Chemical and Biomolecular Engineering Department, The University of Akron, Akron, Ohio 44325-3906, USA.
Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
J Chem Phys. 2019 Nov 28;151(20):204501. doi: 10.1063/1.5126281.
In Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] of this series, a methodology was presented for computing the coefficients of a power series of the Helmholtz energy in reciprocal temperature, β, through density series based on cluster integral expansions. Previously, power series in β were evaluated by thermodynamic perturbation theory (TPT) using molecular simulation of a reference fluid. The present methodology uses cluster integrals to evaluate coefficients of the density expansion at each individual order of temperature. While Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] developed this methodology for square well (SW) spheres, the present work extends the methodology to Lennard-Jones (LJ) spheres, where the reference fluid is the Weeks-Chandler-Andersen potential. Comparisons of TPT coefficients computed from cluster integrals to those from molecular simulation show good agreement through third order in β when coefficients are expressed with effective approximants. Notably, the agreement for LJ spheres is much better than for SW spheres although fewer coefficients of the density series (B-B) are available than for SW spheres (B-B). The coefficients for B(β) of the reference fluid are shown to follow a simple relationship to the virial coefficients of hard sphere fluids, corrected for the temperature dependency of the equivalent hard sphere diameter. This lays the foundation for a correlation of the second virial coefficient of LJ spheres B(β) that extrapolates to infinite order in temperature. This correlation of B(β) provides a basis for estimating the low density limit of TPT coefficients at all orders in temperature, facilitating a recursive extrapolation formula to estimate TPT coefficients of fourth order and higher over the entire density range. The applicability of the resulting equation of state is demonstrated by computing the thermodynamic properties for LJ spheres and comparing to standard simulation results.
在本系列的论文 I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] 中，提出了一种通过基于团簇积分展开的密度级数来计算以倒数温度 β 为变量的亥姆霍兹自由能的幂级数系数的方法。在此之前，通过分子模拟参考流体的热力学摄动理论（TPT）评估了 β 中的幂级数。本方法使用团簇积分在每个温度阶评估密度展开的系数。虽然论文 I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] 为方阱（SW）球发展了这种方法，但本工作将该方法扩展到 Lennard-Jones（LJ）球，其中参考流体是 Weeks-Chandler-Andersen 势。通过有效逼近，将从团簇积分计算得到的 TPT 系数与从分子模拟得到的系数进行比较，结果表明，在β的三阶时，两者吻合较好。值得注意的是，LJ 球的吻合度比 SW 球好得多，尽管密度级数（B-B）的系数比 SW 球少。参考流体的 B(β)系数被证明与硬球流体的第二维里系数存在简单关系，对等效硬球直径的温度依赖性进行了修正。这为 LJ 球的第二维里系数 B(β)的关联奠定了基础，该关联可以在温度的无穷阶外推。这种 B(β)关联为在所有温度阶上估计 TPT 系数的低密度极限提供了基础，从而可以递归外推公式来估计整个密度范围内四阶及更高阶的 TPT 系数。通过计算 LJ 球的热力学性质并与标准模拟结果进行比较，证明了所得状态方程的适用性。
