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Dynamics of Nuclear Spins

  • Ronald Y. Dong
Part of the Partially Ordered Systems book series (PARTIAL.ORDERED)

Abstract

The description of nuclear spin systems in liquid crystals under the influence of radiofrequency pulses requires a quantum mechanical formalism that specifies the state of a spin system by a state function or by a density operator. The density matrix formalism (Section 2.1) is introduced in this chapter. The full Hamiltonian H of a molecular system is usually complex. Fortunately, magnetic resonance experiments can be described by a more simplified spin Hamiltonian. The nuclear spin Hamiltonian acts only on the spin variables and is obtained by averaging the full Hamiltonian over the lattice coordinates. The lattice is defined as all degrees of freedom excluding those of a spin system. Various terms (e.g., chemical shift, dipoledipole interaction) in the spin Hamiltonian are summarized in Section 2.2. In contrast to solids, intermolecular interactions are normally averaged to zero in liquid crystals due to rapid translational and rotational diffusion of molecules in liquid crystalline phases. Furthermore, partial motional averaging of the NMR spectrum should be considered for the liquid crystalline molecules or for the solute molecules dissolved in liquid crystals. The partial averaging of the spin Hamiltonian is a result of anisotropic molecular tumbling motions. This is addressed in Section 2.3. Although the density matrix formalism is a general method, it is particularly suitable for systems in which the lattice may be described classically and in which motional narrowing [2.1]occurs. It is useful for describing pulsed NMR, which is a tool for studying liquid crystals. Deuterium NMR is used to illustrate various pulsed NMR techniques in Section 2.4.

Keywords

Liquid Crystal Density Matrix Spin System Nuclear Spin Spin Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 2.1
    C.P. Slichter, Principles of Magnetic Resonance, 3rd ed. (Springer, New York, 1990).Google Scholar
  2. 2.2
    M. Goldman, Quantum Description of High-Resolution NMR in Liq uids (Clarendon, Oxford, 1988).Google Scholar
  3. 2.3
    J.D. Memory, Quantum Theory of Magnetic Resonance Parameters (McGraw-Hill, New York, 1968).Google Scholar
  4. 2.4
    A. Abragam, The Principles of Nuclear Magnetism (Clarendon, Oxford, 1961).Google Scholar
  5. 2.5
    U. Haeberlen, High Resolution NMR in Solids: Selective Average (Academic, New York, 1976).Google Scholar
  6. 2.6
    M. Mehring, Principles of High Resolution NMR in Solids, 2nd ed. (Springer, Berlin, 1983).CrossRefGoogle Scholar
  7. 2.7
    H.W. Spiess, NMR Basic Principles Prog. 15, 55 (1978).Google Scholar
  8. 2.8
    M.E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957); D.M. Brink and G. R. Satchler, Angular Momentum (Clarendon, Oxford, 1962).MATHGoogle Scholar
  9. 2.9
    A.R. Edmonds, Angular Momentum in Quantum Mechanics (Prince ton University, Princeton, NJ, 1957).MATHGoogle Scholar
  10. 2.10
    C. Zannoni, The Molecular Physics of Liquid Crystals, edited by G.R. Luckhurst and G.W. Gray (Academic, New York, 1979), Chap. 3.Google Scholar
  11. 2.11
    M. Luzar, V. Rutar, J. Seliger, and R. Blinc, Ferroelectrics 58, 115 (1984).CrossRefGoogle Scholar
  12. 2.12
    A. Pines and J.J. Chang, J. Am. Chem. Soc. 96, 5590 (1974); Phys. Rev. A 10, 946 (1974).CrossRefGoogle Scholar
  13. 2.13
    M. Bloom, J.H. Davis, and M.I. Valic, Can. J. Phys. 58, 1510 (1980).ADSCrossRefGoogle Scholar
  14. 2.14
    R.R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon, Oxford, 1987).Google Scholar
  15. 2.15
    A.J. Vega and Z. Luz, J. Chem. Phys. 86, 1803 (1987).ADSCrossRefGoogle Scholar
  16. 2.16
    S. Vega and A. Pines, J. Chem. Phys. 66, 5624 (1977); M. Mehring, E.K. Wolff, and M.E. Stoll, J. Magn. Reson. 37, 475 (1980).ADSCrossRefGoogle Scholar
  17. 2.17
    K.R. Jeffrey, Bull. Magn. Reson. 3, 69 (1981).Google Scholar
  18. 2.18
    J.H. Davis, K.R. Jeffrey, M. Bloom, M.I. Valic, and T.P. Higgs, Chem. Phys. Lett. 42, 390 (1976).ADSCrossRefGoogle Scholar
  19. 2.19
    J. Jeener and P. Broekaert, Phys. Rev. 157, 232 (1967).ADSCrossRefGoogle Scholar
  20. 2.20
    H.W. Spiess, J. Chem. Phys. 72, 6755 (1980).ADSCrossRefGoogle Scholar
  21. 2.21
    R.R. Vold and R.L. Vold, in Advances in Magnetic and Optical Res onance, edited by W.S. Warren (Academic, San Diego, 1991).Google Scholar
  22. 2.22
    R.L. Vold, W.H. Dickerson, and R.R. Vold, J. Magn. Reson. 43, 213 (1981).Google Scholar
  23. 2.23
    P.A. Beckmann, J.W. Emsley, G.R. Luckhurst, and D.L. Turner, Mol. Phys. 50, 699 (1983).ADSCrossRefGoogle Scholar
  24. 2.24
    S. Wimperis, J. Magn. Reson. 86, 46 (1990).Google Scholar
  25. 2.25
    S. Wimperis, J. Magn. Reson. 83, 509 (1989); S. Wimperis and G. Bodenhausen, Chem. Phys. Lett. 132, 194 (1986).Google Scholar
  26. 2.26
    G.L. Hoatson, J. Magn. Reson. 94, 152 (1991).Google Scholar
  27. 2.27
    R.Y. Dong, Bull. Magn. Reson. 14, 134 (1992).Google Scholar
  28. 2.28
    C. Forte, M. Geppi, and C.A. Veracini, Z. Naturforsch. Teil A 49, 311 (1994).Google Scholar
  29. 2.29
    H.Y. Carr and E.M. Purcell, Phys. Rev. 94, 630 (1954).ADSCrossRefGoogle Scholar
  30. 2.30
    S.B. Ahmad, K.J. Packer, and J.M. Ramsden, Mol. Phys. 33, 857 (1977).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ronald Y. Dong
    • 1
  1. 1.Department of Physics and AstronomyBrandon UniversityBrandonCanada

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