Solid State NMR

solid state nmr spectroscopy

1. In The Name Of God

2. همانا در آفرینش آسمانها و زمین و رفت و آمد و شب وروز نشانه هایی است برای صاحبان عقل. (سوره آل عمران: 190)

3. Solid State NMR Spectroscopy [email protected]

4. Solid State NMR Applications The very powerful technique for amorphous solids, powder crystalline samples. Determination of local molecular environments . measurement of internuclear distances (dipolar recoupling) Structure Chirality Enzyme mechanisms Polymorphism

5. Organic complexes Inorganic complexes Zeolites mesoporous solids microporous solids aluminosilicates /phosphates minerals biological molecules Glasses cements food products wood ceramics bones semiconductors metals and alloys archaelogical specimens polymers resins surfaces Solid state NMR has been applied to

6. 6 13 C NMR of glycine Adapted from M. Edén , Concepts in Magnetic Resonance 18A, 24. D. Lide , G. W. A. Milne, Handbook of Data on Organic Compounds: Compounds 10001-15600 Cha-Hex. (CRC Press, 1994). Solid Liquid Powder Spectra

7. Solid and Liquid Factors that average to zero in solution due to random motion are now factors in solid state NMR T 1 is long  lack of motion and modulation of dipole-dipole interaction T 2 is short  mutual spin flips occurring between pairs of spins Each nucleus produces a rotating magnetic field as it precesses in the applied magnetic field Each spin has a static field component that influences Larmor frequency of neighbors Range of frequencies that add to line-width Chemical shift anisotropy Chemical shift varies with orientation relative to B B o Solid-state (ordered structure) Solution-state (random-orientation) 9

8. Line-shape Broadening Factors for Solid Samples Direct Dipolar Coupling ◦ Between at least two nuclear magnetic moments ◦ Heteronuclear and Homonuclear Chemical Shift Anisotropy ◦ Orientation dependence of molecule relative to B o Shorter Spin-Spin (T 2 *) Relaxation ◦ Larger linewidths at half-height Quadrupolar Interaction for Spin > ½ ◦ Between nuclear charge distribution and electric field gradient in the solid Magnetic Susceptibility ◦ Differences of Ho (mag. flux) at solid / liquid interface

9. Shorter Spin-Spin (T 2 *) Relaxation NUCLEAR MAGNETIC RESONANCE IN SOLID POLYMERS, VINCENT J. McBRIERTY , 1993.

10. NMR Interactions in the Solid State In the solid state, all of these interactions can make secular contributions. Spin state energies are shifted resulting in direct manifestation of these interactions in the NMR spectra. 12 1-Zeeman interaction of nuclear spins 2-Direct dipolar spin interaction 3-Indirect spin-spin coupling ( J-coupling) , nuclear-electron spin coupling ( paramagnetic), coupling of nuclear spins with molecular electric field gradients ( quadrupolar interaction). 4-Direct spin-lattice interactions 3,5-Indirect spin-lattice interaction via electrons 3,6-Chemical shielding and polarization of nuclear spins by electrons 4,7-Coupling of nuclear spins to sound fields

11. 1-Zeeman interaction of nuclear spins 2-Direct dipolar spin interaction 3-Indirect spin-spin coupling (J-coupling), nuclear-electron spin coupling (paramagnetic), coupling of nuclear spins with molecular electric field gradients ( quadrupolar interaction). 4-Direct spin-lattice interactions 3,5-Indirect spin-lattice interaction via electrons 3,6-Chemical shielding and polarization of nuclear spins by electrons 4,7-Coupling of nuclear spins to sound fields

12. Nuclear spin interactions The “size” of these external interactions is larger than internal

13. All NMR interactions are anisotropic - their three dimensional nature can be described by second-rank Cartesian tensors, which are 3 × 3 matrices . The NMR interaction tensor describes the orientation of an NMR interaction with respect to the cartesian axis system of the molecule. These tensors can be diagonalized to yield tensors that have three principal components which describe the interaction in its own principal axis system (PAS)

14. Zeeman interaction It can be described with a Hamiltonian or in ternsor form In the magnetic field the two spin states have different energies It is far the strongest interaction and all other types of interaction can be considered as corrections Order of the magnitude:

15. Chemical shielding is an anisotropic interaction characterized by a shielding tensor σ , which can also be diagonalized to yield a tensor with three principal components . Isotropic Chemical shielding

