Orientational Ordering of Solutes in Confined Nematic Solvents: a Possible Way to Probe Director Distributions

We propose a method to study the director distribution in a nematic liquid crystal confined in a slab geometry. It is based on the measurement, by NMR spectroscopy, of the Saupe ordering matrices of a collection of biaxial solute molecules dissolved in the confined nematic liquid crystal of interest. Due to the combined action of the surface anchoring and magnetic field interactions, the director is generally not uniformly aligned within the cell. Consequently, the resulting Saupe ordering matrices may be considered as weighted sums of the corresponding Saupe ordering matrices measured in the bulk nematic phase, and modulated by the director distribution. The determined Saupe ordering matrices may then be taken as the set of data in a fitting process where the fitting function, whose form is deduced from molecular mean field and continuum theories, is dependent on the director distribution; the angle that the director forms with the plain surfaces and the corresponding derivative at the surfaces are taken as fitting parameters. The methodology is preliminarily tested on the virtual nematic phase formed by the Lebwohl-Lasher lattice model, confined between two plain surfaces favoring planar anchoring, and where a number of model cuboidal solutes has been dissolved. We comment on the implemention of the method when applied to real experimental systems.