J. E. Pearson university of London King's College Strand, w.c.2, England
II
Fourier Transform Nuclear Magnetic S
The understanding of the Fourier transform method of nuclear magnetic resonance (nmr) spectroscopy can he facilitated by considering an analogy with a more familiar resonant system than an ensemble of atomic nuclei, namely, a set o f tuning forks. As with nuclei, these will resonate when subjected to an oscillation of the correct frequency. T o determine the resonant frequencies, or frequency spectrum, of the set of tuning forks a variable frequency note from, say, a loudspeaker, can he applied, and the frequency of resonance of each fork noted. An experiment carried out using three tunine forks tuned to 264. 330, and 396 Hz wouldgive the frequency spectrum shown in Fieure 1. This experimental method corres~ondsto the normal nmr method except that it is not to observe directly when a particular set of nuclei are a t resonance. Nuclear resonance is detected indirectly by noting when energy is absorbed. In Fourier transform spectroscopy a short intense "white" signal is applied to the system instead of a variable pure tone. In our analogy with the tuning forks, this could correspond to the firing of a gun near to them or maybe striking the base of them with a hammer. The result of this shock would he to cause all the tuning forks to oscillate simultaneously and in the specific case shown in Figure 1, the musical chord of C major would he heard. If this chord were picked u p by a microphone and displayed on an oscilloscope, the pattern would appear as shown in Figure 2. This is known as a time spectrum. Similarly with nmr, the nuclei are all shocked into oscillation and a signal received, which is a complex waveform made up by the addition of the individual nuclear sienals. This simal is termed a free induction decay or interference pattern.' The method used to shock the nuclei into oscillation depends on the fact that the pulsing of a radio-frequency signal introduces sidebands-the switching on and off causes harmonic distortion. The more narrow the rf pulse, the more intense are the side-bands. Experimentally, the intensity of the pulse is arranged so that the band of frequencies generated is sufficiently broad to excite all the nuclear resonances. The interference patterns decrease in intensity with time, as is clearly shown in Figure 2. The signal from the tuning forks dies away because of factors like the air resis-
tance around each fork while that from the nuclei decays for the followine reason: when the intense radio freauencv . . pulse is applied, the nuclei align themselves along the direction of the a ~ o l i e d~ u l s eand the resonant sienals from all the individuii nuciei act in the same directl'on to give a measurable signal. As time passes this alignment is lost and, since signals from individual nuclei are far too weak to he detected, the observed signal is lost. The time taken to loose this alignment is characteristic of a system and is called the "spin-spin relaxation time" which is given the svmhol TI. The time spectra obtained are not, in themselves, of much use hut they do contain the same information as the more familiar frequency spectra. The conversion, or transformation, of the time spectra into freauencv. soectra in. volves cl~nsiderable numerical analysis, and it is only sinre the introduction of high speed computers that this method of spectroscopy has become practical. In order to understand the transformation process, it is perhaps necessary to remind ourselves of the method of Fourier synthesis. The Fourier theorem states that a periodic function can be synthesized exactly by an infinite series of sines and/or cosines. The interference pattern shown in Figure 2, is, ignoring for now the decay, a periodic function. By simulating this pattern by a series of sines and/or cosines the transformation is obtained since the height of the frequency spectrum at a particular frequency is the magnitude of the sine or cosine term in the series in that point. Of course an infinite series is not used and only sufficient terms to cover the region of interest with sufficient resolution are used. For example, a study at 1 Hz intervals of a 1 KHz range would require a thousand terms. The advantage of studying a system by the Fourier transform method is the great saving in time. In favorable cases a single shock is sufficient to give enough signal and the entire spectrum is obtained in a few milliseconds. This is of course very useful in the study of the kinetics of reactions.
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Figure 1. Frequency spectrumof three tuningforkstuned to 264,330, and 396 Hz.
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Figure 2. Oscilloscope pattern of all three tuning forks vibrating simultaneously (chord of C major). Volume 50, Number 4. April 1973 / 243
