Exact Finite Method of Lattice Statistics. IV. Square Well Lattice Gas

Abstract

The temperature-dependent phase equilibrium of simple classical molecules has been studied, using a model based on the two-dimensional square lattice. The intermolecular potential includes a hard core extending to the first-neighbor distance and a finite interaction (attractive or repulsive) at the second-neighbor distance. The transfer matrix method of calculation is used for lattices of infinite length and finite circumference up to 16 sites. At all temperatures studied there is a single phase transition, which is of first order for attractive interactions at sufficiently low temperatures. The model best describes the equilibrium between solid and gas at low temperatures or the equilibrium between solid and supercritical fluid at high temperatures. The deficiencies in the model which exclude a liquidlike phase are discussed.

Extracting the equation of state of lattice gases from random sequential adsorption simulations by means of the Gibbs adsorption isotherm

“…• The matrix method of Kramers and Wannier [17][18][19][20][21][22][23][24][25][26][27][28][29][30], • The density (or activity) series expansion [15,22,[31][32][33][34][35], • The generalized Bethe method [33,[36][37][38][39][40][41], • The Rushbrooke and Scoins method [42],…”

Exact Finite Method of Lattice Statistics. V. The Thermodynamic Phases of a Triangular Lattice Gas

“…1 In addition to L the second independent intensive variable is the activity Z= exp (/-L/kT The pressure is a zeroth-order property given by the dominant eigenvalue /.. of the transfer matrix, while the densities should be regarded as first-order properties since they are expectation values of appropriate operators over the eigenvector belonging to A. s New features appearing in the present problem arise primarily from the increased range of the potential (to third-neighbor distances).…”

Prediction of Thermodynamic Properties of Complex Fluids

“…In these models, occupancy in the first shell, second shell, and, in some cases, even more distant shells is forbidden. Different types of potential functions also have been considered, including hard spheres [46], square well potentials [47], and repulsions with large positive (but not infinite) energies [48,49]. It has been shown that models with first-neighbor exclusions give second-order phase transitions [50], but models with larger exclusion shells can give a first-order transition [51][52][53].…”

“…Consider equations (36) and (37) as linear approximations for an expansion of the configurational energy in powers of density. Then, the series ... ) ( ) ( Using equations (47) and (48) instead of equations (36) and (37) and leaving only linear, quadratic, and cubic terms, we obtain instead of equation 41:…”

“…Here α a , β a , α b , and β b are temperature dependent coefficients. Note that the quadratic and higher terms in equations(47) and(48) reflect correlations that become important near the critical point but which are not taken into account in the classical mean-field, Ono-Kondo model.…”