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Tracing Water and Cation Diffusion in Hydrated Zeolites of Type LiLSX by Pulsed Field Gradient NMR
Steffen Beckert,† Frank Stallmach,† Helge Toufar,‡ Dieter Freude,† Jörg Kar̈ ger,*,† and Jürgen Haase†
†
Faculty of Physics and Earth Sciences, Leipzig University, Linnéstraße 5, 04103 Leipzig, Germany
Clariant Corporation, P.O. Box 32730, Louisville, Kentucky 40232, United States
‡
ABSTRACT: The pulsed field gradient (PFG) technique of NMR is exploited for
recording the time-dependent mean diffusion path lengths of both the water molecules
(via 1H NMR) and the cations (via 7Li NMR) in hydrated zeolite Li-LSX. The observed
propagation patterns reveal, for both the water molecules and the cations, two types of
transport resistances, acting in addition to the diffusion resistance of the genuine pore
network. They are attributed to the interfaces at the boundary between the purely
crystalline regions (crystallites) within the Li-LSX particles (intergrowths) under study and
to the external surface of either the particles themselves or crystallite aggregates within
these particles. The cation diffusivity is retarded by about 1 order of magnitude in
comparison with the water diffusivity. This notably exceeds the retardation of cation
diffusion in comparison with water in free solution, reflecting the particular influence of the
zeolite lattice on the guest mobility.
■
INTRODUCTION
The unique potentials of zeolites and related crystalline
nanoporous materials for their technological use, notably for
mass separation,1 catalytic conversion,2 selective adsorption,3
sensing,4 and molecular ordering for generating optical
functionality5,6 are intimately correlated with the similarity in
pore sizes and guest dimensions and with their content of
exchangeable cations.7,8 A wide variety of applications of
zeolites, ranging from water softening in detergency9 to
selective removal of radionuclides,10 are based on the exchange
of these cations. Cation content is, moreover, known to deeply
modify the adsorption and diffusion behavior of zeolites11,12 as
well as their catalytic activity,13,14 prompting extensive
experimental studies on cation locations15 and the development
of computer simulation methods and theoretical models.16−19
However, exempt from in situ X-ray diffraction (XRD) and
NMR studies of the variation of cation locations upon
dehydration20,21 and the measurement of cation exchange
rates between the zeolite crystals and the surrounding
solution,22,23 cation migration used to remain beyond the
focus of both experimental and modeling studies.
The advent of the pulsed field gradient (PFG) technique of
NMR24 and its first application to nanoporous host−guest
systems25,26 has provided us with clear and direct evidence
about the rate of intracrystalline diffusion of the guest
molecules in such host materials.27,28 Equivalent information
on the cation mobility, however, is still missing. From cation
exchange measurements, e.g., meaningful information about
intracrystalline diffusivities only results if the overall exchange
rate is indeed controlled by intracrystalline diffusion. The ability
to provide exactly this type of proof has made PFG NMR28−30
a powerful technique for probing molecular mass transfer in
complex systems over microscopic dimensions,31−35 whose
© 2013 American Chemical Society
potentials for diffusion studies of cations in zeolites have
recently been demonstrated.36 It was due to the availability of
extra-large field gradient pulses35,37,38 as a prerequisite for the
measurement of small diffusivities39−43 that such measurements
became possible. These novel options are now exploited for
comparative diffusion studies of cations and water in zeolite LiLSX and for unraveling correlations between guest propagation
and host topology.
■
MATERIALS AND METHODS
Zeolite Synthesis. Zeolite LSX with particle diameters
ranging from about 3 to 10 μm was synthesized by D. Täschner
as described in ref 36. The ion content after the 4-fold exchange
with lithium chloride solution amounts to 90.9% Li+, 3.4% K+
and 5.7% Na+, and the silicon-to-aluminum ratio is Si/Al =
1.02. The zeolite was heated at 363 K for one hour in an open
glass tube (outer diameter of 10 mm with a length of 50 mm)
in an oven containing a water bed. Subsequently, the glass tube
was sealed off at room temperature, with the zeolite bed kept
cooled in liquid nitrogen. After this treatment, the water
content of the zeolite was about 20 wt %. This corresponds to
171 molecules per unit cell. A scanning electron microscopy
(SEM) picture of the LSX crystallites is presented in Figure 1.
