Constant-coupling theory of nematic liquid crystals

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Abstract
The well-known constant-coupling theory of ferromagnetism has been adapted to the problem of the nematic liquid crystal. A cluster variational formulation of the theory is developed. The calculations are based on an effective pair potential which is derived from the most general form of interaction by taking suitable averages. Expressions for the long-range order, short-range order, energy, and free energy are derived. Numerical calculations have been performed for a variety of effective interaction potentials. The temperature dependences of the order parameters and thermodynamic functions have been determined. As required by experiment, the theory is found to display a first-order nematic-isotropic phase transition. The results of the present theory are compared to those of previous calculations; questions concerning the validity of the mean-field theory have been clarified. The numerical results are also compared to a variety of experimental data.