Orientational Order

Abstract

One of the characteristic features of liquid crystals is the existence of long-range orientational order in a mesomorphic phase. Molecules are preferentially aligned along a particular direction in space labeled by a unit vector ň known as the local director. A set of microscopic order parameters was introduced in Chapter 2 for rigid molecules in a uniaxial phase. They may be determined from the splitting or shift of spectral lines in NMR spectra of liquid crystalline molecules. A typical difference between the isotropic phase and the nematic phase is that, in the latter, the measurement of all macroscopic tensor properties is possible. Thus, a macroscopic property can be used to define order parameters without requiring prior knowledge of molecular symmetry or invoking molecular rigidity. Given certain models for the molecules, the macroscopic order parameters may be related to the microscopic order parameters. The macroscopic order parameters are introduced in Section 3.1. The ordering of molecules in mesophases may be described by an orientational distribution function (Section 3.2), which depends in general on three Eulerian angles (ϕ,θ,ψ) as illustrated in Fig. 3.1. It is often difficult to experimentally determine the full distribution function. An expansion of this distribution function in terms of microscopic order parameters is possible.