Principles of NMR spectroscopy

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					Principles of NMR spectroscopy



      Dieter Freude, Institut für Experimentelle Physik I der Universität Leipzig
Skiseminar in the Dortmunder Hütte in Kühtai, Sunday 30 March 2008, 7:308:30 p.m.
              NMR is far from nuclear spectroscopy

 /m 101 100 101 102 103 104 105 106 107 108 109 1010 1011

  10   7
             10  8
                      10 9
                              10    10
                                               101      102       103       104                       102    103         104      105
                                     /Hz                                          /cm1                                           E/eV

  SW        USW              microwaves                         infrared             UV                       X-rays
  HF        VHF      UHF      SHF        EHF           far     middle      near    Qu vacuum                                -rays

                                                                              visible

           radio frequency spectroscopy                        optical spectroscopy                     X-ray spectr.          nuclear sp.


                                                        ½ kT300                                  photoelectron            Möss-
           NMR                 EPR                                                               spectroscopy             bauer
                             S X    Q     W

                                                         lattice                  -, n- outer -
                                                molec.             molec. over                               inner                nuclear
                                                          vibr.                   electr. electrons
                                                rotation         vibration -ton                              electrons            transitions
                                                s                        s
                           NMR is near to Nobel Prizes




Physics 1952                         Chemistry 1991 2002                Medicine 2003




Felix Bloch and Edward Purcell       Richard R. Ernst   Kurt Wüthrich   Paul Lauterbur and   Peter Mansfield
Stanford        Harvard University   ETHZ               ETHZ            Urbana               Nottingham
USA             USA                  Switzerland        Switzerland     USA                  England
                  Some of the 130 NMR isotopes
 nucleus     natural     spin     quadrupole     gyromagnetic      -frequency rel. sensitivity
           abundance               moment              ratio        100 MHz        at natural
               /%                   Q/fm2         /107 Ts      (1H)        abundance
   1
      H     99.985       1/2                    26.7522128         100.000000       1.000
                                                                                 1.45  106
   2
      H     0.015         1         0.2860      4.10662791         15.350609
                                                                                 6.31  104
    6
     Li      7.5          1        0.0808      3.9371709          14.716106
    7
     Li      92.5        3/2         4.01      10.3977013         38.863790        0.272
   11
      B      80.1        3/2        4.059       8.5847044          32.083974        0.132
                                                                                 1.76  104
   13
      C      1.10        1/2                    6.728284           25.145020
                                                                                 1.01  103
   14
      N     99.634        1         2.044       1.9337792           7.226330
                                                                                 3.85  106
   15
      N     0.366        1/2                    2.71261804         10.136784
                                                                                 1.08  05
   17
      O     0.038        5/2        2.558      3.62808            13.556430
   19
      F      100         1/2                    25.18148           94.094008        0.834
                                                                                 9.25  102
  23
     Na      100         3/2         10.4       7.0808493          26.451921
  27
      AI     100         5/2        14.66       6.9762715          26.056890        0.21
                                                                                 3.69  104
   29
      Si     4.67        1/2                    5.3190             19.867187
                                                                                 6.63  102
   31
      P      100         1/2                    10.8394            40.480742
   51
      V     99.750       7/2         5.2       7.0455117          26.302963        0.38
WEB of Science: 35% of NMR studies focus to the nuclei 1H, 25% to 13C, 8% to       31P,   8% to   15N,

4% to 29Si,and 2% to 19F. In these nuclei, we have a nuclear spin I = ½.
If we look at nuclei with a quadruple moment and half-integer spin I > ½, we find    27Al   in 3% of
all the NMR papers and 1% for each of the nuclei 11B, 7Li, 23Na and 51V.
For even numbered spin, only the I = 1-nuclei are frequently encountered: 2H in 4% and            14N

and 6Li in 0.5% of all NMR papers.
                 Chemical shift of the NMR

                                                                 shielded
                   external magnetic field B0
                                                                 magnetic
                                                                   field
                                                                 B0(1)

                   H+                              OH
                                                                  electron
                                                                    shell




We fragment hypothetically a water molecule into hydrogen cation plus hydroxyl anion.
Now the 1H in the cation has no electron shell, but the 1H in the hydroxyl anion is
shielded (against the external magnetic field) by the electron shell. Two signals with
a distance of about 35 ppm appear in the (hypothetical) 1H NMR spectrum.
                   Chemical shift and J-coupling


                                      t/ms
   0    10    20   30       40   50   60   70




                                           t/s
                                                    5       4       3       2      1       0
   0         1          2         3         4                    / ppm

The figure shows at left the free induction decay (FID) as a function of time and at right the
Fourier transformed 1H NMR spectrum of alcohol in fully deuterated water. The individual
spikes above are expanded by a factor of 10. The singlet comes from the OH groups, which
exchange with the hydrogen nuclei of the solvent and therefore show no splitting. The quartet
is caused by the CH2 groups, and the triplet corresponds to the CH3 group of the ethanol. The
splitting is caused by J-coupling between 1H nuclei of neighborhood groups via electrons.

