Seminar. Solid-state NMR Spectroscopy

Transcription

1 Univerza v Ljubljani, Fakulteta za matematiko in fiziko Seminar Solid-state NMR Spectroscopy Author: Katja Kadunc Mentor: prof.dr.janez Seliger Ljubljana, April 2011 Abstract In this seminar repeat some general facts of the nuclear magnetic resonance. Later on, I concentrate on NMR spectroscopy in solids. The interactions of nuclear spins with each other, and other quantities that determine the appearance of NMR spectra and complicate NMR imaging in solids are described. Also some methods of NMR imaging in solids are discussed are that are required to avoid problems that these interactions cause, such as cross-polarization and magic-angle spinning.

2 Contents 1 Introduction 2 2 Nuclear Magnetic Resonance (NMR) Magnetic fields Nuclear magnetization Classical equation of motion: the Bloch equation The impact of short-term high-frequency magnetic disturbances on the magnetization in a static magnetic field Solid-state NMR spectroscopy Nuclear spin interactions Cross-polarization Magic-angle spinning Spinning sidebands Magic angle spinning and cross-polarization Magic angle spinning and off-magic angle spinning Conclusion 14 1

3 1 Introduction Nuclear magnetic resonance (NMR) exploits the interacion of nuclei with magnetic fields. This phenomenon was first described in molecular beams by Isidor Rabi in Eight years later, Felix Bloch and Edward Mills Purcell improved the technique for use on liquids and solids, for which they shared the Nobel Prize in physics in 1952 [1]. Since then, NMR has developed and it is now widley used: for analysis and identification of material, to determinate the detailes in chemical strucutre of the chemicals which are being synthesied, for structual analysis of molecules in solutions and proteins, in condensed matter physics. Another well-known product of NMR technology is the Magnetic Resonance Imaging (MRI), which is utilized extensively in the medical radiology field to obtain image slices of soft tissues in the human body. 2 Nuclear Magnetic Resonance (NMR) 2.1 Magnetic fields NMR is a method which investigates molecular properities by interrogating atomic nuclei with magnetic fields and radio-frequency irradiation. A strong time-invariant magnetic field B 0 is applied to polarize the nuclear magnetic moments. It is oriented along the z-direction of the coordinate system. The strength of B 0 is between 0.5 and 21 T. It defines the NMR frequency ω 0 : ω 0 = γb 0, (1) where γ is gyromagnetic ratio and has a characteristic value for a certain nuclei. B 0 is the magnitude of the strong static magnetic field. For spatial resolution in NMR imaging the polarizing field has to be inhomogeneous. This inhomogeneous part is normally linearly space-depended, so that the field gradient is constant and is generated by a seperate set of coils. Time-dependant radio-frequency magnetic fields B rf (t) are used to stimulate the spectroscopic response and are perpendicular to the static field. B rf (t) oscillates with nuclear resonace frequency ω 0. Typical NMR frequencies are in radio-frequency regime between 10 and 900 MHz. The strength of this excitaion field B rf (t) is 1 mt or less [2]. 2.2 Nuclear magnetization The relevant quantity to NMR is the contribution of the nuclei to macroscopic magnetization. Many nuclei have a property similar to angular momentum which is known as spin. Let us denote overall spin of the nucleus by the spin quantum number I. A non-zero spin has a non-zero magnetic moment µ: µ = γ I. (2) In external magnetic field B 0 which is parallel to z-axis, the nuclear magnetic moment µ experiences a torque N: N = µ B 0. (3) 2

