Univerza v Ljubljani, Fakulteta za matematiko in fiziko
Seminar
Solid-state NMR Spectroscopy
Author:
Katja Kadunc
Mentor:
prof.dr.Janez Seliger
Ljubljana, April 2011
————————————————————————————————————— AbstractIn 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.
Contents
1 Introduction 2
2 Nuclear Magnetic Resonance (NMR) 2
2.1 Magnetic fields . . . 2
2.2 Nuclear magnetization . . . 2
2.3 Classical equation of motion: the Bloch equation . . . 4
2.4 The impact of short-term high-frequency magnetic disturbances on the magnetization in a static magnetic field . . . 5
3 Solid-state NMR spectroscopy 7 3.1 Nuclear spin interactions . . . 7
3.2 Cross-polarization . . . 9
3.3 Magic-angle spinning . . . 11
3.3.1 Spinning sidebands . . . 12
3.3.2 Magic angle spinning and cross-polarization . . . 13
3.3.3 Magic angle spinning and off-magic angle spinning . . . 13
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 1938. 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 B0 is applied to polarize the nuclear magnetic moments. It is oriented along the
z-direction of the coordinate system. The strength of B0 is between 0.5 and 21 T. It
defines the NMR frequency ω0:
ω0 = −γB0, (1)
where γ is gyromagnetic ratio and has a characteristic value for a certain nuclei. B0 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 Brf(t) are used to stimulate the
spectroscopic response and are perpendicular to the static field. Brf(t) oscillates with
nuclear resonace frequency ω0. Typical NMR frequencies are in radio-frequency regime
between 10 and 900 MHz. The strength of this excitaion field Brf(t) is 1 mT or less [2].
2.2
Nuclear magnetization
The relevant quantity to NMR is the contribution of the nuclei to macroscopic magne-tization. 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 B0 which is parallel to z-axis, the nuclear magnetic moment ~µ
experiences a torque ~N :
~
The change of spin d~I is proportional to torque thrust ~N dt. Therefore we can rewrite equation (3):
d~I
dt = ~N = ~µ × ~B0 = γ ~I × ~B0. (4) The change of spin is always perpendicular to the spin itself and to magnetic field. The magnetic moment ~µ precess about ~B0. Frequency of precession is not dependent on the
angle between magnetic field and magnetic moment and it is called the Larmor frequency: ~
ωL= −γ ~B0. (5)
The energy of a magnetic moment ~µ in a magnetic field ~B0 = (0, 0, B0) is given by:
E = −~µ · ~B0 = −µzB0. (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:
µz = γ~m, (7)
where m is magnetic quantum number. Therefore the energy is:
Em = −γ~mB0. (8)
It can assume the values:
−I ≤ m ≤ I. (9)
Figure 1: Energy levels for a nucleus with spin number 1/2 [3].
This means that a nuclear spin with quan-tum number I can be in one of 2I + 1 sta-tionary states in a magnetic field. Nuclei like 1H and 13C with spins I = 1/2 have
two eigenstates. These are referred as spin-up 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 emmited by nuclear spin when it reorients and moves form one energy level to the
next. This energy difference determines the NMR frequency ω0:
∆E = Em− Em−1 = −γ~B0 = ~ω0 = ~2πν0 (10)
The NMR frequency is proportional to the strength of the magnetic field B0 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
due to an increase in magnetic polarization M0 established in magnetic field B0, which
is in thermodynamic equilibrium given by Curie law: ~ M0 = N γ2 ~2I(I + 1) 3kBT ~ B0, (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 nu-clear magnetic moments parallel to the applied field. In thermodynamic equilibrium, all magnetic moments are found in one of the energy eigenstates Em 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:
nm−1 nm = exp −~ω0 kBT . (12)
From this we can caluculate the population difference ∆n = nm − nm−1. In
high-temperature approximation, where kBT ~ω0, 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
Figure 2: Precession of magnetization ~M in magnetic field ~B0.
from the spins to the surrounding lat-tice. This energy transfer takes place in a characteristic time T1 (energy disipation
time or spin-lattice relaxation time). A tipical value for T1 of 1H is 1 second at
high magnetic fields. Since all magnetic moments ~µi precess with different phases
around B0, projections on xy plane are in
average 0, which means that the total equi-lirium magnetization will point along mag-netic field (in our case along the z-axis). In nonequilibrium state magnetization is pre-cessing around B0 (figure 2).
2.3
Classical equation of
mo-tion: 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
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) − ~M0]. (13) The time-dependent magnetization’s ~M (t) thermodynamic equilibrium is at ~M0 = (0, 0, M0)
and ~R is a relaxation matrix:
R = 1/T2 0 0 0 1/T2 0 0 0 1/T1 , (14)
with the longitudinal and transverse relaxation times T1 and T2.
