Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

4 SPECTRAL LINE-BROADENING 145of spinning nuclei is placed in a magnetic field the nuclei will tend to precess in phasewith one another. This results in a net rotating magnetic vector with a componentin the plane perpendicular to the applied field. Now if the nuclei somehow lose theircoherence, the resultant rotating vector decreases. Again, this decay is a first orderprocess associated with a relaxation time which is normally given the symbol T2.The reason for the name “spin-spin” relaxation is that one mechanism for this lossof coherence involves an interchange of spin between two identical nuclei. Anothercause for loss of phase coherence is the local inhomogeneity within the samplecaused by the fact that the molecules might have different neighbours. Sometimesalso placed under this heading is the broadening caused by slight non-uniformitiesin the applied magnetic field. This is an instrumental limitation which means thatthe observed spectrum is broadened because it is really a superposition of spectrafrom molecules in different parts of the sample.For most liquids TI and T2 are of the order of a few seconds or less. They arerelated to the line-width in the Bloch equations and it is possible to derive an exactexpression for the line shape and width in terms of TI and T2 (actually, the linewidth is often determined primarily by T2). In a reacting system the lines areoften broadening further and the experimental line shapes are compared with thesolutions of the Bloch equations to which the appropriate terms have been addedallowing for the exchange5’. The exact method of doing this is rather complicatedand will not be dealt with here; the detailed treatment generally involves the useof computers, especially in exchange systems which involve more than two lines.It is also possible to measure T, directly by the “spin-echo’’ method58, a techniquewhich may also be used for following fast chemical reactions56i59.Ideally, then, the most kinetic information may be obtained from an NMR signalby comparing the observed with the computed pattern. In many cases this is notpossible, or at best very tedious, yet very good approximations of the relevant rateconstants may be obtained in a much more straightforward way.Suppose there are two protons, in environments A and B, in the system underinvestigation, and that they have resonances at frequencies oA and wB, respectively,with no spin coupling between them; the kinetics of possible exchange between Aand B are to be followed. Suppose also that the concentrations of A and B are equal(although this is not an important restriction since the treatment has been extended6’to the more general case where cA # cB). The observed spectrum comprises twolines of equal intensity separated by 6 = /oA-wBl, the chemical shift. The term Tis now introduced, and this represents the mean lifetime of states A and B, or thetime spent by the proton in the environments A and Bt. (If the concentrations ot In some ways the nomenclature is a little confusing. In NMR it is traditional to use TI and Tz todescribe the relaxation times of specific nuclear processes and t the mean lifetime of a nucleus ina particular state. In chemical relaxation methods, however, T refers to the relaxation time. Chemicalrelaxation methods and NMR are similar in that in each, one time function is measured andits variation with concentration is followed. The difference comes in the relationships of therespective time functions to the concentrations.References pp. 176-1 79