Statistical Physics Study of Supercooled Colloidal Liquids and Colloidal Glass Transition

我们不仅通过构建理论，而且通过广泛的计算机模拟，对胶体玻璃相变进行了研究，取得了以下重要成果：1)为了阐明胶体之间的流体动力学相互作用如何在玻璃化相变附近发挥重要作用，我们对硬球系统进行了两种类型的计算机模拟，布朗动力学模拟和分子动力学模拟。通过基于德山最近提出的平均场理论的统一观点的分析，我们首先证明了玻璃化转变的发生离不开流体的相互作用。2)我们从第一原理出发数值求解了德山在2001年导出的密度涨落的非线性随机扩散方程，然后证明了由玻璃化转变附近的非线性密度涨落引起的长寿命空间不均匀是著名的两步弛豫的重要来源。3)德山从非线性随机扩散方程出发，推导出均方位移的非线性方程，从而提出了平均场理论。通过对几种不同的实验和模拟数据的分析，表明该方法不仅适用于胶体悬浮液，也适用于玻璃形成材料。因此，该理论预测了不同玻璃化转变之间的显著相似之处，并提出了一种与传统方法截然不同的方法来理解玻璃化转变，包括对数衰减和任何特征时间的无发散。

We have studied the colloidal glass transitions not only by constructing the theory but also by performing the extensive computer simulations and obtained the following important achievements.1)In order to clarify how the hydrodynamic interactions between colloids play an important role near the glass transition, we have performed two types of computer simulations on the systems of hard spheres, the Brownian-dynamics simulation and the molecular-dynamics simulation. By analyzing the data from a unified point of view based on the mean-field theory proposed recently by Tokuyama, we have thus first shown that the glass transition can not occur without the hydrodynamic interactions.2)We have numerically solved the nonlinear stochastic diffusion equation for the density fluctuations derived in 2001 by Tokuyama from a first principle and then shown that the long-lived spatial heterogeneities caused by the nonlinear density fluctuations near the glass transition are an important origin of a famous two-step relaxation.3)Tokuyama has proposed the mean-field theory by deriving the nonlinear equation for the mean-square displacement from the nonlinear stochastic diffusion equation. It has been shown to be applicable not only for colloidal suspensions but also for glass-forming materials by analyzing several different experimental and simulation data. The theory thus predicts remarkable similarities between different glass transitions and proposes an approach quite different from the conventional ones to understand the glass transition, including a logarithmic decay and no divergence of any characteristic times.