4 The change of spin d I is proportional to torque thrust Ndt. Therefore we can rewrite equation (3): d I dt = N = µ B 0 = γ I B 0. (4) The change of spin is always perpendicular to the spin itself and to magnetic field. The magnetic moment µ precess about B 0. Frequency of precession is not dependent on the angle between magnetic field and magnetic moment and it is called the Larmor frequency: ω L = γ B 0. (5) The energy of a magnetic moment µ in a magnetic field B 0 = (0, 0, B 0 ) is given by: E = µ B 0 = µ z B 0. (6) We can see that only z-component of magnetic moment contributes to energy. Spin is discrete in value and orientation, which means that z-component of magnetic moment is also discrete in value and orientation: µ z = γ m, (7) where m is magnetic quantum number. Therefore the energy is: It can assume the values: E m = γ mb 0. (8) I m I. (9) This means that a nuclear spin with quantum number I can be in one of 2I + 1 stationary states in a magnetic field. Nuclei like 1 H and 13 C with spins I = 1/2 have two eigenstates. These are referred as spinup and spin-down, depending on whether the z component of the magnetic moment is parallel or antiparallel to the magnetic field (figure 1). The energy difference E between the neighbouring energy levels is absorbed or Figure 1: Energy levels for a nucleus with spin emmited by nuclear spin when it reorients number 1/2 [3]. and moves form one energy level to the next. This energy difference determines the NMR frequency ω 0 : E = E m E m 1 = γ B 0 = ω 0 = 2πν 0 (10) The NMR frequency is proportional to the strength of the magnetic field B 0 and also is the fine structure of the resonance which results from shielding of the magnetic field at the site of the nucleus by surrounding electrons. This is called chemical shift. Higher field strengths provide better spectroscopic resolution and also better sensitivity. This is 3

5 due to an increase in magnetic polarization M 0 established in magnetic field B 0, which is in thermodynamic equilibrium given by Curie law: M 0 = N γ2 2 I(I + 1) 3k B T B 0, (11) where I is nuclear spin quantum number, T temperature and N the number of nuclei with spin I in the sample. The polarization is the sum of all components of the nuclear magnetic moments parallel to the applied field. In thermodynamic equilibrium, all magnetic moments are found in one of the energy eigenstates E m with one of the 2I + 1 allowed projections along the z-axis. The differences in population of the energy levels are determining the nuclear magnetic polarization. The relative number of spins in these states is given by the Boltzmann distribution: ( n m 1 = exp ω ) 0. (12) n m k B T From this we can caluculate the population difference n = n m n m 1. In hightemperature approximation, where k B T ω 0, the exponent in equation (12) can be expanded and truncated after the second term. This high-temperature approximation can be used down to rather low temperatures. In this limit the population difference n corresponding to the magnitude of the magnetization is proportional to the strength of the magnetic field. This is expressed by the Curie law (equation 11) and is valid when thermodynamic equilibrium is achived [2]. When an initially unmagnetized sample is put in the magnetic field, the formation of the thermodynamic equilibrium of magnetization requires the transfer od energy from the spins to the surrounding lattice. This energy transfer takes place in a characteristic time T 1 (energy disipation time or spin-lattice relaxation time). A tipical value for T 1 of 1 H is 1 second at high magnetic fields. Since all magnetic moments µ i precess with different phases around B 0, projections on xy plane are in average 0, which means that the total equilirium magnetization will point along magnetic field (in our case along the z-axis). In nonequilibrium state magnetization is precessing around B magnetic field B 0. 0 (figure Figure 2: Precession of magnetization M in 2). 2.3 Classical equation of motion: the Bloch equation The equation of motion of the macroscopic magnetization vector has been derived by Felix Bloch by defining M/γ as angular momentum, which experiences a torque M B in magnetic field B. This means that any magntization component, which is not parallel to the magnetic field precesses around it. By equating the torque to the rate of change 4

