Crossover between solid-like and liquid-like behavior in supercooled liquids

In supercooled liquids, at a temperature between the glass transition temperature (Tg) and the melting point (Tm), thermodynamic properties remain continuous, while dynamic behavior exhibits anomalies. The origin of such thermodynamics-dynamics decoupling has long been a puzzle in the field of glass researches. In this study, we show that this feature can be effectively characterized by the ratio of the characteristic relaxation time associated with the relative and center-of-mass coordinates of nearest-neighbor atomic pairs. In addition, supercooled liquids can be categorized into two distinct "states" based on their dynamics: solid-like and liquid-like behaviors. We further propose four possible paths from the liquid to the final glass state, each exhibiting unique dynamic behaviors. Two of these paths predict a characteristic temperature Tx between Tm and Tg, where a crossover between solid-like and liquid-like behaviors occurs in supercooled liquids. The molecular dynamics simulations of several supercooled liquids reveal that the actual path followed by all these systems undergoes the crossover between solid-like and liquid-like behaviors. This crossover provides a new microscopic perspective, i.e., an easy-to-understand atomic-level picture, for explaining macroscopic dynamic anomalies.