Molecular theory of orientationally ordered liquids: Exact formal expressions and the application of integral-equation methods with results for ferrofluids

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Abstract
The purpose of this paper is to describe a number of theoretical results for fluids consisting of orientationally ordered particles. The model considered assumes perfect orientational order, with all molecules fully aligned in a particular direction with respect to a laboratory fixed frame of reference. However, rotations about the fixed axis are permitted and hence the present theory can be applied to particles which are not axially symmetric. Physically, such a model can represent liquid crystals in a dense nematic phase or fluids of particles aligned by strong electric or magnetic fields. A general formulation is given which allows the hypernetted-chain, Percus-Yevick, and closely related integral-equation approximations to be solved for orientationally ordered systems. For anisotropic fluids it is interesting to analyze the compressibility and pressure tensors and this is done in some detail for particles interacting with both short- and long-range (i.e., dipolar) potentials. The compressibility equation is used to demonstrate microscopically the physical requirement that these tensors be isotropic in a fluid. Also, the conditions placed upon the pair distribution function g(12) by isotropy of the pressure tensor were determined by examining the virial equation of state. For the dipolar case explicit expressions are derived relating the elements of the dielectric tensor to g(12) for an infinite system. Finally, numerical results are presented and discussed for ferrofluids and for another model defined by a closely related but short-range potential.