Lattice Models for Thermotropic Liquid Crystals

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Abstract
The utility of the DiMarzio-Alben lattice model for investigating thermotropic liquid crystals is evaluated, using a system of straight, inflexible rods with hard cores and nearest neighbor attractions on a simple cubic lattice. In the most general case, treated in the Bragg-Williams approximation, the rods, of length-to-breadth ratio x, are divided into a core portion of c segments and two “tail” portions of (x - c)/2 segments each and there are seven different segmental attractive energies: w cc, w ct, w tt, w ee, w cc, w ct, w tt, where c and t denote core and tail segments, respectively, unprimed and primed energies are for interactions between parallel and perpendicular rods, respectively, and w ee is for the end-to-end interaction between the last segments of two parallel rods. In addition, a special case of the model is also treated in the quasi-chemical or Bethe approximation and the Bragg-Williams approach is extended to simple mixtures of hard rods of two different lengths with solvent-solvent, solvent-solute, and solutesolute attractions. By comparing the model predictions with experimental results, it is concluded that: (I) the lattice approach (or, for that matter, any molecular field treatment of a system of inflexible rods with hard cores and intermolecular attractions) does not appear to be useful for considering homologous series of p.ure nematogenic substances; however, it does seem to be of use for studying solute induced nematic → isotropic transitions in nematic solutions; (2) The quasichemical approach does not produce significantly better agreement with experiment than does the Bragg-Williams approach; (3) The model provides a qualitatively decent account of certain aspects of the smectic A → nematic phase transition, suggesting that more sophisticated tattice and/or cell models may be of use in treating both smectic A and more ordered smectic mesophases.

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