A Unified Theory for the Glass Transition Dynamics and its Singularities
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T. ODAGAKI, J. MATSUI, M. FUJISAKI AND M. HIGUCHI Department of Physics, Kyushu University, Fukuoka 812-81, Japan
ABSTRACT Vitrification is a gradual freezing process of supercooled liquids, during which a slow process is separated from the fast diffusive and microscopic motions. The slow process is identified as a non-trapped jump motion and can be characterized by the waiting time distribution (WTD) of the elementary relaxation process. We first show that the WTD can be expressed as a power law function in the long time limit in general with modest assumptions. Defining the glass transition temperature by vanishing diffusivity or the divergence of the mean waiting time, we relate the exponent to the Adam-Gibbs parameter Tsc(T) where T is the temperature and sc(T) is the excess entropy. We also show that the divergence of the fluctuation of WTD leads to a cross over in the non-Gaussianity and present a unified view of the dynamics in the vitrification process.
INTRODUCTION The most important feature of glass formers from the point of view of application is the gradual change in viscosity and other dynamical properties with temperature. This is a clear contrast to crystallization in which the structural arrest takes place suddenly at the freezing point. In this gradual "freezing" process, various characteristic temperatures have been observed, defined or suggested from experiments: From the lowest, the Vogel-Fulcher temperature To [1] at which the viscosity measured near the glass transition temperature is extrapolated to diverge as ,-' exp[DTo/(T-To)], the Kauzmann temperature TK [2], close to To, at which the excess entropy in the supercooled state is extrapolated to vanish, the glass transition temperature T. at which some thermodynamic quantities exhibit anomalies and a cross over temperature T, where liquid-like dynamics changes to solid-like dynamics[3]. In this paper we first present the gradual transition from liquid to amorphous solid state for the dynamical properties of a supercooled binary soft-sphere system obtained by molecular dynamics (MD) simulation. We attribute the slowest mode to a concerted jump motion from the trapped site and the fast motion to the trapped diffusion and rapid oscillation in a trapped region. To characterize the slowness, we introduce the waiting time distribution (WTD) which can be shown to be a power-law function of time in the long time limit. We show the power can be related to a scaled parameter [Tsc(T) Tg sc(Tg)]/Tgsc(Tg), where sc(T) is the excess entropy of the system at temperature T. We also present unique behavior of the non-Gaussianity parameter which may be used as a technique to identify the cross over point. We summarize our results by proposing a unified view of the change in dynamics in the verification process.
163 Mat. Res. Soc. Symp. Proc. Vol. 455 ©1997 Materials Research Society
SEPARATION OF SLOW PROCESS We first present the result of MD simulation for a binary soft-sphere mixture composed of N 1 atoms of mass m, and diameter al and N 2 atoms of mas
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