MAS PFG NMR Diffusometry and MAS NMR Spectroscopy of
Paraffin-Olefin Mixtures Adsorbed in MOF ZIF-8
Magic-Angle Spinning Pulsed Field Gradient Nuclear Magnetic Resonance
as an Established Tool for Diffusometry of Interface Materials
by Dieter Freude, Christian Chmelik, Jörg Kärger, Jürgen Haase
Universität Leipzig, Institut für Experimentelle Physik, Linnéstraße 5, 04103 Leipzig, Germany
B0 = 9  21 T
rotor with sample
in the rf coil
zr
rot  10 kHz
θ
gradient coils for
pulsed field gradients,
maximum 1 T / m
Introduction to pulsed field gradient (PFG) NMR
Spin recovery by Hahn echo without diffusion of nuclei:
p/2
p
r.f. pulse
t
gradient pulse
gmax = 25 T / m
magnetization y
t
d
free induction
Hahn echo
D
B0 z
B0 z
y
y
t
D
B0 z
B0 z
y
5
y
1
4
M
2
M
x
1
3
2
x
5
3
4
x
x
PFG NMR, signal decay by diffusion of the nuclei
PFG NMR diffusion measurements base
on radio frequency (rf) pulse sequences.
They generate a spin echo,
like the Hahn echo (two pulses) or
the stimulated spin echo (three pulses).
p/2
p
p/2
p/2
p
p/2
p/2
rf pulses
FID,
amplitude S


g


d
d
At right, a sequence for alternating
ecd
D
sine shaped gradient pulses and
longitudinal eddy current delay (LED)
consisting of 7 rf pulses, 4 magnetic field gradient pulses of duration d,
intensity g, observation time D, and 2 eddy current quench pulses is presented.
gradient
pulses
The self-diffusion coefficient D of molecules is obtained from the decay of the
amplitude S of the FID in dependence on the field gradient intensity g by the equation
2

d  d
 4d g   

S  S0 exp  D 
  pp   S0 exp D k 
 D 
p
2


 


