Structural aspects of the nematic-isotropic transition in liquid crystals: an investigation using a development of the Lebwohl-Lasher lattice model

Abstract

This paper explores further the predictions of the Lebwohl-Lasher model [1] for the description of order in a liquid crystalline system, especially in the region of the nematic- isotropic transition. The model is based on a lattice, each cell of which contains a director representing the long axis of a rod molecule. The energy of each director is determined by the relative orientations of its six nearest neighbours, and the probability of a director orientation being moved to another chosen at random depends on the Boltzmann function of the difference between the old and the new energies in accord with the normal Monte Carlo procedure. The validity of this model to describe this transition has been demonstrated in several previous studies [2–16] and its simplicity permits calculations over a statistically significant number of molecules. Preliminary studies of the model behaviour have been made below the transition temperature in order to investigate the influence of boundary conditions. The simulated P₂ and P₂/P₄quantities are compared both with experimental data and with the theory of Maier and Saupe [17]. The predictions of the model are analysed in the normal way using the Ornstein-Zernike expression for pairwise correlation functions, while this expression is modified in order to describe the short-range order which is superimposed on the background level of long-range order present in the nematic phase. The model's predictions of enthalpy changes across the transition are compared with calorimetric data from the literature [18]. The opportunity of working with a large model is taken to extend the Zhang plot to test for the presence of first order character within the transition. A structural description of the transition is proposed, based on the molecular director maps, and the identification of more ordered and less ordered regions achieved by the analysis of the distribution of local energies into two sub-distributions with widths in accord with the mean values of their energies. As the transition is approached from above, the isotropic melt structure is seen to contain nematic nuclei which increase in volume fraction with decreasing temperature. At the transition these nuclei appear to join to give a percolating phase having a single orientation across the model. With decreasing temperature within the nematic region, isolated regions of disorder become continually smaller with a corresponding increase in the overall order parameter (P₂). This paper focuses particularly on the structural implications of the predicted nematicisotropic transition. It is recognized that aspects characterizing the physics of the transition can be obtained through averaging energy parameters over very large numbers of cycles, and using models as large as possible. While the 503 model presented here is particularly large by current standards, it is designed in this way to show a representative picture of the structure in the transition region. The aspect of the work reported, despite the availability of a large model, does not seek to generate better averages than previously reported, and the calculation of some such parameters in the earlier sections is to check that the model is behaving properly and in accord with results reported previously.