Pulsed Field Gradient (PFG) NMR Diffusion Measurements. Under the influence of a pair of field gradient pulses,
applied in addition to the sequence of radio frequency pulses
giving rise to the formation of the NMR signal, the intensity of
the spin echo, M, is known to obey the relation29,30,44,45
Received: August 28, 2013
Revised: November 1, 2013
Published: November 1, 2013
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δ were varied between 0.5 and 1.5 ms. Diffusion measurements
were performed using the stimulated24 and (for short
observation times) the Hahn-echo sequences.46
For molecules in an infinitely extended, isotropic medium the
propagator is a Gaussian28
P(z , t ) =
⎧ z2 ⎫
1
⎬
exp⎨−
4πDt
⎩ 4Dt ⎭
(2)
with the mean square width (molecular mean square
displacement) given by the Einstein formula
⟨z 2(t )⟩ =
⎛ 1
⎞
Ψ(γδg , t ) = exp( −γ 2δ 2g 2Dt ) = exp⎜ − γ 2δ 2g 2⟨r(t )2 ⟩⎟
⎝ 6
⎠
∞
∫−∞ P(z,t )cos(γδgz)dz
(3)
with the self-diffusivity D. Inserting eqs 2 and 3 into eq 1 leads
to the familiar expressions
Figure 1. SEM pictures of the parent material of type Na,K-LSX.
Reprinted from Freude et al.36 with permission.
M(δg )
≡ Ψ(γδg,t ) =
M(0)
∞
∫−∞ z 2P(z,t )dz = 2Dt
(1)
(4)
with g and δ denoting, respectively, the amplitude and duration
of the gradient pulses. t stands for the observation time of the
PFG NMR experiment, i.e., the time interval between the two
gradient pulses (where, for simplicity, the pulse width δ is
implied to be negligibly small in comparison with t). The
symbol γ (= 2.67 × 108 T−1 s−1 for protons and 1.04 × 108 T−1
s−1 for 7Li) denotes the gyromagnetic ratio of the nucleus
under study. P(z,t) stands for the probability that, during time t,
an arbitrarily selected molecule within the sample is shifted over
a distance z, i.e., in the direction of the applied field gradient.
This interrelation between the signal attenuation curve
Ψ(γδg,t) and the “mean propagator” P(z,t)29,30,44,45 gives rise
to the matchless versatility of PFG NMR for the exploration of
molecular mass transfer in complex systems.
The present measurements were carried out by means of a
home-built NMR spectrometer at a proton resonance
frequency of 400 MHz. The spectrometer is equipped with a
pulsed field gradient (PFG) unit35,37 allowing field gradient
amplitudes g up to a value of 39 T/m. The field gradient widths
For normal diffusion in infinitely extended homogeneous
systems, one may even abandon the requirement of pulse
gradient widths δ to be negligibly small in comparison with the
distance t between the two field gradient pulses. In this case one
obtains, quite generally, a relation of the form of eq 4 in which
only the separation between the two gradient pulses t is
replaced by t − δ/3.24 Throughout this study, we have
considered the thus corrected pulsed separation as the
observation time.
On considering diffusion in nanoporous materials and, in
particular, in zeolites, one must be aware that some of the
prerequisites for deriving eq 4 are not strictly fulfilled anymore
(see chapter 11 of ref 28 for details). This concerns, in
particular, the fact that one cannot assume absolute uniformity
of the material. As a consequence, we have to expect a
distribution of diffusivities so that the observable PFG NMR
signal attenuation is not a single exponential anymore. It rather
results as the weighted mean over many exponentials of the
type of eq 4 with the (different) diffusivities corresponding to
the differences in material structure and/or composition.
