固体中半整数四极核的自旋扩散

摘要/Abstract

摘要：

首先介绍固态中自旋扩散的一般理论，包括半经典描述和建立在投影算子理论上的密度矩阵描述. 接着以丰核环境中相互偶合的自旋-1/2系统以及自旋-3/2系统为典型列举了自旋扩散速率的计算. 最近藉助多量子魔角旋转(MQMAS)方法实现半整数四极核的多量子谱自旋扩散实验，可以测量固体粉末中半整数四极核体系四极张量相对方向. 结合作者最近的计算机模拟和实验测量结果对这一新兴方向作了重点介绍，尤其指出了射频
脉冲强度、宽度及样品旋转速度对交叉峰线型的影响.

关键词: 固体核磁共振, 半整数四极核, 自旋扩散

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

中图分类号:

O482.53

刘志宏, 邓风, 丁尚武. 固体中半整数四极核的自旋扩散[J]. 波谱学杂志, 2004, 21(1): 99-125.

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.

参考文献

[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.