Mode Coupling Theory and Trapping Model of Glass Transition

1.证明了过冷液体中原子的跳跃速率分布函数为幂函数，其幂函数由慢弛豫模和快弛豫模的贡献之比决定。利用Fuchs等人推导的硬球系统弛豫时间与波数的关系，结合模式耦合理论，确定了在给定的尝试频率下，快模和慢模之间的迁移率边缘。利用迁移率边与陷阱模型中的关键参数之间的关系来确定玻璃化转变温度和Vogel-Fulcher温度，结果表明，玻璃化转变发生在迁移率边缘关闭之前，而迁移率边缘关闭的温度对应于Vogel-Fulcher温度。在玻璃化转变温度附近，易碎玻璃的比热由表征REL…的相同参数[Tsc(T)-TgSc(Tg)]来表示更多的原子动力学之轴。从理论上分析了双原子分子在过冷态的驰豫过程，证明了密度涨落的磁化率可以表示为质心运动和内部自由度运动的贡献之和。分子动力学模拟表明，双原子分子过冷液体的转动弛豫与平移运动的弛豫分离，产生Arrhenius类型的Johari-Goldstein过程。建立了计算能量景观图所描述的非平衡体系比热的理论框架。将该框架应用于具有两个能盆的氢气，得到了比热随观测时间的温度变化关系。结果表明，根据两个熔池之间的跳跃速率，得到了退火态和淬火态的平均值，并得到了冷却速率与退火度的关系。较少

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