 An NMR spectrum is not shown as a function of the frequency  = ( / 2)  B0(1),
 but rather on a ppm-scale of the chemical shift  = 106  (ref ) /L, where the
 reference sample is tetramethylsilane (TMS) for 1H, 2H, 13C, and 29Si NMR.
Chemical shift range
of some nuclei                                           1, 2H   TMS
                                                                 6, 7Li   1M LiCl
                                                  11B                      BF3O(C2H5)2
                                                 13C    MS = (CH3)4Si
                                       14, 15N                 NH4+
                                                  19F                                 CFCl3
                                                           23Na                 1M NaCl
                                             27Al                           [Al(H2O)6]3+
                                                  29Si                       TMS = (CH3)4Si
                                                 31P                            85% H3PO4
                                                                          51V                 VOCl3
                                    129, 131Xe                                                 XeOF4
Ranges of the chemical shifts of a few
nuclei and the reference substances, 1000    100          10           0   10        100 1000
relative to which shifts are related.                              / ppm
NMR spectrometer

                                  Bruker's
                                  home
                                  page




   H. Pfeifer:
   Pendulum feedback
   receiver
   Diplomarbeit,
   Universität Leipzig,
   1952




                  AVANCE 750
                   wide-bore in
                        Leipzig
NMR spectrometer for liquids
       Structure determination by NMR



           CH3                          45          40     35          30            25          20          15           10 ppm 5




                                 2.5




                                                                                                                                                1.0
 O




                                                                                                                                              ppm
                                 2.0
                                                                                                                                      0.8




                                                                                                                                                1.5
                                                                                                                                     ppm
                                                                                                                                     0.9



  HC               CH3
                                 1.5
                                                                                                                                     1.0

H 3
HH                                                               2.5                 2.0               1.5          ppm     1.0




                                                                                                                                                2.0
                   C              ppm

                                         Integral
                                 1.0




                                                                                                                                  3.01
                                                                                                                                  3.20
                                                                                                        2.10




                                                                                                                                  3.14
                                                                0.94
                                                    1.00




                                                                       1.09

                                                                              0.98

                                                                                          1.12
         Campher




                                                                                                                                                2.5
                                        45
                                         2.5          40      35
                                                               2.0             30                25
                                                                                                 1.5           20           15
                                                                                                                            1.0    10
                                                                                                                                 ppm        ppm 5
                                                            2.5                       2.0                      1.5        ppm 1.0




       Structure                                                       NMR-Spektrum
                                                                         1 C-NMR
                                                                        13H-NMR
                                                                        HC-COSY
                                                                        HH-COSY
                                                                        NOESY
                                                                              HETCOR
                       R. Meusinger, A. M. Chippendale, S. A. Fairhurst,
                       in “Ullmann’s Encyclopedia of Industrial Chemistry”, 6th ed., Wiley-VCH, 2001
How works NMR: a nuclear spin I = 1/2 in an magnetic field B0
    B0, z
               Many atomic nuclei have a spin, characterized by the nuclear spin
              quantum number I. The absolute value of the spin angular momentum is
              y                                   L   I (I  1).
                     The component in the direction of an applied field is
              x
                                   Lz = Iz   m  =  ½  for I = 1/2.
              Atomic nuclei carry an electric charge. In nuclei with a spin, the rotation
    L           creates a circular current which produces a magnetic moment µ.
                        An external homogenous magnetic field B results in
    B0, z             a torque T = µ  B with a related energy of E =  µ·B.

                    The gyromagnetic (actually magnetogyric) ratio  is defined by
              y                                µ =  L.
                        The z component of the nuclear magnetic moment is
              x                      µz =  Lz =  Iz    m .
                         The energy for I = 1/2 is split into 2 Zeeman levels
         
                            Em =  µz B0 =   mB0 =  B0/2 = L/2.
    L         Pieter Zeeman observed in 1896 the splitting of optical spectral lines in the field of an electromagnet.
                                       Larmor frequency
Classical model: the torque T acting on a magnetic dipole is defined
                                                                                                           B0, z
as the time derivative of the angular momentum L. We get
                                 dL 1 dμ                                                                         M
                              T          .
                                  dt  dt
By setting this equal to T = µ  B , we see that                                                                       y
                                         dμ
                                              μ  B.                                                                 x
                                         dt                                                                L
The summation of all nuclear dipoles in the unit volume gives us the magnetization.
For a magnetization that has not aligned itself parallel to the external magnetic field,
it is necessary to solve the following equation of motion:
                                          dM
                                               M  B.
                                          dt
We define B  (0, 0, B0) and choose M(t  0)  |M| (sina, 0, cosa). Then we obtain
       Mx  |M| sina cosLt, My  |M| sina sinLt, Mz  |M| cosa with L = B0.
The rotation vector is thus opposed to B0 for positive values of . The Larmor frequency
is most commonly given as an equation of magnitudes: L = B0 or  L   B0 .
                                                                           2
     Joseph Larmor described in 1897 the precession of electron orbital magnetization in an external magnetic field.
     Macroscopic magnetization
hL « kT applies at least for temperatures above 1 K             energy
and Larmor frequencies below 1 GHz. Thus,              Em = ½               Nm = ½
spontaneous transitions can be neglected, and the                     E = hL
probabilities P for absorption and induced emission
                                                       E
are equal. It follows P = B+½,½ wL= B½,+½ wL, where B m = ½               Nm = ½
refers to the Einstein coefficients for induced
transitions and wL is the spectral radiation density at the Larmor frequency.
A measurable absorption (or emission) only occurs if there is a difference in the two
occupation numbers N. In thermal equilibrium, the Boltzmann distribution applies to
N and we have            N1/ 2       B0      h
                                 exp       exp L .
                         N1/ 2        kT       kT
If L  500 MHz and T  300 K, hL/kT  8  105 is very small, and the exponential
function can be expanded to the linear term:
                      N1/ 2  N1/ 2 h L
                                           8  10 5.
                          N1/ 2       kT
                   Longitudinal relaxation time T1


