Phenyl ring dynamics and chain reorientation in liquid crystal polymers: A deuteron spin relaxation study

A detailed description of phenyl ring dynamics and spin relaxation in a highly ordered main chain/side chain liquid crystal polymer is presented. Models for the different motional processes are discussed with reference to experimental measurements of the deuteron spectral densities, $J_M{\mathrm{(M\omega }}_0\mathrm{),}$ measured in the smectic A and nematic phases between 330 K and 500 K, and measured as a function of orientation at 410 K, close to the minima in the relaxation times for Zeeman and quadrupolar order, $T_{\text{1Z}}$ and $T_{\text{1Q}}.$ Intramolecular motion of phenyl rings about the para-axis is regarded as a diffusive process in a two-fold symmetric potential. Theoretical analysis of this model provides the rate constants and amplitudes for passage across the potential barriers and libration within the minima. These are governed entirely by the height of the potential barrier, the potential shape, and the diffusion constant. It is demonstrated that other models for the intramolecular ring dynamics cannot simultaneously account for the magnitudes of the observed $J_M{\mathrm{(M\omega }}_0)$ in the vicinity of the $T_{\text{1Z}}$ and $T_{\text{1Q}}$ minima. Large amplitude reorientation of the polymer chain is regarded as rotational diffusion in an orienting potential. In order to reproduce both the temperature and orientation dependences of the $J_M{\mathrm{(M\omega }}_0\mathrm{),}$ an additional low amplitude motion of the polymer about the main chain axis, with correlation times in the ${10}^{\text{−9}}\hspace{0.17em}\mathrm{s}$ regime at $\text{T∼400\hspace{0.17em}}\mathrm{K},$ must be included. This is modeled as a one-dimensional diffusion process modulated by a harmonic potential, representing torsional motion of the extented polymer chains. Analysis of the experimental deuteron spin relaxation data yields values for the correlation times and amplitudes for each of the individual processes, providing estimates for the parameters describing each of the potentials which modulate the intramolecular and whole molecule motion, as well as the temperature dependences of the various diffusion constants.