6 of angular momentum, and by adding a relaxation term that allows the establishment of thermodynamic equilibrium with time, we get the Bloch equation: d M dt = γ M(t) B(t) R[ M(t) M 0 ]. (13) The time-dependent magnetization s M(t) thermodynamic equilibrium is at M 0 = (0, 0, M 0 ) and R is a relaxation matrix: 1/T R = 0 1/T 2 0, (14) 0 0 1/T 1 with the longitudinal and transverse relaxation times T 1 and T 2. The longitudinal relaxation time T 1 is the spin-lattice relaxation time (as mentioned above) which is characteristic for accumulation of the magnetization parallel to the magnetic field. The transverse relaxation time T 2 is the time constant for disappearance of magnetization components perpendicular to the magnetic field. T 2 is in liquids close to T 1, while in solids it can be orders of magnitude shorter. Transverse magnetization components are generated by application of resonant radio-frequency irradiation. We can see this by solving the Bloch equation, which gives us the following relation for the z component of magnetization: M z (t) = M 0 (1 e t/t 1 ), (15) which is desciribing how magnetizaion relaxes into its termodynamical equilibrium state along z-axis [2]. 2.4 The impact of short-term high-frequency magnetic disturbances on the magnetization in a static magnetic field To solve the Bloch equations the magnetic field B(t) is written as a sum of the strong static magnetic field B 0 and a weak, time-dependent radio-frequency field B rf (t), which is perpendicular to B 0 : B(t) = B 0 + B rf (t). (16) The radio-frequency field is usually applied with linear polarization: 2B 1 cos(ω L t + ϕ) B rf (t) = 0 0, (17) where ϕ describes a phase offset which can be manipulated by the transmitter electronics. To simplify the calculation let us move from laboratory frame to a rotating coordinate frame, which rotates around the z-axis of the laboratory frame with Larmor frequency ω L : z = z, x = xcos(ω L t) + ysin(ω L t), (18) y = ycos(ω L t) xsin(ω L t). 5

7 In laboratory frame the linearly polarized radio-frequency field can be written as a sum of two circular polarized components: 2B 1 cos(ω L t + ϕ) B 1 cos(ω L t + ϕ) B 1 cos(ω L t + ϕ) B rf (t) = 0 = B 1 sin(ω L t + ϕ) + B 1 sin(ω L t + ϕ). (19) The first component rotates with rotating coordinate frame, so within this frame we see this component as static. The second component rotates around the z-axis with twice Larmor frequency. Therefore, it does not impact the direction of magnetization significantly and can be discarded. If we apply the radio-frequncy field perpendicular to the thermodynamic equilibrium magnetization M 0, the magnetization is exposed to a nonvanishing magnetic field in the rotating frame. For this reason, it experiences a torque and rotates in this field with frequency: ω 1 = γb 1, (20) where B 1 is the magnitude of the rotating field component. The duration t p for which the radio-frequncy field is turned on, is adjustable in NMR spectrometers. Therefore, we can manipulate the angle of precession α around the axis of the radio-frequncy field: α = ω 1 t p. (21) This gives us the possibility to apply pulses with arbitrary flip angles and so-called π/2 and π pulses. Figure 3: Magnetization in rotating coordinate frame, which rotates with frequency ω rf. (a) On resonance the rotating radio-frequency field component B 1 appears static. The magnetization M 0 rotates around B 1 field with frequency ω 1. (b) When the radio-frequency field is turned off the magnetization rotates around the z-axis of the rotating frame with frequency Ω 0 if the radio-frequency is set off resonance. (c) The phase coherance among magnetization components making up the xy part of the vector sum M is lost in time due to differences in local NMR frequencies which fluctuate with time [2]. By changing the phase ϕ, the direction of the field B 1 can be set anywhere within the xy plane of the rotating frame. For example, when choosing ϕ = 0, 90, 180, 270, the field B 1 is parallel to the +x, +y, -x and -y axes. Due to spin-spin interaction, the phase correlation between the spins is lost in time. Consequently the signal of magnetization in xy plane is reducing as given by the Bloch equation (13): M xy = M 0xy e t/t 2. (22) 6

