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
7
8
10
10
SW
USW
HF
VHF
9
10
10
10
 /Hz
101
102
microwaves
UHF
SHF
EHF
103
 /cm1
infrared
far
middle
102
104
UV
near
103
104
105
E/eV
X-rays
-rays
Qu vacuum
visible
radio frequency spectroscopy
optical spectroscopy
½ kT300
NMR
EPR
S X
Q
X-ray spectr.
photoelectron
spectroscopy
nuclear sp.
Mössbauer
W
lattice
molec.
molec. over
vibr.
rotation
vibration -ton
s
s
-, n- outer electr. electrons
inner
electrons
nuclear
transitions
NMR is near to Nobel Prizes
Physics 1952
Chemistry 1991 2002
Medicine 2003
Felix Bloch and Edward Purcell
Stanford
Harvard University
USA
USA
Richard R. Ernst
ETHZ
Switzerland
Paul Lauterbur and
Urbana
USA
Kurt Wüthrich
ETHZ
Switzerland
Peter Mansfield
Nottingham
England
Some of the 130 NMR isotopes
nucleus
1
H
H
6
Li
7
Li
11
B
13
C
14
N
15
N
17
O
19
F
23
Na
27
AI
29
Si
31
P
51
V
2
natural
abundance
/%
99.985
0.015
7.5
92.5
80.1
1.10
99.634
0.366
0.038
100
100
100
4.67
100
99.750
spin
1/2
1
1
3/2
3/2
1/2
1
1/2
5/2
1/2
3/2
5/2
1/2
1/2
7/2
quadrupole
moment
Q/fm2
0.2860
0.0808
4.01
4.059
2.044
2.558
10.4
14.66
5.2
gyromagnetic
ratio
/107 Ts
26.7522128
4.10662791
3.9371709
10.3977013
8.5847044
6.728284
1.9337792
2.71261804
3.62808
25.18148
7.0808493
6.9762715
5.3190
10.8394
7.0455117
-frequency rel. sensitivity
100 MHz
(1H)
100.000000
15.350609
14.716106
38.863790
32.083974
25.145020
7.226330
10.136784
13.556430
94.094008
26.451921
26.056890
19.867187
40.480742
26.302963
at natural
abundance
1.000
1.45  106
6.31  104
0.272
0.132
1.76  104
1.01  103
3.85  106
1.08  05
0.834
9.25  102
0.21
3.69  104
6.63  102
0.38
WEB of Science: 35% of NMR studies focus to the nuclei 1H, 25% to 13C, 8% to
4% to 29Si,and 2% to 19F. In these nuclei, we have a nuclear spin I = ½.
31P,
If we look at nuclei with a quadruple moment and half-integer spin I > ½, we find
all the NMR papers and 1% for each of the nuclei 11B, 7Li, 23Na and 51V.
8% to
27Al
15N,
in 3% of
For even numbered spin, only the I = 1-nuclei are frequently encountered: 2H in 4% and
and 6Li in 0.5% of all NMR papers.
14N
Chemical shift of the NMR
external magnetic field B0
H+
shielded
magnetic
field
B0(1)
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
0
1
2
3
4
5
4
3
/ ppm
2
1
0
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
11B
13C
1M LiCl
BF3O(C2H5)2
MS = (CH3)4Si
14, 15N
NH4+
19F
CFCl3
23Na
27Al
1M NaCl
[Al(H2O)6]3+
29Si
TMS = (CH3)4Si
31P
85% H3PO4
51V
129, 131Xe
Ranges of the chemical shifts of a few
nuclei and the reference substances, 1000
relative to which shifts are related.
100
VOCl3
XeOF4
10
0
10
 / ppm
100 1000
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
45
40
35
30
25
20
15
10 ppm 5
0.8
ppm
1.5
2.0
O
ppm
1.0
2.5
CH3
0.9
Structure
452.5
40
352.0
2.5
1.0
ppm
2.0
1.5
30
3.14
3.01
3.20
2.10
1.12
0.98
1.09
0.94
1.00
1.0
Campher
2.0
25
1.5
2.0
20
1.5
15
10
1.0
ppm
ppm 1.0
2.5
2.5
ppm
C
1.0
Integral
CH3
1.5
H
C
3
HHH
ppm 5
13
1H-NMR
NMR-Spektrum
HC-COSY
HH-COSY
NOESY
C-NMR
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
x
L
B0, z
x
L
The component in the direction of an applied field is
Lz = Iz   m  =  ½  for I = 1/2.
Atomic nuclei carry an electric charge. In nuclei with a spin, the rotation
creates a circular current which produces a magnetic moment µ.
An external homogenous magnetic field B results in
a torque T = µ  B with a related energy of E =  µ·B.
y

