SPIN DIFFUSION OF HALF-INTEGER QUADRUPOLAR SPINS IN SOLIDS

Abstract

Abstract:

This review first summarizes the general theory of spin diffusion in solids, including semi-classical description and the more exact approach, i.e., density matrix method based on projection operator formalism. The calculation of spin diffusion rate is demonstrated with two typical cases: a spin-1/2 pair and the central transition of a spin-3/2 pair. The analysis of spectral spin diffusion of halfinteger quadrupolar spins is emphasized, highlighting the influence of pulse strength, width as well as sample spinning speed.

Key words: solid state NMR, half-integer spin nuclei, spin diffusion

CLC Number:

O482.53

LIU Zhi-Hong, DENG Feng, DING Shang-Wu. SPIN DIFFUSION OF HALF-INTEGER QUADRUPOLAR SPINS IN SOLIDS[J]. Chinese Journal of Magnetic Resonance, 2004, 21(1): 99-125.

References

[1] Bloembergen N. The interaction of nuclear spins in a crystalline lattice[J]. Physica, 1949, 15: 386-426.

[2] Abragam A. Principle of Nuclear Magnetism[M]. London: Oxford, 1961.

[3] Douglass D C, Mcbrierty V J. Compatibility in PVF2/PMMA and PVF2/PEMA blends as studied by pulsed NMR[J]. Macromolecules, 1978, 11: 766-773.

[4] McBrierty V J. Heterogeneity in polymers as studied by Nuclear Resonance[J]. Faraday Discuss Chem Soc, 1979, 68: 86-99.

[5] Caravatti P, Deli J A, Bodenhuasen G, et al. Direct evidence of microscopic homogeneity in disordered solids[J]. J Am Chem Soc, 1982, 104: 5 506-5 507.

[6] Szevernyi N M, Sullivan M J, Maciel G E. Observation of spin exchange by Two-Dimensional Fourier transform 13C transform cross polarization/Magic-Angle Spinning[J]. J Magn Reson, 1982, 47: 462-475.

[7] Henrichs P M, Linder M. Carbon-13 spin diffusion in the determination of intermolecular structure in solids[J]. J Magn Reson, 1984, 58: 458-461.

[8] Caravatti P, Neuenschwander P, Ernst R R. Characterization of heterogeneous polymer blends by two-dimensional proton spin diffusion spectroscopy[J]. Macromoleecules, 1985, 18: 119-122.

[9] Cheung T T P. Spin diffusion in NMR in solids[J]. Phys Rev B, 1981,23: 1 404-1 418.

[10] Suter D, Ernst R R. Spin diffusion in resolved solid-state NMR spectra[J]. Phys Rev B, 1985, 32: 5 608-5 627.

[11] Linder M, Hohener A, Ernst R R. Orientation of tensorial interactions determined from two-dimensional NMR powder spectra[J]. J Chem Phys, 1980, 73: 4 959-4 970.

[12] De Paul S M, Tomaselli M, Pines A, et al. Reversal of radio-frequency-driven spin diffusion by reorientation of the sample spinning axis[J]. J Chem Phys, 1998, 108: 826-829.

[13] Ding S, Mcdowell C A. Theoretical calculations of CPMAS spectral lineshapes of half-integer quadrupole spin systems[J]. Mol Phys, 1995, 85: 283-288.

[14] Meier B H. Polarization transfer and spin diffusion in Solid-State NMR[J]. Adv Magn Op Reson, 1994, 18: 1-26

[15] Kubo A, McDowell C A. ³¹P spectral spin diffusion in crystalline solids[J]. J Chem Phys, 1988, 89: 63-70.

[16] Ye C, Eckman R, Pines A. Spin Diffusion and orientation dependence of deuterium T1 in solids[J]. J Magn Reson, 1983, 55: 334-337.
[17] Dowell N G, Ashbrook S E, McManusa J, et al. Relative orientation of quadrupole tensors from Two-Dimensional Multiple-Quantum MAS NMR[J]. J Am Chem Soc, 2001, 123: 8 135-8 136.