8 Another reason for the dephasing of magnetic moments with time are inhomogeneities in field B 0, which have an impact on the total relaxation time T 2 : 1 T 2 = 1 T T inh. (23) Typically the spin-spin relaxation time T 2 is notably smaller than the spin-lattice relaxation time T 1 so that the signal decreases mainly due to spin-spin interaction and field inhomogeneities. This is called the free induction decay (FID). 3 Solid-state NMR spectroscopy The appearance of NMR spectra is determined by various interactions of nuclear spins with each other, and other quantities like the local and applied magnetic field, the electric field gradient and the coupling to the lattice or the surroundings. This quantities have impact on resonance frequencies, lineshapes and relaxation times. The description of spin interactions in solids is more complicated than in liquids due to slow molecular motion on the NMR timescale. This interactions complicate NMR imaging of solids and often require completely different experimental tehniques from those used for liquids and biomedical objects. 3.1 Nuclear spin interactions The resonance frequencies and therefore the separation of the energy levels of the nuclear spin states are determined by the interaction energies of the spins. The larges interaction next to the Zeeman interaction is the quadrupolar interaction, followed by the dipoledipole coupling, the chemical shift and the indirect coupling. The quadrupole interaction: Nuclei with spin quantum number I > 1/2 exhibit an electric quadrupole moment, which couples to the electric field gradient caused by the electrons surrounding the nucleus. This means, that this interaction is a valuable sensor for the electronic structure. In rigid aromatic and aliphatic compounds, the quadrupole splitting of 2 H is of the order of 130 khz. The quadrupole interaction is expressed by the Hamilton operator: eq Ĥ Q = [2I(2I 1) ]ÎQÎ (24) The interaction is quadratic with respect to spin vector Î and it is described by the quadrupole coupling tensor Q, which is proportional to the tensor od the electric field gradient. The average value of 1 Tr(Q) = 0. Therefore, the quadrupole interaction and 3 quadrupole splitting cannot be observed under fast isotropic motion as in liquids. 7

9 Figure 4: Quadrupole coupling of the 2 H nucleus to the electric field gradient of a C- 2 H bond. Left: Geometry of the interaction and principal axes of the coupling tensor. Middle: NMR spectrum for a single molecular orientation. Right: The average over all orientations is the powder spectrum [2]. The dipole-dipole interaction describes the coupling of two magnetic moments through space. The Hamilton operator for an isolated 13 C- 1 H (in general these are named as S and I spins) pair can be written as: Ĥ D = µ 0 2 γ I γ S r 3 (1 3cos 2 θ)îz Ŝz (25) where γ I and γ S are proton and carbon the gyromagnetic ratios, r is the lenght of the internuclear vector, I and S are the proton and carbon spin operator, Figure 5: Geometrical construction for dipoledipole interaction. B 0 is the magnetic field and the C-H vector of length r makes the angle θ with the field direction [5]. and θ is the angle between internuclear vector and external magnetic field. This equation is the secular part of dipolar Hamilton operator that comutates with Zeeman Hamilton operator and causes the shift of resonance frequency in the first order of the perturbation theory. Because of the 1 3cos 2 (θ) dependence of the dipoledipole interaction, the interaction vanishes when θ is 54.7 (the magic angle). For liquids in which the molecules are moving rapidly, the term 1 3cos 2 (θ) must be integraded over a sphere, as all angles θ are sampled. This integration produces the result that the dipole-dipole interaction is zero for molecules in solution. The r 3 dependence means that generally only directly bonded and nearest neighbouring protons will contribute to dipolar boardening at a specific carbon nucleus. This dependence on distance is a highly valuable source of information about the structual geometry of molecules. The dipole-dipole coupling has no effect on the resonance frequencies in liquids, but it is the dominating mechanism for relaxation in many solid samples. Magnetic shielding appears when the external magnetic field is shielded at the site of the nucleus by the surounding electrons. The local field is given by: B = (1 σ)b 0, (26) where 1 is an identity matrix and σ is the shielding tensor, which is different for different materials. This shieldnig is specific for a particular electronic enviroment and thus of the 8

