Mode Coupling Theory and Trapping Model of Glass Transition

1. 结果表明，过冷液体中原子的跳变率分布函数由幂律函数给出，幂由慢弛豫模式和快弛豫模式的贡献比决定。利用Fuchs等人利用模式耦合理论导出的硬球系统弛豫时间的波数依赖性，确定了给定尝试频率下快、慢模之间的迁移率边缘。利用捕获模型中迁移率边与关键参数之间的关系确定了玻璃化转变温度和Vogel-Fulcher温度，结果表明，在迁移率边关闭之前，玻璃化转变发生，迁移率边关闭时的温度对应于Vogel-Fulcher温度。在玻璃化转变温度附近，易碎玻璃形成物的比热用[TSc(T)-TgSc(Tg)]来标度，这与表征原子动力学更轴化的参数相同。对双原子分子在过冷状态下的弛豫过程进行了理论分析，结果表明，对密度波动的敏感性可以表示为质心运动和内自由度运动的贡献之和。通过分子动力学模拟，表明双原子分子过冷液体的旋转弛豫与平动弛豫分离，产生Arrhenius型的Johari-Goldstein过程。建立了能量景观图描述的非平衡系统比热计算的理论框架。将该框架应用于具有两个能量盆的氢气，得到了比热随观测时间的温度依赖关系。结果表明，退火和淬火平均取决于两个流域之间的跳跃速率，并得到冷却速率与退火程度之间的关系。少

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