High-resolution solid-state MAS NMR
Fast rotation (160 kHz) of the sample
about an axis oriented at the angle
54.7° (magic-angle) with respect to the
zr
static magnetic field removes all
rot broadening effects with an
angular dependency of
2
B0
3 cos   1
.
2
θ
  arccos
1
 54.7o
3
Chemical shift anisotropy,
internuclear dipolar interactions,
first-order quadrupole interactions, and
inhomogeneities of the magnetic susceptibility
are averaged out.
It results an enhancement in spectral resolution
by line narrowing for solids and for soft matter.
The transverse relaxation time is prolonged.
MAS PFG NMR  diffusometry with spectral resolution
Example: n-butane + isobutane in zeolite Na-X
Example: ethene + ethane in MOF ZIF-8
δ = 0.5 ppm
ωr = 0 kHz
d / ppm
4
2
0
-2
δ = 0.02 ppm
ωr = 10 kHz
d / ppm
2.0
1.5
1.0
0.5
Spectral resolution is necessary for studies of mixture diffusion
Metal-Organic Frameworks (MOFs)
Potential applications in storage, separations, and catalysis caused a remarkable progress
of research activities on metal-organic frameworks (MOFs) [1,2]. The mass transfer of
molecular mixtures inside the nanopores and through the outer surface is essential for the
applicability of the particular system which is zeolitic imidazolate framework 8 (ZIF-8) [3,4]
in the present study. Direct access to the transfer through the outer surface and the
mobility in the framework was obtained by our previous IR and interference microscopic
investigations [5]. It could be shown that the self-diffusivity exceeds the transport
diffusivity if molecular clustering dominates the molecular mobility. For the understanding
of the molecular transport detailed information about the self-diffusion of the adsorbed
molecules are needed.
One of the major differences of MOFs compared to classical nanoporous materials, such as
zeolites, is the flexibility of the host lattice. Also for the new MOF subclass of ZIFs (zeolitic
imidazolate frameworks) such effects were reported. Gücüyner et al. [6] found a gateopening effect upon adsorption of an ethene/ethane mixture on ZIF 7. Although a similar
effect was not observed in recent permeation measurements through a ZIF 8 membrane for
this mixture, the existence of a structural change upon adsorption cannot be ruled out in
general.
[1]
[2]
[3]
[4]
[5]
[6]
U. Mueller, M. Schubert, F. Teich, H. Puetter, K. Schierle-Arndt, J. Pastre, J. Mater. Chem. 16 (2006) 626-636.
G. Feréy and C. Serre, Chem. Soc. Rev., 38 (2009) 1380-1399.
H. Bux, F.Y. Liang, Y.S. Li, J. Cravillon, M. Wiebcke, J. Caro, J. Am. Chem. Soc. 131 (2009) 16000-16001.
X.C. Huang, Y.Y. Lin, J.P. Zhang, X.M. Chen, Angew. Chem. Int. Ed., 45 (2006) 1557-1559.
C. Chmelik, H. Bux, J. Caro, L. Heinke, F. Hibbe, T. Titze, J. Kärger, Phys. Rev. Lett. 104 (2010) 085902.
C. Gücüyener, J. van den Bergh, J. Gascon, F. Kapteijn, J. Am. Chem. Soc. 132 (2010) 17704-17706.
ZIF = zeolitic imidazolate framework, ZIF-8 ↔ SOD
Cage-cut: potential landscape
mIM bridge
window size:
ca. 3.4 Å
crystal size: 10 nm … 400 µm
cavity size: ca. 12 Å
unit cell: a = b = c  17 Å
synthesis: H. Bux, J. Caro, Hannover
Solid-state NMR spectroscopy and diffusometry
Magic-angle spinning NMR spectroscopy
on 1H and 13C nuclei in the ZIF-8 framework
and in the adsorbed molecules was
performed in the field of 17.6 Tesla.
Diffusometry on 1H nuclei of the adsorbed
molecules and the molecules in the gas
phase was done in the temperature range
283363 K.
1H
MAS NMR spectroscopy
ethane
1H
MAS NMR spectrum of the as-synthesized MOF ZIF8 measured at a Larmor frequency of L =750 MHz, a
MAS frequency of rot = 17 kHz and a temperature of
T = 322 K. Asterisks denote spinning side bands.
1H
ethene
MAS NMR spectrum of a ZIF-8 sample loaded
with two ethene and two ethane molecules per cavity.
The spectrum was measured at L =750 MHz,
rot = 10 kHz, T = 303.
13C
NMR spectroscopy
13C CP {1H} MAS NMR
13C
ethane
13C
CP MAS NMR spectrum of the non-loaded (dotted line)
ZIF-8 sample and the sample loaded with four molecules
ethene plus four molecules ethane per cavity (solid line),
measured at L = 188 MHz, rot = 10 kHz and T = 303 K.
Inlets increase the chemical shift scale by 10.
13C
MAS NMR
ethene
MAS NMR proton decoupled spectrum of the MOF ZIF-8
loaded with four ethene and four ethane molecules p.c.,
measured at L = 188 MHz, rot = 10 kHz, T = 303.
Diffusometry of gas phase molecules
δ = 0.5 ppm
We obtain D = 1.6 × 105 m2s1
for both, the ethene and ethane,
gas phase diffusivities.
Decay of MOF of the signals of gas phase
molecules in ZIF-8 loaded with two ethene and
two ethane molecules per cavity, measured at
L =750 MHz, rot = 10 kHz, T = 303 K with a
Hahn-echo pulse sequence with a pulse distance
of 10 ms with two mono-polar gradient pulses
