Diffusion Theory in Liquid Crystals

Abstract

An adaptation of liquid and solid state diffusion theory is made here to diffusion in liquid crystals. Kirkwood's diffusion theory is modified to take into account anisotropic viscosity, molecular order and the detailed geometry of the molecules. For p-azoxyanisole the dffusivities parallel and perpendicular to the director are 4.25 × 10−4 and 2.87 × 10-6 cm2/s, respectively, at 122°C which are very close to experimental values and which give the ratio D∥/D⊥ = 1.48. The unmodified Kirkwood theory gives a ratio of 3.0 which is more than twice the experimental value. The rotational diffusivity in PAA is Dr = 6.95 × 108/s and during the time Dr −l the translational motion perpendicular to the director is 6.4Å in the modified Kirkwood theory, which indicates a coupling between translational and rotational motion. In addition, D∥ is found inversely proportional to molecular length. An analysis of the temperature dependence of D indicated that dD/dT could not vanish over a 20°C temperature range if usual activation energies for translation and rotation in liquids are considered.