10 chemistry. The shielding is dependent on the strength of the magnetic field, therefore the Hamilton operator is Ĥ σ = γîσb 0. (27) The average value of σ = 1 Tr(σ) is observed in liquids and also in solids by using the 3 line-narrowing techniques. Magnetic shielding determines the chemical shift in high-resolution NMR. The resonance frequency ω L is different from the NMR frequency ω 0 of the nucleus by ω L = (1 σ)ω 0 (28) The NMR frequency of free nuclei is difficult to measure, so the chemical shift is tabulated with reference to a standard. Relative values, which give the frequency difference to the standard compound normalized by the NMR frequency of the nucleus, are being used to eliminate the field dependence. δ = ω L ω s ω s (29) δ is the relative chemical shift and values are given in ppm. The spread of resonace frequencies in the spectral resolution increases with the increasing field strength. The indirect coupling is mediated by a polarization of the orbital angular momentum of the electrons. This coupling is difficult to obsereve in solid-state NMR because of the larger linewidth in solids. The indirect coupling is written as Ĥ J = Îi JÎj, (30) where Îi and Îj are the spin vector operators of the coupling nuclei and J is a coupling 1 tensor. Its trace is different from zero: Tr(J) = J so that the indirect coupling is 3 observed not only in solids but also under fast isotropic motion such as in liquids. J is the coupling constant and because of the the indirect coupling is also known as the J coupling. 3.2 Cross-polarization Cross-polarization is usually used to assist in observation od rare nuclei (like 13 C and 29 Si). When observing rare nuceli, we come across some problems: 1. The low abundance of the nuceli means that the signal-to-noise ratio is inevitably poor. 2. The relaxation times of low abundance nuceli are usually very long (because of the absence of strong homonuclear dipolar interactions which can stimulate the relaxation transition). The longer relaxation time means longer gaps must be left between scans, which means longer time to collect a spectrum. 9

11 By using cross-polarization these problems can be avoided. A significant gain in signal-to-noise ration can be achieved if magnetization is transferred to the rare spins S from abundant spins I (like 1 H). Cross-polarization can be achieved in a double-resonance experiment. Transverse magnetization of the I spins is generated by a 90 pulse at a frequency ω rfi. Afterwards the transmitter is not turned off, only the radio-frequency phase is shifted by 90. Therefore, the B 1I field is now applied parallel to the I magnetization. This technique is called spin-locking, because the I magnetization is locked along the B 1I field (if this field is the dominant magnetic field that the I spins experience in the frame rotating with frequency ω rfi around the z-axis). The B 1I field is the dominant magnetic field that the I spins experience if its amplitude ω 1I = γ 1I B 1I is larger than the frequency offset ω LI ω rfi and the other interactions of the I spin. While the I spins are locked in the transverse plane, another radio-frequency field B 1S at frequency ω rfs is applied to the S spins. If the magnitudes B 1S and B 1I of both applied fields are matched by the Hartmann- Hahn condition γ S B 1S = γ I B 1I, (31) Figure 6: Illustration of cross polarization: (a) Timing diagram of radio-frequency excitation for cross-polarization of 1 H magnetization to 13 C, DD denotes heteronuclear dipolar decoupling. (b) Precession of 1 H magnetization components during cross-polarization with a frequency ω 1H around the magnetic field B 1H in the coordinate system, rotating with frequency ω rfh. (c) Precession of 13 C magnetization components during cross-polarization with a frequency ω 1C around the magnetic field B 1C in the coordinate system, rotating with frequency ω rfc [2]. then each spin species precesses with the same frequency ω 1 = γb 1 around the axis of its radio-frequency field in its own rotating frame. Both rotating frames share the same z-axis, consequently there is an oscillation of local I and S magnetizations components along the z-axis with the same frequency. This frequency match allows the exchange of magnetization between both spins species. But because only the I spins were polarized at the beginnig, magnetization is transferred form the I to the S spins. The efficiency of cross-polarization is determined by the size of the dipolar interaction between I and S spins, and by the relaxation times T 1ρI and T 1ρS (longitudinal relaxation times in the rotating frame for both spin species) of the spin-locked I and S magnetization. By variation of the contact time T CP (the length of the spin-locked time), local differences in the dipolar interaction and in the T 1ρI relaxation times can be exploited to selectively polarize different chemical and morphological structures. The dipolar interaction between I and S spins is made ineffective by high-power dipolar decoupling (DD). If the decoupler is turned off for a short time t D, the magnetization of the S spins strongly coupled to the I spins dephases and only the magnetization of the 10

