Investigation of Nematic Ordering Using Raman Scattering

Abstract

Consider a uniformly oriented nematic liquid crystal sample within which the direction of average molecular alignment is described by a unit vector n called the director. While the molecules, on the average, are oriented with their long axes parallel to n, at any instant in time a particular molecule may be oriented with its long axis at some angle θ with respect to n due to thermal fluctuations. The azimuthal angle φ about the director can be shown by symmetry to be unimportant. Thus, the angular distribution function f(θ) is symmetric about n and depends only on the angle θ. With the assumption that n and -n are equivalent physical states of the system, f(θ) can be expanded in terms of Legendre polynomials in the form⁽¹⁾