Martha A. Cotter

Lattice Models for Thermotropic Liquid Crystals

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-...

Lattice model for a binary mixture of hard rods of different lengths. Application to solute induced nematic→isotropic transitions

A statistical mechanical treatment for two‐component mixtures of hard rods placed on a simple cubic lattice is presented. Each mixture is composed of two types of rods of different length‐to‐breadth ratios; and the pressure‐to‐temperature ratios are chosen so that the system is anisotropic when only longer rods are present but isotropic when composed of only shorter rods. Such solutions can be induced to undergo a first‐order anisotropic‐isotropic phase transition, with a small two phase region, by increasing the concentration of the shorter rods. The dependence of this transition on the parameters of the model is described and deviations from ideal solution behavior are discussed. Recent experimental data are cited and compared with the results of the lattice calculation.

The van der Waals theory of nematic liquids

This paper describes the van der Waals theory of nematic liquids, an approximate molecular theory in which very short-range intermolecular repulsions are approximated by hard-rod exclusions, and somewhat longer-ranged intermolecular attractions are subject to a self-consistent mean-field treatment. The rationale, underlying assumptions, idealizations and approximations of the theory are presented in detail and the numerical results so far reported are summarized, together with the results of extensive new calculations, which provide a quite accurate test of the theory in its present state. Finally, the current status of the theory, its relative strengths and weaknesses, and the prospects for extending and improving it are discussed.

Molecular Theories of Nematic Liquid Crystals

Abstract In this paper, the current state of the art of molecular theories of nematic mesophases is reviewed. For this purpose, the many theories of nematogens which have been proposed are grouped into two classes: (1) the Maier-Saupe theory and its extensions and variants, which assume that nematic long-range order is primarily due to anisotropic intermolecular attractions and (2) the hard-rod and van der Waals theories, which assume that nematic order results primarily from excluded volume effects. These two types of theories are discussed in turn, with particular emphasis on the basic assumptions and approximations, the relative strengths and weaknesses, and the most fruitful applications of each of them. Finally, prospects for improving and extending current molecular theories are examined briefly.

Generalized van der Waals theory of nematic liquid crystals: An alternative formulation

An alternative formulation of the generalized van der Waals theory of nematic liquid crystals is presented and discussed briefly. The derivation is considerably more straightforward than that of Gelbart and Baron and is closely analogous to the usual derivation of the van der Waals equation of state.

Generalized van der Waals theory of nematic liquid crystals: Requirements for self‐consistency

In the generalized van der Waals (GVDW) theory of nematic liquid crystals, nematogenic molecules are assumed to interact via hard core repulsions and longer ranged attractive forces, and the latter are treated in the mean field approximation. The resulting expression for the configurational Helmholtz free energy Ac as a functional of the orientational distribution function f (Ω) is N−1Ac[ρ,T;f (Ω)]=N−1Ac[ρ,T;f (Ω)] + N−1V(a)N(ρ) =N−1Ac[ρ,T;f (Ω)] + 1/2Ff (Ω) ? (ρ,Ω) dΩ, where ρ is the number density, Ac[f (Ω)] is the free energy functional for a system of molecules with only hard core repulsions, ?(a)N is the GVDW average of the total potential energy of attraction V(a)N, and ? (ρ,Ω) is the pseudopotential describing the interaction between a molecule with orientation Ω and the mean field produced by intermolecular attractions. In this paper, it is shown that the theory exhibits statistical mechanical self‐consistency if and only if both N−1?(A)Nand?(Ω)are directly proportional to the first power of the d...