Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures

Abstract

New proposals for the equation of state of four-and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

Structural and Thermodynamic Properties of Hard-Sphere Fluids

“…We should also mention that the ideas presented here in connection with the EOS for additive multicomponent HS mixtures have also been used for nonadditive systems and for hard-hypersphere systems with arbitrary spatial dimensions. 126,177,180,[226][227][228] Finally, it should be clear that there are many facets of the equilibrium and structural properties of many other hard-core systems that may be studied following the ideas presented here but that up to now have not been considered. For instance, the generalization of the RFA approach to square-well or square-shoulder mixtures and the surplus mapping of the single-component EOS to that of nonadditive HS mixtures appear as interesting challenges.…”

“…(4.9) This allows us to interpret that, in the e1 approximation, the excess compressibility factor Z(η) − 1 is just a linear combination of η/(1 − η) and Z s (η) − 1 with densityindependent coefficients such that the exact second and third virial coefficients are retained. 179,180 From Eq. (2.17) one can obtain the excess free energy per particle as [see first step in Eq.…”

“…(4.39) when expressed in terms of surplus quantities. 11,179,180,198 Note that the effective rescaled packing fraction is just the rescaled packing fraction of the mixture divided by λ.…”

“…This simple interpretation allows for a successful straightforward extension of the sp approximation to hard disks 179 and hard hyperspheres. 180 From the thermodynamic relation ∆ p η 2 ∂β T ∆a/∂η, where the surplus pressure is defined in Eq. (4.20), Eq.…”

Statistical Mechanics and Thermodynamics of Liquids and Crystals

“…In the first of these articles [18], the focus is on the virial equation of state for mixtures of hard hyperspheres. While such systems obviously have no counterpart in the real world, they still represent a useful playground where to explore the effectiveness of approximations routinely employed in three dimensions.…”