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Unprecedented Insight into Diffusion by Monitoring the Concentration of Guest Molecules in Nanoporous Host Materials.

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Host?Guest Systems
DOI: 10.1002/anie.200602892
Unprecedented Insight into Diffusion by
Monitoring the Concentration of Guest Molecules
in Nanoporous Host Materials**
Jrg Krger,* Pavel Kortunov, Sergey Vasenkov,
Lars Heinke, Dhananjai B. Shah, Rainer A. Rakoczy,
Yvonne Traa, and Jens Weitkamp*
Nanoporous materials[1] may be visualized as sponges with
holes of molecular dimensions. They are a key to novel and
environmentally friendly technologies for the isolation of
value-added products through heterogeneous catalysis and
mass separation.[2?4] They also offer potential for gas sensors
and opto-electronic devices.[5?7] Recent progress in synthesis
methods has led to an explosion in the number of structure
types[8] and, thus, to a broad spectrum of nanoporous
To understand the functionality of these host materials,
knowledge of the distribution of adsorbed guest molecules
and its temporal evolution are necessary. A number of
techniques, broadly classified as either macroscopic or microscopic, are available for characterizing diffusion in porous
materials. However, conventional techniques, such as uptake
and release experiments,[9, 10] are not capable of providing
information on the temporal evolution of internal concentration profiles. These techniques measure changes in macroscopic properties, from which information about the intrinsic
processes must be deduced on the basis of numerous model
Nor is the required information about internal concentration profiles accessible by microscopic techniques such as
quasi-elastic neutron scattering[10, 12] and pulsed field gradient
(PFG) NMR spectroscopy,[10, 13] since these methods measure
[*] Prof. Dr. J. Krger, Dr. P. Kortunov, L. Heinke
Fakultt f%r Physik und Geowissenschaften
Universitt Leipzig
Linn0strasse 5, 04103 Leipzig (Germany)
Fax: (+ 49) 341-97-32-549
Prof. Dr. S. Vasenkov
Department of Chemical Engineering
University of Florida, P.O. Box 116005
Gainesville, FL 32611-6005 (USA)
Prof. Dr. D. B. Shah
Department of Chemical & Biomedical Engineering
Cleveland State University, 2121 Euclid Avenue
Cleveland, OH 44115 (USA)
Dr. R. A. Rakoczy, Dr. Y. Traa, Prof. Dr. J. Weitkamp
Institute of Chemical Technology
Universitt Stuttgart
70550 Stuttgart (Germany)
Fax: (+ 49) 711-685-64065
[**] We gratefully acknowledge financial support from the Deutsche
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2006, 45, 7846 ?7849
only the average molecular displacements in the sample.
NMR imaging techniques (such as MR tomography),[13] which
have become indispensable in medical diagnosis, are still far
from the necessary spatial (down to micrometers) and
temporal (down to seconds) resolution.
From this point of view, the introduction of interference
microscopy to zeolite science has been a breakthrough.[14, 15]
The technique is based on the principle that the optical
density of zeolite crystallites (or other transparent media)
depends on the amount and nature of the guest molecules. As
a consequence, the phase shift between two light beams, one
passing through the crystal and the other through the
surrounding atmosphere, is a measure of the average guest
concentration along the direction of the light beam through
the crystal. The mean concentration (that is, the total amount
of molecules in the beam direction) can be deduced by
analyzing the interference pattern of the two beams. The
experimental method is illustrated in Figure 1.
Figure 1. Interference microscopy. a) Two light beams, one passing
through the crystal and the other through the surrounding atmosphere
(L 10 mm). b) The interference microscope. c) Interference pattern
arising from the two beams passing through media with different
optical properties. d) Concentration profiles at different times, calculated from interference patterns.
The introduction of interference microscopy to zeolite
science and technology has far-reaching consequences, since it
allows the in situ detection of the spatial evolution of the
concentration distribution in solid host systems. As a result, for
the first time, experimentally measured concentration profiles
can be directly compared with the predictions of the classical
Fick5s equations. According to Fick5s first law [Eq. (1)], the
particle flux j is proportional to the gradient of the particle
concentration c. In general, the proportionality factor, the
(transport) diffusivity D, is a function of particle concentration.
