Calculation of third to eighth virial coefficients of hard lenses and hard, oblate ellipsoids of revolution employing an efficient algorithm

Virial coefficients of hard, homonuclear dumbbells in two- to four-dimensional Euclidean spaces

We calculated virial coefficients up to the eighth order for hard dumbbells in two-, three-, and four-dimensional Euclidean spaces employing Mayer-sampling Monte Carlo simulations. We improved and extended available data in two dimensions, provide virial coefficients in R^{4} in dependence on their aspect ratio, and recalculated virial coefficients for three-dimensional dumbbells. Highly accurate, semianalytical values for the second virial coefficient of homonuclear, four-dimensional dumbbells are provided. We compare the influence of the aspect ratio and the dimensionality to the virial series for this concave geometry. Lower-order reduced virial coefficients B[over ̃]_{i}=B_{i}/B_{2}^{i-1} depend in first approximation linearly from the inverse excess part of their mutual excluded volume.

Equation of state of hard lenses: A combined virial series and simulation approach

We provide highly accurate equation-of-state data for the isotropic phase of hard lenses obtained by means of cluster Monte Carlo simulations. This data is analyzed using a virial approach considering coefficients up to the order eight and Carnahan-Starling type closure relations for the virial series. The comparison with previously investigated systems consisting of hard, oblate ellipsoids of revolution allows insights into the detailed influence of the particle geometry. We propose a generalized Carnahan-Starling approach as a heuristic equation of state for the isotropic phase of hard lenses that in first approximation shows the same dependence on the excess part of the excluded volume as identified for oblate, hard lenses of revolution.

Virial coefficients of hard hyperspherocylinders in R^{4}: Influence of the aspect ratio

We provide second- to sixth-order virial coefficients of hard hyperspherocylinders in dependence on their aspect ratio ν. Virial coefficients of an anisotropic geometry in four dimensions are calculated employing an optimized Mayer-sampling algorithm. As the second virial coefficient of a hard particle is identical to its excluded hypervolume, the numerically obtained second virial coefficients can be compared to analytical relations for the excluded hypervolume based on geometric measures of the respective, convex geometry in dependence on its aspect ratio ν.

Reexamining equations of state of oblate hard ellipsoids of revolution: Numerical simulation utilizing a cluster Monte Carlo algorithm and comparison to virial theory

We provide highly accurate equation-of-state data determined by means of cluster Monte Carlo simulations for the isotropic phase of oblate hard ellipsoids of revolution. Both equation-of-state data and phase boundaries of the isotropic phase are obtained from relatively large ensembles with typically 1000 particles. The comparison of simulation data with a virial approach gives evidence for the importance of high-order so-far-unknown virial coefficients and therewith many-particle interactions in dense, isotropic systems of anisotropic particles. While a virial approach with a rescaled Carnahan-Starling correction for the unknown, higher-order virial coefficients reproduces the simulation data of moderately anisotropic particles with high accuracy, we suggest for highly anisotropic shapes a simple, heuristic equation of state as a suitable approach.

Extended law of corresponding states: square-well oblates

The vapour-liquid coexistence collapse in the reduced temperature,T_r=T/T_c, reduced density,ρ_r=ρ/ρ_c, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension, and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ= 1/3) with varying short-range square-well interactions collapse into a single master curve in theΔB2*-ρ_rplane, whereΔB2*=(B2(T)-B2(Tc))/v0,B₂is the second virial coefficient, andv₀is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.