Potential-energy landscape , supercooled

The concept of fragility is a qualitative one and is related to deviations of the relaxation time of a liquid from Arrhenius-like behavior and to the topology of the potential energy landscape of the system. The classification of liquids into strong and fragile thus provides a fundamental framework for quantitatively describing equilibrium and dynamical properties of supercooled liquids and glassy states of matter [1-6,8,9,22,37,38,52,54—56,88-91,103]. 

In Section VII we conclude our results and discuss several issues arising from our proposals. We revisit our original motivation—that is, to find a simple model, in the sense of dynamical systems, that captures several common aspects of slow dynamics in liquid water, or more generally supercooled liquids or glasses. Our attempt is to make clear the relation and compatibility between the potential energy landscape picture and phase space theories in the Hamiltonian dynamics. Importance of heterogeneity of the system is discussed in several respects. Unclarified and unsolved points that still remain but should be considered as crucial issues in slow dynamics in molecular systems are listed. 

We may list differences between the liquid water system and the FPU model the latter will be examined in the next section as a representative system in the study of many-dimensional Hamiltonian systems. The most important difference would be that the FPU model describes a lattice vibration around an equilibrium point and the potential energy function possesses a single minimum, whereas there are infinitely many local potential minima and the potential energy landscape generally becomes ragged in the case of the liquid water system. The reason why the character of the potential landscape could be so important is that the raggedness is considered as an origin of slow motions in liquid water or supercooled liquids. 

In Section II we define energy landscapes, and we present the formahsm that relates potential energy minima to the thermal properties of supercooled liquids and glasses. Section III discusses the characterization of voids in dense particle packings, and how this approach, combined with energy minimization techniques, can yield powerful new insights into the mechanical... 

Structural Models for Supercooled Liquids. - This approach focuses on the molecular order in the supercooled liquid. The potential energy surface or landscape (r ) where = n, 2. .. is a 3A-dimensional vector in phase space has a characteristic appearance in the various states of matter. In a liquid, the 4>-landscape has a distribution of many shallow energy minima. In a crystal there are a few steep and deep minima representing the collapse of the system into the crystalline states with long-range order. In a liquid simulation, each of these deep minima, or inherent structures as they are called, will be surromided... 

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