Closed virial equations for hard parallel cubes andsquares

作     者：Leslie V. Woodcock 

作者机构：不详 

出 版 物：《Natural Science》 (自然科学期刊（英文）)

年 卷 期：2011年第3卷第7期

页      面：622-632页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Virial Equations Liquid Theory 

摘      要：A correlation between maxima in virial coefficients (Bn), and “kissing numbers for hard hyper-spheres up to dimension D = 5, indicates a virial equation and close-packing relationship. Known virial coefficients up to B7, both for hard parallel cubes and squares, indicate that the limiting differences Bn – Bn-1 behave similar to spheres and disks, in the respective expan-sions relative to maximum close packing. In all cases, the difference Bn – Bn-1 is approaching a negative constant with similar functional form in each dimen-sion. This observation enables closed-virial equa-tions-of-state for cubes and squares to be obtained. In both the 3D and 2D cases, the virial pressures begin to deviate from MD thermodynamic pressures at densities well below crystallization. These results consolidate the general conclusion, from previous papers on spheres and disks, that the Mayer cluster expansion cannot represent the thermodynamic fluid phases up to freezing as commonly assumed in statistical theories.