H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.
J Chem Phys. 2010 Dec 14;133(22):224505. doi: 10.1063/1.3511719.
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
我们描述了一种基于动理学密度泛函理论（DDFT）的测试粒子方法，用于研究构成流体的粒子的相关时间演化。我们的理论提供了一种通过将自部分和独特部分视为二元流体混合物的两个组成部分来计算范霍夫分布函数的方法，其中“自”部分只有一个粒子，“独特”部分由所有其他粒子组成，并使用 DDFT 来计算两个组成部分的密度分布的时间演化。我们将此方法应用于布朗硬球的体相流体，并将结果与范霍夫函数和来自布朗动力学计算机模拟的中间散射函数进行比较。我们在低和中等密度下使用非常简单的 Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] 过剩自由能泛函近似得到了很好的一致性。由于 DDFT 基于平衡亥姆霍兹自由能泛函，我们可以探测到动力学的基础自由能景观。在平均场近似下，我们发现随着粒子密度的增加，这个景观会发展出一个最小值，而对一个受限模型的精确处理表明，对于一个遍历性的流体，这个景观应该是单调的。我们讨论了在高密度下可能对缓慢、玻璃态和被捕获的动力学的影响。