Figure 2. PFG NMR attenuation plots for water diffusion at 25 °C (a) and for the diffusion of the lithium cations at 100 °C (b) in hydrated zeolite
Li-LSX.
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Figure 3. Effective diffusivities of water at 25 °C (a) and of the lithium cations at 100 °C (b) in hydrated zeolite Li-LSX. The straight lines represent
the best fit of eq 5 to the experimental data in the short- and long-time ranges.
decrease with increasing observation time, indicating the
existence of transport resistances on the diffusion paths of
the species (the water molecules and lithium cations,
respectively) under study. Judging from the micrographs of
the crystals, see Figure 1, there are two sources of transport
resistances which one might expect: at the outer surface of the
zeolite particles and at the boundary between the individual
crystallites out of which the particles are, obviously, composed.
Figures 3a and b are seen to exhibit, for both species, two
distinctly differing regimes of time dependence. They are,
tentatively, expected to be correlated with the two types of
resistances. For quantitatively correlating the effective diffusivities experimentally determined with relevant structural and
transport parameters, we are going to distinguish between the
results of “short-range” and “long-range” measurements. Shortrange measurements refer to displacements smaller than the
distance between transport resistances within the zeolite
particles, most likely correlated with barriers formed at the
interfaces between the individual crystallites which are found to
form the zeolite particles. They are thus expected to reflect
molecular diffusion within the genuine micropore space,
affected by confinement effects at the boundaries between the
individual crystallites. Long-range measurements refer to
displacements exceeding the sizes of the individual crystallites
but still within the interior of the individual zeolite particles.
They are, correspondingly, expected to reflect mass transfer
under the combined effect of the micropores and transport
resistances at their mutual interfaces, subject to the confinement by the size of the particles, i.e., by the surface of the
agglomerates seen in Figure 1.
For quantitative analysis we refer to the well-known
analytical expression28,47−49
However, even under these conditions, by a series expansion of
the cosine in eq 1, eq 4 is easily seen to be still correct for small
enough gradient pulse intensities gδ, with the mean square
displacement taken over the total system (and the diffusivity,
correspondingly, denoting the weighted mean over all
diffusivities in the sample). It is this diffusivity to which we
refer in our study. If distinction from the genuine self-diffusivity
as introduced with eq 2 is needed, the diffusivity as resulting
from the PFG NMR measurements is referred to as Deff.
A second deviation from the ideal case of an infinitely
extended medium originates from the finite size of the particle
under study, including the presence of a possible substructure.
The confinement of the guest molecules to certain regions will
obviously lead to a decrease in their propagation rates. In the
Results and Discussion section, exactly this consequence is
exploited for estimating the sizes of the regions to which guest
propagation is confined, using the adequate analytical solutions.
There is, however, also a second consequence of the finite
particle size. As soon as a perceptible number of molecules are
able to leave the individual crystallites, the mean square
displacement shall be dramatically affected by their contribution
when the rate of mass transfer through the intercrystalline space
notably exceeds the rate of intracrystalline diffusion. Since the
long-range diffusivity is, essentially, given by the product
pinterDinter of the relative amount of molecules in the
intercrystalline space and their diffusivity, it is easily seen to
notably exceed, at sufficiently high temperatures, the
diffusivities of the remaining part of molecules, corresponding,
with eq 4, to a much larger decay of the contribution of these
molecules to the overall PFG NMR signal attenuation curve. It
may, therefore, be easily subtracted.
■
RESULTS AND DISCUSSION
Deff (t ) = D −
Figures 2a and b show selected PFG NMR attenuation curves
as the primary data of our diffusion studies with water and the
lithium cations in hydrated zeolite Li-LSX. The full lines
represent the best fit of eq 4 to our attenuation data. The
resulting diffusivities are plotted, as a function of the square
root of the observation time, in Figures 3a and b.