16. chemical shielding anisotropy gives rise to frequency shifts with the following orientation dependence: In order to calculate powder patterns (for any anisotropic NMR interaction), one must calculate frequencies for a large number of orientations of the interaction tensor with respect to the magnetic field - many polar angles over a sphere: Ɵ, φ

17. Chemical shifts in single crystals Shielding depends on molecular (i.e. crystal) orientation: 23

18. Powder patterns Spectra from powdered samples are sums over individual crystallite orientations: (Shape reflects probability of particular orientation) axial symmetry ( h = 0) Well-defined powder patterns can analysed to determine chemical shift tensor components Loss of resolution (and sensitivity) is usually unacceptable 24

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20.             Rossum , Solid State NMR and proteins (2009) J. Duer , Solid State NMR spectroscopy (2002) Chemical Shift Anisotropy More shielding -> lower chemical shift

21. More shielding -> lower chemical shift. Dependent on angular orientation More shielded   Chemical Shift Anisotropy

22. 28 Chemical Shift Anisotropy

23. Powder Pattern Chemical shift is dependent on orientation of nuclei in the solid Distribution of chemical shifts Averaged to zero for isotropic tumbling Leads to extensive line-width broadening in solid-state NMR Progress in Nuclear Magnetic Resonance Spectroscopy 6 46 (2005) 1–21 29

24. Why is the chemical shift orientation dependent ? Molecules have definite 3D shapes, and certain electronic circulations (which induced the local magnetic fields) are preferred over others . Molecular orbitals and crystallographic symmetry dictate the orientation and magnitude of chemical shielding tensors.

25. Nuclear Pair Internuclear distance Dipolar coupling 1 H, 1 H 10 120 1 H, 13 C 1 30 1 H, 13 C 2 3.8 Nuclear Pair 1 H, 1 H 10 120 1 H, 13 C 1 30 1 H, 13 C 2 3.8 Dipolar coupling causes huge line broadening J. Duer , Solid State NMR spectroscopy (2002) Dipole-Dipole Coupling

26. When two spins (nuclei I and S) are close (≤10 Å) in a magnetic field ... ◦ One spin affects local magnetic field at another spin ◦ Changes frequency of paired nuclei ◦ Interaction depends on I-S distance and angle between I-S and Bo z y x 1 H 13 C q B r The degree by which spin I affects the magnetic field at spin S is determined by the dipolar coupling constant (d): In solution, random motion averages dipolar coupling to zero In solids, orientations are static  defined by crystal lattice

27. Direct dipole coupling Useful for molecule structure studies and provides a good way to estimate distances between nuclei and hence the geometrical form of the molecule

28. The dipolar interaction results from interaction of one nuclear spin with a magnetic field generated by another nuclear spin , and vice versa. This is a direct through space interaction .

29. Dipolar hamiltonian can be expanded into the dipolar alphabet , which has both spin operators and spatially dependent terms. Only term A makes a secular contribution for heteronuclear spin pairs, and A and B (flip flop) both make contributions for homonuclear spin pairs: H DD =A+B+C+D+E+F

30. In a solid-state powder sample every magnetic spin is coupled to every other magnetic spin; dipolar couplings serve to severely broaden NMR spectra. In solution molecules reorient quickly; nuclear spins feel a time average of the spatial part of the dipolar interaction +3cos2 2-1, over all orientations 2,N. The dipolar interaction tensor is symmetric and traceless, meaning that the interaction is symmetric between the two nuclei, and there is no isotropic dipolar coupling: For a heteronuclear spin pair in the solid state, the (3cosƟ 2 - 1) term is not averaged by random isotropic tumbling: the spatial term will have an effect on the spectrum!

31. So, for an NMR spectrum influenced only by the Zeeman and AX dipolar interaction, the frequencies for A can be calculated as: For a homonuclear spin pair, the flip flop term (B) is also important: So the frequencies of the transitions can be calculated as:

32. Presence of many dipolar interactions (e.g. between 1 H’s) results in featureless spectra : The dipolar interaction

33. In a single crystal with one orientation of dipolar vectors, a single set of peaks would be observed

34. in a powder, the spectra take on the famous shape known as the Pake doublet A - A A - X m x = +1/2 m x = -1/2

35. The Pake doublet was first observed in the 1 H NMR spectrum of solid CaSO 4 .H 2 O . The Pake doublet is composed of two subspectra resulting from the α and β spin states of the coupled nucleus.

