High-density equation of state for a lattice gas

Abstract

For the lattice gas models of arbitrary geometry and dimensions with absolute repulsion between particles at zero distance (a hard core identical to a single lattice site) and arbitrary repulsion or attraction at other distances, the "hole-particle" symmetry of the system potential energy has been stated and an equation of state has been derived on the basis of the classical Gibbs statistics. The equation is completely analogous to the well-known virial equation of state, except that it is more accurate at high-density states, while the virial equation has the low-density limitation. Both equations contain the common set of the so-called irreducible integrals, related to the corresponding virial coefficients, and can be used together to describe the behavior of a lattice gas in a wide range of densities.

Equation of state for all regimes of a fluid: From gas to liquid

“…In these circumstances, the irreducible integrals cannot be used at all, and the corresponding equations mentioned above will always remain inapplicable to condensed states of matter (with rare exceptions like the equations based on the "hole-particle" symmetry for some specific models of matter [13,12]). The only possibility to make the CE behavior adequate in high-density regimes is to use the equations in terms of reducible cluster integrals as certain functions of volume (or density), {b n (V)}.…”

Lattice Gas Condensation and its Relation to the Divergence of Virial Expansions in the Powers of Activity

“…A new statistical approach has been proposed recently [1][2][3] for a wide range of lattice gas models, in which the "particle-hole" symmetry inherent in such models is used. For the general well-known virial equation of state (VEOS) [4,5]…”

“…whose applicability is limited to low particle density , a symmetric VEOS (SVEOS) equation was obtained [1]:…”

“…Both Eqs. (1) and (2) also include the same mutual set of irreducible cluster integrals, { }, which are related to the corresponding virial coefficients [5].…”

“…For an adequate comparison to be done between the behaviors of series expansions in powers of the density [Eqs. (1) and (2)] and activity [Eqs. (4) and (5)] -and, even more so, for the research of the series divergence in Eqs.…”