Instrumentation Spin-Echo Fourier Transform Nuclear Magnetic Resonance Spectroscopy
Dallas L. Rabenstein and Thomas T. Nakashima Department of Chemistry University of Alberta Edmonton, Alberta, Canada T6G 2G2
time domain. Fourier transformation of the second half of the echo yields a frequency domain spectrum. In this article, we describe the S E F T N M R experiment and several of its applica tions to illustrate some of the possibil ities with multiple pulse techniques.
The SEFT NMR Experiment Pulsed Fourier transform (FT) methods for measuring high resolution nuclear magnetic resonance spectra have greatly increased the range of practical applications of NMR. Typi cal examples include the routine mea surement of spectra for 13 C and other isotopically dilute nuclei at the natu ral abundance level and the measure m e n t of high resolution spectra for in dividual compounds in samples as complex as whole red blood cells. T h e usual pulsed F T N M R experi ment involves the application of a sin gle, high-powered pulse of radiofrequency radiation, followed by comput er acquisition of a time-domain signal, the free induction decay (FID) (1, 2). Fourier transformation of the FID yields the familiar frequency domain spectrum. State-of-the-art spectrome ters also have the capability for doing multiple-pulse experiments, i.e., ex periments in which a series of careful ly timed pulses are applied prior to ac quisition of the FID. Most such exper iments were developed for the purpose of measuring relaxation times. How ever, with the versatility of today's spectrometers, they are being used in creasingly by the N M R spectroscopist in a variety of other applications. In deed, with today's spectrometers, the spectroscopist is often limited only by his imagination in devising multiplepulse experiments to solve a particular problem. Of the various multiple-pulse tech niques, the spin-echo Fourier trans form ( S E F T ) technique is one of the simplest and most useful. In its sim plest form, two precisely timed pulses give rise to a spontaneous echo in the 0003-2700/79/A351 -1465$01.00/0 © 1979 A m e r i c a n Chemical Society
Figure 1A is a schematic representa tion of the S E F T N M R experiment. Following the two rf pulses, there is a spontaneous echo in the time domain. T h e origin and shape of the echo can be accounted for in terms of the be havior of the nuclear magnetization in a rotating three-axis coordinate sys tem (Figure IB). T h e spectrometer magnetic field H0 is applied along the z' axis, and the x' and y' axes rotate around the z' axis at the spectrometer carrier frequency. Because the two possible orientations of the individual nuclear magnetic moments for spin one-half nuclei have slightly different populations and the nuclei in each or ientation are randomly distributed around Ho, the ensemble of nuclei in the sample gives rise to a net macro scopic magnetization, Mu, which is colinear with and in the direction of H0.
T h e component of the net magneti zation projected in the x'y' plane gives rise to the N M R signal. At equilibri um, this is zero. In the pulsed N M R experiment, the system is perturbed by application of one or more rf pulses along x', each of which will rotate M0 about the x' axis through an angle a given by Equation 1 a = yH1tw
(1)
y is the magnetogyric ratio, H\ the in tensity of the magnetic component of the rf pulse, and tw the length of the pulse (usually in the range of micro seconds). In the simplest S E F T exper iment, there are two pulses; Hi is the same for both pulses and tw is changed so t h a t the first pulse rotates Mo through 90° about x' and the sec ond pulse through a further 180°. Following the 90° pulse, the mag netization is colinear with y' (Figure IB). This is a nonequilibrium condi tion, and thus the magnetization re laxes by several processes. Of interest to us here is relaxation of the compo nent in the x'y' plane since it is this magnetization which gives the N M R signal. This component decays expo nentially by spin-spin relaxation ac cording to
Figure 1 . Schematic representations A is the spin-echo sequence and Β shows the behavior of the nuclear magnetization during the spinecho sequence. Τ indicates the time before the beginning of the experiment or between successive pulse sequences
ANALYTICAL CHEMISTRY, VOL. 5 1 , NO. 14, DECEMBER 1979 • 1465 A
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