Deuteron spinalattice relaxation in the presence of an activation energy distribution: Application to methanols in zeolite NaX

A new method is introduced for analyzing deuteron spinalattice relaxation in molecular systems with a broad distribution of activation energies and correlation times. In such samples the magnetization recovery is strongly non-exponential but can be fitted quite accurately by three exponentials. The considered system may consist of molecular groups with different mobility. For each group a Gaussian distribution of the activation energy is introduced. By assuming for every subsystem three parameters: the mean activation energy E0, the distribution width I and the pre-exponential factor I0 for the Arrhenius equation defining the correlation time, the relaxation rate is calculated for every part of the distribution. Experiment-based limiting values allow the grouping of the rates into three classes. For each class the relaxation rate and weight is calculated and compared with experiment. The parameters E0, I and I0 are determined iteratively by repeating the whole cycle many times. The temperature dependence of the deuteron relaxation was observed in three samples containing CD3OH (200% and 100% loading) and CD3OD (200%) in NaX zeolite and analyzed by the described method between 20 K and 170 K. The obtained parameters, equal for all the three samples, characterize the methyl and hydroxyl mobilities of the methanol molecules at two different locations.