L   I (I  1).
The gyromagnetic (actually magnetogyric) ratio  is defined by
µ =  L.
The z component of the nuclear magnetic moment is
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.
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
as the time derivative of the angular momentum L. We get
d L 1 dμ
T

.
dt  d t
By setting this equal to T = µ  B , we see that
dμ
  μ  B.
dt
B0, z
M
y
L
x
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
Em = ½
and Larmor frequencies below 1 GHz. Thus,
spontaneous transitions can be neglected, and the
probabilities P for absorption and induced emission
are equal. It follows P = B+½,½ wL= B½,+½ wL, where BEm = ½
refers to the Einstein coefficients for induced
energy
Nm = ½
E = hL
Nm = ½
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


T1

n  n0 1  e ,




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



T1
n  n0 1  2e 




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
echo, see next page) corresponds to
21/2=2/T2=1/2
1/2
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/ 2 
1
.
T2
Note that no second moment exists for a Lorentian line shape. Thus,
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
(
)
M2 / s =
≈ 7.12 × ( 1/ 2 / Hz ) .
2 =  1/ 2 / Hz
(T2 / s)
ln 4
-2
Correlation time c, relaxation times T1 and T2
G   f t f t   
 
G   G0 exp  
 c




2 c
8 c
1 1  I I  1 




2
2 
6

T1 5 r 4 0  1  L c  1  2L c  
4
2
ln T1,2
T1
T1 min

5 c
2 c
1 1 4  2 I I  1 



3 c 

2
2 
6

T2 5 r
4 0 
1  L c  1  2L c  
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
frame rotating with  gives, by neglecting the part that
oscillates with the twice radio frequency,
H0 i + Hrf i =   Iz + rf Ix,
where  = L   denotes the resonance offset and
the subscript i stays for the interaction representation.
M
y
x
B0 z
y
Magnetization phases develop in this interaction
representation in the rotating coordinate system like
b = rf  or a =  t.
Quadratur detection yields value and sign of a.
M
x’
Bloch equation and stationary solutions
We define Beff  (Brf, 0, B0 /) and introduce the Bloch equation:
M x e x  M y e y M z  M 0 e z
dM
  M  Beff 

dt
T2
T1
Stationary solutions to the Bloch equations are attained for dM/dt  0:
Mx

  L T22

Brf M0  2  Hrf ,
2 2
2 2
1    L  T2   BrfT1T2
My 
T2
Brf M0  2  Hrf ,
2 2
2 2
1    L  T2   BrfT1T2
1    L  T22
Mz 
M0 .
2 2
2 2


1    L T2   BrfT1T2
2
Hahn echo
B0 z
M
B0 z
B0 z
y
y
y
B0 z
B0 z
y
y
5
1
4
M
M
x
3
1
x
2
2
x
3
5
x
4
x
/2 pulse FID,
 pulse
around the dephasing
around the
rephasing
echo
y-axis
x-magnetization x-axis
x-magnetization
magnetization rf pulses
/2

a(r,t) = (r)·t
a(r,t) =  a(r,) + (r)·(t  )
free induction

t
echo

t
T2 and T2*
/2

t
t
2
2
T2
G( ) = e
t
T2
G(t ) = e
EXSY, NOESY, stimulated spin echo


t1
0
FID

t2
tmix
t1
FID
after mixing
time
stimulated
echo
NMR diffusometry (PFG NMR)
Pulsed field gradient NMR diffusion
measurements base on NMR pulse
sequences that generate a spin echo,
like the Hahn echo (two pulses) and the
stimulated spine echo (three pulses).
At right, the 13-intervall sequence for
alternating gradients consisting of
7 rf pulses, 4 gradient pulses of duration
, intensity g, and diffusion time  and







rf pulses
free induction
decay



g


gradient pulses


ecd
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
rotor with sample
in the rf coil
B0
zr
rot
θ
Fast rotation (160 kHz) of the sample about
an axis oriented at 54.7° (magic-angle) with
respect to the static magnetic field removes
all broadening effects with an angular
dependency of
3 cos2   1
2
gradient coils for
MAS PFG NMR
  arccos
1
 54.7o
3
That means
chemical shift anisotropy,
dipolar interactions,
first-order quadrupole interactions, and
inhomogeneities of the magnetic
susceptibility.
It results an enhancement in spectral
resolution by line narrowing also for soft
matter studies.
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

