Small-angle scattering from hexagonal liquid crystals

In this paper, we discuss the scattering behavior of two-dimensional hexagonal liquid crystals with micellar cylinders as a building unit. We treat the hexagonal phase as an accumulation of ordered domains of finite size that typically consists of one hundred parallel cylinders whose axes are perpendicular to the lattice plane. When we suppose that no specific orientation is preferred, the lengths of the cylinders are rather large compared to their diameter, and the polydispersity of the size of the cylinders is negligible; it is therefore possible to split the scattering intensity into a product of the so-called form factor and the structure factor. This product approximation is the basic condition for the use of the generalized indirect Fourier transformation ( GIFT) method and the deconvolution (DECON) method to evaluate the small-angle scattering data of hexagonal phases. The GIFT method provides the parameters of the structure factor model and the pair distance distribution function of the cylinders. Via the DECON technique, we can calculate the radial contrast profile of the cylinders from the pair distance distribution function that is obtained by the GIFT method.