Siderius Daniel W, Gelb Lev D
Department of Chemistry and Center for Materials Innovation, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
J Chem Phys. 2009 Aug 28;131(8):084503. doi: 10.1063/1.3207883.
Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.
我们运用分子模拟和理论，研究了晶格上硬球流体的液相热力学和结构性质。我们开展这项工作的目的是为晶格密度泛函理论[D. W. 西迪里厄斯和L. D. 格尔布，《朗缪尔》25, 1296 (2009)]及相关微扰理论提供参考数据。在此模型中，硬球位于精细离散的立方晶格的格点上，格点间距在硬球直径的十分之一到三分之一之间。我们精确计算了第二、第三和第四维里系数作为晶格间距的函数。通过蒙特卡罗模拟，我们测量了几种晶格间距下过量化学势随密度的变化。然后将这些结果用一种方便的函数形式进行参数化，可立即用于晶格密度泛函理论。特别令人感兴趣的是确定那些能产生与非晶格流体性质相似的晶格间距。我们发现晶格上流体的性质强烈依赖于晶格间距，一般来说，随着晶格分辨率的提高，其性质趋近于非晶格流体，但并非平滑趋近。这些观察结果与较大晶格间距的结果[A. Z. 帕纳吉奥托普洛斯，《化学物理杂志》123, 104504 (
