Mode Coupling Theory and Trapping Model of Glass Transition

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1. It was shown that the jump rate distribution function of atoms in supercooled liquids is given by a power law function and that the power is determined by the ratio of the contribution of slow and fast relaxation modes.2. Using the wave number dependence of the relaxation time for a hard sphere system derived by Fuchs et al with the mode coupling theory, the mobility edges between fast and slow modes were determined for a given attempt frequency. The relation between the mobility edges and the key parameter in the trapping model was exploited to determine the glass transition temperature and the Vogel-Fulcher temperature and it was shown that the glass transition occurs before the mobility edges are closed and the temperature at which the mobility edges are closed corresponds to the Vogel-Fulcher temperature.3. The specific heat of fragile glass formers near the glass transition temperature was shown to be scaled by [TSc(T)-TgSc(Tg)] which is the same parameter chracterizing the rel … More axation of atomic dynamics.4. The relaxation process of diatomic molecules in the supercooled state was analyzed theoretically and it was shown that the susceptibility for the density fluctuation can be written as sum of the contributions due to the motion of the center of mass and the motion of the internal degree of freedom.5. By the molecular dynamics simulation, the rotational relaxation of a diatomic molecular supercooled liquid was shown to separate from the relaxation of the translational motion, giving rise to the Johari-Goldstein process of the Arrhenius type.6. The theoretical frame work was established to calculate the specific heat of non-equilibrium systems described by the energy landscape picture. The frame work was applied to the hydrogen gas which has two energy basins and the temperature dependence of the specific heat was obtained as a function of the observation time. It was shown that annealed and quenched averages are obtained depending on the jump rate between two basins and the relation between the cooling rate and the degree of annealing are obtained. Less