36. J-coupling Nuclear spins are coupled with the help of the molecular electrons It is exclusively intramolecular The mechanism responsible for the multiplet structure It can be viewed only in solution-state NMR spectra where the spectral lines are narrow enough to observe the interaction

37. Notably, NMR of half-integer quadrupolar nuclei has become quite commonplace , and allowed investigation of a broad array of materials . The only integer quadrupolar nuclei investigated regularly are 2 H (very common) and 14 N (less common).

38. Electric Q uadrupole C oupling Nucleus with the electric quadrupole moment int e r a cts strongly with the electric field gradients generated by surrounding electron clouds Size of quadrupole interaction, w Q , depends on nucleus e.g. 2 H has a relatively low quadrupole moment symmetry of site e.g. no field gradients at cubic symmetry site Liquids : quadrupolar nuclei relax quickly, resulting in broad lines Solids : NMR can be complex, but may be very informative… Quadrupole interaction is totaly averaged in liquids, but in solids is the strongest after Zeeman In solids we often need to take into account second order contributions

39. an asymmetric distribution of nucleons giving rise to a non-spherical positive electric charge distribution The asymmetric charge distribution in the nucleus is described by the nuclear electric quadrupole moment, eQ , which is measured in barn (which is ca. 10 -28 m 2 ). eQ is an instrinsic property of the nucleus , and is the same regardless of the environment.

40. Quadrupolar nuclei interact with electric field gradients ( EFGs) in the molecule: EFGs are spatial changes in electric field in the molecule . Like the dipolar interaction, the quadrupolar interaction is a ground state interaction, but is dependent upon the distribution of electric point charges in the molecule and resulting EFGs. The EFGs at the quadrupolar nucleus can be described by a symmetric traceless tensor, which can also be diagonalized :

41. The magnitude of the quadrupolar interaction is given by the nuclear quadrupole coupling constant: For a quadrupolar nucleus in the centre of a spherically symmetric molecule , the EFGs cancel one another resulting in very small EFGs at the quadrupolar nucleus. As the spherical symmetry breaks down, the EFGs at the quadrupolar nucleus grow in magnitude :

42. The quadrupolar interaction, unlike all of the other anisotropic NMR interactions, can be written as a sum of first and second order interactions: Below, the effects of the first- and second-order interactions on the energy levels of a spin - 5/2 nucleus are shown:

43. The first order interaction is proportional to C Q , and the second-order interaction is proportional to C Q 2 / ν , and is much smaller. Notice that the first-order interaction does not affect the central transition . The first-order quadrupolar interaction is described by the hamiltonian (where Ɵ and φ are polar angles )

44. Perturbation theory can be used to calculate the second-order shifts in energy levels (note that this decreases at higher fields)

45. only the first-order quadrupolar interaction is visible , with a sharp central transition, and various satellite transitions that have shapes resembling axial CSA patterns. Static spectra of quadrupolar nuclei are shown below for the case of spin 5/2:

46. the value of C Q is much larger. The satellite transitions broaden and disappear and only the central transition spectrum is left (which is unaffected by first-order interactions). It still has a strange shape due to the orientation dependence of the second- order quadrupolar frequency.

47. A number of methods have been developed and considered in order to minimize large anisotropic NMR interactions between nuclei and increase S/N in rare spin (e.g., 13 C, 15 N) NMR spectra High-Resolution Solid-State NMR Magic-angle spinning Cross Polarization

48. Magic Angle Spinning (MAS) 54.74 o

49. Notice that the dipolar and chemical shielding interactions both contain 3cos 2 Ɵ - 1 terms. In solution, rapid isotropic tumbling averages this spatial component to zero. Magic-angle spinning introduces artificial motion by placing the axis of the sample rotor at the magic angle (54.74) with respect to B - the term 3cos 2 Ɵ - 1 = 0 when θ = 54.74. The rate of MAS must be greater than or equal to the magnitude of the anisotropic interaction to average it to zero. Magic-angle spinning

50. Simulating the “tumbling” of molecules http://www.rs2d.com/english/images/protasis/doty/doty.jpg Magic Angle Spinning

