Theoretical Study of Glass Transition and Slow Dynamics

本研究项目的主题是以统一的方式理解玻璃化过程的动力学性质，并阐明玻璃形成过程的物理机制。对捕获扩散模型（TDM）进行了较深入的研究，给出了模型的理论基础。我们还进行了分子动力学模拟，研究了过冷液体动力学性质的变化，将TDM扩展到包含囚禁运动和非囚禁跳跃运动，得到了动力学结构因子。我们证明了主弛豫时间服从Vogel-Fulcher定律，得到了与实验定性相符的非高斯性，并设计了一种新的分析方法（log-科尔-科尔分析），用它可以很容易地发现弛豫的本质。我们发现Vogel-Fulcher定律的主要弛豫时间，玻色子-本文提出了一个由振荡和两种随机运动组成的理想三模模型，并证明了该模型能再现过冷液体的动力学特性。本文还对三模模型的基础作了广泛的讨论，并指出在具有随机运动的活化过程的系统中，通常也能观察到类似的动力学特性活化能我们还表明，发散的各种时刻表示的动力学转变和温度乘以过剩熵从其值的玻璃化转变点的差异可以作为转换的标度参数。

The main theme of the present research project is to understand the dynamical properties of vitrification process in a unified manner and to elucidate the physics of the glass forming process. We studied the trapping diffusion model (TDM) more throughly and gave the theoretical foundation of the model. We also performed a molecular dynamics simulation to find out the changes in dynamical properties of supercooled liquids.We extended the TDM to include the trapped motion as well as the non-trapped jump motion and obtained the dynamical structure factor. We showed that the main relaxation time obeys the Vogel-Fulcher law and obtained the non-Gaussianity which agees qualitatively with experiments.We also devised a new technique (log-Cole-Cole analysis) with which we can find easily the nature of the relaxation.The extensive MD simulation was carried out for a binary soft shpere system covering the liquid state, supercooled liquid state and glassy state. We found the Vogel-Fulcher law for the main relaxation time, Boson-peak and the fast process.We proposed an ideal three model mode consisting of an oscillation and two kinds of stochastic motions and showed that this model can reproduce the dynamical charasteristics of supercooled liquids.The foundation of the TDM was discussed extensively and it was shown that similar dynamics would be commonly observed in systems with activation processes with randam activation energies. We also showed that the divergence of various moments signifies the dynamical transitions and that the difference of temerature multiplied by the excess entropy from its value the glass transition point can serve as the scaling parameter for the transition.