Orientational relaxation for small wavevectors of rod-like Brownian particles

Abstract

We present a theorical study of the kinetic orientational relaxation of a colloidal monodispersed system of stiff and long rods, for small wavevectors. This process is described by the dynamic structure factor. The relationship between this factor with the fluctuations of the second order parameter is provided in the limit of wavevectors going to zero. The second order parameter is computed with the Smoluchowski formalism, neglecting hydrodynamic interactions, and using the Maier-Saupe potential for the rods interaction. Considering suitable properties, the isothermal orientation susceptibility proposed is able to localize the isotropic and nematic concentrations in qualitative agreement with well known computer simulations results. At relaxation our model predicts a single value for the maximum of the orientation property proposed, which it is reached at different times, according to the concentration.