Introduction to Solid State NMR In solution NMR, spectra consist of a series of very sharp transitions, due to averaging of anisotropic NMR interactions by rapid random tumbling. By contrast, solid-state NMR spectra are very broad, as the full effects of anisotropic or orientation-dependent interactions are observed in the spectrum. High-resolution NMR spectra can provide the same type of information that is available from corresponding solution NMR spectra, but a number of special techniques/equipment are needed, including magic-angle spinning, cross polarization, special 2D experiments, enhanced probe electronics, etc. 150 100 50 0 ppm Solution 13 C NMR Solid State 13 C NMR The presence of broad NMR lineshapes, once thought to be a hindrance, actually provides much information on chemistry, structure and dynamics in the solid state. Origins of Solid-State NMR Original NMR experiments focused on 1 H and 19 F NMR, for reasons of sensitivity. However, anisotropies in the local fields of the protons broadened the 1 H NMR spectra such that no spectral lines could be resolved. The only cases where useful spectra could be obtained was for isolated homonuclear spin pairs (e.g., in H2O), or for fast moving methyl groups. Much of the original solid state NMR in the literature focuses only upon the measurement of 1 H spin-lattice relaxation times as a function of temperature in order to investigate methyl group rotations or motion in solid polymer chains. The situation changed when it was shown by E.R. Andrew and I.J. Lowe that anisotropic dipolar interactions could be supressed by introducing artificial motions on the solid - this technique involved rotating the sample about an axis oriented at 54.74° with respect to the external magnetic field. This became known as magic-angle spinning (MAS). In order for the MAS method to be successful, spinning has to occur at a rate equal to or greater than the dipolar linewidth (which can be many kHz wide). On older NMR probe designs, it was not possible to spin with any stability over 1 kHz! 5000 0 -5000 Hz 19 F NMR of KAsF6 1 J(75 As,19 F) = 905 Hz Rdd(75 As,19 F) = 2228 Hz static (stationary sample) MAS, rot = 5.5 kHz High-Resolution Solid-State NMR 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:  Magic-angle spinning: rapidly spinning the sample at the magic angle w.r.t. B0, still of limited use for “high-gamma” nuclei like protons and fluorine, which can have dipolar couplings in excess of 100 kHz (at this time, standard MAS probes spin from 7 to 35 kHz, with some exceptions)  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!  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 -1 H 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!  Cross Polarization: When combined with MAS, polarization from abundant nuclei like 1 H, 19 F and 31 P can be transferred to dilute or rare nuclei like 13 C, 15 N, 29 Si in order to enhance signal to noise and reduc waiting time between successive experiments. Magic-Angle Spinning Notice that the dipolar and chemical shielding interactions both contain (3cos2 -1) terms. In solution, rapid isotropic tumbling averages this spatial component to zero (integrate over sind). Magic-angle spinning introduces artificial motion by placing the axis of the sample rotor at the magic angle (54.74() with respect to B0 - the term 3cos2  - 1 = 0 when  = 54.74(. The rate of MAS must be greater than or equal to the magnitude of the anisotropic interaction to average it to zero. B0 M M = 54.74( 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). Magic-Angle Spinning Here is an example of MAS applied in a 31 P CPMAS NMR experiment: 0 -200200400 ppm iso static spectrum rot = 3405 Hz rot = 3010 Hz The span of this spectrum is 6  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. Magic-Angle Spinning Here is an example of a 119 Sn CPMAS NMR spectrum of Cp*2SnMe2 at 9.4 T: 250 200 150 100 50 0 -50 ppm rot = 5 kHz rot = 3 kHz static spectrum 208 scans 216 scans 324 scans Even with MAS slower than the breadth of the anisotropic interaction, signal becomes localized under the spinning sidebands, rather than spread over the entire breadth as in the case of the static NMR spectrum. Notice the excellent signal to noise in the MAS spectra, and poor signal to noise in the static spectrum, despite the increased number of scans. iso = 124.7 ppm iso = 124.7 ppm Cross Polarization Cross polarization is one of the most important techniques in solid state NMR. In this technique, polarization from abundant spins such as 1 H or 19 F is transferred to dilute spins such as 13 C or 15 N. The overall effect is to enhance S/N: 1. Cross polarization enhances signal from dilute spins potentially by a factor of I/ 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. The end result is that one does not have to wait for slowly relaxing dilute nuclei to relax, rather, the recycle delay is dependent upon the T1 of