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ANALYTICAL CHEMISTRY, VOL. 50, NO. 6, MAY 1978
Dispersion versus Absorption: Analysis of Line-Broadening Mechanisms in Nuclear Magnetic Resonance Spectrometry D. Christopher Roe and Alan G. Marshall* Department of Chemistry, University of British Columbia, Vancouver, B.C. V6T 1 W5, Canada
Stephen H. Smallcombe NMR Research, Varian Instrument Division, 6 1 1 Hansen Way, Palo Alto, Calif. 94303
I n nuclear magnetic resonance (NMR) spectrometry, absorption and dispersion spectra are readily obtained by Fourier transformation of the free induction decay following a pulse excitation. For a single Lorentzian line (corresponding to a free induction decay described by a single exponential), a plot of dispersion vs. absorption (DISPA) gives a perfect semicircle. Theoretically (see preceding paper), various inhomogeneous line-broadening mechanisms can be identified from a single data set, based on the direction and magnitude of the displacement of an experimental DISPA curve from a reference semicircle whose diameter is the experimental maximum absorption peak height. I n this paper, we present experimental DISPA plots illustrating: ( a ) Lorentzian line shape, (b) detection of two unresolved components in an NMR absorption signal, (c) several distributions in chemical shift, (d) chemical exchange, and ( e ) effect of phase misadjustment. Phasing will not be a problem in practice. Agreement with theory is excellent, and suggests that the DISPA plot should prove useful in detecting and distinguishing between a variety of linebroadening mechanisms in actual NMR experiments.
One of the most basic problems in nuclear magnetic resonance ( N M R ) spectrometry is how to analyze a broad absorption signal into its individual components. Once the broadening m e c h a n i s m has been established, it is often straightforward to fit t h e observed absorption line shape to that mechanism, by varying the parameter(s) which broaden the line (e.g.. chemical exchange rate; width of specified distributions in chemical shift, relaxation time, or correlation time; and the like). However, since it is often possible to obtain relatively precise theoretical fits for more t h a n one broadening m e c h a n i s m to the s a m e experimental d a t a . it is necessary to find reliable criteria for establishing the correct broadening mechanism. Prior criteria have typically relied on multiple experiments, conducted a t different concentrations, different temperatures, and different applied (static or oscillating) magnetic fields or field gradients. However: such multivariate experiments are difficult to control (and thus difficult to interpret) and of course require additional experiments. In the preceding article, it was shown that a simple graphical display of data from a singie NMR experiment could distinguish between several possible line-broadening mechanisms. In this paper, that graphical display of dispersion vs. absorption (DISPA) is applied to a variety of experimental N M R examples. T h e examples are chosen to include many of the theoretical cases treated in the previous article.
EXPERIMENTAL 'H and "F NMR free induction decays (FID's) were obtained using a Varian XL-100 FT-NMR spectrometer, with Varicui 620L computer. The I9F radiofrequency transmitter and detector were homebuilt, as described elsewhere ( I ) . FID's were stored on
magnetic tape. using a Computer Operations CO-600 reel-to-reel tape deck. Following exponential weighting ("sensitivity enhancement") where specified. and Fourier transformation and phasing in the usual way, a display of normalized dispersion vs. normalized absorption could be generated either on an oscilloscope or on the XL-100 flatbed recorder, using a special program written by S. H. Smallcombe. The program scales the absorption maximum peak height to a specifiable number of centimeters which then becomes the length of the DISPA abscissa (the dispersion spectrum is vertically scaled by the same factor); the high-frequency half of the dispersion spectrum is plotted vs. the corresponding half of the absorption spectrum, starting at the center of the absorption peak. Virtually all existing commands in the present L'arian "SS-FT" Fourier transform software program are unaffected. While correct spectral phasing is critical (see below), adequate phasing was readily achieved in practice by monitoring the absorption spectrum during phase adjustment in the usual way. All samples were run in 5-mm diameter tubes. and sample spinning was used for all homogeneous samples only. For nondeuterated solvents, data were collected using external 'H lock, but with prior magnet shimming based on 2D lock for a separate deuterated solvent sample. Spectral width and acquisition time were adjusted so that there would be a large number of digital points (for instance, 220) in the absorption peak envelope, but with sufficient spectral width that the absorption signal had decreased essentially to zero at the edges of the display (i.e., a spectral width of at least 10 absorption line widths) in order to obtain an accurate baseline. Linear baseline flattening was occasionally used to avoid distortions in the spectra. Finally, care was taken (where necessary) to narrow the spectral window sufficiently that only one peak was \