The resulting diffusivities are immediately seen to depend on
the observation time. Not unexpectedly, the diffusivities
4
D3/2 t
3 πR
(5)
which correlates the “effective” diffusivity Deff(t), resulting from
the application of eq 4 to the PFG NMR attenuation curves,
with the genuine, intrinsic diffusivity D if mass transfer is
confined to spheres of radius R. The straight lines in the longtime part of the Deff(t)-vs-√t plots in Figures 3a and b
represent the best fits to the Deff data points for the long-range
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calculated on the basis of eq 5 may exceed the real ones. An
estimate of the extent of this shift is in the focus of ongoing
simulation work.
The increase in the genuine micropore diffusivities Dmicro for
both the cations and the water molecules in comparison with
the long-range diffusivities Dlong‑range within the zeolite particles
has been seen to be the immediate consequence of the
additional impediment of propagation on the boundaries
between the different crystallites which the diffusants have to
overcome on their diffusion paths over larger distances, with eq
6 providing a quantitative expression of this interrelation. The
influence of internal surface barriers is known to decrease with
increasing temperature.53−56 This may be easily referred to the
fact that the activation energy for barrier permeation exceeds, in
general, the activation energy for diffusion in the genuine pore
network. Also in the present case, the genuine intracrystalline
diffusivities Dmicro of both the lithium ions and the water
molecules are seen to differ by not more than a factor of about
3 from the intraparticle long-range diffusivities.
In ref 36, the diffusivity of the lithium ions in hydrated zeolite
Li-LSX at 100 °C was determined to be (2.0 ± 0.8) × 10−11 m2
s−1. The order of magnitude of these measurements, which
have been performed with an observation time of t = 2 ms
without any further variation, has been confirmed in the present
study using the identical samples. In addition, by an extensive
variation of the observation time, it has been revealed that an
observation time of even as short as the considered 2 ms is not
yet short enough to exclude corruption by confinement within
the individual crystallites. By extrapolation to zero observation
time via eq 5 the true (i.e., unperturbed by boundary effects)
value of DmicroLi+ is now estimated to be (4.0 ± 0.9) × 10−11 m2
s−1.
A comparison between the magnitudes of the water and
cation diffusivities is complicated by the difference in the
measuring temperature. Their choice, however, was a
consequence of the measuring conditions. A dramatic decrease
in the cation mobility with decreasing temperature, together
with an accompanying reduction in the transverse relaxation
times, excluded any meaningful 7Li PFG NMR measurement
with hydrated Li-LSX at temperatures below the chosen 100
°C. On the other hand, with temperatures higher than the
chosen room temperature, the increasing water diffusivities give
rise to increasing diffusion path lengths. With eq 3, the rootmean-square displacements are thus, for even the shortest
possible observation time of 2 ms, found to amount to 1.7 μm,
notably exceeding the size of the individual crystallites
appearing from both the micrograph (see Figure 1) and the
confinement effects as traced by the short-range PFG NMR
measurements (see Rmicro data in Figure 3). PFG NMR
measurements of water diffusion at 100 °C do allow, therefore,
reliable measurement of only intraparticle long-range diffusivity.
Since the diffusivities of genuine micropore diffusion have to
definitely exceed the intraparticle long-range diffusivities and
are, moreover, known to be approached by them at sufficiently
high temperatures, a comparison with the cation diffusivities
may clearly be also based on the intraparticle long-range
diffusivities of the water molecules.
Figure 4 shows the PFG NMR signal attenuation curve for
water in the hydrated Li-LSX samples, corresponding to those
shown in Figure 2a for 25 °C, measured now at 100 °C for the
shortest possible observation time, i.e., t = 2 ms. In the
beginning of the attenuation curve we note a very fast decay
which has to be correlated with those water molecules which, at
measurements. With eq 5, the corresponding diffusivities and
radii of confinement result to be DH2O,long‑range = 1.1× 10−11 m2
s−1, Rparticle(H2O) = 1.3 μm, and DLi,long‑range = 1.3 × 10−11 m2 s−1,
Rparticle(Li) = 2.41 μm.
