Phase transitions in lattice models of one-, two-, and three-component molecular systems

Abstract

Through the study of model systems, equilibrium statistical mechanics has been successfully used to elucidate the nature of phase transitions and critical phenomena. Two such models, the Ising model and the lattice gas, have been extensively studied. Example of these models were used in the present work to study orientational ordering in molecular liquids, enantiomeric phase separation, and phase separation in three-component solutions. A lattice gas model for carbon tetrachloride was considered in which the sites of a bcc lattice are either vacant or occupied by a molecule in either of the two orientations in which the bonds of the molecule point toward neighboring sites. The liquid-vapor equilibrium was studied within the Guggenhiem approximation. The condensed phase in the model exhibits the same type of short-range orientational ordering proposed by Nishikawa and Murata to exist in liquid carbon tetrachloride. A lattice gas model for enatiomeric phase separation was considered in which the two enatiometric forms of a tetrahedral molecule, consisting of a central carbon atom bonded to four different groups, are adsorbed onto a triangular lattice, such that the carbon is above a lattice site, the bond to a certain one of the groups points perpendicular to and away from the plane of the lattice, and the bonds to the remaining three groups point toward neighboring lattice sites. For a reasonable choice of intermolecular interactions such as may exist between the zwitterion forms of an amino acid, the phase diagram was investigated using a Guggenheim approximation with two order parameters. Enantiomeric phase separation into two symmetric condensed phases was found to occur at low temperatures. A model three-component solution, introduced by Wheeler and Widom, was considered in which the bonds of a lattice are covered by rod-like molecules of type AA, BB, or AB. The ends of molecules near a common lattice site interact. The ordered phases on the square and simple cubic lattices were investigated using the Peierls argument. For the model on the honeycomb lattice, exact isothermal coexistence curves were obtained for the phase separation into AA rich and BB rich phases.