Two-order-parameter model of the liquid–glass transition. I. Relation between glass transition and crystallization

Recently we proposed a two-order-parameter model of liquid to understand the liquid–glass transition, liquid–liquid transition, and anomalies of water-type liquids in a unified manner. Here we discuss the relation between our model and previous models of the liquid–glass transition, focusing on the difference in the basic standpoint among the models. We argue that (i) actual liquids universally have a tendency of spontaneous formation of locally favored structures and (ii) liquid–glass transition is controlled by the competition between long-range density ordering toward crystallization and short-range bond ordering toward the formation of locally favored structures due to the incompatibility in their symmetry. Thus, we regard vitrification as phenomena that are intrinsically related to crystallization. Previous models, on the other hand, regard vitrification as a result of (a) an homogeneous increase in the density and the resulting cooperativity in molecular motion or (b) the frustration intrinsic to a liquid state itself. Accordingly, they presuppose the kinetic avoidance of crystallization and thus do not put focus on ‘crystallization’. This leads to the essential difference in the physical picture between our model and previous models. By comparing models, we aim at gaining further insight into what is the physical origin of the liquid–glass transition and its possible connection with crystallization.