For mass transfer affected by both the diffusion resistance of
the genuine pore space and transport resistances at the interface
between the subunits (crystallites) within the zeolite particles,
effective medium theory provides an expression of the
type28,50−52
1/D long‐range = 1/D + 1/(α S)
(6)
with D denoting the diffusivity within the genuine pore space
and α and S denoting, respectively, the permeability and the
separation of additional transport barriers.
The resulting radii reproduce the sizes of the smaller and
medium particles, in agreement with the expected behavior.
Given the large distribution of the particle sizes, one cannot
exclude that the larger particles are, in reality, agglomerates of
smaller particles so that it is not unexpected that their particle
sizes may exceed the Rparticles values determined in our diffusion
studies.
For rationalizing the origin of the time dependence of the
effective diffusivities in the short-time range, it is helpful to refer
to the influence of spherical boundaries on the PFG NMR
signal attenuation in a more general way. With eq 3, the mean
diffusion path lengths during t in a given direction (we choose
that perpendicular to the boundary) are seen to be ⟨z2(t)⟩1/2 =
(2Dt)1/2.
The effect of confinement by a sphere of radius R may thus,
in first-order approximation, be assumed to affect a shell of
thickness (2Dt)1/2, while the remaining part of the sphere
remains unaffected. Within this approximation, the effective
diffusivity results as
Deff =
4
πR3
3
− 4πR2(2Dt )1/2
4
πR3
3
D+
4πR2(2Dt )1/2
4
πR3
3
Dred
(7)
where the confinement by the boundary of the sphere, which
the molecules within this layer are able to experience, is taken
into account by introducing a “reduced” diffusivity Dred < D. If
the “reduced” diffusivity Dred is set equal to
D(1 − 4/(9(2π)1/2)), eq 7 is seen to coincide with eq 5. We
note that, also in this more general approach, the effective
diffusivity decreases linearly with the square root of time. As a
first-order approach, we are therefore going to use eq 5 for also
analyzing the effective diffusivities in the short-time range. Now
the corresponding diffusivities and radii of confinement result
to be DH2O,micro = 3.45 × 10−11m2 s−1, Rmicro(H2O) = 0.28 μm and
DLi,micro = 4 × 10−11m2 s−1, Rmicro(Li)= 0.44 μm. Just as the
particle sizes resulting from analyzing the effective diffusivities
in the long-time range, now also the sizes of the individual
constituents, i.e., the sizes of the “crystallites” as resulting from
the short-time analysis, are seen to be of the order of magnitude
revealed by the SEM picture in Figure 1.
Confinement by an impermeable boundary (as implied for
the external particle surface) on the mean square displacement
clearly exceeds the effect of confinement by the boundaries
between the subunits within one zeolite particle which, at least
to some degree, allow a passage of the diffusants. Dred must
therefore be expected to be even closer to the genuine
intracrystalline diffusivity D so that the prefactor of the √t term
in eq 5 becomes smaller. Correspondingly, the radii R
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hydrated zeolite Li-LSX at 100 °C of about (3.5 ± 0.5) × 10−10
m2 s−1.
This value confirms the estimate of the water diffusivity at
100 °C in ref 36 which has been based on the rate of water
exchange with the surrounding atmosphere. This value is
slightly smaller than the water diffusivity in zeolite Na-X (D ≈ 5
× 10−10 m2 s−1) determined in the very first PFG NMR
measurement of intracrystalline zeolitic diffusion 40 years ago,25
which, quite recently, was confirmed by molecular dynamics
(MD) simulations and quasi-elastic neutron scattering experiments.57 In addition to the influence of transport resistances at
the crystallite boundaries, the difference between the water
diffusivities in zeolites Na-X and Li-LSX can easily be referred
to the different amount and nature of the cations.
Figure 5 shows the diffusivities in aqueous lithium chloride
solution at both room temperature and 100 °C. In comparison
with these data, the diffusivities in hydrated zeolite Li-LSX for
either component (Figure 3) are seen to be significantly (by
about 2 orders of magnitude) reduced. This reduction is more
pronounced for the cations. Their diffusivity in Li-LSX is seen
to be nearly 1 order of magnitude smaller than the water
diffusivities, while in aqueous lithium chloride solution, they
differ by not more than a factor of about two. Both effects may
be easily referred to the existence of the zeolite lattice. It is
expected to slow down the random motion of all guests and is,
in addition, the carrier of the negative charges whichin
contrast to the mobile anions in solutionare now fixed in
space, leading to an additional slowing down of the positively
charged cations.
