Rates from the coalescence of relaxation times

Abstract

A method has been developed for obtaining intramolecular exchange rates in liquids from the coalescence of nonselective 13C spin-lattice relaxation times for the general case in which T 1 at the two sites can have any relative values. Regression analysis and curve fitting of the relaxation data to the double-exponential solution of the Bloch equations modified for exchange yields the exchange rate k and the true spin-lattice relaxation times for each site ( T 1 A and T 1 B). The method has been applied to the exchange of methyl groups by amide bond rotation in dimethyl-formamide (DMF). Comparison of the true relaxation times with those obtained by single-exponential analysis ( T 1 A (eff) and T 1 B (eff)) at several temperatures provides insight into the double-exponential behavior of relaxation times in exchanging systems. A computer simulation model of the relaxation behavior demonstrates that the peculiar temperature dependence of T 1 (eff) at sites A and B is a superposition of exchange effects on dipole-dipole relaxation. For DMF, the exchange rate constants derived from the double-exponential analysis agree reasonably well with the literature values. All T 1 measurements are made in the temperature range below the initiation of any lineshape changes.