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Unformatted text preview: 07Mar2011 Chemistry 21b – Spectroscopy Lecture # 26 – Fourier Transform & Multi-Dimensional NMR For the “simple” NMR spectra discussed in Lecture 25, one means of recording the chemical shift spectrum is to sweep the static magnetic field strength B across each of the peaks. Another is to sweep the RF frequency associated with B 1 . Signal averaging can then be used to improve the overall signal-to-noise ratio (SNR). The disadvantage of these techniques is that the swept field scanning times are long, and so the inherent sensitivity is low. Much better sensitivity can be obtained when operating NMR spectrometers in a pulsed mode . To see how this works, let’s consider again the nature of the magnetization of an NMR sample under the application of a static magnetic field for a spin 1/2 system (so for protons, 13 C, 15 N, etc.). As Figure 26.1 reminds us, in the absence of a magnetic field there are equal numbers of up and down spins ( α and β ), and the net magnetization M is zero. Upon the application of B along the laboratory z-axis, a net magnetization along the z-axis is established, and the spins precess about the field at the Larmor frequency. Figure 26.1 – Magnetization for a spin 1/2 sample. (a) In the absence of the static magnetic field, the population of α and β spin states are equal, while (b) in the presence of the field M is non-zero and the precession of the spins occurs at the Larmor frequency ν = γ N B/ 2 π . Fourier Transform NMR (FT-NMR) Now, let us suppose that the sample is exposed to an intense RF pulse with RF magnetic field strength B 1 and with a frequency equal to the Larmor frequency. If the 198 pulse is applied orthogonal to the static B field and is strong enough, the magnetization will precess into the xy plane. Since the magnetization is rotated by 90 degrees, such a pulse is called a π/ 2 pulse, and is illustrated graphically in Figure 26.2. Because the spins are now precessing at the Larmor frequency in the xy plane, the signal induced by these precessing spins can be detected by a fixed coil in the laboratory. Figure 26.2 – Illustration of a π /2 pulse. (a) If an intense RF pulse is applied for the correct length of time, the net magnetization vector is rotated into the xy plane. (b) For an observer fixed in the laboratory reference frame, the magnetization vector precesses in the xy plane at the Larmor frequency, and thus induces a current in the fixed coils that can be amplified and detected with standard RF circuitry. Remember that NMR transitions are magnetic dipole allowed, and that the frequency is very low, in the few hundred MHz range for even the strongest fields presently achievable. Thus, the Einstein A-coefficients are very small and the transitions are very easy to saturate. Once the pulse is turned off, protons with the same chemical shift will be precessing at the same frequency and with the same phase . Let’s imagine for the sake of simplicity that there are only two chemically distinct protons to worry about. Afterof simplicity that there are only two chemically distinct protons to worry about....
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This note was uploaded on 01/03/2012 for the course CH 21b taught by Professor List during the Fall '10 term at Caltech.
- Fall '10