Figure 4. 1H PFG NMR signal attenuation curve for water diffusion in
hydrated zeolite Li-LSX at 100 °C for an observation time of 2 ms.
The diffusivity, D (H2O, long-range) = (2.5 ± 0.5) × 10−10 m2 s−1, has
been determined, via eq 4, from the slope of the broken line shown in
the representation which approaches the slope in the attenuation curve
for small values of (γδg)2t if one omits the very first steep decay which
has to be attributed to water molecules which exchange, during the
observation time, between different particles.
this high temperature, are able to leave the crystals, even during
this shortest possible observation time. For considering the
effective diffusivity within the zeolite particles, their contribution to the overall signal has to be subtracted. The resulting
signal attenuation curve is shown by the broken line. From the
very first part of this attenuation curve, the mean diffusivity
results to be (2.5 ± 0.5) × 10−10 m2 s−1. Also this diffusivity is,
strictly speaking, an effective diffusivity, Deff, resulting from
diffusion within a finite, spherical volume. For an order-ofmagnitude estimate of the difference between this value and the
true intraparticle diffusivity, we consider the magnitude of the
second term on the right-hand side of eq 5. For this estimate
we approach the value of the true diffusivity appearing in this
term by the value of the effective diffusivity, 2.5 × 10−10 m2 s−1,
and the particle radius R = 1.3 μm as resulting from the longrange data analysis given in Figure 3a. In this way, the second
term is estimated to 10−10 m2 s−1, yielding a water diffusivity in
■
CONCLUSIONS AND OUTLOOK
For the first time, PFG NMR diffusion measurements are
shown to provide a complete view on cation self-diffusion in
hydrated zeolite particles. By varying the observation times and,
hence, the diffusion path lengths covered in the experiments,
the propagation patterns are found to be closely related with
the morphology of the zeolite specimens under study. The view
on guest dynamics is completed by the PFG NMR results of
water diffusion, yielding diffusivities exceeding the cation
diffusivities by about 1 order of magnitude. This is a remarkable
Figure 5. Diffusivities of water (●) and of lithium ions (■) in an aqueous solution of LiCl at 25 °C (a) and at 100 °C (b) determined by 1H and 7Li
PFG NMR, respectively, (this study) and comparison with literature data for the lithium diffusivities (□).58
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difference since, in the free aqueous solution, water diffusivities
are found to exceed the cation diffusivities by not more than a
factor of 2. Diffusivities in the hydrated zeolite are notably
reduced in comparison with aqueous solution, by more than 2
orders of magnitude for the cations and slightly less than 2
orders of magnitude for water. The time dependence of the
diffusivities of both the cations and the water molecules reveals
two types of additional transport resistances which may be
attributed to the interfaces between the individual crystallites
forming the zeolite particles and to the external surface of these
particles or of larger subunits within the particles.
With the entity of diffusion data in hydrated zeolite Li-LSX as
provided by the present PFG NMR studies we dispose of a
scenario of the dynamics of exchangeable cations and guest
molecules in zeolites of unprecedented completeness. These
novel options are, notably, accompanied by a recent breakthrough in the modeling of cation exchange isotherms in
zeolites which, following previous studies of water and
hydrogen adsorption,59−61 have been based on grand ensemble
Monte Carlo simulations.62 The combination of these two
options for an in-depth study of the laws of the exchange
dynamics of the cations in hydrated zeolites is, doubtlessly,
among the most attractive tasks of future zeolite research.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was supported by Deutsche Forschungsgemeinschaft
under the projects AVANCE 750, HA 1893/9-1 and GK 1056/
2 and by the Fonds der Chemischen Industrie.
■
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