Nuclear-spin relaxation in molecular solids with reorienting methyl and t-butyl groups: The spectral density and the state of the solid

We have measured the temperature T dependence of the proton Zeeman relaxation rate R in polycrystalline 1,3-di-t-butylbenzene (1,3-DTB) at Larmor frequencies of ω/(2π)=8.50, 22.5, and 53.0 MHz. The relaxation is caused by the modulation of the methyl proton dipole-dipole interactions by the reorientation of the t-butyl groups [C(${\mathrm{CH}}_3$${)}_3$] and their three constituent methyl groups (${\mathrm{CH}}_3$).

There are two solid phases which either have a large hysteresis of at least 90 K, or are both stable below 200 K. The sample melts at 262 K. We interpret the high-temperature phase R-versus-$T^{\mathrm{-}1}$ data with three models. First, we adopt a one-correlation-time model using a Davidson-Cole spectral density which suggests that there is a distribution of correlation times, or, equivalently, a distribution of activation energies for t-butyl and methyl group reorientation. In this case, the methyl and t-butyl reorientation is characterized by a cutoff activation energy of 17±1 kJ/mol which is to be compared with 18±1 kJ/mol in 1,4-DTB [P. A. Beckmann, F. A. Fusco, and A. E. O’Neill, J. Magn. Reson. 59, 63 (1984)] in which there is only the one phase. Second, we adopt two two-correlation-time models using Bloembergen-Purcell-Pound spectral densities; one based on the dynamical inequivalence of the methyl groups in each t-butyl group and one based on the dynamical inequivalence of different t-butyl groups, either because of intramolecular effects or because of intermolecular (crystal-structure) effects. In the low-temperature phase of 1,3-DTB, R(ω,T) is unusual in that it is Larmor-frequency dependent in the short-correlation-time limit (i.e., temperatures above the relaxation rate maximum). We have fit the data with a Havriliak-Negami spectral density (which reduces to a Davidson-Cole spectral density when one of the parameters becomes unity which, in turn, reduces to a Bloembergen-Purcell-Pound spectral density when an additional parameter becomes unity). The fit, with an effective activation energy of 10±3 kJ/mol, suggests that this low-temperature phase in 1,3-DTB is a glassy state. We relate the Havriliak-Negami spectral density to the Dissado-Hill spectral density which has a fundamental microscopic basis and which has been used to interpret a vast quantity of dielectric relaxation data as well as some mechanical relaxation data.