Theoretical Study of Glass Transition and Slow Dynamics

本课题的研究主题是统一地了解玻璃化过程的动力学特性，阐明玻璃形成过程的物理特性。对捕集扩散模型（TDM）进行了较为深入的研究，并给出了该模型的理论基础。我们还进行了分子动力学模拟，以了解过冷液体动力学性质的变化。我们将TDM扩展到包括捕获运动和非捕获跳跃运动，并得到了动态结构因子。证明了主弛豫时间服从Vogel-Fulcher定律，得到了与实验定性一致的非高斯性。我们还设计了一种新的技术（log-Cole-Cole分析），用它我们可以很容易地找到松弛的性质。对一个涵盖液态、过冷液态和玻璃态的二元软球系统进行了广泛的MD模拟。我们发现了主要弛豫时间、玻色子峰和快速过程的Vogel-Fulcher定律。我们提出了一个由振荡和两种随机运动组成的理想三模型模型，并表明该模型可以再现过冷液体的动力学特性。广泛讨论了TDM的基础，并表明在具有随机活化能的激活过程的系统中通常会观察到类似的动力学。我们还证明了各种矩的散度表示动力学转变，并且温度差乘以玻璃化转变点的多余熵值可以作为转变的标度参数。

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.