Krishnan S H, Ayappa K G
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India.
J Chem Phys. 2006 Apr 14;124(14):144503. doi: 10.1063/1.2183312.
An accurate model for the density of states (DOS) for strongly inhomogeneous and bulk fluids has been proposed based on gamma distributions. The contribution to the density of states from the collective dynamics is modeled as an incomplete gamma distribution and the high frequency region is obtained from the solution of the memory equation using a sech memory kernel. Using only the frequency moments as input, the model parameters for the collective dynamics are obtained by matching moments of the resulting distribution. The model results in an analytical expression for the self-diffusivity of the fluid. We present results for soft sphere fluids confined in slit-shaped pores as well as bulk soft sphere liquids. Comparisons of the DOS, velocity autocorrelation functions, and memory kernels with molecular dynamics simulations reveal that the model predicts features in the DOS over the entire frequency range and is able to capture changes in the DOS as a function of fluid density and temperature. As a result the predicted VACFs, memory kernels, and self-diffusivities are accurately predicted over a wide range of conditions. Since the frequency moments for bulk liquids can be obtained from pair correlation functions, our method provides a direct route from fluid structure to dynamics. For fluids confined in slit-shaped pores, where the frequency moments are obtained from molecular dynamics simulations, the predicted self-diffusivities capture the resulting oscillations due to variations in the solvation pressure, and in the case of smooth walled pores, the predictions are superior to those obtained using kinetic theory.
基于伽马分布，提出了一种针对强非均匀和体相流体的态密度（DOS）精确模型。集体动力学对态密度的贡献被建模为不完全伽马分布，高频区域则通过使用双曲正割记忆核求解记忆方程得到。仅将频率矩作为输入，通过匹配所得分布的矩来获得集体动力学的模型参数。该模型得出了流体自扩散系数的解析表达式。我们给出了限制在狭缝形孔中的软球流体以及体相软球液体的结果。将态密度、速度自相关函数和记忆核与分子动力学模拟进行比较表明，该模型在整个频率范围内预测了态密度的特征，并且能够捕捉态密度随流体密度和温度的变化。结果，在广泛的条件下准确预测了预测的速度自相关函数、记忆核和自扩散系数。由于体相液体的频率矩可以从对关联函数中获得，我们的方法提供了一条从流体结构到动力学的直接途径。对于限制在狭缝形孔中的流体，其频率矩通过分子动力学模拟获得，预测的自扩散系数捕捉了由于溶剂化压力变化而产生的振荡，并且在光滑壁孔的情况下，预测结果优于使用动力学理论获得的结果。