All degrees of freedom of the system except for the spin (e.g. nuclear oscillations,
rotations, translations, external fields) are called the lattice. Setting thermal
equilibrium with this lattice can be done only through induced emission. The
fluctuating fields in the material always have a finite frequency component at the
Larmor frequency (though possibly extremely small), so that energy from the spin
system can be passed to the lattice. The time development of the setting of
equilibrium can be described after either switching on the external field B0 at time
t  0 (difficult to do in practice) with
                                                t
                                                    
                                    n  n0 1  eT1 ,
                                                   
                                                   
T1 is the longitudinal or spin-lattice relaxation time an n0 denotes the difference in
the occupation numbers in the thermal equilibrium. Longitudinal relaxation time
because the magnetization orients itself parallel to the external magnetic field.
T1 depends upon the transition probability P as
                             1/T1 = 2P  2B½,+½ wL.
                        T1 determination by IR


                      The inversion recovery (IR) by -/2




                                                              



                           0                         
                                                          
                                         n  n0 1  2e 
                                                       T1
                                                         
                                                         


By setting the parentheses equal to zero, we get 0  T1 ln2 as the passage of zero.
 Line width and T2
                                                          fLorentz
                                                  1
A pure exponential decay of the free
induction (or of the envelope of the             1/2                               21/2=2/T2=1/2
echo, see next page) corresponds to
         G(t) = exp(t/T2).
                                                                                                    
                                                                            0
The Fourier-transform gives fLorentz = const.  1 / (1 + x2) with x = (  0)T2,
see red line. The "full width at half maximum" (fwhm) in frequency units is
                                          1
                              1/ 2        .   Note that no second moment exists for a Lorentian line shape. Thus,
                                         T2     an exact Lorentian line shape should not be observed in physics.



Gaussian line shape has the relaxation function G(t) = exp(t2 M2 / 2) and a line
form fGaussian = exp (2/2M2), blue dotted line above, where M2 denotes the
second moment. A relaxation time can be defined by T22 = 2 / M2. Then we get
                                             2 
                                                 2
                      2
                          2 = ( 1/ 2 / Hz )      ≈ 7.12 × ( 1/ 2 / Hz ) .
               -2                                                          2
         M2 / s =
                  (T2 / s)                    ln 4
           Correlation time c, relaxation times T1 and T2

                                                   
   G    f t f t       G   G0 exp   
                                                   
                                                  c

                                                               ln T1,2
    1 1  I I  1 
              4   2
                           2 c         8 c    
                                             
    T1 5 r 6
             4 0   1    2 1  2  2                            T1
                             L c           L c  
                                                               T1 min
 1 1 4  2 I I  1             5 c          2 c      
                      3 c                             
T2 5 r  6
             4 0                                     2 
                               1  L c  1  2L c  
                                           2
                                                                            T2
                                                               T2   rigid
                                                                                 1/T

The relaxation times T1 and T2 as a function of the reciprocal absolute temperature
1/T for a two spin system with one correlation time. Their temperature dependency
can be described by c  0 exp(Ea/kT).

It thus holds that T1  T2  1/c when Lc « 1 and T1  L2 c when Lc » 1.
T1 has a minimum of at Lc  0,612 or Lc  0,1.
        Rotating coordinate system and the offset
For the case of a static external magnetic field B0 pointing in z-direction and the
application of a rf field Bx(t) = 2Brf cos(t) in x-direction we have for the
Hamilitonian operator of the external interactions in the laboratory sytem (LAB)
                          H0 + Hrf = LIz + 2rf cos(t)Ix,
where L = 2L =  B0 denotes the Larmor frequency, and the nutation
frequency rf is defined as rf =  Brf.
                                                                   B0 z
The transformation from the laboratory frame to the                 M
frame rotating with  gives, by neglecting the part that             y
oscillates with the twice radio frequency,
                             H0 i + Hrf i =   Iz + rf Ix,                x
                                                                  B0 z
where  = L   denotes the resonance offset and
the subscript i stays for the interaction representation.
                                                                     y

 Magnetization phases develop in this interaction
                                                                           M
 representation in the rotating coordinate system like                             x’
                      b = rf  or a =  t.
 Quadratur detection yields value and sign of a.
     Bloch equation and stationary solutions

We define Beff  (Brf, 0, B0 /) and introduce the Bloch equation:

        dM                M x e x  M y e y M z  M0 e z
             M  Beff                   
        dt                       T2              T1

Stationary solutions to the Bloch equations are attained for dM/dt  0:


           Mx   
                             L T22        Brf M0  2  Hrf ,
                  1    L  T2   BrfT1T2
                               2 2      2 2


                               T2
           My                                 Brf M0  2  Hrf ,
                  1    L  T2   BrfT1T2
                               2 2    2 2


                      1    L  T22
                                     2

           Mz                               M0 .
                1    L  T2   BrfT1T2
                             2 2     2 2
                                                               Hahn echo
B0 z                                     B0 z              B0 z                           B0 z                   B0 z
   M
                                            y                                                                       y
  y                                                            y   5                         y   1
                                                                               4                         2
                                                M                                                                       M
                                                    x                      3                             3                  x
                                                                   1   2                         5   4
                                 x                                                 x                         x