[18] Dowell N G, Ashbrook S E, Wimperis Stephen. Relative orientation of quadrupole tensors from High-Resolution NMR of powdered solids[J]. J Phys Chem A , 2002, 106: 9 470-9 478.

[19] Fryddman, Harwood. Isotropic spectra of half-integer quadrupolar spins from bidimensional Magic-Angle Spinning NMR[J]. J Am Chem Soc., 1995, 117: 5 367-5 368.

[20] Medek A, Harwood J S, Frydman. Multiple-quantum magic-angle spinning NMR: A new method for the study of quadrupolar nuclei in solids[J]. J Am Chem Soc, 1995, 117: 12 779-12 787.

[21] Fernandez C, Amoureux J P. 2D multiquantum MAS-NMR spectroscopy of ²⁷Al in aluminophosphate molecular sieves[J]. Chem Phys Lett, 1995, 242: 449-454.

[22] Wu G, Rovnyak D, Sun B, et al. High-resolution multiple quantum MAS NMR spectroscopy of half-integer quadrupolar nuclei[J]. Chem Phys Lett, 1996, 249: 210-217.

[23] Fernandez C, Amoureux J P. Triple-quantum MAS-NMR of quadrupolar nuclei[J]. Solid State Nucl Magn Reson, 1996, 5: 315-321.

[24] Brown S P, Heyes S J, Wimperis S. Two-dimensional MAS multiple-quantum NMR of quadrupolar nuclei removal of inhomogeneous second-order broadening[J]. J Magn Reson A , 1996, 119: 280-284.

[25] Baltisberger J H, Xu Z, Stebbins J F, et al. Triple-quantum two-dimensional ²⁷Al magic-angle spinning nuclear magnetic resonance spectroscopic study of aluminosilicate and aluminate crystals and glasses[J]. J Am Chem Soc, 1996, 118: 7 209-7 914.

[26] Ding S, McDowell C A. Shaped pulse excitation in multi-quantum magic-angle spinning spectroscopy of half-integer quadrupole spin systems[J]. Chem Phys Lett, 1997, 270: 81-86.

[27] Wang S H, Xu Z, Baltisberger J H, et al. Multiple-quantum magic-angle spinning and dynamic-angle spinning NMR spectroscopy of quadrupolar nuclei[J]. Solid State Nucl Magn Reson , 1997, 8: 1-16.

[28] Fernandez C, Delevoye L, Amoureux J P, et al. ²⁷Al -¹H cross polarization triple-quantum magic angle spinning NMR[J]. J Am Chem Soc, 1997, 119: 6 858-6 862.

[29] Pruski M, Lang D P, Fernandez C, et al. Multiple-quantum magic-angle spinning NMR with cross-polarization: Spectral editing of high-resolution spectra of quadrupolar nuclei[J]. Solid State Nucl Magn Reson, 1997, 7: 327-331.

[30] Marinelli L, Frydman. On the origin of spinning sidebands in MQMAS NMR experiments[J]. Chem Phys Lett, 1997, 275: 188-198.

[31] Ding S, McDowell C. Multiple-quantum MAS NMR spectroscopy of spin-3/2 quadrupolar spin systems using shaped pulses[J]. J Magn Reson, 1998, 135: 61-69.

[32] Chapentier T, Fermon C, Virlet J. Efficient time propagation technique for MAS NMR simulation: Application to quadrupolar nuclei [J]. J Magn Reson, 1998, 132: 181-190.

[33] Chapentier T, Fermon C, Virlet J. Numerical and theoretical analysis of multiquantum magic-angle spinning experiments[J]. J Chem Phys, 1998, 109: 3 116-3 130.

[34] Fernandez C, Lang D P, Amoureux J P, et al. Measurement of heteronuclear dipolar interactions between quadrupolar and spin -1/2 nuclei in solids by multiple-quantum REDOR NMR[J]. J Am Chem Soc, 1998, 120: 2 672-2 673.

