title: Freezing transition of hard hyperspheres.
abstract: We investigate the system of D-dimensional hard spheres in D-dimensional space, where D>3. For the fluid phase of these hyperspheres, we generalize scaled-particle theory to arbitrary D and furthermore use the virial expansion and the Percus-Yevick integral equation. For the crystalline phase, we adopt cell theory based on elementary geometrical assumptions about close-packed lattices. Regardless of the approximation applied, and for dimensions as high as D=50, we find a first-order freezing transition, which preempts the Kirkwood second-order instability of the fluid. The relative density jump increases with D, and a generalized Lindemann rule of melting holds. We have also used ideas from fundamental-measure theory to obtain a free energy density functional for hard hyperspheres. Finally, we have calculated the surface tension of a hypersphere fluid near a hard smooth (hyper-)wall within scaled-particle theory.
authors.affiliation: University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Reimar
authors.initials: R
authors.lastname: Finken
authors.forename: Matthias
authors.initials: M
authors.lastname: Schmidt
authors.forename: Hartmut
authors.initials: H
authors.lastname: Löwen