Proton spin-lattice relaxation due to tunnelling motions

Abstract

A theory of proton spin-lattice relaxation due to the rotation of hindered methyl groups is described. The theory bridges the gap between low temperatures when the motion may be described as a tunnelling rotation, and high temperatures when it is better visualized as a random jumping between three equivalent orientations. In this higher temperature range the theory reduces to that of Bloembergen, Purcell and Pound (1948). Two kinds of thermally activated transitions are identified between eigenstates of the tunnelling methyl group. Together these give rise to a frequency spectrum for the motion which differs very considerably from the Lorentzian spectrum assumed by the BPP theory. As a consequence, the temperature dependence of the spin-lattice relaxation time should be much more complex at low temperatures than has previously been recognized. The theory offers an explanation for some hitherto unexplained published results and indicates that T1 studies are a sensitive way of studying the details of low temperature rotational motion.