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A general, feasible approach is presented for the evaluation of the statistical thermodynamics of interacting lattice gases. Exact solutions are obtained for lattice systems of infinite length and increasing finite width, using the matrix method which treats all densities on an equivalent basis. Through the application of symmetry reduction and the use of an electronic computer to perform logical as well as arithmetical operations, widths of up to 24 sites for two-dimensional lattices can be handled. For examples studied, rapid convergence is obtained away from transition regions and in the vicinity of phase transitions the behavior appears to be a sufficiently regular function of the width to allow meaningful extrapolation to systems of infinite width. Two problems of two-dimensional lattice gases are solved as illustrations of the technique: the square and triangular lattice gases with infinite repulsive interactions preventing the simultaneous occupancy of adjacent lattice sites (excluded-volume effect). Both systems exhibit phase transitions which are most likely second order at densities of 74.2% (square) and 83.7% (triangular) of the close-packed density. For both lattices the compressibility is infinite at the transition point, becoming infinite linearly with the logarithm of the width of the lattice for the square lattice and perhaps slightly more strongly for the triangular lattice.

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Thermodynamic properties have been obtained using the matrix method for a two-dimensional honeycomb-lattice gas of hard molecules which prevent simultaneous occupancy of nearest-neighbor sites. Exact results have been obtained for cylinders of infinite length and finite circumference from 6 to 18 sites. Uniform trends with increasing circumference lend confidence to extrapolations used to infer the behavior of systems of infinite width. We find a great similarity with the corresponding square-lattice gas and a second-order phase transition at activity z=7.92±0.08, reduced pressure p/kT=1.12±0.05, and relative density ρ/ρ0=0.845±0.02. The compressibility appears to be infinite at the transition.

A molecular theory of phase transitions in fatty acid monolayers at the air/water interface is proposed based on rotational ordering of molecules about their longitudinal axes. The first order statistical mechanical lattice model of Bell, Mingins, and Taylor (BMT) which is an equilibrium diluted Ising model is used to describe the monolayer behavior of some simple aliphatic carboxylic acids. The interaction energy parameters in the BMT model are adjusted to give reasonable agreement with the experimentally observed chain length dependence, and the energies thus obtained are compared with those calculated for interacting aliphatic carboxylic acid dimers by the technique of perturbative configuration interaction using localized orbitals (PCILO). It is concluded that intermolecular rotational ordering due to the anisotropy of the intermolecular potential plays a significant role in simple fatty acid monolayer phase behavior. A possible experimental test of the,model is briefly described.

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Report of a teaching approach designed to encourage students in physical chemistry and modern physics courses to develop their creative abilities by requiring their participation in four specific study methods, as opposed to mere fact memorization.