Noah-Vanhoucke Joyce E, Andersen Hans C
Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2007 Aug 14;127(6):064502. doi: 10.1063/1.2752153.
We use computer simulation results for a dense Lennard-Jones fluid for a range of temperatures to test the accuracy of various binary collision approximations for the memory function for density fluctuations in liquids. The approximations tested include the moderate density approximation of the generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip [Statistical Mechanics. Part B. Time-Dependent Processes, edited by B. J. Berne (Plenum, New York, 1977)], the binary collision approximation (BCA) and the short time approximation (STA) of Ranganathan and Andersen [J. Chem. Phys. 121, 1243 (2004); J. Phys. Chem. 109, 21437 (2005)] and various other approximations we derived by using diagrammatic methods. The tests are of two types. The first is a comparison of the correlation functions predicted by each approximate memory function with the simulation results, especially for the self-longitudinal current correlation (SLCC) function. The second is a direct comparison of each approximate memory function with a memory function numerically extracted from the correlation function data. The MGBE memory function is accurate at short times but decays to zero too slowly and gives a poor description of the correlation function at intermediate times. The BCA is exact at zero time, but it predicts a correlation function that diverges at long times. The STA gives a reasonable description of the SLCC but does not predict the correct temperature dependence of the negative dip in the function that is associated with caging at low temperatures. None of the other binary collision approximations is a systematic improvement on the STA. The extracted memory functions have a rapidly decaying short time part, much like the STA, and a much smaller, more slowly decaying part of the type predicted by a mode coupling theory. Theories that use mode coupling commonly include a binary collision term in the memory function but do not discuss in detail the nature of that term. It is clear from the present work that the short time part of the memory function has a behavior associated with brief binary repulsive collisions, such as those described by the STA. Collisions that include attractive as well as repulsive interactions, such as those of the MGBE, have a much longer duration, and theories that include them have memory functions that decay to zero much too slowly to provide a good first approximation of the correlation function. This leads us to speculate that the memory function for density fluctuations can be usefully regarded as a sum of at least three parts: a contribution from repulsive binary collisions (the STA or something similar to it), another short time part that is related to all the other interactions (but whose nature is not understood), and a longer time slowly decaying part that describes caging (of the type predicted by the mode coupling theory).
我们使用一系列温度下稠密 Lennard-Jones 流体的计算机模拟结果，来测试用于液体密度涨落记忆函数的各种二元碰撞近似的准确性。所测试的近似包括 Mazenko 和 Yip [《统计力学。B 部分。时间相关过程》，由 B. J. Berne 编辑（Plenum，纽约，1977 年）] 的广义玻尔兹曼 - 恩斯科格记忆函数（MGBE）的中等密度近似、Ranganathan 和 Andersen [《化学物理杂志》121, 1243 (2004); 《物理化学杂志》109, 21437 (2005)] 的二元碰撞近似（BCA）和短时间近似（STA），以及我们通过图解方法推导的各种其他近似。测试分为两类。第一类是将每个近似记忆函数预测的关联函数与模拟结果进行比较，特别是对于自纵向电流关联（SLCC）函数。第二类是将每个近似记忆函数与从关联函数数据中数值提取的记忆函数进行直接比较。MGBE 记忆函数在短时间内是准确的，但衰减到零的速度太慢，并且对中间时间的关联函数描述不佳。BCA 在时间为零时是精确的，但它预测的关联函数在长时间时发散。STA 对 SLCC 给出了合理的描述，但没有预测到与低温下的笼效应相关的函数中负凹陷的正确温度依赖性。其他二元碰撞近似都没有在 STA 的基础上有系统的改进。提取的记忆函数有一个快速衰减的短时间部分，很像 STA，还有一个由模式耦合理论预测的类型的小得多、衰减更慢的部分。使用模式耦合的理论通常在记忆函数中包含一个二元碰撞项，但没有详细讨论该项的性质。从目前的工作可以清楚地看出，记忆函数的短时间部分具有与短暂的二元排斥碰撞相关的行为，例如 STA 所描述的那些碰撞。包括吸引和排斥相互作用的碰撞，如 MGBE 中的那些碰撞，持续时间要长得多，并且包含它们的理论的记忆函数衰减到零的速度太慢，无法为关联函数提供一个好的一阶近似。这使我们推测，密度涨落的记忆函数可以有效地看作至少由三部分组成：来自排斥二元碰撞的贡献（STA 或与其类似的东西）、与所有其他相互作用相关的另一个短时间部分（但其性质尚不清楚），以及描述笼效应的长时间缓慢衰减部分（模式耦合理论预测的类型）。
