1324
JOSEPH H. NOGGLE
The Study of the Hindered Rotation of Methyl Groups Using Nuclear Magnetic Resonance by Joseph H. Noggle Department of Chemistrg, Unizersity of Wisconsin, Madison, Wisconsin 66706 (Received October 3, 1367)
The nuclear magnetic relaxation of 13C and 2D in an anisotropically rotating methyl group is considered and formulas are derived for the TI of a I3C nucleus in 13CH3and WDa and for the TI of a 2D nucleus in CD,. The conditions for validity of these formulas and their application to the study of methyl group motion in solids and glasses are discussed. It is suggested that the study of 13C and 2D relaxation in 13CD8is the best method for obtaining information relating to such motions. Such a method could be used for separating effects due to the hindered internal rotation of methyl groups and the main chain motion in macromolecules. The effects of cross-correlation are considered and found to be negligible.
A. Introduction Nuclear magnetic resonance (nmr) has been often used to study the motion of molecules or parts of molecules in solids or polymers.'j2 This work has been recently reviewed by ref 2 . One of the more interesting areas has been the study of hindered internal rotation of methyl groups attached to polymer^.^ The data thus obtained are difficult to interpret quantitatively because of the complicated interactions of the methyl protons both with themselves and with protons on other parts of the molecule. The study of 13C nmr in such cases has much to recommend it. The principal relaxation mechanism of the 13C nucleus will probably be due to dipole-dipole interactions with the directly attached protons. Under some conditions (described herein) this relaxation will be exponential and a formula is derived for the T I thus obtained. Another simple case which can be studied is the relaxation of 2D in a CD3 group. This is even simpler than C13and formulas for the deuterium TI are presented. The T iof 13C in W D 3 is also given. B. The Equation of Motion Before it behooves One to make certain that the equation of motion is a simple exponential. The relaxation of spin I due to dipole-dipole coupling with spin S is given by ref 4 and will not in general be exponential. The solution of these simultaneous differential equations for ('E) and ('Z) under the conditions that (S,(t = 0)) = So will be exponential provided the spin X has an additional mechanism of relaxation so that it relaxes much more efficiently than I . Under the condition that
and TISS
