Nuclear-spin-relaxation study of internal motion in two organic molecular solids

We investigate proton spin-lattice relaxation in two powdered organic molecular solids with reorienting methyl (${\mathrm{CH}}_3$) and tert-butyl [C${\left({\mathrm{CH}}_3\right)}_3$] groups: 3,5-di-tert-butylphenol (DTBP) and 1,3,5-tri-tert-butylbenzene (TTBZ). The temperature and Larmor frequency dependence of the relaxation rate is considerably more complicated than would be expected on the basis of random reorientations of the ${\mathrm{CH}}_3$ and C${\left({\mathrm{CH}}_3\right)}_3$ groups. The spectral densities describing the relaxation are broader, and show more structure, than those customarily used to interpret relaxation data. Assuming that the spectral densities may be expressed as linear superpositions of Lorentzians, we are able to obtain a single, nonexponential correlation function which leads to satisfactory fits of the data. Assuming also the validity of the Arrhenius relation, $\tau ={\tau }_{\infty }\exp \left(\frac{E}{\mathrm{kT}}\right)$, with a constant ${\tau }_{\infty }$, we find that the barriers to rotation for the ${\mathrm{CH}}_3$ and C${\left({\mathrm{CH}}_3\right)}_3$ groups may be characterized by a distribution of activation energies consisting of a wide background and one (DTBP) or two (TTBZ) $\delta$ functions.