C-13 NUCLEAR MAGNETIC-RELAXATION IN MACROMOLECULES WITH SIDE-CHAINS UNDERGOING MULTIPLE INTERNAL ROTATIONS - EFFECTS OF THE DISTRIBUTION OF CORRELATION TIMES AND OVERALL ANISOTROPIC MOTION

Dipolar nuclear magnetic relaxation in macromolecules having side chains which undergo multiple interned rotations has been investigated for two cases: (1) the motion of the molecule as a whole is anisotropic and (2) there is a distribution of correlation times in the main chain. It is assumed that the internal rotations of the side chain occur by random jumps among sites 1, 2, and 3, two of which are equivalent. The rates of internal rotations are specified by three jump rates, W1 (1 → 2 or 1 → 3), W2 (2 → 1 or 3 → 1), and W3 (2 ⇄ 3). The theoretical equations for spin-lattice relaxation times (T1), spin-spin relaxation times (T2), and Nuclear Overhauser Enhancements (NOE) of 13C {1H} are given. Some numerical calculations of T1 and NOE are presented for two typical conditions of internal rotations of an alkyl side chain: (1) W1 = vW2, W3 = 0 and (2) W1 = vW2, W3 = W2. The effects of an overall anisotropic motion of the macromolecule and of the distribution of correlation times in the main chain on the 13C relaxation of the side chain are discussed. The frequency dependence of this latter is also examined. © 1979, American Chemical Society. All rights reserved.