TANAKA LAB. Physics of Soft Condensed Matter The University of Tokyo Graduate School of Engineering Department of Applied Physics The University of Tokyo Institute of Industrial Science Department of Fundamental Engineering
Entrance > Research > Liquid, Glass, Gel > Two-Order Parameter Model > Two-Order-Parameter Description of Glass Transition Covering Its Strong to Fragile Limit
Polymer, Liquid Crystal, Colloid, Membrane, ProteinLiquid, Glass, GelLight and Soft Matter
Liquid-Liquid Transition in the Molecular LiquidCritical-Like Phenomena Associated with Liquid-Liquid TransitionLiquid-Liquid Transition under Spatial ConfinementSimple View of Waterlike AnomaliesTwo-Order-Parameter Description of Critical Phenomena and Phase Separation of Supercooled LiquidsTwo-Order-Parameter Description of Glass Transition Covering Its Strong to Fragile LimitFrustration on the Way to Crystallization in GlassGlass Transition in a Polydispersed Colloidal SystemGlass Transition and Jamming in a Driven Granular SystemAging and Shear Rejuvenation of a Colloidal GlassKinetics of Crystallization under a Glass Transition TemperatureViolation of the Incompressibility of Liquid by Simple Shear Flow

Two-Order-Parameter Description of Glass Transition Covering Its Strong to Fragile Limit

Two-Order-Parameter Description of Glass Transition Covering Its Strong to Fragile Limit 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 T of the corresponding pure system without frustration and the Vogel–Fulcher temperature T_0. Glass transition is then characterized by these two transitions: (A) a transition from an ordinary-liquid state to a Griffiths-phase-like state at T, 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 T_0 and the resulting divergence of the lifetime of metastable islands, namely, the relaxation time. Between T and T_0, a system has a complex free-energy landscape characteristic of the Griffiths-phase-like state, which leads to the non-Arrhenius behavior of relaxation and dynamic heterogeneity below T. 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.”

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