Two-order-parameter description of liquids. I. A general model of glass transition covering its strong to fragile limit

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Abstract
Here we propose a simple physical model that may universally describe glass-transition phenomena from the strong to the fragile limit. Our model is based on the idea that there always exist two competing orderings in any liquids, (i) density ordering leading to crystallization and (ii) bond ordering favoring a local symmetry that is usually not consistent with the crystallographic symmetry. The former tries to maximize local density, while the latter tries to maximize the quality of bonds with neighboring molecules. For the phenomenological description of these competing ordering effects [(i) and (ii)] hidden in many-body interactions, we introduce density and bond order parameters, respectively. This leads to the following picture of a liquid structure: Locally favored structures with finite, but long lifetimes are randomly distributed in a sea of normal-liquid structures. Even simple liquids suffer from random disorder effects of thermodynamic origin. We argue that locally favored structures act as impurities and produce the effects of “fluctuating interactions” and “symmetry-breaking random field” against density ordering, in much the same way as magnetic impurities for magnetic ordering in spin systems. Similarly to random-spin systems, thus, we predict the existence of two key temperatures relevant to glass transition, the density ordering (crystallization) point Tm* of the corresponding pure system without frustration and the Vogel–Fulcher temperature T0. Glass transition is then characterized by these two transitions: (A) a transition from an ordinary-liquid state to a Griffiths-phase-like state at Tm*, which is characterized by the appearance of high-density metastable islands with medium-range order, and (B) another transition into a spin-glass-like nonergodic state at T0 and the resulting divergence of the lifetime of metastable islands, namely, the α relaxation time. Between Tm* and T0, a system has a complex free-energy landscape characteristic of the Griffiths-phase-like state, which leads to the non-Arrhenius behavior of α relaxation and dynamic heterogeneity below Tm*. This simple physical picture provides us with a universal view of glass transition covering the strong to fragile limit. For example, our model predicts that stronger random-disorder effects make a liquid “stronger,” or “less fragile.”