                                     /2 pulse FID,              pulse
                                     around the dephasing      around the   rephasing     echo
                                       y-axis   x-magnetization x-axis    x-magnetization

                                      /2                                          
       magnetization rf pulses




                                            a(r,t) = (r)·t
                                                                                                                                   t
                                                                                       a(r,t) =  a(r,) + (r)·(t  )
                                          free induction
                                                                                                                            echo
                                                                                                                                 t
             T2 and T2*



/2           

                                   t

                                   t
             2

        2                     t

G( ) = e
        T2                    T2
                      G(t ) = e
         EXSY, NOESY, stimulated spin echo




                       

        t1            t2               t1
                     tmix


 0                                                         time
                                   FID
      FID                      after mixing
                                              stimulated
                                                 echo
                    NMR diffusometry (PFG NMR)
Pulsed field gradient NMR diffusion                                                          
                                                                                                                 rf pulses
measurements base on NMR pulse
                                                                                                                 free induction
sequences that generate a spin echo,                                                                             decay
like the Hahn echo (two pulses) and the                                                
                                                                       g                                         gradient pulses
stimulated spine echo (three pulses).
At right, the 13-intervall sequence for                                  
alternating gradients consisting of                                                                 ecd
                                                                 
7 rf pulses, 4 gradient pulses of duration
, intensity g, and diffusion time  and
2 eddy current quench pulses is described.


The self-diffusion coefficient D of molecules in bulk phases, in confined geometries and in
biologic materials is obtained from the amplitude S of the free induction decay in dependence
on the field gradient intensity g by the equation
                              4 g   2          
                 S  S0 exp  D               p  
                             
                                            2       
 Application of MAS technique in addition to PFG (pulsed field gradient) improves drastically
 the spectral resolution, allowing the study of multi-component diffusion in soft matter or
 confined geometry.
The difference between solid-state and liquid NMR,
              the lineshape of water


                                         solid water (ice)



                                                       / kHz
 -40    -30    -20    -10    0    10        20        30     40



                                 liquid water



                                                       / Hz
 -0.4   -0.3   -0.2   -0.1   0    0.1       0.2       0.3    0.4
           High-resolution solid-state MAS NMR

                                           Fast rotation (160 kHz) of the sample about
      rotor with sample
                                           an axis oriented at 54.7° (magic-angle) with
      in the rf coil            zr
                                           respect to the static magnetic field removes
B0                                         all broadening effects with an angular
                                    rot   dependency of
                                                             3 cos   1
                                                                   2
       θ
                                                                  2
                                           That means
                                           chemical shift anisotropy,
               gradient coils for          dipolar interactions,
                MAS PFG NMR                first-order quadrupole interactions, and
                   1                       inhomogeneities of the magnetic
       arc cos      54 .7o
                   3                       susceptibility.

                                           It results an enhancement in spectral
                                           resolution by line narrowing also for soft
                                           matter studies.
   Laser supported high-temperature MAS NMR
 for time-resolved in situ studies of reaction steps
in heterogeneous catalysis: the NMR batch reactor



                                       B0



                                      MAS Rotor
                                        7 mm

                                  Cryo Magnet


                                    CO2 Laser
Some applications of solid-state
     NMR spectroscopy


    Dieter Freude, Institut für Experimentelle Physik I der Universität Leipzig
 Skiseminar in the Dortmunder Hütte in Kühtai, 31 March 2008, 7:308:30 p.m.
            NMR on the top

WEB of Science refers for the year 2006 to about
16 000 NMR studies, mostly on liquids, but including
also 2500 references to solid-state NMR.
Near to 12 000 studies concern magnetic resonance
imaging (MRI).
The next frequently applied technique, infrared
spectroscopy, comes with about 9 000 references in the
WEB of Science.
    Solid-state NMR on porous materials

 1H MAS NMR spectra including TRAPDOR
 29Si MAS NMR
 27Al 3QMAS NMR
 27Al MAS NMR
 1H MAS NMR in the range from 160 K to 790 K

           1H
            MAS NMR on molecules
         adsorbed in porous materials
 Hydrogen exchange in bezene loaded H-zeolites
 In situ monitoring of catalytic conversion of molecules
  in zeolites by 1H, 2H and 13C MAS NMR
 MAS PFG NMR studies of the self-diffusion
  of acetone-alkane mixtures in nanoporous silica gel
      1H   MAS NMR spectra, TRAPDOR



      1H   MAS NMR with 27Al dephasing
                  
                                            t2
              t1               t1

                                           time

0      FID                          echo
                   1H    MAS NMR spectra, TRAPDOR
Without and with dipolar dephasing by 27Al high power irradiation and difference spectra are
shown from the top to the bottom. The spectra show signals of SiOH groups at framework
defects, SiOHAl bridging hydroxyl groups, AlOH group.