12 weakly coupled S spins survives. In this way magnetization can be selectively transferred, for example, from 1 H to 13 C of rigid crystalline and of mobile amorphous regions, or of protonated and unprotonated nuclei. In the beginning the S magnetization M(t CP ) is bulit up with a constant T CH (characteristic time for the strength of the dipolar coupling between spis species). The magnetization passes through a maximum with the increasing cross-polarization time t CP. Then it is weakened by the influence of the relaxation times T 1ρH and T 1ρC in the rotating frames of I and S spins: where M(t CP ) = M 0 λ [ 1 exp ( λt CP T CH )] exp ( t ) CP, (32) T 1ρH λ = 1 + T CH T 1ρC T CH T 1ρH. (33) This cross-polarization is the basic one most often used in practice. Other variation exist and other techniques can be used. For example, the spin-lock fields can be ramped off and on adiabatically (adiabatic cross-polarization by demagnetization an remagnetization in the rotating frame). This gives better efficiency than Hartmann-Hahn cross-polarization, but is also experimentally more demanding. High-power decoupling is the most effective tool to measure the spectra of rare spins S in the presence od abundant spins I. To measure this spectra, the heteronuclear dipolar coupling between I and S spins has to be suppressed. For I decoupling during aquisition of S magnetization a strong continuous or pulsed radio-frequency field of amplitude ω 1I is applied at the spin frequency ω rfi. The decoupling efficiency depends on two factors: 1. The amplitude ω 1I = γb 1I of the decoupling field has to be large compared to the strength of the heteronuclear dipolar interaction (for the decoupling of 13 C and 1 H this means that γb 1H > 2π100kHz should be chosen). 2. The modulation of the heteronuclear dipolar coupling by the flip-flop transistors in the sistem of abundant I spins, which communicate by the homonuclear dipole-dipole interaction. 3.3 Magic-angle spinning Magic-angle spinnig (MAS) is used in the vast majority of solid-state NMR experiments, where its primary task is the removal of the effects of chemical shift anisotropy, to assist in the removal of heteronuclear dipolar coupling effects, to narrow lines from quadrupolar nuclei and for removing the effects of homonuclear dipolar coupling from NMR spectra. This last application requires high spinning speed, and is therefore not so widely spread. They are using spinning frequencies up to 50 khz [6]. In solutions the effects of chemical shift anisotropy, dipolar coupling etc., are rarely observed in solution NMR spectra. This is a result of the rapid movement of the molecules which means that the angle θ between the orientation of the shielding/dipolar tensor and the applied magnetic field is rapidly averaged, which also averages the 1 3cos 2 θ dependence to zero on the NMR timescale (the rate of change of molecular orientation is fast relative to the chemical shift anisotropy). The same can be achieved for solids by the magic angle spinning. If we incline our sample for the angle θ R to the applied field and start to spin it, 11

13 the angle θ, which is describing the orientation of the interaction tensor fixed in a molecule in the sample, varies with time as the molecule rotates with the sample. The average 1 3cos 2 θ in these circumstances is 1 3cos 2 θ = 1 2 (1 3cos2 θ R )(1 3cos 2 β), (34) where angles θ R and β are defined in figure 7. The angle β is fixed for a given nucleus in a rigid solid, but it takes on all possible values in a powder sample (like the angle θ). The angle θ R is under the control of the experiment. When it is set to 54.74, (1 3cos 2 θ R ) becomes zero, and consequently the average 1 3cos 2 θ is Figure 7: The sample is placed in a gas driven spinner. The rotation axis is inclined by the angle θ R = The chemical shielding tensor is represented by an ellipsoid and its fixed in the molecule to which it applies and so rotates with sample. The angle θ is the angle between B 0 and the principal z-axis of the shielding tensor and β is the angle between the z-axis of the shielding tensor and the spinning axis [6]. zero also. Providing that the spinnig rate is fast so that the angle θ is averaged rapidly compared to the anisotropy of the interaction, the interaction anistoropy averages to zero Spinning sidebands The rate of the sample spinning must be fast in comparison to the anisotropy of the interaction (3 or 4 times larger that the anisotropy) in order for magicangle spinning to reduce a powder pattern to a single line at the isotropic chemical shift. If the spinning speed is not high enough, a set of spinning sidebands are produced in addition to the line at the isotropic chemical shift. The sidebands are sharp lines, set at the spinning speed apart from the line of isotropic chemical shift, which is not necessarily the most intense line. It can be determined which line is the line of isotropic chemical shift, because this is the only line that does not change its position, when different spinning speed is applied. The spinning sidebands are used to determine details of the anisotropic interactions which are being averaged by the MAS [6]. Figure 8: The effects of slow speed MAS, where spinning sidebands appear with a center line at isotropic chemical shift and lines spaced at the spinning frequency. The intensities of the sidebands are less intense with increasing spinning speed [6]. 12

