Alternative formulation of the induced surface and curvature tensions approach

Abstract

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace-Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not an exponential one, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.

Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics

“…Recently the IST concept was generalized further in order to include the effects of curvature tension for quantum hard-spheres, 10,11 for two-component classical mixtures of hard spheres and hard-discs. 12 The novel EoS based on the concept of induced surface and curvature tensions (ISCT) is able to accurately model the EoS of hard spheres up to the packing fraction η ≡ k ρ k V k 0.45 (where ρ k is the particle number density of the k-th sort of particles and V k is their eigenvolume) and the EoS of hard discs (2-dimensional spheres) up to the packing fraction η ≡ k ρ k S k 0.7 (here S k denotes the eigensurface of the k-th sort of particles).…”

“…21,22 In fact, one can regard the results of Refs. 10-12 as a GCE generalization of the morphological thermodynamics approach to the mixtures of quantum particles with hard-core interaction 10,11 and the ones of classical hard spheres and hard discs. 12 According to the concept of morphological thermodynamics 21,22 the change of free energy of a convex rigid body B placed into the fluid away from its critical point and from wetting and drying transitions is solely expressed in terms of system pressure p, mean surface tension coefficients Σ, and two bending rigidities K (or curvature tension coefficient) and k: −∆Ω = pV B + ΣS B B + KC B + kX B , where the coefficients V B , S B , C B and X B are, respectively, the volume of B, its surface, mean curvature integrated over the surface area and mean Gaussian curvature also integrated over the surface area.…”

“…These coefficients are introduced according to the concept of the ISCT. 5,[10][11][12] In Ref. 12 one can find various examples demonstrating that for α k > 1 and β k > 1 the system (54)-(56), and its generalizations for classical and quantum hard spheres, 11 as it is mentioned in the Introduction, are able to provide an accurate description of the EoS properties of hard spheres up to the packing fraction η ≡ k ρ k V k 0.45 and even the one of hard discs up to the packing fraction η ≡ k ρ k S k 0.7.…”

“…5,[10][11][12] In Ref. 12 one can find various examples demonstrating that for α k > 1 and β k > 1 the system (54)-(56), and its generalizations for classical and quantum hard spheres, 11 as it is mentioned in the Introduction, are able to provide an accurate description of the EoS properties of hard spheres up to the packing fraction η ≡ k ρ k V k 0.45 and even the one of hard discs up to the packing fraction η ≡ k ρ k S k 0.7. In other words, in the GCE formulation the ISCT EoS with a few parameters only is able to reproduce the EoS of classical hard spheres and hard discs in the entire gaseous phase 12,13 of such systems.…”

“…is a decreasing function of system pressure, 5,[10][11][12] i.e. at high pressures the ratios Σ p and K p tend to vanish and, thus, the effective excluded volumes of particles are compressible to some extent.…”