Slow dynamics of banana-shaped molecules: a theoretical approach to analyze 2H-NMR T2 relaxation times

In the present work, we analyze pulsed deuterium NMR experiments performed on the isotropic and nematic phases of the banana-shaped liquid-crystalline mesogen 4-chloro-1,3-phenylene bis{4-4'-(11-undecenyloxy) benzoyloxy} benzoate (ClPbis11BB) selectively deuterated on the central ring. Starting from a previous evidence of unusual slow dynamics in the isotropic phase (Domenici V. et al., J. Phys. Chem. B 2005, 109, 769), a quantitative and model-supported analysis of the deuterium NMR data is performed here by accounting for slow-motional modulation of the magnetic anisotropies through the full solution of the stochastic Liouville equation. Focusing on the quadrupolar echo experiments performed in the nematic phase, the analysis of the transverse relaxation rate has been carried out by considering single-molecule motions and fluctuations of the local director. The main conclusions are: (a) director fluctuations are not relevant on driving the signal relaxation; (b) molecular reorientations about transverse axes control the dynamic regime of the signal relaxation and impose a full slow-motional treatment; (c) the small amplitude tumbling of the molecule within the wells of orientational potential occurs with characteristic times up to the microsecond. The outcome of our analysis has to be taken as indicative of very slow dynamics concerning out-of-plane motions of the molecules. Besides the specific application, this paper also offers the methodological tools to treat the pulsed deuterium NMR experiment in the slow-motional regime of reorientational motions and provides a detailed comparison with the usually employed fast-motional approximation.