Initial stage of spinodal decomposition in a rigid-rod system

The initial stage of spinodal decomposition is investigated for a rigid-rod system. Spinodal decomposition proceeds through either of two mechanisms: (1) The randomly aligned rods rotate toward a common director with no inherent length scale. (2) The rods diffuse axially and segregate into regions of common alignment with a selected length scale [script-l]. Previous studies on spinodal decomposition yielded radically different conclusions about which mechanism is dominant. A computational method is employed to analyze the growth rate and properties of the dominant fluctuation mode through an eigenvalue analysis of the linearized Doi diffusion equation in Fourier space. The linearized operator is discretized in Fourier mode and orientation space (k,theta,phi) space, and the maximum eigenvalue and corresponding eigenvector of the operator are calculated. Our analysis generalizes the results of previous studies and shows that the conflicts seen in those studies are due to differences in the diffusivities for rotational motion, motion perpendicular to the rod axis, and motion along the rod axis. For a given system density, a plot of the dominant perturbation wave number k(max) as a function of the diffusivity ratios shows two separate regions corresponding to mechanisms (1) and (2). High rotational diffusivity corresponds to mechanism (1), whereas high axial diffusivity corresponds to mechanism (2). The transition between the two mechanisms depends on the ratio of diffusivities and on system density. Also, the dominant wave number increases with increasing density indicating that a deeper quench into the spinodal regime leads to a smaller characteristic length scale.