Equations of the state of hard sphere fluids based on recent accurate virial coefficients B₅-B₁₂

By using the recently published simulation data for the compressibility factor (M. N. Bannerman, L. Lue and L. V. Woodcock, J. Chem. Phys., 2010, 132, 084507; S. Pieprzyk, M. N. Bannerman, A. C. Branka, M. Chudak and D. Heyes, Phys. Chem. Chem. Phys., 2019, 21, 6886) and the recently published numerical virial coefficients B₅-B₁₂ (R. J. Wheatley, Phys. Rev. Lett., 2013, 110, 200601; C. Zhang and B. M. Pettitt, Mol. Phys., 2014, 112, 1427; A. J. Schultz and D. A. Kofke, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2014, 90, 023301) of hard sphere fluids, we herein report the updated versions of the equations of the state of hard sphere fluids based on the asymptotic expansion method (J. Tian, H. Jiang, Y. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2009, 11, 11213), the Padé approximants (N. Clisby and B. McCoy, J. Stat. Phys., 2006, 122, 15) and the exponential approximants (N. S. Barlow, A. J. Schultz, S. J. Weinstein and D. A. Kofke, J. Chem. Phys., 2012, 137, 204102) and compare them with other recently published equations. It is found that the so-called mKLM equation describes the relation of the compressibility factor versus the packing fraction with the highest accuracy. The asymptotic expansion method based equation Z(-5, 2) is recommended to well describe both the virial coefficients and the compressibility factor.