(after the rf pulses) with a duration of 500 µs.
The gradient intensity was varied between 0.0
and 0.1 T m1.
Note the advantage of MAS PFG NMR
diffusometry with respect to the
PFG NMR diffusometry without
spectral resolution:
The latter would consider the sum
of all unresolved signals for the
determination of one averaged
self-diffusion coefficient.
Diffusometry of the adsorbed molecules
2D-presentation of the signal decay of MOF
ZIF-8 loaded with two ethene and two ethane
molecules per cavity, measured at T = 363 K
with gradient pulse duration and observation
time of 2 ms and 200 ms, respectively.
The gradient intensity was varied between
0.05 and 0.5 T m1.
Diffusometry of the adsorbed molecules
Loading per cavity \ Temperature
283 K
303 K
323 K
343 K
363 K
D (ethene) / 101 m2s1
2 ethene + 2 ethane
0.65
0.82
0.99
1.11
1.21
D (ethane) / 101 m2s1
2 ethene + 2 ethane
0.11
0.14
0.18
0.23
0.27
D (ethene) / 101 m2s1
4 ethene + 4 ethane
0.79
0.95
0.97
1.22
1.25
D (ethane) / 101 m2s1
4 ethene + 4 ethane
0.13
0.20
0.20
0.25
0.29
Self-diffusion coefficients, D, of molecules in two mixtures of ethene
and ethane molecules adsorbed in MOF ZIF-8 in dependence on T.
D is given in units of 10-10 m2s-1 and has a variance of ±10%.
Diffusometry comparisons
-9
DT or D / m s
2 -1
10
-10
10
ethene
ethane
-11
10
0
1
2
3
4
5
6
7
c / molecules per cage
8
Transport diffusion coefficients DT
(triangles in the figure) which
were derived in dependence on
the concentration c of molecule
mixtures ethene/ethane or singlecomponent molecules from gas
sorption uptake experiments by
infra-red microscopy, IRM, on a
large single crystal (300 µm size)
at T = 298 K [1, 2].
Open and solid triangles denote the mixtures and single-components, respectively. Inverted and upright triangles denote ethene and
ethane, respectively. The ethene/ethane ratios in the gas mixtures are 1/1.5 and 1.9/1. The latter ratio is denoted by upright bars in the
open triangles. The concentration c corresponds to the sum of ethene plus ethane molecules per cage. Solid pentagons on the bottom
denote the self-diffusion coefficient of ethane determined by tracer IR microscopy [1]. Solid asterisks (ethene) and solid spheres (ethane)
at c = 4 and c = 8 mixture molecules per cage were taken from the MAS PFG NMR data in the table above for 283 and 303 K.
[1] C. Chmelik, H. Bux, J. Caro, L. Heinke, F. Hibbe, T. Titze, J. Kärger, Phys. Rev. Lett. 104 (2010) 085902.
[2] H. Bux, C. Chmelik, R. Krishna and J. Caro, J. Membr. Sci. 369 (2011) 284-289.
Conclusions
 1H and 13C MAS NMR spectroscopy show that there are no by-products or compounds with different
short-range order in the synthesis products of ZIF-8. 13C NMR spectroscopy gives a weak hint for
a preferential adsorption of the molecules close to the methyl-groups of the imidazole-rings.
However, no evidence for a gate-opening effect or another structural change upon adsorption of an
ethene/ethane mixture is found. Four well-resolved signals were assigned to ethene and ethane molecules,
which are adsorbed in the ZIF-8 crystals or non-adsorbed in the gas phase. The corresponding self-diffusion
coefficients could be determined separately.
 The microscopic MAS PFG NMR diffusivities are in agreement with the mesoscopic diffusivities of IR
microscopy. The diffusion selectivity is Dethene:Dethane = 5.5 at a loading of 4 molecules per cavity by both
techniques. By accounting for the influence of the thermodynamic factor IRM transport diffusivities and
NMR self-diffusivities could be directly transferred into each other. The latter is expected only
for porous structures consisting of large cavities with narrow windows. The agreement between the results
from both techniques is exceptionally good, if we consider the uncertainties in the determination of the
absolute concentration and the diffusivities and the fact that crystals from different batches were
investigated.
 The different diffusivities of ethene and ethane can be rationalized by the different size of molecules.
This conclusion is supported by the higher activation energies of ethane diffusion compared to ethene.
A possible difference in the guest-host interaction between the saturated and non-saturated molecule has
no impact on the mobility of the molecules.
 MAS PFG NMR gives access to a multitude of different aspects of guest diffusion and adsorption. In
particular if combined with non-equilibrium methods as IR microscopy a most detailed picture on molecular
transport can be obtained which facilitates its understanding on a molecular level.
 Article in Press: Christian Chmelik, Dieter Freude, Helge Bux, Jürgen Haase, Micropor. Mesopor. Mater.
(2011), doi:10.1016/j.micromeso.2011.06.009