1H
MAS NMR spectra, TRAPDOR
27Al dephasing
MAS NMR with

t1
t2
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.
2.2 ppm
4.2 ppm
2.9 ppm
2.2 ppm
H-ZSM-5
activated
at 550 °C
1.7 ppm
2.9 ppm
1.7 ppm
H-ZSM-5
activated 4.2 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
 / ppm
0
2
4
10
8
6
4
2
 / ppm
0
2 4
1H
MAS NMR of porous materials
Disturbed bridging OH groups in zeolite
H-ZSM-5 and H-Beta
SiOH
Bridging OH groups in small channels
and cages of zeolites
SiOHAl
Bridging OH groups in large channels
and cages of zeolites
SiOHAl
CaOH, AlOH,
LaOH
OH groups bonded to extra-framework aluminium species
which are located in cavities or channels and which are
involved in hydrogen bonds
AlOH
Silanol groups at the external
surface or at framework defects
SiOH
Metal or cation OH groups in large cavities
or at the outer surface of particles
7
6
5
Cation OH groups located in sodalite cages
of zeolite Y and in channels of ZSM-5
which are involved in hydrogen bonds
4
3
MeOH
2
1
ppm
0
1
2
2
4
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
alkali and
alkaline earth
silicates
Q1
Q2
Q3
Q4
Q3
Si(3Si, 1OH)
Si(4 Al)
Si(3 Al)
4
Q
Si(2 Al)
aluminosilicatetype zeolites
Si(1 Al)
Si(0 Al)
Si(2 Zn
)
Q4
60
70
80
zincosilicate-type zeolites
VP-7, VPI-9
Si(1 Zn
)
100
90
ppm
110
120
130
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
Si
Al

Take-away message from this page:
400
4
 nI
n 0
n
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.
MAS NMR
6-fold
coordinated
27Al
aluminophosphates
aluminoborates
aluminates
aluminosilicates
4-fold
3-fold
coord. coordinated
5-fold
coordinated
aluminophosphates
aluminoborates
aluminates
aluminosilicates
aluminophosphates
aluminoborates
aluminates
aluminosilicates
aluminosilicates
120
110 100
90
80
70
60
50
ppm
40
30
20
10
0
10 20
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-OAl 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
coordinated
five-fold
coordinated
six-fold
coordinated
L = 195 MHz
Rot = 15 kHz
L = 130 MHz
Rot = 10 kHz
100
Take-away message:
80
60
40
20
 / ppm
0
20
40
60
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
O
O
O
O
O
Al
Si
Si
O O
O O
O O
H H
multiple-site jumps
along several
aluminum atoms
O
NH4+
O
Al
H
O O
O
H
O
O
O
Al
Si
Si
Al
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
fwhm of the sideband envelope / kHz
40 °C
10
20
120°C
17 kHz
10
 = rigid/2
3,2 kHz
1
 = rigid/2
2H
1H
MAS NMR, zeolite H-Y, loaded
with mit 0.6 NH3 per cavity
MAS NMR, deuterated
zeolite H-ZSM-5, loaded with
0.33 NH3 per crossing
1
0,1
1,5
2,0
2,5
3,0
3,5 4,0 4,5
1000 T 1/ K1
5,0
5,5
2,5
3,0
3,5
4,0
4,5
5,0
1
1
1000 T  / K
5,5
6,0
The correlation time corresponds to the mean residence time of an ammonium ion at an
oxygen ring of the framework.
c 
1
15  rigid
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
2H
1D 1H EXSY (exchange spectroscopy)
/2
/2
t1
/2
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
H-Y loaded with 0.35 ammonia
molecules per cavity. Mixing times
are between tm = 3 s and15 s.
OH
97 °C
 / ppm 10
0
2
4
6
8
10
12
0
2
4
6
8
10
12
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.
mixing time tm / s
Basis of the data processing
diagonal peaks
I AA (t m ) 