                                   4.2 ppm                                           2.2 ppm

                                   2.9 ppm                         2.9 ppm               1.7 ppm
      H-ZSM-5                           2.2 ppm          H-ZSM-5
      activated                                          activated 4.2 ppm
      at 550 °C                              1.7 ppm     at 900 °C

                                               without dephasing


                                                  with dephasing

           4.2 ppm                                            2.9 ppm
                                        2.9 ppm
                                                           4.2 ppm

                                              difference spectra

         10    8     6    4        2     0    2   4       10    8   6     4   2   0    2 4
                               / ppm                                       / ppm
           1H      MAS NMR of porous materials

                         SiOH       Disturbed bridging OH groups in zeolite
                                    H-ZSM-5 and H-Beta

                                              Bridging OH groups in small channels
                             SiOHAl           and cages of zeolites

                                       Bridging OH groups in large channels
                 SiOHAl                and cages of zeolites

                                             CaOH, AlOH,      Cation OH groups located in sodalite cages
                                             LaOH             of zeolite Y and in channels of ZSM-5
                                                              which are involved in hydrogen bonds

                                             OH groups bonded to extra-framework aluminium species
                         AlOH                which are located in cavities or channels and which are
                                             involved in hydrogen bonds

                                      SiOH                    Silanol groups at the external
                                                              surface or at framework defects

    Metal or cation OH groups in large cavities
                                                      MeOH
    or at the outer surface of particles

7          6         5          4      3          2       1         0      1        2         2     4
                                                  ppm
              29Si    MAS NMR spectrum of silicalite-1




SiO2 framework consisting of 24 crystallographic different silicon sites per unit cell (Fyfe 1987).
                       29Si   MAS NMR
                Q0
                        Q1                                     alkali and
                                                             alkaline earth
                                   Q2                           silicates
                                              Q3
                                                                           Q4

  Q3                                               Si(3Si, 1OH)

                                   Si(4 Al)
                                        Si(3 Al)            aluminosilicate-
      4
  Q                                                           type zeolites
                                              Si(2 Al)
                                                         Si(1 Al)
                                                                           Si(0 Al)

                       Si(2 Zn                zincosilicate-type zeolites
  Q4                   )                             VP-7, VPI-9
                                         Si(1 Zn
                                        )
60       70    80         90        100        110            120        130
                                 ppm
Determination of the Si/Al ratio by 29Si MAS NMR

For Si/Al = 1 the Q4 coordination represents a SiO4 tetrahedron that is surrounded by four
AlO4-tetrahedra, whereas for a very high Si/Al ratio the SiO4 tetrahedron is surrounded
mainly by SiO4-tetrahedra. For zeolites of faujasite type the Si/Al-ratio goes from one
(low silica X type) to very high values for the siliceous faujasite. Referred to the siliceous
faujasite, the replacement of a silicon atom by an aluminum atom in the next coordination
sphere causes an additional chemical shift of about 5 ppm, compared with the change
from Si(0Al) with n = 0 to Si(4Al) with n = 4 in the previous figure. This gives the
opportunity to determine the Si/Al ratio of the framework of crystalline aluminosilicate
materials directly from the relative intensities In (in %) of the (up to five) 29Si MAS NMR
signals by means of the equation

                                            400
                          Si         
                               Al           4

                                           nI
                                          n 0
                                                    n
Take-away message from this page:
Framework Si/Al ratio can be determined by 29SiMAS NMR. The problem is that the
signals for n = 04 are commonly not well-resolved and a signal of SiOH (Q3) at
about 103 ppm is often superimposed to the signal for n = 1.
  29Si    MAS NMR shift and Si-O-Si bond angle a
Considering the Q4 coordination alone, we find a spread of 37 ppm for zeolites in the
previous figure. The isotropic chemical shift of the 29Si NMR signal depends in addition on
the four Si-O bonding lengths and/or on the four Si-O-Si angles ai, which occur between
neighboring tetrahedra. Correlations between the chemical shift and the arithmetical mean
of the four bonding angles ai are best described in terms of


                    r  cos a cos a  1
The parameter r describes the s-character of the oxygen bond, which is considered to be
an s-p hybrid orbital. For sp3-, sp2- and sp-hybridization with their respective bonding
angles a = arccos(1/3)  109.47°, a = 120°, a = 180°, the values r = 1/4, 1/3 and 1/2 are
obtained, respectively. The most exact NMR data were published by Fyfe et al. for an
aluminum-free zeolite ZSM-5. The spectrum of the low temperature phase consisting of
signals due to the 24 averaged Si-O-Si angles between 147.0° and 158.8° (29Si NMR
linewidths of 5 kHz) yielded the equation for the chemical shift

             ppm  287 .6 r  21 .44
Take away message from this page:
Si-O-Si bond angle variations by a distortion of the short-range-order in a crystalline
material broaden the 29Si MAS NMR signal of the material.
                                              27Al     MAS NMR
coordinated
                                                                    aluminophosphates
   6-fold



                                                                       aluminoborates
                                                                   aluminates
                                                                   aluminosilicates
                                                  aluminophosphates
coordinated
   5-fold




                                                      aluminoborates
                                                       aluminates
                                               aluminosilicates
                                      aluminophosphates
coord. coordinated
          4-fold




                       aluminoborates
                             aluminates
                           aluminosilicates
3-fold




