Modeling of dynamics in liquid crystals from deuterium NMR

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Abstract
We present a superimposed rotations model that incorporates a three-site jump model to describe the trans–gauche isomerism of a hydrocarbon chain and a small step rotational diffusion model to describe the reorientation of a mesogen in an ordering potential. The model can be used to interpret the spectral densities of motion measured in liquid crystals by deuterium NMR relaxation studies. Under the simplifying assumption that rotation about each carbon–carbon bond is free, the jump model reduces to the free rotation model. Both the jump model and the free rotation model are examined using the reported J1 and J2 values in the literature for the nematogen 5CB-d15. Analytical solutions of rotational diffusion constants by numerical computation are given. The temperature dependence of these rotational diffusion constants provides the activation energies for these diffusion processes. In conjunction with the free rotation model, we found that the contribution to spin relaxation due to director fluctuations appears to show an odd–even effect along the pentyl chain of 5CB.