To predict the evolution of the concentration distribution
c(x,t), Equation (1) is combined with the law of conservation
of matter [Eq. (2)], yielding Fick5s second law [Eq. (3)].
@D @c 2
ў D№c№xоо 2
@t @x
@c @x
j М D
Angew. Chem. Int. Ed. 2006, 45, 7846 ?7849
For simplicity, Equations (1) to (3) have been written for
the special case of a one-dimensional concentration profile.
Concentration gradients cannot be determined along the
direction of observation by using interference microscopy,
owing to its measuring principle. The situation described by
Equation (3) (with x as a coordinate along an axis perpendicular to the light beam and, therefore, to the observation
direction) correctly represents our experimental conditions,
as is demonstrated below.
We performed adsorption and desorption experiments
with methanol on a ferrierite zeolite, the structure of which is
depicted in Figure 2 a, and determined the concentration
Figure 2. Temporal evolution of concentration profiles of methanol in a
ferrierite crystal for a pressure step from 0 to 80 mbar. a) Shape and pore
structure of the ferrierite crystal. b) Concentration profiles in the z direction
at y = 25 mm. c) Two-dimensional concentration profiles in the y and
z directions. d) Concentration profiles in the y direction at the center of the
crystal (z = 120 mm) and at two locations near the edges. A relative
concentration of 1.0 corresponds to the equilibrium concentration of
methanol in ferrierite at 80 mbar.
profiles of methanol in the crystal interior. The ferrierite
crystal was activated under high vacuum at a temperature of
673 K for 4 h. To ensure the complete removal of organic
residues, the sample was heated in an oxygen atmosphere at
973 K for 4 h prior to the activation. The observed adsorption
profiles, which are presented in Figure 2 b?d, yield two
astonishing results:
a) Almost immediately after the onset of adsorption, a
concentration profile associated with the rooflike part of
the crystal is established. During desorption, this part of
the profile disappears equally rapidly.
b) Concentration gradients, which indicate the direction of
mass transfer into the crystal during adsorption and out of
the crystal during desorption, are observed exclusively in
the y direction for the central part of the crystal.
Both of these results can be unambiguously attributed to
the particular features of the channels that run along the
z direction of the ferrierite crystal. These channels are
surrounded by 10-rings (formed by 10 silicon and 10 oxygen
atoms). As the channels that run along the y direction of the
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ferrierite crystal are composed of smaller 8-rings, intracrystalline mass transfer is expected to proceed much faster in the
z direction. Thus, the rooflike part of the crystal is occupied
by guest molecules immediately after the onset of adsorption
and is emptied immediately after the onset of desorption
(result (a)). The occurrence of such high-speed transport
processes in channels of molecular dimensions has been
reported several times.[16]
Another interesting feature of the concentration profiles
is that in the central parallelepiped part of the crystal, there
are no concentration gradients (and hence no fluxes) in the
z direction. Apparently, the channels along the z direction are
blocked in this part of the crystal, whereas they are wide open
in the rooflike part of the crystal, which is defined by inclined
faces. The formation of similar pore or channel blockages is a
relatively common structural feature of nanoporous materials.[5] As a consequence of this blockage, any mass transfer in
the central (and by far the largest) part of the crystal can only
occur in the y direction, along the 8-ring channels, as indicated
by the concentration gradients (result (b)). This particular
pattern of pore blocking in ferrierite leads to the situation that
mass transfer in the main part of the crystal occurs only in the
y direction, even though the molecular mobility (diffusivity)
is much larger in the z direction because of the larger pore
size. Electron microscopy studies of intracrystalline guest
concentrations have found analogous patterns of guest
distribution in ferrierite.[17]
An extensive set of internal concentration profiles have
been measured as a function of time. The concentration
profiles for a pressure step from 0 to 5 mbar at different times
during the adsorption of methanol in a ferrierite crystal are
shown in Figure 3. The concentration profiles obtained in this
manner are much more informative than similar profiles that
have previously been obtained for diffusion in solids[18, 19] and
fluids.[20] Moreover, interference microscopy is nondestructive
and is an ideal method for in situ measurements.
