Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

144 EXPERIMENTAL METHODS FOR FAST REACTIONSterest. If the sensitivity of measurement is high, it is often found that the peaks havea fine structure. This arises from an interaction between the protons on neighbouringatoms which results in a splitting of the energy levels of the spin states. The magnitudeof this splitting, or “spin-spin interaction” J, is independent of the oscillatingfrequency a and the background field H,. In the application of NMR to the studyof fast kinetics the shape and width of the spectral lines are vitally important, andit will now be considered how the line-broadening comes aboutt.So far the only mechanism considered for changing the magnetic quantum numberis that in which an interaction occurs between the precessing nucleus and anoscillating external magnetic field of the same, or approximately the same, frequency.If this were the only path for the transference of energy, resonance would notbe observed; energy would only be absorbed until the numbers of nuclei in the upperand lower states had been equalized. As in other forms of spectroscopy, it is necessaryfor the species in their excited states to be continually losing their excessenergy to the surroundings by some form of radiationless transfer so that further absorptionof energy can occur. The energy is transferred by “nuclear relaxation”, whichis exactly analogous to chemical relaxation in that it is a kinetically first-order processand the relaxation time is the time taken for the population difference to dropto l/e of its original value. There are two important types of nuclear relaxation:(a) Longitudinal Relaxation (sometimes called spin-lattice relaxation). A particularspinning nucleus is surrounded by many others of the same type which areundergoing constant thermal motion. Such thermal motion is associated with smalllocal magnetic fields oscillating in a random manner, and it will sometimes happenthat the nucleus experiences a rotating magnetic field whose angular frequency componentm is equal to its own precessional frequency a,,. It is then possible for aninteraction to occur, and a transition will take place from one spin state to the other.Such a transition can occur in either direction, i.e., the upper spin state can relaxto the lower or vice versa, corresponding to the gain or loss in translational androtational energy by the surrounding molecules. Thus a dynamic equilibrium ismaintained, and the relaxation time of this process is usually referred to as TI.TI is of the order of a few seconds for most liquids.The line-width of an NMR signal is related to the lifetime of the nucleus in a givenspin-state, and in fact the order of magnitude of the broadening can be estimatedfrom the Heisenberg Uncertainty Principle. If the uncertainty in the frequency ofabsorption is Am, the energy difference AE, the mean lifetime At and Planck’s constanth, then AE.At % h/2n. But AE = h.Aw and so Am is about 112nAt. In otherwords, the line width, on a frequency scale, associated with longitudinal relaxationis of the order of T;’.(b) Transverse Relaxation (sometimes called spin-spin relaxation). When a groupNMR has also been used to measure the concentration of a reactant during a chemical reaction.This application involves, in principle, the same considerations as the use of visible spectroscopyto monitor concentration and will not be considered further.