                                               aluminosilicates

                     120   110 100   90   80     70     60    50       40   30   20     10   0   10 20
                                                             ppm
       27Al    MAS NMR shift and Al-O-T bond angle
Aluminum signals of porous inorganic materials were found in the range -20 ppm to 120 ppm
referring to Al(H2O)63+. The influence of the second coordination sphere can be demonstrated
for tetrahedrally coordinated aluminum atoms: In hydrated samples the isotropic chemical
shift of the 27Al resonance occurs at 7580 ppm for aluminum sodalite (four aluminum atoms
in the second coordination sphere), at 60 ppm for faujasite (four silicon atoms in the second
coordination sphere) and at 40 ppm for AlPO4-5 (four phosphorous atoms in the second
coordination sphere).
In addition, the isotropic chemical shift of the AlO4 tetrahedra is a function of the mean of the
four Al-O-T angles a (T = Al, Si, P). Their correlation is usually given as

                      /ppm = -c1a / + c2.
c1 was found to be 0.61 for the Al-O-P angles in AlPO4 by Müller et al. and 0.50 for the Si-O-
Al angles in crystalline aluminosilicates by Lippmaa et al. Weller et al. determined c1-values
of 0.22 for Al-O-Al angles in pure aluminate-sodalites and of 0.72 for Si-O-Al angles in
sodalites with a Si/Al ratio of one.
Aluminum has a nuclear spin I = 5/2, and the central transition is broadened by second-order
quadrupolar interaction. This broadening is (expressed in ppm) reciprocal to the square of the
external magnetic field. Line narrowing can in principle be achieved by double rotation or
multiple-quantum procedures.
        27Al       3QMAS NMR study of AlPO4-14
                                                                             1/ ppm
                                                                                 0
                                                            position 5

                                                                                 10


                                                                                 20

                                                  position 3
                                                                                 30


                                     position 1                                  40
                                          position 2

                            2/ ppm 40      30        20      10        0


AlPO4-14, 27Al 3QMAS spectrum (split-t1-whole-echo, DFS pulse) measured at 17.6 T with a
rotation frequency of 30 kHz.
The parameters CS, iso = 1.3 ppm, Cqcc = 2.57 MHz, h = 0.7 for aluminum nuclei at position 1, CS, iso = 42.9 ppm,
Cqcc = 1.74 MHz, h = 0.63, for aluminum nuclei at position 2, CS, iso = 43.5 ppm, Cqcc = 4.08 MHz, h = 0.82,
for aluminum nuclei at position 3, CS, iso = 27.1 ppm, Cqcc = 5.58 MHz, h = 0.97, for aluminum nuclei at position 5,
CS, iso = 1.3 ppm, Cqcc = 2.57 MHz, h = 0.7 were taken from Fernandez et al.
                        27Al
                    MAS NMR spectra
       of a hydrothermally treated zeolite ZSM-5
                        four-fold            five-fold            six-fold
                        coordinated          coordinated          coordinated

                      L = 195 MHz
                      Rot = 15 kHz




                     L = 130 MHz
                     Rot = 10 kHz



                             100   80   60    40     20      0   20   40   60
                                                    / ppm
Take-away message:
A signal narrowing by MQMAS or DOR is not possible, if the line broadening is
dominated by distributions of the chemical shifts which are caused by short-range-order
distortions of the zeolite framework.
               Mobility of the Brønsted sites
             and hydrogen exchange in zeolites
        H          H one-site jumps around
                       one aluminum atom
                                               NH4+
         O         O
                   O            O          O          O

             Al           Si        Si         Al

             O O          O O       O O        O O
                                           H                    H

             H H                O          O          O         O           O

    multiple-site jumps             Al       Si         Si        Al
    along several
    aluminum atoms
                                    O O        O O        O O       O O

Proton mobility of bridging hydroxyl groups in zeolites H-Y and H-ZSM-5 can be monitored in
the temperature range from 160 to 790 K. The full width at half maximum of the 1H MAS NMR
spectrum narrows by a factor of 24 for zeolite H-ZSM-5 and a factor of 55 for zeolite 85 H-Y.
Activation energies in the range 20-80 kJ mol have been determined.
                                                     Narrowing onset and correlation time


                                                                                                                         40 °C
  fwhm of the sideband envelope / kHz




                                        10                                                                    20
                                                          120°C
                                                                                                              10                                      17 kHz

                                                                                       3,2 kHz                                    = rigid/2
                                         1
                                                                 = rigid/2
                                                                                                                           2H     MAS NMR, deuterated
                                                    1H MAS NMR, zeolite H-Y, loaded                                            zeolite H-ZSM-5, loaded with
                                                                                                              1
                                                    with mit 0.6 NH3 per cavity                                                0.33 NH3 per crossing
                                        0,1
                                              1,5   2,0   2,5   3,0    3,5 4,0 4,5     5,0   5,5                   2,5   3,0     3,5   4,0   4,5    5,0   5,5   6,0
                                                                      1000 T 1/ K1                                                    1000 T  / K
                                                                                                                                                1     1



The correlation time corresponds to the mean residence time of an ammonium ion at an
oxygen ring of the framework.
                                                                                                        1
                                                                                         c 
                                                                                                   15  rigid

                                                                          2H NMR, H-Y: at50 °Cc=5 µs
                                                                          1H NMR, H-Y: at 40 °C  =20 µs
                                                                                                 c
                                                                          2H NMR, H-ZSM-5: at 120 °C  =3,8 µs
                                                                                                       c
   1D 1H EXSY (exchange spectroscopy)


    /2              /2                           /2
              t1                      tm                 FID           t2

                                                                       time
     0
               EXSY pulse sequence
Evolution time t1 = 1/4  .
 denotes the frequency difference of the exchanging species.


