NMR relaxation of rigid molecules in the nematic phase of a discotic liquid crystal

Frequency and temperature dependent NMR relaxation measurements were performed on deuteriated benzene, pyrene and triphenylene dissolved in the nematic phase of a discotic liquid crystal. The results show a strong frequency dependence of the spectral densities. Based on the symmetries of the system and the usual model for director fluctuations this frequency dependence should be equal for J₁ and J₂. From fitting the commonly used model of rotational diffusion and director fluctuations to the data we see that this is not the case for benzene and triphenylene, even though the fits themselves are satisfactory. Values for the elastic constants, effective viscosity and translational diffusion in similar discotic liquid crystals do not account quantitatively for the frequency dependence of benzene. For both pyrene and triphenylene quantitative comparison was impossible due to lack of translational diffusion data. We also find that the so-called cut-off wave-length is of the order of the dimensions of the liquid crystal molecules, just as in ordinary nematics.