[35] Ding S, McDowell C. Quantification of multi-quantum magic-angle spinning spectra of half-integer quadrupolar spin systems[J]. Chem Phys Lett, 1999, 307: 215-219.

[36] Madhu P K, Goldbourt A, Frydman L, et al. Sensitivity Enhancement of the MQMAS NMR Experiment by Fast Amplitude Modulation of the Pulses[J].Chem Phys Lett, 1999,307: 41-47.

[37] Gan Z. Isotropic NMR spectra of half-integer quadrupolar nuclei using satellite transitions and magic-angle Spinning[J]. J Am Chem Soc, 2000, 122: 3 242-3 243.

[38] Ashbrook S E, Wimperis S. Single- and multiple-quantum cross-polarizatin in NMR of quadrupolar nuclei in static samples[J]. Mol Phys, 2000, 98: 1-26.

[39] Ashbrook S E, Wimperis S. Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei[J]. J Magn Reson, 2000, 147: 238-249.

[40] Wi S, Frydman. Residual dipolar couplings between quadrupolar nuclei in high resolution solid state NMR: Description and observations in the high-field limit[J]. J Chem Phys, 2000, 112: 3 248-3 261.

[41] Nijman M, Ernst M, Kentgens A P M, Meier B H. A rotational-resonance NMR experiment for half-integer quadrupolar spin systems[J]. Mol Phys, 2000, 98: 161-168.

[42] Bak M, Rasmussen J T, Nielsen N C. SIMPSON: A General Simulation Program for Solid-State NMR Spectroscopy[J]. J Magn Reson, 2000, 147: 296-330.

[43] Povnyak D, Baldus M, Griffi R G. Multiple-quantum cross polarization in quadrupolar spin systems during magic-angle spinning[J]. J Magn Reson, 2000, 142: 145-152.

[44] Madhu P K, Goldbourt A, Frydman L, et al. Fast radio-frequency amplitude modulation in multiple-quantum magic-angle-spinning nuclear magnetic resonance: Theory and experiments[J]. J Chem Phys, 2000, 112: 2 377-2 391.

[45] Vosegaard T, Florian P, Grandinetti P J, et al. Pure absorption-mode spectra using a modulated RF mixing period in MQMAS experiments[J]. J Magn Reson, 2000, 143: 217-222.

[46] Vosegaard T, Florian P, Massiot D, et al. Multiple quantum magic-an-gle spinning using rotary resonance excitation[J]. J Chem Phys, 2001, 114: 4 618-4 624.

[47] Wi S, Heise H, Pines A. Reintroducing anisotropic interactions in magic-angle-spinning NMR of half-integer quadrupolar nuclei: 3D MQMAS[J]. J Am Chem Soc, 2002, 124: 10 652-10 653.

[48] Eden M, Grinshtein J, Frydman L. High resolution 3D exchange NMR spectroscopy and the mapping of connectivities between halfinteger quadrupolar nuclei[J]. J Am Chem Soc, 2002, 124: 9 708-9 709.

[49] Wi S, Logan J W, Sakellariou D, et al. Rotary resonance recoupling for half-integer quadrupolar nuclei in solid-state nuclear magnetic resonance spectroscopy[J]. J Chem Phys,2002, 117: 7 024-7 033.

[50] Liu Z, Deng F, Ding S. Effects of pulse width and spinning speed on spectral spin diffusion of spin-3/2 quadrupolar Nuclei[J]. J Chem Phys, 2004, 120: 740.

[51] Smitht S A, Levante T O, Meier B H, Ernst R R. Computer simulations in magnetic resonance. An object-oriented programming approach[J]. J Magn Reson Ser A, 1994, 106: 75-105.

[52] Baks M, Rasmussen, Nielsen N C. SIMPSON:a general simulation program for solid-state NMR spectroscopy[J]. J Magn Reson, 2000, 147: 296-330.