Thermally activated methyl and $t$-butyl group reorientation in solids

We reinterpret proton spin-lattice relaxation measurements in solid 1,4-di-$t$-butylbenzene (1,4-DTB) [P. A. Beckmann, F. A. Fusco, and A. E. O'Neill, J. Magn. Reson. 59, 63 (1984)] in light of a recent study of solid 1,3-DTB [P. A. Beckmann, A. I. Hill, E. B. Kohler, and H. Yu, Phys. Rev. B 38, 11098 (1988)]. We investigate the relationship between the spectral density that characterizes the intramolecular reorientation of the $t$-butyl groups and their constituent methyl groups in DTB, and the $t$-butyl group environment which dictates the symmetry of the local electrostatic potential. For both isomers, if one assumes a sixfold potential, then a spectral density characteristic of a distribution of correlation times (or a nonexponential correlation function) is required, but if one assumes a lower, threefold symmetry due to crystal effects (for both isomers) or due to intramolecular effects (for the 1,3-isomer), then the relaxation-rate data can be interpreted in terms of a unique correlation time for intramolecular reorientation. For the case where only methyl groups are reorienting (i.e., either no $t$-butyl group reorientation or no $t$-butyl groups at all) one can only use the model which characterizes the reorientation in terms of a distribution of correlation times (or a nonexponential correlation function). Recent work in methyl-substituted phenanthrenes [K. G. Conn, P. A. Beckmann, C. W. Mallory, and F. B. Mallory, J. Chem. Phys. 87, 20 (1987)] is used to make the latter point.