Toward an accurate equation of state for hard polyhedron fluids

An alternative to corrected high-order virial expansions to derive an accurate equation of state for fluids made up of bodies of extreme nonsphericity is proposed. Instead of empirically corrected virial expansions of high order, we use the virial coefficients within the functional form of the hard convex body equation of state. The balance between the accuracy of the equation and the number of the used virial coefficients and adjustable parameters is examined. First, for the fluid of tetrahedra, the recommended equation with only three virial coefficients and four adjustable parameters is considered for the complete set of fourteen polyhedron fluids. An excellent agreement with simulation data is achieved for all the models. The next equation in accuracy is the equation of Tian et al. [Phys. Chem. Chem. Phys. 21, 13109 (2019)], which employs seven virial coefficients and two adjustable parameters. The results are also compared with purely theoretical equations, which are considerably inferior and have unpredictable accuracy for different models.