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Stochastic approach to glass transitions

玻璃化转变的随机方法

基本信息

批准号：
02640275
负责人：
ODAGAKI Takashi
金额：
$ 0.96万
依托单位：
Kyoto Institute of Technology, Faculty of Engineering and Design
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

The main theme of the research project is to elucidate the dynamical properties of supercooled liquids near the glass transition, applying tlie trapping diffusion model to the stochastic dynamics of atoms seen in the supercooled liquids. We devised an efficient method to locate the glass transition point on the basis of the peak position of the non-Gaussian parameter. This method is powerful compared to the other methods, since the former uses only the informations at finite times. We used this method to fix the glass transition point for the soft-sphere liquid. In order to test the validity of the present model and compare the model with the softsphere system, we studied the waiting time distribution function and derived the explicit relation between the parameter in the model and the softsphere systems. We also studied the effect of the finite observation time. We showed that due to the subanomalous diffusion, the time required for the determination of physical quantities within a given accuracy increases before the glass transition point is reached. We also investigated the intermediate scattering function and the dynaurical structure factor and showed that the subanomalous regime of the trapping diffusion yields the characteristics of the alpha-relaxation, where the dynamical structure fac'Lor as a function of frequency decreases in a power-law form or the intermediate scattering function decreases stretched-exponentially in time.

该研究项目的主题是阐明玻璃化转变附近过冷液体的动力学特性，将捕获扩散模型应用于过冷液体中原子的随机动力学。我们设计了一种根据非高斯参数的峰值位置来定位玻璃化转变点的有效方法。与其他方法相比，该方法非常强大，因为前者仅使用有限次数的信息。我们使用这种方法来确定软球液体的玻璃化转变点。为了检验该模型的有效性并将模型与软球系统进行比较，我们研究了等待时间分布函数，并推导了模型中的参数与软球系统之间的显式关系。我们还研究了有限观察时间的影响。我们表明，由于亚反常扩散，在达到玻璃化转变点之前，在给定精度内确定物理量所需的时间会增加。我们还研究了中间散射函数和动态结构因子，并表明俘获扩散的亚反常状态产生了 α 弛豫特征，其中动态结构 fac'Lor 作为频率的函数以幂律形式减小，或者中间散射函数随时间呈指数拉伸减小。