14 3.3.2 Magic angle spinning and cross-polarization Another common practice in analytical solid-state NMR studies of 13 C in organic molecules is the combination of cross polarization and MAS (also known as CP MAS). MAS averages the anisotropy of the chemical shielding so that signals that are observed in solid are similar to the liquid state NMR spectra. Cross-polarization enhances the signal of the rare spins. When the sample spinning speed is large enough to effectively modulate the homonuclear and heteronuclear dipolar couplings, the polarization enhancement of low-γ nuclei by CP under MAS from high-γ becomes difficult. The is a result of reduced efficiency of the original Hartmann-Hahn at high spinnnig speeds (above 15 khz) from a broad frequency region to narrow frequency bands spaced at the spinning frequency, and the CP efficiency becomes sensitive to chemical shift, radio-frequency inhomogeneities and the fluctuations in the overall radio-frequency power and the spinning speed. The CP process can be made less sensitive to these effects by the use of time-dependant phase and amplitude modulations of the spin-lock fields applied for polarization transfer [2] Magic angle spinning and off-magic angle spinning When measuring the NMR spectra of 13 C in static sample, the wideline resonances of different carbons overlap.these wideline signals can be compacted into narrow lines by the use of MAS with spinning speed larger than the anisotropies. This results as better resolution and sensitivity, but we lose information about the anisotorpic character of the interaction. The resonances can no longer be used as a protractor, and such spectra do not contain informatin about molecular order. If we are prepared to sacrifice spectral resolution, we can partly regain this information in two ways: 1. By spinning the sample with a frequency ω R which is small compared to the anisotropy, spinning sidebands arise at separations ω R from each centre frequency ω L (isotropic chemical shift). Information about principal axes of the coupling tensor, and about molecular order and mobility can be derived by an analysis of spinning sidebands (figure 9c). 2. By fast sample spinning at an angle θ R different for the magic angle (off-magic angle spinning or OMAS) the anisotropies of the coupling tensor are scaled by the factor (1 3cos 2 ω R )/2. This partialy narrows the wideline resnonaces and the overlapping is reduced while protractor propterty can be retained with reduced angular resolution (figure 9d). 13

15 Figure 9: 1 H decoupled 13 C spectra of isotactic polypropylene. (a) Static sample, where the wideline resonances of the different carbons overlap. (b) MAS spectrum with fast spinning. Narrow signals are observed at the isotropic chemical shitfs only. (c) MAS spectrum with slow spinning, where sideband signals are observed in addition to the centre line. (d) OMAS spectrum with fast spinning. Each resonance forms a powder spectrum with reduced width, which can serve as a protractor [2]. 4 Conclusion Solid-state NMR spectroscopy is challenging due to different interactions between nucleus that complicate the NMR. Different methods have been developed to avoid these problems. Solid-state NMR spectroscopy is therefore an important source of information in many differnet areas of science, such as physics, chemistry, pharmaceuticals and many others because it helps us determine the basic elements and structure of our sample. References [1] magnetic resonance, April 2010 [2] B.Blümich, NMR Imaging od materials (Oxford University Press, 2000) [3] April 2010 [4] April 2010 [5] April 2010 [6] M.J.Duer, Solid-state NMR spectroscopy, principles and applications (Blackwell Science, 2001) 14