Demagnetization field effects in two-dimensional solution NMR

Concepts in Magnetic Resonance

Volumn 8, Issue 2, 1996, Pages 77-103

  Levitt, Malcolm H ^a  

^a STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030306713     PISSN: 10437347     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0534(1996)8:2<77::AID-CMR1>3.0.CO;2-L     Document Type: Article

References (41)

1. H. T. Edzes, "The Nuclear Magnetization as the Origin of Transient Changes in the Magnetic Field in Pulsed NMR Experiments," J. Magn. Reson., 1990, 86, 293.
2. R. Bowtell, R. M. Bowley, and P. Glover, "Multiple Spin Echoes in Liquids in a High Magnetic Field," J. Magn. Reson., 1990, 88, 643.
3. A. S. Bedford, R. Bowtell, and R. M. Bowley, "Multiple Spin Echoes in Multicomponent Liquids," J. Magn. Reson., 1991, 93, 516.
4. R. Bowtell, "Indirect Detection via the Dipolar Demagnetizing Field," J. Magn. Reson., 1992, 700, 1.
5. Q. He, W. Richter, S. Vathyam, and W. S. Warren, "Intermolecular Multiple-Quantum Coherences and Cross Correlations in Solution Nuclear Magnetic Resonance," J. Chem. Phys., 1993, 98, 6779.
6. W. S. Warren, W. Richter, A. H. Andreotti, and B. T. Farmer, "Generation of Impossible Cross-Peaks Between Bulk Water and Biomolecules in Solution NMR," Science, 1993, 262, 2005.
7. W. Richter, S. Lee, W. S. Warren, and Q. He, "Imaging with Intermolecular Multiple-Quantum Coherences in Solution NMR," Science, 1995, 267, 654.
8. P. Broekaert and J. Jeener, 12th European NMR Conference, Oulu, Finland, June 1994.
9. P. Broekaert and J. Jeener, "Suppression of Radiation Damping in NMR in Liquids by Active Electronic Feedback," J. Magn. Reson. A, 1995, 113, 60.
10. A. Vlassenbroek, Doctoral Thesis, "Radiation Damping in High Resolution NMR," Université Libre de Bruxelles, 1993.
11. J. Jeener, A. Vlassenbroek, and P. Broekaert, "Unified Derivation of the Dipolar Field and Relaxation Terms in the Bloch-Redfield Equations of Liquid NMR," J. Chem. Phys., 1995, 103, 1309.
12. 3He," Phys. Rev. B, 1979, 19, 5666.
13. A. Abragam and M. Goldman, "Nuclear Magnetism: Order and Disorder," Chapter 3, Section F, Clarendon, Oxford, 1982.
14. D. Einzel, G. Eska, Y. Hirayoshi, T. Kopp, and P. Wölfle, "Multiple Spin Echoes in a Normal Fermi Liquid," Phys. Rev. Lett., 1984, 53, 2312.
15. M. A. McCoy and W. S. Warren, "Three-Quantum Nuclear Magnetic Resonance Spectroscopy of Liquid Water: Intermolecular Multiple-Quantum Coherences Generated by Spin-Cavity Coupling," J. Chem. Phys, 1990, 93, 858.
16. W. S. Warren, Q. He, M. McCoy, and F. C. Spano, "Reply to Comment on 'Is Multiple-Quantum Nuclear Magnetic Resonance of Water Real?'," J. Chem. Phys., 1992, 96, 1659.
17. The equivalence of classical and quantum demagnetizing field treatments has been disputed by Warren et al. (5-7, 15, 16) who claimed that some experimental results cannot be explained quantitatively by the classical model. Claims were made that "the modified Bloch equations provide an incorrect representation of the quantum mechanical evolution," and that the (classical) demagnetizing field approach cannot fully explain the two-dimensional cross peaks because this method "throws away correlations" (the quotations are from ref. 5). Warren et al. supported these statements by erroneous simulations of the classical fields. All evidence suggests that carefully-applied classical models of radiation damping and demagnetizing fields do explain all the experimental resuits, and that the modified Bloch equations are in full accordance with quantum statistical mechanics. In fact, full quantitative agreement between experiments and simulations has only been reached with classical calcuations. The inclusion of spin-lattice relaxation, radiation damping, and molecular diffusion is essential for full quantitation, and these effects are incorporated only with great difficulty into macroscopic quantum calculations.
18. R. P. Feynman, R. B. Leighton and M. Sands, in The Feynman Lectures on Physics, Vol. 2, Addison-Wesley, London, 1964, pp. 36-12.
19. K-H. Hellwege, Einführung in die Festkörperphysik Springer, Berlin, 1976.
20. C. Kittel, Introduction to Solid-State Physics, 6th ed., Wiley, New York, 1986, pp. 479-485.
21. If each component contains J-coupled spins, a simple classical treatment of the spin dynamics is of course inappropriate. In that case the "classical" model should be replaced by a "semiclassical" model in which the spin dynamics within each molecule are treated quantum mechanically, by well-developed techniques (25), but with an extra term taking into account the macroscopic demagnetizing field from the net spin magnetization. However, claims have been made that semiclassical models of this kind are not always accurate. See ref. (17).
