Micah J. Green, Department of Chemical Engineering, Massachusetts Institute of Technology, 25 Ames St., 66-258, Cambridge, MA 02139, Robert A. Brown, Boston University, President's Office, 1 Sherborn Street, Boston, MA 02215, and Robert C. Armstrong, MIT, Department of Chemical engineering, MIT, 25 Ames street, Room 66-360, Cambridge, MA 02139.
The spinodal decomposition of rodlike liquid crystals is simulated for a one-dimensional system with both periodic boundaries and hard-wall boundaries. The nonhomogeneous Doi equation for the rigid-rod distribution function is discretized by the finite element method and integrated forward in time using a parallel, semi-implicit scheme. The simulation uses a discretized form of the full nonhomogeneous Onsager intermolecular potential which models interactions of the rods on the scale of a single rod length. This intermolecular potential makes it possible to characterize nonhomogeneous structures and interfaces in terms of the rod length with no adjustable parameters. The method is applied to isotropic-nematic spinodal decomposition and to the behavior of misaligned nematic grains. The effects of rotational and translational diffusivity ratios are computed, and the mechanisms for alignment and phase separation are analyzed. The initial stages of spinodal decomposition are also simulated in Fourier space in order to study the functional dependence of the dominant perturbation mode and wavenumber. These results mark the first full computation of the evolution of the distribution function for spinodal decomposition in nonhomogeneous rigid-rod systems.