protons, fluorine, etc. Polarization is transferred during the spin locking period, (the contact time) and a %/2 pulse is only made on protons: 1 H 13 C (%/2)x Spin Locking Mixing Acquisition Decoupling Relaxtion Delay Relaxtion Delay -CT -AQ -R Contact Time y Cross Polarization Cross polarization requires that nuclei are dipolar coupled to one another, and surprisingly, it even works while samples are being spun rapidly at the magic angle (though not if the spinning rate is greater than the anisotropic interaction). Hence the acronym CPMAS NMR (Cross Polarization Magic-Angle Spinning NMR) 1 H 13 C70H 71H 1 H 13 C 70C 71C Polarization Lab frame: 70H > 70C Rf rotating frame: 71H w 71C The key to obtaining efficient cross polarization is setting the Hartmann-Hahn match properly. In this case, the rf fields of the dilute spin (e.g., 71C-13) is set equal to that of the abundant spin (e.g., 71H-1) by adjusting the power on each of the channels: C-13BC-13 = H-1BH-1 If these are set properly, the proton and carbon magnetization precess in the rotating frame at the same rate, allowing for transfer of the abundant spin polarization to carbon: Extremely different frequencies Matched frequencies Single Crystal NMR It is possible to conduct solid-state NMR experiments on single crystals, in a similar manner to X-ray diffraction experiments. A large crystal is mounted on a tenon, which is mounted on a goniometer head. If the orientation of the unit cell is known with respect to the tenon, then it is possible to determine the orientation of the NMR interaction tensors with respect to the molecular frame. tenon crystal Here is a case of single crystal 31 P NMR of tetra-methyl diphosphine sulfide (TMPS); anisotropic NMR chemical shielding tensors can be extracted. NMR Interactions in the Solid State In the solid-state, there are seven ways for a nuclear spin to communicate with its surroundings: Electrons Nuclear spin I Nuclear spin S Phonons 1 1 7 6 2 53 3 4 4 B0, B1, external fields 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   ext   int  ext  0   1  [Tr{ 2 }]1/2  int  II   SS   IS   Q   CS   L NMR Interactions in the Solid State Nuclear spin interactions are distinguished on the basis of whether they are external or internal: Interactions with external fields B0 and B1 The “size” of these external interactions is larger than int: The hamiltonian describing internal spin interactions:  II and  SS: homonuclear direct dipolar and indirect spinspin coupling interactions  IS: heteronuclear direct dipolar and indirect spin-spin coupling interactions  Q: quadrupolar interactions for I and S spins  CS: chemical shielding interactions for I and S  L: interactions of spins I and S with the lattice 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. For most cases, we can assume the high-field approximation; that is, the Zeeman interaction and other external magnetic fields are much greater than internal NMR interactions. Correspondingly, these internal interactions can be treated as perturbations on the Zeeman hamiltonian.  I#A#S [Ix, Iy, Iz] Axx Axy Axz Ayx Ayy Ayz Azx Azy Azz Sx Sy Sz  I#Z#B0,  I#Z#B1, B0 [B0x, B0y, B0z] [0,0, B0], B1 2[B1x, B1y, B1z]cos&t Z I 1, 1 1 0 0 0 1 0 0 0 1  PAS A11 0 0 0 A22 0 0 0 A33 NMR Interaction Tensors All NMR interactions are anisotropic - their three dimensional nature can be described by second-rank Cartesian tensors, which are 3 × 3 matrices. A22 A11 A33 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): Such interaction tensors are commonly pictured as ellipsoids or ovaloids, with the A33 component assigned to the largest principal component. Nuclear spins are coupled to external magnetic fields via these tensors:  DD M i 1/2, and an asymmetric distribution of nucleons giving rise to a non-spherical positive electric charge distribution; this is in contrast to spin-1/2 nuclei, which have a spherical distribution of positive electric charge. + + _ _ + + _ _ nuclear charge distribution electric field gradients in molecule Spin-1/2 Nucleus Quadrupolar Nucleus + 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 m2 ). eQ is an instrinsic property of the nucleus, and is the same regardless of the environment. 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. prolate nucleus eQ > 0 oblate nucleus eQ < 0 VPAS V11 0 0 0 V22 0 0 0 V33 V Vxx Vxy Vxz Vyx Vyy Vyz Vzx Vzy Vzz Solid-State NMR of Quadrupolar Nuclei The EFGs at the quadrupolar nucleus can be described by a symmetric traceless tensor, which can also be diagonalized: V22 V11 V33 The principal components of the EFG tensor are defined such that V11  V22  V33 . Since the EFG tensor is traceless, isotropic tumbling in solution averages it to zero (unlike J and )). 