1 











1

exp



D
t

1

exp



D
t




m
m  M A0

2 
D
D



1 



IBB (t m )   1  exp-   D t m    1   exp   D tm  MB0
2 
D
D


cross peaks
1
1
I AB (t m )  IBA (t m )  exp σ  D t m  exp σ  D t m M A 0
2
 BD
 
1
LAA
2
1
1






 exp  σ  D t m  exp  σ  D t m MB0
2
 AD
1
1
2
LAA  LBB 



2
 LBB  D    LAB LAB 
2
dynamic matrix (without spin diffusion):
 LAA
L  
 LBA
LAB 
1 T
  R  K   1A
LBB 
 0
0  1A
  
1 T1B   1  A
1 B 

 1 B 
Laser supported 1H MAS NMR of H-zeolites
773 K
723 K
1/2 / kHz
10
1
673 K
623 K
573 K
423 K
297 K
40
20
0 20
 / ppm
40
0.1
1.0
1.5
2.0 2.5 3.0
1000 T  / K
3.5
Spectra (at left) and Arrhenius plot
(above) of the temperature dependent
1H MAS NMR measurements which
were obtained by laser heating. The
zeolite sample H-Y was activated at
400 °C.
Proton transfer between Brønsted sites and
benzene molecules in zeolites H-Y
85 H-Y with
fully deuterated
benzene at
400 K
t
10
8
4
 /ppm
0
intensity
t /min
0
200 400
In situ 1H MAS NMR spectroscopy
of the proton transfer between
bridging hydroxyl groups and
benzene molecules yields
temperature dependent exchange
rates over more than five orders of
magnitude.
600 800
F1
92 H-Y with
benzene at
520 K with a
mixing period
of 500 ms
H-D exchange and
NOESY MAS NMR
experiments were
performed by both
conventional and
laser heating up to
600 K.
2
4
6
8
F2
8
6
4
2
 /ppm
Exchange rate
as a dynamic measure of Brønsted acidity

k /min
Arrhenius plot of the H-D
and H-H exchange rates for
benzene molecules in the
zeolites 85 H-Y and 92 H-Y.
The values which are
marked by blue or red were
measured by laser heating
or conventional heating,
respectively.

10

10
10
10
92 H-Y
85 H-Y


1.5
1.9
2.3
2.7 1000
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 preexponential 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
at 323 K
1.7
*
*
*
*
–CH=
2.0
5.0
5.6
13
1.7
20 h
at 323 K
5.9
18.5 h
65 min
17
*
*
*
*
4 min
6
1H
4
2
/ ppm
0
MAS NMR spectra of n-but-1-ene-d8
adsorbed on H-FER2 (T=360K).
Hydrogen transfer occurs from the acidic
hydroxyl groups of the zeolite to the
deuterated butene molecules. Both methyl
and methene groups of but-2-ene are
involved in the H/D exchange. The ratio
between the intensities of the CH3 and
CH groups in the final spectrum is 3:1.
5 min
6
2H
4
 / ppm
2
0
MAS NMR spectra of n-but-1-ene-d8
adsorbed on H-FER (T = 333K). n-But1-ene undergoes readily a double-bondshift reaction, when it is adsorbed on
ferrierite. The reaction becomes slow
enough to observe the kinetics , if the
catalyst contains only a very small
concentration of Brønsted acid sites.
200
160
120
 / ppm
80
40
0
13C
CP/MAS NMR spectra of
[2-13C]-n-but-1-ene adsorption on
H-FER in dependence on reaction
time. Asterisks denote spinning
side-bands. The appearance of the
signals at 13 and 17 ppm and
decreasing intensity of the signal at
126 ppm show the label
scrambling.
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
B0
rotor with sample
in the rf coil


zr





rf
pulses
FID
rot
θm
r. f.




g pulses
g
Gz
gradient
coil


T
g gradient pulses
θm  arccos
 ecd

2

    
 4 g  
  S / S 0  exp  D
 
  

3
 




1
 54.7 o
3
MAS PFG NMR diffusion experiment
CH3 (n-but)
ωr = 0 kHz
ωr = 1 kHz
*
 ppm
4
**
**
2
CH2 (n-but)
*
0
CH3 (iso)
Δδ = 0.4 ppm
CH (iso)
-2
gradient
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
Δδ
 / ppm
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
at 10 kHz of the 1:10 acetone and octane
mixture absorbed in Em material as function
of increasing pulsed gradient strength for a
diffusion time  = 600 ms:
Semi-logarithmic plot of the decay of the CH3
signal of ketone in binary mixture with acetone
at 298 K. The diffusion time is  = 600 ms and
a gradient pulse length is  = 2 ms:
Em / acetone + alkane (C6,C7,C8,C9)
octane
CH2
1
 = 600 ms
 = 2 ms
acetone
CH3
gradient
strength
S / S0
CH3
0,1
nonane C9
octane C8
heptane C7
hexane C6
2.8 2.4 2.0 1.6 1.2 0.8 0.4
 / ppm
Acetone diffusivity in alkane mixture
2 -1
D / ms
-11
1,2x10
-11
1,0x10
-12
8,0x10
6
0,05
0,10
g
% ( = 600 ms)
% ( = 800 ms)
% ( = 1200 ms)
-11
1,4x10
0,01
0,00
7
8
9
Carbon number of alkane solvent
10
2
0,15
2
0,20
0,25
-2
/ T m
Diffusion coefficient of acetone in mixture within Em
in dependence of the number of carbons in the
alkane solvent. The measurements were carried
out with diffusion time  = 600 ms,  = 800 ms and
 = 1200 ms and the gradient pulse length  = 2 ms.
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