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NMR Diffusometry and MAS NMR Spectroscopy
of Functionalized Mesoporous Proton Conductors
Magic-Angle Spinning Pulsed Field Gradient Nuclear Magnetic Resonance
as a New Tool for Diffusometry of Interface Materials
by Dieter Freude1, Monir Sharifi2, and Michael Wark2
1Universität
2Leibniz
Leipzig, Inst. für Experimentelle Physik, Linnéstraße 5, 04103 Leipzig, Germany
Universität Hannover, Inst. für Phys. Chem. und Elektrochemie, Callinstraße 3a, 30167 Hannover, 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
p/2
p
p/2
p/2
p/2
p/2
rf pulses
t
t
g
t
t
At right, a sequence for alternating
d
d
sine shaped gradient pulses and
tecd
D
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.
free induction
decay, FID,
amplitude S
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 t 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
CH3 (iso)
CH 3 (n-but)
ωr = 0 kHz
FAU Na-X , n-butane + isobutane
d / ppm
4
2
0
CH2 (n-but)
CH (iso)
Δδ = 0.4 ppm
gradient
strength
-2
δ = 0.02 ppm
ωr = 10 kHz
d / ppm
2.0
1.5
1.0
0.5
2.0
1.0
d / ppm
Δδ
Spectral resolution is necessary for studies of mixture diffusion
and functionalized mesoporous proton conductors as well.
From left: 1H MAS NMR spectra of imidazol composite b, hydrated composite c, and sulfonic acid functionalized composite
Functionalized mesoporous proton conductors
R. Marschall, M. Sharifi, M. Wark: Proton conductivity of imidazole functionalized
ordered mesoporous silica, Microporous Mesoporous Mater. 123 (2009) 21–29:
The proton conductivity of highly ordered high surface mesoporous silica material
Si-MCM-41 functionalized with imidazole groups was studied by impedance
spectroscopy in the temperature range of 60–140 C. Samples were characterized by
X-ray diffraction, nitrogen adsorption and FT-infrared spectroscopy in addition.
The degree of functionalization, spacer chain length between silica host and
functional imidazole group, and the relative humidity was varied.
R. Marschall, I. Bannat, A. Feldhoff, L. Wang, G. Q. Lu, M. Wark: SO3H-functionalized
Si-MCM-41 with superior proton conductivity, small 5 (2009) 854–859:
Mesoporous silica particles of around 100 nm diameter functionalized with sulfonic
acid groups are prepared using a simple and fast in situ co-condensation procedure.
Structural data are determined via electron microscopy, nitrogen adsorption, and
X-ray diffraction. Proton conductivity values of the functionalized samples are
measured via impedance spectroscopy.
Solid-state NMR spectroscopy
Magic-angle spinning NMR spectroscopy on 1H, 13C, and 29Si nuclei in the
functionalized mesoporous proton conducting materials was performed in
the fields of 9.4 and 17.6 Tesla mainly at room temperature.
1H
N
MAS NMR spectroscopy
HO3S
Si
Si
N
O
H
H2O +
H+

H3O+
H3O+
 10
H2O
Imidazole-MCM-41
O
H
SO3H-MCM-41
13C
N
N
CP {1H} MAS NMR spectroscopy
Si
Imidazole-MCM-41
HO3S
Si
SO3H-MCM-41
29Si
and 29Si CP {1H} MAS NMR spectroscopy
Imidazole-MCM-41
29Si
CP {1H} MAS NMR
Si (OSi)3 (OH)1
CH2Si (OSi)2 (OH)1
Si (OSi)2 (OH)2
Si (OSi)4
29Si
CH2Si (OSi)3
MAS NMR (one-pulse)
29Si
5%
5%
100%
relative concentration
MAS NMR Bloch decay spectra
yield quantitative information
about linking of functional groups.
1H
MAS PFG NMR diffusometry
2D-presentation of the signal decay of
sample SO3H-MCM-41 (grafting)
measured at 353 K. The self-diffusion
coefficient is obtained from the decay of
the 7-ppm-signal. Methylen signals in the
range 14 ppm are relatively increased,
since their relaxation times are longer.
The diffusion time was 20 ms and
1-ms-alternating-gradient-pulses were
used.
2

d t d
 4d g   

S  S0 exp  D 
  pp   S0 exp D k 
 D 
2

 p  


Fitting of the values S for the 7-ppm-signal
yields a self-diffusion coefficient of
D = 7.9  10-9 m2s-1.
The figure left demonstrates the advantage of
MAS PFG NMR diffusometry with respect to
the well-established PFG NMR diffusometry.
The latter would consider the sum of all
unresolved signals for the determination of
the self-diffusion coefficient.
Nernst-Einstein equation
and conductivity models
The Nernst-Einstein equation gives the direct-current conductivity sdc as a function
of the concentration C of the proton vehicles, the charge e of a single vehicle, the
self-diffusion coefficient D and the temperature T, with kB as Boltzmann constant:1
The concentration can be obtained from solid-state NMR data and weight and
volume of the sample in the NMR rotor. Then we obtain from the equation above
sdc = 0.036 S cm1. A comparison with the value obtained directly by impedance
spectroscopy [R. Marschall, J. Rathousky, M. Wark, Ordered functionalized silica
materials with high proton conductivity, Chem. Mater. 19 (2007) 6401-6407]
shows that the calculated values are higher by one order of magnitude.
Models of the conductivity in solid ionic conductors describe a macroscopic behavior.
Diffusion can be studied by several techniques giving a macroscopic or microscopic
picture. NMR diffusometry monitors diffusion path lengths in the order of magnitude of
micrometer during observation times 11000 ms. The comparison of conductivities,
which were directly measured, with those obtained by the Nernst-Einstein equation
from NMR diffusivity data, can be used for the verification of conductivity models.
1 P.
Colomban, A. Novak, Proton Conductors: classification and conductivity, in: Proton coductors. Solids, membranes
and gels – materials and devices, (P. Colomban, Eds.), Cambridge University Press, 1992, p. 38-60
Conclusions
 The development of functionalized mesoporous materials for proton exchange
membrane fuel cells (PEM cells) at higher temperatures (140 °C) is a key area in the
research for new environmentally friendly ways of energy generation.
 A conductivity of s = 103 S cm1 can be obtained at 140 °C for the sulfonic acid
functionalized mesoporous material Si-MCM-41.
 1H MAS NMR spectroscopy yield information about the spacer and the nature of the
proton vehicle for the conductivity
 13C CP MAS NMR shows the structure of the spacer and functional group
 29Si MAS NMR gives quantitative results about the anchorage of the spacer to the
mesoporous host material.
 1H MAS PFG diffusometry determines selectively the diffusivity of the proton vehicles
in the cell material.
 A comparison between conductivities, which were directly measured by impedance
spectroscopy, with values obtained by the Nernst-Einstein equation from the selfdiffusion coefficient, which was obtained by 1H MAS PFG NMR, is helpful for the
evaluation of conductivity models.
Diffusion Fundamentals IV
Basic Principles of Theory,
Experiment and Application
August 21rd - 24th, 2011
Troy, NY, USA

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