The longitudinal relaxation time T1 is the spin-lattice relaxation time (as mentioned
above) which is characteristic for accumulation of the magnetization parallel to the mag-netic field. The transverse relaxation time T2 is the time constant for disappearance of
magnetization components perpendicular to the magnetic field. T2 is in liquids close to
T1, while in solids it can be orders of magnitude shorter. Transverse magnetization
com-ponents 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:
Mz(t) = M0(1 − e−t/T1), (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
distur-bances 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 B0 and a weak, time-dependent radio-frequency field Brf(t), which
is perpendicular to B0:
B(t) = B0 + Brf(t). (16)
The radio-frequency field is usually applied with linear polarization:
Brf(t) = 2B1cos(ωLt + ϕ) 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 ωL:
z0 = z,
x0= xcos(ωLt) + ysin(ωLt),
y0 = ycos(ωLt) − xsin(ωLt).
In laboratory frame the linearly polarized radio-frequency field can be written as a sum of two circular polarized components:
Brf(t) = 2B1cos(ωLt + ϕ) 0 0 = B1cos(ωLt + ϕ) B1sin(ωLt + ϕ) 0 + B1cos(ωLt + ϕ) −B1sin(ωLt + ϕ) 0 . (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 M0, 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:
ω1 = −γB1, (20)
where B1 is the magnitude of the rotating field component. The duration tp 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 = ω1tp. (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 ωrf. (a) On
resonance the rotating radio-frequency field component B1 appears static. The magnetization
M0 rotates around B1 field with frequency ω1. (b) When the radio-frequency field is turned
off the magnetization rotates around the z-axis of the rotating frame with frequency Ω0 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 ~B1 can be set anywhere within the xy
plane of the rotating frame. For example, when choosing ϕ = 0◦, 90◦, 180◦, 270◦, the field ~
B1 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):
Another reason for the dephasing of magnetic moments with time are inhomogeneities in field ~B0, which have an impact on the total relaxation time T2∗:
1 T2∗ = 1 T2 + 1 Tinh . (23)
Typically the spin-spin relaxation time T2 is notably smaller than the spin-lattice
relax-ation time T1 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 dipole-dipole 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 2H is of the order of 130 kHz. The quadrupole interaction is expressed by
the Hamilton operator:
d HQ =
eQ
[2I(2I − 1)~]bIQbI (24)
The interaction is quadratic with respect to spin vector bI 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 13Tr(Q) = 0. Therefore, the quadrupole interaction and quadrupole splitting cannot be observed under fast isotropic motion as in liquids.
Figure 4: Quadrupole coupling of the2H nucleus to the electric field gradient of a C-2H 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 isolated13C-1H (in general these are named
as S and I spins) pair can be written as:
b HD = µ0~2γIγS r3 (1 − 3cos 2 θ) bIz· cSz (25)
where γIand γSare proton and carbon the gyromagnetic ratios, r is the lenght of the
inter-nuclear vector, I and S are the proton and carbon spin operator,
Figure 5: Geometrical construction for dipole-dipole interaction. B0 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 internu-clear vector and external magnetic field. This equation is the secular part of dipo-lar Hamilton operator that comutates with Zeeman Hamilton operator and causes the shift of resonance frequency in the first or-der of the perturbation theory. Because of the 1 − 3cos2(θ) dependence of the
dipole-dipole interaction, the interaction vanishes when θ is 54.7◦ (the magic angle).
For liquids in which the molecules are
mov-ing rapidly, the term 1 − 3cos2(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 car-bon 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)B0, (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
chemistry. The shielding is dependent on the strength of the magnetic field, therefore the Hamilton operator is
b
Hσ = γbIσB0. (27)
The average value of σ = 13Tr(σ) is observed in liquids and also in solids by using the line-narrowing techniques.
Magnetic shielding determines the chemical shift in high-resolution NMR. The resonance frequency ωL is different from the NMR frequency ω0 of the nucleus by
ωL= (1 − σ)ω0 (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 = ωL− ωs ωs
(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
b
HJ= bIiJbIj, (30)
where bIi and bIj are the spin vector operators of the coupling nuclei and J is a coupling
tensor. Its trace is different from zero: 13Tr(J) = J so that the indirect coupling is 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 13C and 29Si). 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.
Figure 6: Illustration of cross polarization: (a) Timing diagram of radio-frequency excitation for cross-polarization of 1H magnetization to
13C, DD denotes heteronuclear dipolar
decou-pling. (b) Precession of 1H magnetization com-ponents during cross-polarization with a fre-quency ω1H around the magnetic field B1H in
the coordinate system, rotating with frequency ωrf H. (c) Precession of13C magnetization
com-ponents during cross-polarization with a fre-quency ω1C around the magnetic field B1C in
the coordinate system, rotating with frequency ωrf C [2].
By using cross-polarization these prob-lems 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 1H).
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 ωrf I.
