CRITICAL DYNAMICS OF LIQUID CRYSTAL ABOVE THE ISOTROPIC - NEMATIC PHASE TRANSITION

Dynamics of liquid crystals above the isotropic-nematic phase transition point is studied. The phase transition is of first-order, but nearly critical. Near the transition point the correlation length (zeta) of molecular orientational order could be comparable to the inverse of a light scattering momentum transfer k. We study the non-linear effects in the dynamics of molecular orientation under such a condition. We first derive the complete quadratic dynamic equations for molecular orientation and translational velocity, based on Mori's theory of the generalized Langevin equation. Our problem differs from the well studied problem of binary fluids in (1)the parameter is not conservative and (2)there are linear cross couplings between the order parameter and translational velocity. A mode-mode coupling method equivalent to the bubble diagram expansion is applied to solve the non-linear equations. The lowest order calculation shows that the effect of non-linear couplings becomes significant when (zeta) is comparable to 1/k. The effect on the polarized and depolarized spectrum of light scattering is discussed. We also investigate if non-linear couplings would dominate the critical relaxation processes as in the case of binary fluids. We show that if non-linear couplings do dominate the critical relaxations we would obtain a result contradictory to the assumption. Thus we prove that in the isotropic-nematic transition region mode-mode couplings can not be the dominant mechanism of relaxations.