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Abstract
A monomer-dimer system with excluded volume interactions and weak long range attractive interactions is studied on a two dimensional square lattice. The anisotropic version of the exact series expansion method of Nagle-Temperley has been used to obtain the entropy as a function of densities of horizontal and vertical dimers. Both isotropic and anisotropic long range dispersion interactions are taken into account in an approximation of the mean field type. Numerical analysis of the system yields three types of phase diagrams depending on the ratio R = ωa/ωi of the parameters specifying the strengths of anisotropic ωa and isotropic ωi interactions. For small values of R (type I) the nematic-isotropic phase transition is second order while for larger R (type II and III) a tricritical point appears below which the phase transition is first order. If R is large enough (type III) the vapour pressure curve remains entirely in the nematic stability region. There is no crystallization in this model. Lines of classical points of first order (vapour-liquid) and second order (isotropic-nematic) as well as a line of triple points and a line of tricritical points are shown on a generalized phase diagram which is discussed in detail.
The work was carried out within the Research Project 03.10 and was supported in part by United States National Science Foundation Grant DMR 78-10226. It was presented at the 7th International Symposium on Liquid Crystals, Bordeaux, 1978.
The work was carried out within the Research Project 03.10 and was supported in part by United States National Science Foundation Grant DMR 78-10226. It was presented at the 7th International Symposium on Liquid Crystals, Bordeaux, 1978.
Notes
The work was carried out within the Research Project 03.10 and was supported in part by United States National Science Foundation Grant DMR 78-10226. It was presented at the 7th International Symposium on Liquid Crystals, Bordeaux, 1978.