We can now use the temporal evolution of the concentration profiles to determine diffusivities through the microscopic application of Fick5s laws. The knowledge of the
concentration profiles at different times allows us to calculate
the rate of change of concentration with time ( @t ) at any
coordinate y, as well as the first and second spatial derivatives
@2 c
of the concentration (@y and @y2 ) at any y and t. The diffusivities
were determined from the profiles in two steps. In the first
step, diffusivities were calculated at the center of the
concentration profiles, because at this position all of the
profiles are flat (with slopes of zero). Hence, Equation (3) has
only two terms,
and D can be calculated from the knowledge
@2 c
of @t and @y2 . The result provides an initial estimate of the
variation of the diffusivity with concentration. In the second
step, this information is used in conjunction with the shapes of
the profiles at other locations to obtain better estimates of the
diffusivities and their dependence on concentration. This type
of analysis opens up a completely new avenue for the
microscopic determination of diffusivities. Since local diffusivity is a direct indicator of structural peculiarities, important
structural information that was previously obscured is now
Several features of the experimental technique and
analysis require further explanation. The concentration
profiles shown in Figure 3 were determined from the twodimensional data sets in Figure 2 c, and these were determined from the primary interference patterns (Figure 1 c) by
taking the weighted averages over adjacent data points. As a
consequence of this necessary smoothing procedure, minor
structural defects, such as occur in highly structured materials,[5] may be masked. In particular, mass transfer in the
x direction, which is not possible in the ideal structure of
ferrierite (Figure 2 a), but which may occur due to structural
defects, may be hidden. Moreover, in the analysis according to
Fick5s second law, a complete homogeneity of the crystal is
assumed; that is, the diffusivity D(c,x) is assumed to be solely
a function of concentration D(c), which is the same throughout the crystal. Because of all these considerations, perfect
agreement between theory and experiment is not likely.
Figure 4 provides an overview of the diffusivities determined from the various uptake and release experiments. The
intracrystalline diffusivity is a strong function of concentration and varies by nearly two orders of magnitude. In Figure 4,
as in all other Figures, the concentration is expressed as a
Figure 3. Temporal evolution of concentration profiles of methanol in
the y direction in the ferrierite crystal (near the edge, at z = 2 mm) for a
pressure step from 0 to 5 mbar. The method of evaluating the terms
@2 c
@y2 and @t is also indicated.
Figure 4. Diffusivities evaluated as a function of concentration for
different pressure steps: desorption from 5 to 0 mbar (filled stars),
desorption from 10 to 0 mbar (open spheres), adsorption from 0 to
20 mbar (open stars), and desorption from 40 to 0 mbar (filled
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2006, 45, 7846 ?7849
fraction of the equilibrium concentration of methanol adsorbed by ferrierite at 80 mbar, which is estimated from our work
and published data[21] to be 0.163 cm3 g1 4 mmol g1
8.5 molecules/unit cell. All experiments consisted of consecutive cycles of adsorption and desorption on the same
single crystal,[22] a technique which is unprecedented.
We have verified the calculated values of diffusivity by
comparing the experimental concentration profiles (Figure 3)
with those calculated from the numerical solution of Fick5s
second law using the estimated D(c) values (Figure 4). The
excellent agreement between the two sets of profiles for both
adsorption and desorption validates the method of analysis.
Thus, the information obtained on the temporal evolution
of the internal concentration profiles leads to fully selfconsistent results for the relevant transport parameters,
namely, the concentration dependence of the intracrystalline
diffusivity. In view of the increasing number and variety of
nanoporous materials, the application spectrum of this new
method for the investigation of diffusion and internal pore
structure is essentially unlimited.
The practical relevance of this finding is illustrated by
considering adsorption and desorption under the conventional conditions of uptake and release experiments. The
information available from uptake experiments (transient
sorption curves) can also be obtained by integrating the
concentration profiles corresponding to the central part of the
crystal. The transient sorption curves determined in this
manner agree well with theoretical predictions based on the
microscopically determined (?differential?) diffusivities.
However, there is no way to determine the differential
diffusivities from the sorption curves. With the microscopic
diffusion measurements reported herein, precisely these
quantities can now be determined, offering new prospects
for diffusion measurements on nanoporous materials.
Received: July 19, 2006
Published online: October 24, 2006
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[19] H. Mehrer in Diffusion in Condensed Matter: Methods, Materials, Models (Eds: P. Heitjans, J. KMrger), Springer, Berlin, 2005,
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Keywords: host?guest systems З interference microscopy З
micropore diffusion З nanoporous materials З zeolites
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