液体晶格模型的图解动力学理论。II. 理论与模拟结果的比较。

Feng Edward H, Andersen Hans C

Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA.

J Chem Phys. 2004 Aug 22;121(8):3598-604. doi: 10.1063/1.1773134.

We compare the predictions of the mean field, the two site multiple scattering, and the simple mode coupling approximation developed in the previous paper for the dynamics of a tagged particle in an excluded volume lattice gas with the results of computer simulations. The tagged particle has a transition rate of gamma while the background particles have transition rates of alphagamma. We consider the tracer diffusion coefficient and the incoherent intermediate scattering function (IISF) for low, intermediate, and high concentrations of particles and for simple square and cubic lattices. In general, the approximate kinetic theories are more accurate in predicting simulations results at low concentrations, high dimensions, and large alpha. For the tracer diffusion coefficient, the mean field approximation is the least accurate, the two site multiple scattering approximation is more accurate, and the simple mode coupling approximation is the most accurate; all three approximate theories overestimate the simulation results. For the IISF, the mean field approximation is quantitatively accurate in the limit of small concentration and large alpha but in general decays too quickly. The two site multiple scattering approximation is quantitatively accurate at low and intermediate concentrations for large wave vectors; it is always more accurate than the mean field approximation and always decays more quickly than the simulation results. The simple mode coupling approximation is the most accurate of the three approximations in most cases and especially so for small wave vectors, high concentration, and small alpha; unfortunately, its predictions are not quantitatively accurate in these highly nonmean field regimes. We discuss the implications of these results for developing diagrammatic kinetic theories.

我们将前一篇论文中针对被排除体积晶格气体中标记粒子动力学所发展的平均场、双位点多重散射以及简单模式耦合近似的预测结果，与计算机模拟结果进行比较。标记粒子的跃迁速率为γ，而背景粒子的跃迁速率为αγ。我们考虑了低、中、高粒子浓度以及简单正方晶格和立方晶格情况下的示踪扩散系数和非相干中间散射函数（IISF）。一般来说，近似动力学理论在预测低浓度、高维度和大α时的模拟结果时更为准确。对于示踪扩散系数，平均场近似最不准确，双位点多重散射近似更准确，简单模式耦合近似最准确；所有这三种近似理论都高估了模拟结果。对于IISF，平均场近似在低浓度和大α的极限情况下在定量上是准确的，但一般衰减太快。双位点多重散射近似在大波矢的低、中浓度下在定量上是准确的；它总是比平均场近似更准确，并且总是比模拟结果衰减得更快。简单模式耦合近似在大多数情况下是这三种近似中最准确的，特别是对于小波矢、高浓度和小α的情况；不幸的是，在这些高度非平均场区域中其预测在定量上并不准确。我们讨论了这些结果对发展图解动力学理论的意义。