Short-range correlations and the effective orientational energy in liquid crystals

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Abstract
Experiment and theory have shown that the orientational free energy of nematic liquid crystals contains both a translational entropy term and an orientational energy term, which are of the same order of magnitude. It has been proposed recently that the energy term is due to the total attractive interaction energy, which is modulated by order‐dependent radial correlations between the rodlike molecular cores. In this paper we confirm this proposal by a calculation of the pair correlations in a fluid of short rods. It turns out that the only point of some difficulty is to explain the relatively small ’’experimental’’ value of the orientational energy −W2 η2/2, where η=orientational order parameter, for the length (l) to diameter (d) ratios common in liquid crystal molecules (l/d≳3). Our results indicate that to get reasonable values of W2/W0 (−W0/2=internal energy for η=0), for l/d≳3/2, it is important to take account of short‐range orientational order. Also, there is the suggestion that the dispersion energy between the rodlike molecules varies more slowly than 1/R6 at short distances R. The calculation of the pair correlation function in this paper is based on the Ornstein–Zernike (OZ) equation. The orientational order and the direct correlation function (DCF) are assumed known, and the resulting OZ equation for the correlation function is put into a simple variational form. (A simplified version of the DCF suggested by Pynn is used.) The variational problem is solved approximately by using a trial correlation function which emphasizes the small‐distance correlations.