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: Co NH3 NH3 NH3NH3 NH3 NH3 Co NH3 NH3 NH3NH3 Cl NH3 Co Br NH3 NH3NH3 Cl Br Increasing EFGs, increasing quadrupolar interaction The magnitude of the quadrupolar interaction is given by the nuclear quadrupole coupling constant: CQ = eQ#V33/h (in kHz or MHz) The asymmetry of the quadrupolar interaction is given by the asymmetry parameter,  = (V11 - V22)/V33, where 0    1. If  = 0, the EFG tensor is axially symmetric.  Q  (1) Q   (2) Q Solid-State NMR of Quadrupolar Nuclei 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:  Z Q  Q (1) (2) +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 mS The first order interaction is proportional to CQ, and the secondorder interaction is proportional to CQ 2 /0, and is much smaller (shifts in energy levels above are exaggerated). Notice that the first-order interaction does not affect the central transition.  (1) Q 1 2 Q (,3) [I 2 z I(I1)/3] where Q (,3) (&Q/2) [3cos2 1 sin2cos23] &Q 3e2qQ/[2I(2I 1)U]  (2) Q 1 6 &Q[3I 2 z I(I1)  (I 2 x I 2 y)] &(2) Q &2 Q 16&0 (I(I1) 3 4 )(1 cos2)(9cos2 1) Solid-State NMR of Quadrupolar Nuclei The first-order quadrupolar interaction is described by the hamiltonian (where  and 1 are polar angles): quadrupole frequency, where eq = V33 If the quadrupolar interaction becomes larger as the result of increasing EFGs, the quadrupolar interaction can no longer be treated as a perturbation on the Zeeman hamiltonian. Rather, the eigenstates are expressed as linear combinations of the pure Zeeman eigenstates (which are no longer quantized along the direction of B0. The full hamiltonian is required: Perturbation theory can be used to calculate the second-order shifts in energy levels (note that this decreases at higher fields) when  = 0. Solid-State NMR of Quadrupolar Nuclei Static spectra of quadrupolar nuclei are shown below for the case of spin 5/2: -Q/2Q/2 -Q -2Q Q 2Q 0  = 90(  = 0(  = 41.8( A = (S(S + 1) - 3/4)Q / 160 +1/2 Û-1/2 0 0 +A 0 - (16/9)ABA -1/2 Û-3/2 -3/2 Û-5/2 +3/2 Û+1/2 +5/2 Û+3/2 In A, only the first-order quadrupolar interaction is visible, with a sharp central transition, and various satellite transitions that have shapes resembling axial CSA patterns. In B, the value of CQ is much larger. The satellite transitions broaden anddisappear 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 secondorder quadrupolar frequency. P2(cos) (3cos2 1) P4(cos) (35cos4 30cos2  3) &(2) Q rot A0  A2P2(cos)  A4P4(cos) MAS NMR of Quadrupolar Nuclei Unlike first-order interactions, the second-order term is no longer a second-rank tensor, and 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: Pn(cos), where P0(cos) = 1, and The averaged value of 7Q (2) under fast MAS is written as where A2 and A4 are functions of 7Q, 70 and  as well as the orientation of the EFG tensor w.r.t. the rotor axis, and  is the angle between the rotor axis and the magnetic field. So the second-order quadrupolar interaction cannot be completely averaged unless the rotor is spun about two axes simultaneously at  = 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). MAS NMR of Quadrupolar Nuclei MAS lineshapes of the central transition of half-integer quadrupolar nuclei look like this, and are very sensitive to changes in both CQ and : Solid-State 27 Al NMR spin = 5/2 9.4 T  = 0.3 40 20 0 -20 -40 -60 -80 -100 ppm 9.0 CQ (MHz) 7.0 5.0 4.0 3.0 1.0 40 20 0 -20 -40 -60 -80 ppm CQ = 6.0 MHz  = 0.0  = 0.2  = 0.4  = 0.6  = 0.8  = 1.0 However, in the presence of overlapping quadrupolar resonances from several sites, the spectra can be very difficult to deconvolute, especially in the case of disordered solids where lineshapes are not well defined! One can use DOR or DAS techniques, but this requires expensive specialized probes. Fortunately a technique has been developed which can be run on most solid state NMR probes, known as MQMAS (multiple quantum magic-angle spinning) NMR. MQMAS NMR MQMASNMR is used to obtain high-resolutionNMR spectra of quadrupolar nuclei. It involves creating a triple-quantum (or 5Q) coherence. During the 3Q evolution, the second-order quadrupolar interaction is averaged; however, sincewe cannot directly observe the 3Q coherence, itmust be converted to a 1Q coherence for direct observation. +2 +1 0 -1 -2 +3 -3 11 t1 12 t2 23 NaMQMASNMR ofNa2SO3 rot = 9 kHz Solid State NMR: Summary Solid state NMR is clearly a very powerful technique capable of looking at a variety of materials. It does not require crystalline materials like diffraction techniques, and can still determine local molecular environments. A huge variety of solid state NMR experiments are available for measurement of internuclear distances (dipolar recoupling), deconvolution of quadrupolar/dipolar influenced spectra, probing site symmetry and chemistry, observing solid state dynamics, etc. Solid state NMR has been applied to: 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 Most of the NMR active nuclei in the periodic table are available for investigation by solids NMR, due to higher magnetic fields, innovative pulse sequences, and improved electronics, computer and probe technology.