The effect of a broad activation energy distribution on deuteron spin-lattice relaxation.

Deuteron NMR spectra and spin-lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20-150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low-temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.