MAS frequency should be a multiple of 


Two series of measurements should be performed at each temperature:
Offset  right of the right signal and offset  left of the left signal.
                  Result of the EXSY experiment
                                             Intensity
                                                                     ammonium ions
Stack plot of the spectra of zeolite                                 OH
H-Y loaded with 0.35 ammonia
molecules per cavity. Mixing times
are between tm = 3 s and15 s.

                              97 °C



                                             0      2    4       6        8       10   12
          / ppm 10       0

Intensities of the signals of ammonium
ions and OH groups for zeolite H-Y
loaded with 1.5 ammonia molecules per
cavity. Measured at 87 °C in the field of
9,4 T. The figure on the top and bottom
correspond to offset on the left hand side
and right hand side of the signals,
respectively.
                                             0      2    4       6        8       10   12
                                                             mixing time tm / s
                  Basis of the data processing
diagonal peaks
               1                                                 
I AA (tm )        1  exp   D tm    1   exp   D tm  MA0
               2 
                      D                         D                   
           1                                                
IBB (tm )   1  exp-   D tm    1   exp   D tm  MB0
           2    D                         D                   
cross peaks
I AB (t m )  IBA (t m )  e xp σ  D t m  e xp σ  D t m M A 0
                          1                                                1
                          2                                               BD

                      
                        1
                          e xp σ  D tm  e xp σ  D tm MB0 1
                        2                                           AD

                     LBB  D    LAB LAB             LAA  LBB 
                                                              1
           1
             LAA
                                                 1
                                 2            2
           2                                                  2
dynamic matrix (without spin diffusion):

   LAA LAB              1 T   0  1A                             1 B 
  
L           R  K   1A
                          0                                             
   LBA LBB                  1 T1B   1  A
                                                                     1 B 
                                                                             
Laser supported 1H MAS NMR of H-zeolites

                                     10

                      773 K




                               1/2 / kHz
                                             1
                      723 K


                      673 K
                                   0.1
                      623 K          1.0         1.5    2.0 2.5 3.0      3.5
                                                       1000 T  / K

                      573 K    Spectra (at left) and Arrhenius plot
                               (above) of the temperature dependent
                      423 K    1H MAS NMR measurements which
                               were obtained by laser heating. The
                       297 K   zeolite sample H-Y was activated at
                               400 °C.
40   20       0 20   40
           / ppm
    Proton transfer between Brønsted sites and
        benzene molecules in zeolites H-Y

                                               In situ 1H MAS NMR spectroscopy
                                               of the proton transfer between
                                               bridging hydroxyl groups and
                      85 H-Y with
                      fully deuterated         benzene molecules yields
                      benzene at               temperature dependent exchange
                      400 K                    rates over more than five orders of
                                         t     magnitude.


    10      8     4    0                                                                              F1
                                                                               92 H-Y with
             /ppm                           H-D exchange and                  benzene at
                                                                                                       2
                                                                               520 K with a
    intensity                                NOESY MAS NMR                     mixing period
                                                                               of 500 ms
                                             experiments were                                          4

                                             performed by both
                                             conventional and                                          6

                               t /min        laser heating up to
0        200 400   600 800                   600 K.                                                    8




                                                                      F2   8      6      4     2    /ppm
                                 Exchange rate
                    as a dynamic measure of Brønsted acidity
         
k /min

       
                                                     Arrhenius plot of the H-D
  10                                                 and H-H exchange rates for
                                                     benzene molecules in the
       
                                                     zeolites 85 H-Y and 92 H-Y.
  10                                                 The values which are
                                  92 H-Y
                                                     marked by blue or red were
                        85 H-Y
                                                   measured by laser heating
  10
                                                     or conventional heating,
                                                     respectively.
       
  10
              1.5      1.9       2.3       2.71000
                                              T/K

        The variation of the Si/Al ratio in the zeolite H-Y causes a change of the
        deprotonation energy and can explain the differences of the exchange rate of
        one order of magnitude in the temperature region of 350600 K. However, our
        experimental results are not sufficient to exclude that a variation of the pre-
        exponential factor caused by steric effects like the existence of non-framework
        aluminum species is the origin of the different rates of the proton transfer.
     In situ monitoring of catalytic conversion of
   molecules in zeolites by 1H, 2H and 13C MAS NMR

                                                                                                                              126
                                                                                                   1.0
                       CH3–                                                                                  17 min
                       1.7                                                                                   at 323 K   *             *

                                                                                                               *                               *

         –CH=                                                                              2.0
                                                                              5.0
         5.6                                                                                                                                                 13
                                                                                    1.7
                                                                                                                                                        17
                                                                    5.9                                      20 h
                                                   18.5 h                                                    at 323 K   *             *
65 min
                                                                                                               *                               *
               4 min                                        5 min
                             6   4             2   0                                                          200       160   120         80       40             0
                                                                          6         4          2         0                       / ppm
                                     / ppm
                                                            2H
                                                                                      / ppm                 13C
  1H MAS NMR spectra of n-but-1-ene-d8                         MAS NMR spectra of n-but-1-ene-d8                 CP/MAS NMR spectra of
  adsorbed on H-FER2 (T=360K).                              adsorbed on H-FER (T = 333K). n-But-             [2-13C]-n-but-1-ene adsorption on
  Hydrogen transfer occurs from the acidic                  1-ene undergoes readily a double-bond-           H-FER in dependence on reaction
  hydroxyl groups of the zeolite to the                     shift reaction, when it is adsorbed on           time. Asterisks denote spinning
  deuterated butene molecules. Both methyl                  ferrierite. The reaction becomes slow            side-bands. The appearance of the
  and methene groups of but-2-ene are                       enough to observe the kinetics , if the          signals at 13 and 17 ppm and
  involved in the H/D exchange. The ratio                   catalyst contains only a very small              decreasing intensity of the signal at
  between the intensities of the CH3 and                    concentration of Brønsted acid sites.            126 ppm show the label scrambling.
  CH groups in the final spectrum is 3:1.