51. Magic Angle Spinning (MAS) Zero z component ( B z ) if the angle (q) relative to B is 54.7356° All dipolar interactions disappear at this angle All chemical shift anisotropy disappear at this angle Quadrupole broadening is also reduced Simulate a uniform distribution of magnetic moments in a powder by spinning the sample very fast at 54.44 o B z = 0 68 z y x 1 H 13 C q B r

52. Samples are finely powdered and packed tightly into rotors, which are then spun at rates from 1 to 35 kHz, depending on the rotor size and type of experiment being conducted. If the sample is spun at a rate less than the magnitude of the anisotropic interaction , a manifold of spinning sidebands becomes visible, which are separated by the rate of spinning (in Hz). Here is an example of MAS applied in a 31 P CPMAS NMR experiment: The span of this spectrum is S . 500 ppm, corresponding to a breadth of about 40000 Hz (31 P at 4.7 T). The isotropic centreband can be identified since it remains in the same position at different spinning rates.

53. Magic-Angle-Spinning Spectrum

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55. Sodium silicate glasses BO NBO Na 2 Si 2 O 5 Na 2 Si 3 O 7 Na 2 Si 4 O 9 600 0 -600 ppm Static 17 O NMR spectra bridging (BO) and non-bridging (NBO) oxygens

56. Structure of glasses (I) BO NBO

57. Structure of glasses (II) Q 4 Q 2 Q 1 Q 3

58. 29 Si NMR spectra for sodium silicate glasses static MAS Q 4 Q 3 + Q 2 0 -100 -200 ppm -60 -80 -100 mole % Na 2 O 34 37 41 Q 2 Q 3

59. Unlike first-order interactions, the second-order term is not averaged to zero by MAS. The second-order quadrupolar frequency can be expressed in terms of zeroth - , second- and fourth-order Legendre polynomials:

60. So the second-order quadrupolar interaction cannot be completely averaged unless the rotor is spun about two axes simultaneously at β = 30.55° and 70.12°. There are experiments called DOR (double rotation - actual special probe that does this ) and DAS (dynamic angle spinning - another special probe).

61. Decoupling static static with low power decoupling static with high power decoupling decoupling + MAS solution-state spectrum In the mechanism of decoupling a strong rf field is applied so that magnetic moments are flipped randomely back and forth to narrow the anisotropic broadeneng of the resonance lines 84

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66. Magic Angle Spinning (MAS) Spin Samples at 54.44 o to reduce line-width Spinning speed must be greater than static line-width to be studied (powder pattern width) Normal speed limit is 35 kHz Sample holder rotor Sample holder at MAS MAS probe rotor at MAS 89

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68. Fast rotation (1 - 60 kHz) of the sample about an axis oriented at 54.7° (magic-angle) with respect to the static magnetic field removes all broadening effects with an angular dependency of That means chemical shift anisotropy, dipolar interactions, first-order quadrupole interactions, and inhomogeneities of the magnetic susceptibility . It results an enhancement in spectral resolution by line narrowing also for soft matter studies . High-resolution solid-state MAS NMR rotor with sample in the rf coil z r  rot θ gradient coils for MAS PFG NMR B 91

69. Solid-state NMR spectroscopy Magic-angle spinning NMR spectroscopy on 1 H, 13 C, and 29 Si nuclei in the functionalized mesoporous proton conducting materials was performed in the fields of 9.4 and 17.6 Tesla mainly at room temperature. 92

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71. 13 C NMR of alanine with 1 H decoupling without decoupling static spinning (5 kHz) CH CH 3 CO 2 NH 3 – + CH CH 3 CO 2 – * * 94

72. 1 H NMR of organic solids Static sample MAS 20 10 - 10 proton chemical shift (ppm) ~25 kHz MAS N H 4 C H C H 3 + 1 H NMR is difficult in organic solids due to strong dipolar couplings between protons Useful resolution can be obtained, especially for H-bonded sites, with relatively fast spinning (>20 kHz) using just MAS 95

73. 1 H MAS NMR spectroscopy Imidazole-MCM-41 Si N OH N Si OH HO 3 S SO 3 H-MCM-41  10 H 2 O H 3 O + H 2 O + H +  H 3 O + 96

