Scattering from uniform, cylindrically symmetric particles in liquid crystal phases

Abstract

Theory is presented for the analysis of the intraparticle component of diffraction patterns from uniaxial fluid phases of cylindrically symmetric particles via a series expansion method. Diffraction from micelles, for example, can be modeled as the scattering from uniform particles, which are considered here. Knowledge of the particle self-correlation function enables the intraparticle component of the scattering to be calculated. The series expansion approach allows direct information on the orientational ordering of the particles to be extracted in terms of Legendre polynomial order parameters. Provided that high rank order parameters can be extracted from the scattering data, the full orientational distribution function can be obtained. However, at small Q, over a Q range which decreases with increasing particle anisotropy, it is shown that high rank order parameters cannot be measured so that the full distribution function is not obtainable. Scattering coefficients for monodisperse uniform cylinders, spherocylinders and ellipsoids are calculated and compared to each other.