Spin—Echo NMR Studies of Chemical Exchange. I. Some General Aspects

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Abstract
The applicability to chemical‐exchange studies of the Carr—Purcell nuclear magnetic resonance spin‐echo method has been investigated for the case of two exchanging sites with equal T 2 0, the transverse relaxation time ``in the absence of exchange.'' Theoretical calculations indicate that the decay of the echo amplitudes should be exponential, or very nearly exponential in all cases, the apparent decay constant T 2 being a function of T 2 0, of δω the chemical shift between the sites, of τ the lifetime between exchanges, and also of tcp the rf pulse separation. Values of the apparent T 2 for different values of these parameters were obtained by numerical methods with a high‐speed computer. These values agree with an approximate equation derived by Meiboom, except at slow exchange and large pulse separation. A method is described for calculating the exchange rate from the observed dependence upon tcp of the apparent T 2. This method has several advantages over the high‐resolution NMR methods. A knowledge of δω and T 2 0 is not required; these quantities are also determined from the spin‐echo data. Larger values of exchange rate (shorter lifetimes) can be determined accurately. The spin‐echo method does have the serious drawback that it lacks ``resolution.'' The method was applied to the hindered internal rotation of N,N‐dimethyltrichloroacetamide (DMTCA) and dimethylcarbamyl chloride (DMCC) as a function of temperature. The resultant activation energies of 14.6 and 14.0 kcal/mole and frequency factors of 3.5×1012 and 7.1×1010, respectively, are appreciably higher than previously reported values. Comparative determinations were carried out using the high‐resolution NMR methods. The relatively large differences in the results from the various methods and from different laboratories indicate that systematic errors are present, several possibilities for which are discussed. A simple arrangement is described for generating the Carr—Purcell pulse sequence with three waveform generators and two pulse generators.