  We studied the dynamics of isotropic-nematic transitions in liquid
crystalline polymers by integrating time-dependent Ginzburg-Landau equations.
In a concentrated solution of rodlike polymers, the rotational diffusion
constant Dr of the polymer is severely suppressed by the geometrical
constraints of the surrounding polymers, so that the rodlike molecules diffuse
only along their rod directions. In the early stage of phase transition, the
rodlike polymers with nearly parallel orientations assemble to form a nematic
polydomain. This polydomain pattern with characteristic length l, grows with
self-similarity in three dimensions (3D) over time with a l~1/4 scaling law. In
the late stage, the rotational diffusion becomes significant, leading a
crossover of the growth exponent from 1/4 to 1/2. This crossover time is
estimated to be of the order t~1/Dr. We also examined time evolution of a pair
of disclinations placed in a confined system, by solving the same
time-dependent Ginzburg-Landau equations in two dimensions (2D). If the initial
distance between the disclinations is shorter than some critical length, they
approach and annihilate each other; however, at larger initial separations they
are stabilized.
