Deuterium spin relaxation and guest motion in the n-nonadecane/urea clathrate

Abstract

Deuterium spin-lattice relaxation are reported as a function of temperature and crystal orientation at two magnetic field strengths for bulk methylene and terminal methyl deuterons of n-nonadecane-d₄₀ urea clathrate. Jeener-Broekaert pulse sequences were used to measure simultaneously the rates of growth of Zeeman order and decay of quadrupolar order, from which the spectral densities of motion J ₁(ω₀) and J ₂(2ω₀) were determined. Relaxation data for the methylene groups are analysed with the aid of five different models, in order to determine features of the motion that transcend the validity of any particular model. It is found that out-of-plane (‘wobble’) motion of the CD₂ groups occurs over a restricted range of angles (on the order of 20°–30° depending on the choice of quadrupole coupling constant) which changes only slightly between -35°C and 56°C. In this temperature range the rate of the CD₂ wobble is slower by a factor of 5–10 than that of overall alkane rotation about the long axis, although the exact ratio is somewhat model-dependent. Rate constants for both types of motion are also model-dependent, but are found to be of the order of 10¹⁰ s^-1 – 10¹¹ s^-1. A more limited analysis of the methyl relaxation data indicates that fast internal rotation about the C₃ axis contributes to the measured spectral densities. Regardless of which model is used to interpret the spin relaxation rates, the quadrupole coupling constant needed to account for relaxation data is somewhat larger than the value obtained directly from the N.M.R. spectrum. This general result arises because part of the motion which results in a reduction of the equilibrium spectral splitting is slow enough to contribute measurably to relaxation.