Af-terwards the transmitter is not turned off, only the radio-frequency phase is shifted by 90◦. Therefore, the B1I field is now
ap-plied parallel to the I magnetization. This technique is called spin-locking, because the I magnetization is locked along the B1I field (if this field is the dominant
mag-netic field that the I spins experience in the frame rotating with frequency ωrf I around
the z-axis). The B1I field is the dominant
magnetic field that the I spins experience if its amplitude ω1I = −γ1IB1I is larger
than the frequency offset ωLI − ωrf I and
the other interactions of the I spin. While the I spins are locked in the transverse plane, another radio-frequency field B1S at
frequency ωrf S is applied to the S spins. If
the magnitudes B1S and B1I of both
ap-plied fields are matched by the Hartmann-Hahn condition
γSB1S = γIB1I, (31)
then each spin species precesses with the same frequency ω1 = −γB1 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 T1ρI and T1ρS (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 TCP (the length of the spin-locked time), local differences
in the dipolar interaction and in the T1ρI 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 tD, the magnetization of
weakly coupled S spins survives. In this way magnetization can be selectively transferred, for example, from 1H to 13C of rigid crystalline and of mobile amorphous regions, or of
protonated and unprotonated nuclei. In the beginning the S magnetization M (tCP) is
bulit up with a constant TCH (characteristic time for the strength of the dipolar coupling
between spis species). The magnetization passes through a maximum with the increasing cross-polarization time tCP. Then it is weakened by the influence of the relaxation times
T1ρH and T1ρC in the rotating frames of I and S spins:
M (tCP) = M0 λ 1 − exp −λtCP TCH exp − tCP T1ρH , (32) where λ = 1 + TCH T1ρC − TCH T1ρH . (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 ω1I
is applied at the spin frequency ωrf I. The decoupling efficiency depends on two factors:
1. The amplitude ω1I = −γB1I of the decoupling field has to be large compared to the
strength of the heteronuclear dipolar interaction (for the decoupling of 13C and 1H this means that |γB1H| > 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 inter-action.
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 spec-tra. 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 mag-netic field is rapidly averaged, which also averages the 1 − 3cos2θ 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 θRto the applied field and start to spin it,
Figure 7: The sample is placed in a gas driven spinner. The rotation axis is inclined by the an-gle θR = 54.74◦. 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 B0 and the principal z-axis of the shielding
ten-sor and β is the angle between the z-axis of the shielding tensor and the spinning axis [6].
the angle θ, which is describing the ori-entation of the interaction tensor fixed in a molecule in the sample, varies with time as the molecule rotates with the sample. The average h1−3cos2θi in these circumstances is h1 − 3cos2θi = 1 2(1 − 3cos 2 θR)(1 − 3cos2β), (34) where angles θRand β are defined in figure
7.
The angle β is fixed for a given nucleus in a rigid solid, but it takes on all pos-sible values in a powder sample (like the angle θ). The angle θR is under the
con-trol of the experiment. When it is set to 54.74◦, (1 − 3cos2θ
R) becomes zero, and
consequently the average h1 − 3cos2θi is
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. 3.3.1 Spinning sidebands
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 side-bands are less intense with increasing spinning speed [6].
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 magic-angle spinning to reduce a powder pat-tern to a single line at the isotropic chem-ical 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 side-bands are sharp lines, set at the spin-ning speed apart from the line of isotropic chemical shift, which is not necessarily the most intense line. It can be deter-mined 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 de-termine details of the anisotropic interac-tions which are being averaged by the MAS [6].
3.3.2 Magic angle spinning and cross-polarization
Another common practice in analytical solid-state NMR studies of13C in organic molecules is the combination of cross polarization and MAS (also known as CP MAS). MAS av-erages 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]. 3.3.3 Magic angle spinning and off-magic angle spinning
When measuring the NMR spectra of 13C 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 ωR which is small compared to the anisotropy,
spinning sidebands arise at separations ωRfrom each centre frequency ωL(isotropic
chem-ical 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 θR different for the magic angle (off-magic angle
spinning or OMAS) the anisotropies of the coupling tensor are scaled by the factor (1 − 3cos2ωR)/2. This partialy narrows the wideline resnonaces and the overlapping is reduced
Figure 9: 1H decoupled 13C 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 nu-cleus 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] http://en.wikipedia.org/wiki/Nuclear magnetic resonance, April 2010 [2] B.Bl¨umich, NMR Imaging od materials (Oxford University Press, 2000) [3] http://www.process-nmr.com/images/nmr1.h1.gif, April 2010 [4] http://www.cis.rit.edu/htbooks/nmr/, April 2010
[5] http://spin.niddk.nih.gov/NMRPipe/mfrintro/images/dcABDiagram.jpg, April 2010 [6] M.J.Duer, Solid-state NMR spectroscopy, principles and applications (Blackwell Science,
