Principle of corresponding states for hard polyhedron fluids
We introduce an equation of state for hard polyhedra and validate our new theory with simulations performed for 22 different shapes spanning a range of particle anisotropy. The derived expression not only shows excellent agreement with simulations but also exhibits ‘corresponding states’-like behaviour across shape space, allowing for a systematic reduction of thermodynamic properties onto a single master curve. Additionally, we propose a scaling-type argument for predicting the order–disorder transition packing fraction for hard polyhedron fluids that accurately captures the observed transitions in simulations. Our works suggest that hard-polyhedron systems can be thought of as perturbations about a hard-sphere where corrections in the principle axes of inertia and excess volume account for differences in relative orientation between neighbouring particles and each polyhedron's intrinsic asphericity, respectively. Additionally, our theory greatly benefits from requiring only knowledge of the inherent geometry for a polyhedron of interest with no necessary fitting parameters and thus provides a good heuristic rule of thumb for targeting relevant regions of simulation interest for novel systems of hard polyhedra.