Translational Diffusion in Liquid Crystals

Finally, restricted 7-motion within an apex angle 0o [Eq. (7.80)] has been employed to interpret [7.11] spectral densities of aromatic deuterons in the nematic and smectic A phases of 50.7-d4. Assuming that a-, and 7-motion are completely uncorrelated, and neglecting the -motion [i.e., set / (0) = /3 t)], the spectral densities were evaluated by describing the a-motion by a simplified model of uniaxial free rotational diffusion about the director and the 7-motion by the reduced correlated functions given in Eq. (7.80). It remains to be examined whether the anisotropic viscosity model in conjunction with restricted 7-motion [i.e., Eq. (7.82)] would be better in interpreting spectral densities of motion in various smectic phases. Also, there is still no convincing NMR evidence for biased 7-motion in nematic or smectic A phases. 

It is again supposed that translational diffusion motions of molecules can be described by a diffusion equation. The theory of spin relaxation by translational diffusion can, in principle, be formulated [7.16]. The review by Kruger [7.57] provides an exhaustive description and interpretation of the behavior of mass diffusion in different thermotropic mesophases. The mass diffusion is anisotropic in mesophases and, in general, will be given by a second-rank tensor D, the symmetry of which is related to the symmetry of the mesophase under consideration. For a uniaxial system with the z axis along the director, the translational diffusion tensor is 

An exception to this has been found in the smectic A phase of octyloxy-p -pentylphenyl thiolbenzoate [7.59]. Furthermore, the activation energy for Dy is much higher than both the activation energy for transverse diffusion and the corresponding value for nematics. Using a parametrized form of the momentum autocorrelation function, Chu and Moroi [7.60] calculated the anisotropy in the translational diffusion constants for nematics as 

FIGURE 7.4. Plots of translational diffusion constants versus the reciprocal of temperature in PA A [after Ref. (7.64)]. 

FIGURE 7.5. Schematic diagrams of the domain distribution and molecular stacking in the planar samples of the discotic nematic Nd), hexagonal Dh), and rectangular (Dr) mesophases. The coordinate system depicts the direction of B and of the field gradients relative to the samples. 

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