         Kinetics of a double-bond-shift reaction, hydrogen exchange
             and 13C-label scrambling of n-butene in H-ferrierite
                  MAS PFG NMR for NMR diffusometry
                 rotor with sample                                                                                                     
                 in the rf coil                              zr
       B0                                                                                                                                                    rf
                                                              rot                                                                                           pulses
                                                                                                                                                             FID
               θm                                                       r. f.
                                                                                                                                    
                                                                                                                 g                                           g pulses
                                                                        Gz
                                                  gradient                                                                
                                                    coil                                 T                                                    ecd
                                                                                                      
                                  g gradient pulses
                                                                                                      4 g  
                                                                                                               2
                                                                                                                         
                                             1                                    S / S 0  exp  D                
                            θm  arccos
                                              3
                                                 54.7 o
                                                                                                                  3    

                                                                                      MAS PFG NMR diffusion experiment
                                                                                                                 CH3 (iso)
                                                                                                   CH3 (n-but)

ωr = 0 kHz                                                                                       CH2 (n-but)                       Δδ = 0.4 ppm
ωr = 1 kHz                   *    **         **     *                                 CH (iso)
                        4          2         0          -2                                                                                           gradient
              ppm
                                                                                                                                                     strength
                                                         δ = 0.02 ppm

ωr = 10 kHz
              ppm       2.0        1.5        1.0             0.5

                    FAU Na-X , n-butane + isobutane
                                                                                                                                       2.0             1.0        / ppm
                                                                                                                                                     Δδ
     MAS PFG NMR studies of the self-diffusion
of acetone-alkane mixtures in nanoporous silica gel



 The self-diffusion coefficients of mixtures of acetone with several alkanes were studied by
 means of magic-angle spinning pulsed field gradient nuclear magnetic resonance (MAS
 PFG NMR). Silica gels with different nanopore sizes at ca. 4 and 10 nm and a pore
 surface modified with trimethylsilyl groups were provided by Takahashi et al. (1). The silica
 gel was loaded with acetone –alkane mixtures (1:10). The self-diffusion coefficients of
 acetone in the small pores (4 nm) shows a zigzag effect depending on odd or even
 numbers of carbon atoms of the alkane solvent as it was reported by Takahashi et al. (1)
 for the transport diffusion coefficient.

 (1) Ryoji Takahashi, Satoshi Sato, Toshiaki Sodesawa and Toshiyuki Ikeda: Diffusion coefficient of ketones in liquid media within
     mesopores;Phys. Chem. Chem. Phys.5 (2003) 2476–2480
          Stack plot of the 1H MAS PFG NMR spectra                                        Semi-logarithmic plot of the decay of the CH3
          at 10 kHz of the 1:10 acetone and octane                                        signal of ketone in binary mixture with acetone
          mixture absorbed in Em material as function                                     at 298 K. The diffusion time is  = 600 ms and
          of increasing pulsed gradient strength for a                                    a gradient pulse length is  = 2 ms:
          diffusion time  = 600 ms:                                                                     Em / acetone + alkane (C6,C7,C8,C9)
                                        octane
                                                                                                    1                                           = 600 ms
                                       CH2
                                                                                                                                                = 2 ms
                                                  CH3

                      acetone




                                                                                          S / S0
                        CH3                                                    gradient
                                                                                                   0,1
                                                                               strength
                                                                                                              nonane C9
                                                                                                              octane C8
                                                                                                              heptane C7
                                                                                                              hexane C6
                                           2.8 2.4 2.0 1.6 1.2 0.8 0.4                        0,01
                                                        / ppm
                     Acetone diffusivity in alkane mixture
                                                                                                  0,00           0,05      0,10        0,15     0,20        0,25
                                                                                                                                2     2   -2
                                                                                                                            g       / T m
               -11
          1,4x10                                             % ( = 600 ms)
                                                             % ( = 800 ms)
                                                             % ( = 1200 ms)
               -11
                                                                                   Diffusion coefficient of acetone in mixture within Em
          1,2x10
2 -1




                                                                                   in dependence of the number of carbons in the
 D / ms




               -11
                                                                                   alkane solvent. The measurements were carried
                                                                                   out with diffusion time = 600 ms,  = 800 ms and
          1,0x10


               -12
                                                                                    = 1200 ms and the gradient pulse length  = 2 ms.
          8,0x10



                       6          7          8            9              10
                              Carbon number of alkane solvent
                  Horst Ernst
I acknowledge Moisés Fernández
support from    Clemens Gottert
             Johanna Kanellopoulos
                  Bernd Knorr
                Thomas Loeser
                 Toralf Mildner
               Lutz Moschkowitz
                Dagmar Prager
                Denis Schneider
              Alexander Stepanov

       Deutsche Forschungsgemeinschaft
             Max-Buchner-Stiftung

				
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