X-ray scattering patterns of model liquid crystals from computer simulation: Calculation and analysis

Abstract

We have simulated the x-ray scattering patterns for the isotropic, nematic, smectic A, and smectic B phases formed by the Gay–Berne model mesogen GB(4.4,20.0,1,1). We have used these scattering patterns for two quite different purposes. First, they have been employed to confirm the previous identification of the phases formed by this Gay–Berne mesogen, building on the considerable knowledge base created from x-ray scattering studies of real liquid crystal phases. Second, we have analyzed the simulated scattering patterns to obtain quantitative structural information about the mesophases using several approximate routes. The structural parameters include the nearest neighbor separation, the layer spacing, and translational order parameters of the smectic phase and the singlet orientational distribution function of the nematic phase. Since these quantities have already been determined from previous simulations, we are able to provide a unique test of the approximations used to extract them from the scattering patterns. The success of this investigation has required the use of sensibly large systems and so we have sought to understand, in a quantitative manner, how the size and geometry of the system influences the scattering pattern.