quasi-equilibrium, metastable or nonequilibrium state, characterized by long structural relaxation times. Therefore, investigations on the dynamical properties of the supercooled liquids are essential to understanding the nature of the liquid-to-glass transition, which are the main issues of this article. The article reviews recent molecular dynamics studies on the dynamical properties of highly supercooled liquids and glasses and the theoretical developments about the liquid-glass transition based on mode-coupling approximations, generalized nonlinear hydrodynamic equations and a trapping diffusion model which have extensively been studied over the past decade. The molecular dynamics simulations prove to be an extremely useful and increasingly valuable aid to the elucidation of glass transition phenomena and the study of amorphous structures, but care is needed in the interpretation of the simulation results on the dynamical properties of such highly supercooled liquids and glasses, in which dynamical slowing down is essential, and consequently the relaxation time exceeds far over the order of the time investigated in computer experiments. We examine a variety of results on the dynamical behaviors obtained by molecular dynamics simulations and theoretical works from different points of view, and elucidate the dynamical singularity near the transition, which we call “quasi critical phenomena”, as in the second-order phase transition.