Author(s)

Leslie V. Woodcock

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A correlation between maxima in virial coefficients (B_n), 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 B_n – B_n-1 behave similar to spheres and disks, in the respective expan-sions relative to maximum close packing. In all cases, the difference B_n – B_n-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.

Virial Equations Liquid Theory

Woodcock, L. (2011) Closed virial equations for hard parallel cubes andsquares. Natural Science, 3, 622-632. doi: 10.4236/ns.2011.37085.