Dynamics of the 13C spin-exchange process in solids: A theoretical and experimental study

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Abstract
Spin exchange between rare nuclei such as 13C occurs readily when the rare nuclei are coupled to a reservoir of abundant spins such as 1H, but the mechanism by which the abundant spins enable the exchange process has not fully been clarified. Two different equations to describe the rate of spin exchange in terms of the magnitude of the dipolar coupling between the carbons and the nature of the carbon–proton interaction have been proposed. The derivation of one of the equations with the projection‐operator formalism is described in this paper; the derivation of the other is outlined. Neither equation fully explains the results from a single crystal of glycine, 90% enriched at the carbonyl position. The discrepancies appear to result from the assumptions used in the derivations. Good agreement with experimental results can be obtained with an equation expressed in terms of the degree of overlap of the signals from each type of carbon in the normal nuclear magnetic resonance (NMR) spectrum if allowance is made for the fact that the surrounding protons affect the environments of both carbons in a pair undergoing spin exchange in a similar manner.