A Universal Equation of State for Hard Polyhedra

The empirical formulation of the ideal gas law marked a major turning point in the development of theoretical models aimed at describing fluid behaviors. Its extension to real systems, however, often result in deviations upon comparison with experimental observations due to the presence of both excluded volume and attractive interactions in non-ideal particles. Consideration of particle shape further complicates the development of a universal theoretical framework, although there have been several attempts with varying degrees of accuracy for convex shapes. Here, we introduce a new equation of state for hard polyhedra. The derived expression not only shows excellent agreement with simulations, but also suggests a “corresponding state”-like behavior, allowing for a reduction across shape space onto a single master curve as well as prediction of the order-disorder transition density for polyhedra.