Seventh Virial Coefficients for Hard Spheres and Hard Disks
Seventh Virial Coefficients for Hard Spheres and Hard Disks
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DOI：
10.1063/1.1840521
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发表时间：
1967-06
影响因子：
4.4
通讯作者：
F. Ree;W. G. Hoover
中科院分区：
文献类型：
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作者：
F. Ree;W. G. Hoover
第七维里系数B7被表示为修正的星积分之和，而不是通常的Mayer星积分。新图包含Mayerf函数和f(≡1+f)函数。这简化了B7的计算。也就是说，取代了Mayer公式中出现的468个星积分，现在只有171个修改后的星积分出现在B7的评估中。此外，对于具有硬核的D维粒子，这171个积分强烈依赖于D的维数。对于硬棒、硬盘和硬球，分别至多有一个、78个和164个这些积分对B7有非零贡献。当用硬球和硬盘势用蒙特卡罗积分来计算这些积分时，我们得到B7的值如下：硬球B7/(B2)6=0.0138±0.0004；硬盘B7/(B2)6=0.1141±0.0005。对于硬球，截断的压力七项维里级数与分子动力学数据的结果在10%以内是一致的。
The seventh virial coefficient B7 is expressed as a sum of modified star integrals instead of the usual Mayer star integrals. The new graphs contain both Mayer f functions and f(≡1+f) functions. This simplifies the calculation of B7. That is, instead of the 468 star integrals that appear in Mayer's formulation, only 171 modified star integrals now appear in the evaluation of B7. Furthermore, for D‐dimensional particles with a hard core, these 171 integrals are strongly dependent on the number of dimensions D. For hard rods, hard disks, and hard spheres, respectively, at most one, 78, and 164 of these integrals give a nonvanishing contribution to B7. When Monte Carlo integration is used to evaluate these integrals using hard‐sphere and hard‐disk potentials we obtain the following values of B7: hard spheres, B7/(B2)6=0.0138±0.0004; hard disks, B7/(B2)6=0.1141±0.0005. For hard spheres, the truncated seven‐term virial series for the pressure agrees within 10% with the results of the molecular dynamics data t...