74. MAS reduces linewidth from 5000 Hz to 200 Hz High power decoupling reduces linewidth from 5000 Hz to 450 Hz MAS & high power decoupling reduces linewidth from 5000 Hz to 2 Hz Similar to liquid state sample Spin ½ Nuclei with Low Magnetogyric ratios ( 13 C, 15 N, 2 9Si, 31 P, 113 Cd ) Combine MAS with high power 1 H decoupling High power is required because of very large 1 H line-widths Low sensitivity of nuclei requires long acquisition times 97

75. Dilution: This occurs naturally for many nuclei in the periodic table, as the NMR active isotope may have a low natural abundance (e.g., 13 C, 1.108% n.a .), and the dipolar interactions scales with r-3 . However, this only leads to “high-resolution” spectra if there are no heteronuclear dipolar interactions (i.e., with protons, fluorine)!Also, large anisotropic chemical shielding effects can also severely broaden the spectra!

76. Multiple-Pulse Sequences: Pulse sequences can impose artifical motion on the spin operators (leaving the spatial operators, vide infra) intact. Multipulse sequences are used for both heteronuclear (very commong ) and homonuclear (less common) decoupling - 1H NMR spectra are still difficult to acquire, and use very complex, electronically demanding pulse sequences such as CRAMPS (combined rotation and multiple pulse spectroscopy). Important 2D NMR experiments as well!

77. Cross Polarization When combined with MAS, polarization from abundant nuclei like 1H, 19F and 31P can be transferred to dilute or rare nuclei like 13C, 15N, 29 Si in order to enhance signal to noise and reduce waiting time between successive experiments.

78. Cross polarization is one of the most important techniques in solid state NMR. In this technique, polarization from abundant spins such as 1H or 19F is transferred to dilute spins such as 13C or15N . The overall effect is to enhance S/N: Cross polarization enhances signal from dilute spins potentially by a factor of γ I / γ S where I is the abundant spin and S is the dilute spin. 2. Since abundant spins are strongly dipolar coupled , they are therefore subject to large fluctuating magnetic fields resulting from motion . This induces rapid spin-lattice relaxation at the abundant nuclei. Polarization is transferred during the spin locking period, (the contact time) and a П /2 pulse is only made on protons: the proton and carbon magnetization precess in the rotating frame at the same rate, allowing for transfer of the abundant spin polarization to carbon Cross Polarization

79. Cross-polarization combined with MAS (CP-MAS ) Exchange polarization from 1 H to 13 C 2 ms 50 ms 1 H 90 o pulse generates xy magnetization (B 1H ) Spin-lock pulse keeps magnetization in xy plane precessing at : g H B 1H /2 p Hz 13 C pulse generates xy magnetization that precesses at: g C B 1C /2 p Hz Polarization transfer occurs if: g H B 1H / 2p Hz = g C B 1C /2 p Hz Hartmann Hahn matching condition D E = g h B o / 2 p 1 Ha 1 Hb 13 C a 13 C b g H B 1H / 2 p g C B 1C / 2 p Polarization transfer 102

80. Outline of what is happening Transfer of polarization from 1H to low- g nuclei 104 x z y x z y x z y x z y x z y x z y 1 H X ( p /2) y (Spin Lock) x (Spin Lock) x 1 H X (p /2) y Spin Lock Decouple

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82. Cross-polarization combined with MAS (CP-MAS ) Simultaneously pulse 1 H to 13 C Use RF energy to equilibrate energy states The increase in the 13 C signal depends on the strength of the dipolar interaction and the duration of the mixing or contact time g H B 1H / 2p Hz = g C B 1C /2 p Hz 108

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84. Cross-polarization combined with MAS (CP-MAS ) Example of CP-MAS 13 C spectrum Cross-polarization increases the 13 C population difference by the factor g H / g C Increases signal sensitivity 110

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86. 13 C CP { 1 H} MAS NMR spectroscopy Imidazole-MCM-41 Si HO 3 S SO 3 H-MCM-41 N N Si 112

87. 29 Si CP {1H} MAS NMR spectroscopy Imidazole-MCM-41 29 Si CP {1H} MAS NMR 29 Si MAS NMR (one-pulse) Si (OSi-) 3 (OH) 1 Si (OSi - ) 4 Si (OSi-) 2 (OH) 2 -CH 2 Si (OSi-) 2 (OH) 1 -CH 2 Si (OSi-) 3 100% 5% 5% relative concentration 29 Si MAS NMR Bloch decay spectra yield quantitative information about linking of functional groups. 113