22. J. Jeener, Ampère Summer School, Basko Polje, Yugoslavia, 1971.
23. Cross-peaks also can be observed even in the absence of resolved spin-spin couplings, if there are cross-correlated relaxation mechanisms on the two involved spins. These effects depend on the close proximity of the participating nuclei and are different from the phenomena discussed in this article. See S. Wimperis and G. Bodenhausen, "Relaxation-Allowed Cross-Peaks in Two-Dimensional NMR Correlation Spectroscopy," Mol. Phys., 1989, 66, 897; I. Bertini, C. Luchinat, and D. Tarchi, "Are True Scalar Proton-Proton Connectivities Ever Measured in COSY Spectra of Paramagnetic Molecules?" Chem. Phys. Lett., 1993, 203, 445.
24. Cross-peaks also can be observed even in the absence of resolved spin-spin couplings, if there are cross-correlated relaxation mechanisms on the two involved spins. These effects depend on the close proximity of the participating nuclei and are different from the phenomena discussed in this article. See S. Wimperis and G. Bodenhausen, "Relaxation-Allowed Cross-Peaks in Two-Dimensional NMR Correlation Spectroscopy," Mol. Phys., 1989, 66, 897; I. Bertini, C. Luchinat, and D. Tarchi, "Are True Scalar Proton-Proton Connectivities Ever Measured in COSY Spectra of Paramagnetic Molecules?" Chem. Phys. Lett., 1993, 203, 445.
25. K. Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York, 1986.
26. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford, 1987.
27. In the examples given, the external field direction is specified explicitly for the sake of concreteness. In principle, the results are more general, because the magnetic flux density inside the sample can always be represented as a vector sum of the magnetic flux density generated by the sample and the magnetic flux density generated from outside.
28. B. I. Bleaney and B. Bleaney, Electricity and Magnetism, Oxford University Press, Oxford, 1976.
29. B. I. Bleaney and B. Bleaney, Electricity and Magnetism, Oxford University Press, Oxford, 1967, pp. 296-300.
30. C. Kittel, Introduction to Solid-State Physics, 6th ed., Wiley, New York, 1986, p. 366.
31. This is a little oversimplified. Vlassenbroek has pointed out (J. Jeener, pers. commun.) that, because the total Zeeman energy is conserved, the total longitudinal magnetization of the sample cannot be modified by the if demagnetizing field. The rf demagnetizing field in fact leads to a spatial redistribution of Zeeman energy and z magnetization within the sample volume, without changing the sum of these quantities.
32. A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1961.
33. J. Jeener, "Superoperators in Magnetic Resonance," Adv. Magn. Reson., 1982, 10, 1.
34. M. H. Levitt and L. Di Bari, "The Steady State in Magnetic Resonance Pulse Experiments," Phys. Rev. Lett., 1992, 69, 3124.
35. M. H. Levitt and L. Di Bari, "The Homogeneous Master Equation and the Manipulation of Relaxation Networks," Bull. Magn. Reson., 1994, 16, 92.
36. In their preliminary articles, Warren et al. (5, 6) truncated the power series expansion of Eq. [50] after the second term. It has been argued (ref. 11) that the entire exponential is required to reproduce the full richness of the classical description.
37. That the selection of coherence orders by field gradient sequences works "as usual" is not obvious. Normally, the participants in a multiple-quantum coherence are separated by a distance so small that the magnetic field gradient affects them identically. This is no longer the case for the postulated macroscopic multispin coherences. For example, microscopic zero-quantum coherences are unaffected by field gradient pulses, but this is not true for a macroscopic zero-quantum coherence involving two spins on opposite ends of the sample, where the gradient field on the two spins has opposite sign. Nevertheless, it seems that a close examination of the problem shows that the usual selection rules still apply, if signals from the entire sample volume are averaged (W. S. Warren, pers. commun.). However, there is potential for error if the wavelength of the magnetization helices established by the field gradient pulses is not very much smaller than the effective sample volume.
38. A. C. Rose-Innes and E. H. Rhoderick, Introduction to Superconductivity, Pergamon, Oxford, 1978.
39. The analogy is not flawless: H and E have identical properties only if there are no electric currents flowing in the material. See Ref. 27.
40. Again the analogy is not complete. The flux of D is only conserved if the enclosed volume does not contain any free electric charges. See Ref. 27.
41. C. Tang and J. S. Waugh, "Dynamics of Classical Spins on a Lattice: Spin Diffusion," Phys. Rev. B, 1992, 45, 748.