How aluminum distributes during synthesis and rearranges after processing within the zeolite framework is a central question in heterogeneous catalysis, as it determines the structure and location of the catalytically active sites of the one of the most important classes of industrial catalysts. Here, exploiting the dipolar interaction between paramagnetic metal ions, we derive the spatial distribution of single aluminum sites within the ZSM-5 zeolite framework in the nanometer range, in polycrystalline samples lacking long-range order. We use a Monte Carlo approach to validate the findings on a pristine ZSM-5 sample and demonstrate that the method is sensitive enough to monitor aluminum redistribution induced in the framework by chemical stress.
How aluminum distributes during synthesis and rearranges after processing within the zeolite framework is a central question in heterogeneous catalysis, as it determines the structure and location of the catalytically active sites of the one of the most important classes of industrial catalysts. Here, exploiting the dipolar interaction between paramagnetic metal ions, we derive the spatial distribution of single aluminum sites within the ZSM-5 zeolite framework in the nanometer range, in polycrystalline samples lacking long-range order. We use a Monte Carlo approach to validate the findings on a pristine ZSM-5 sample and demonstrate that the method is sensitive enough to monitor aluminum redistribution induced in the framework by chemical stress.
The chemistry and catalysis
of zeolites are driven by the presence of aluminum ions in tetrahedral
coordination at so-called crystallographic T sites, which, for charge
compensation, introduce Brønsted (H+) or redox (transition
metal cations) functionalities that serve as catalytic active sites.[1,2] To harness the catalytic potential of such sites and implement catalyst
performances by design, a precise description of the Al site distribution
is required. In particular, knowledge of the (i) Si/Al ratio; (ii)
the distribution of the Al atoms among crystallographic unique lattice
sites; and (iii) the relative proximity of lattice Al atoms (i.e.,
the distribution of interatomic Al–Al distances among framework
Al-site pairs) is crucially needed. Experimentally, the last two points
are particularly taxing to achieve.[3,4] In fact, although
the spatial density of Al atoms is decisive in determining the turnover
rate of a catalytic reaction, its experimental assessment remains
an open challenge. In the literature, there are several types of evidence
pointing toward a nonrandom distribution of aluminum within the zeolite,[4,5] but very few experimental methods are available to directly determine
the long-range spatial distribution of such sites in disordered polycrystalline
materials. Here, we address this for the ZSM-5 zeolite, a particularly
interesting case for this topic in light of its high industrial interest[6] and its inherent topological complexity.[7]ZSM-5 is commercially one of the most widely
used Si-rich (Si/Al
> 12) zeolites. It has an MFI structure characterized by the intersection
of straight and sinusoidal 10-membered ring channels (of approximately
5.5 Å in diameter) and larger spherical voids at the channel
junctions (of ∼10 Å in diameter). The MFI topology comprises
either a monoclinic (P21/n symmetry)
or orthorhombic structure (Pnma symmetry) with 24
and 12 crystallographically distinct T sites, respectively, the 24
T sites of the monoclinic form corresponding to the 12 T sites of
the orthorhombic form.[8] The T1, T2, T3,
T5, T6, T7, T9, and T12 sites are accessible within channel intersections,
while T4 and T10 are within the sinusoidal channel, and T8 and T11
are within the straight channel.The high Si/Al ratios and the
very similar scattering factors for
Al and Si make the determination of the Al atoms at the different
T sites of ZSM-5 by X-ray diffraction (XRD) very difficult. To circumvent
the problem, Seff and co-workers[9,10] exchanged the protons
of H-ZSM-5 with the much heavier thallium or cesium cations (i.e.,
Tl-ZSM-5 and Cs-ZSM-5) providing evidence by XRD that the distribution
of Al over the T sites is not random. The same indications have been
obtained by energy dispersive X-ray spectroscopy (EDX)[11] and atomic probe tomography (APT).[12]27Al NMR techniques,[13−15] often assisted by DFT
modeling,[16] have proven very useful in
assessing the distribution of Al species in zeolite catalysts at atomic
length scales, providing evidence for the nonrandom nature of the
Al site distribution suggesting that the number of distinct Al sites
could be as low as 3 over 24 possible substitution sites. More recently,
the preferential incorporation of Al at distinct tetrahedral sites
of as-synthesized ZSM-5 (containing the organic structure directing
agent) has been proposed based on a combination of DFT calculations
and two-dimensional 29Si–27Al NMR experiments,[17] while by means of 27Al MQMAS NMR
at 22.3 T the distribution of aluminum over the tetrahedral sites
and their evolution after steam treatment has been assessed.[15] The general conclusion from these studies is
that the Al siting is neither random nor controlled by a simple rule
but depends on synthetic protocols and postsynthesis treatments.[16] In this context, while the combination of specific
spectroscopic techniques and DFT modeling can provide structural insights
at the atomic length scale, the determination of the long-range spatial
distribution of Al sites in Si-rich zeolites remains an open challenge
of particular interest.To address this issue, in this contribution,
we selectively labeled
isolated aluminum sites in ZSM-5 zeolite (Figure a,b) with paramagnetic ZnI ([Ar]3d104s1, S = 1/2)[18,19] and exploited the long-range dipolar interaction between electron
spins to measure their distribution within the zeolite framework.
Figure 1
Overview
of the ZnI-loaded ZSM-5 structure and the physical
principle of magnetic dipole–dipole interaction. (a) Pictorial
rendering of the ZnI-loaded ZSM-5 sample. The zeolite framework
is reported in white (oxygen) and gray (silicon), while Zn ions are
depicted as purple spheres. (b) Close-up on the geometrical structure
of the ZnI site as derived by EPR spectroscopy data.[18,19] The purple arrow represents the electron spin. Color code: purple:
zinc; white: oxygen; gray: silicon; sage: aluminum. (c) Room-temperature
Q-band (33.7658 GHz) echo-detected EPR spectrum of ZnI;
see also Figure S2. The arrow marks the
field position used to record the RIDME time trace. (d) Schematic
representation of the magnetic dipole-magnetic dipole interaction
between two electron spins in the presence of an external magnetic
field. The interspin vector, r, makes an angle θ
with the external applied magnetic field, B0.
Overview
of the ZnI-loaded ZSM-5 structure and the physical
principle of magnetic dipole–dipole interaction. (a) Pictorial
rendering of the ZnI-loaded ZSM-5 sample. The zeolite framework
is reported in white (oxygen) and gray (silicon), while Zn ions are
depicted as purple spheres. (b) Close-up on the geometrical structure
of the ZnI site as derived by EPR spectroscopy data.[18,19] The purple arrow represents the electron spin. Color code: purple:
zinc; white: oxygen; gray: silicon; sage: aluminum. (c) Room-temperature
Q-band (33.7658 GHz) echo-detected EPR spectrum of ZnI;
see also Figure S2. The arrow marks the
field position used to record the RIDME time trace. (d) Schematic
representation of the magnetic dipole-magnetic dipole interaction
between two electron spins in the presence of an external magnetic
field. The interspin vector, r, makes an angle θ
with the external applied magnetic field, B0.The formation of monovalent Zn
cations (ZnI) results
from the spontaneous ionization of Zn atoms only at isolated Al–OH
sites (Figure c,d
and Figures S1 and S2), as demonstrated
by EPR studies.[18,19] ZnI features some
intriguing properties that emerge from its geometric and electronic
structure, namely, long spin relaxation times even at room temperature
(Tm ≈ 2 μs and T1 ≈ 16 μs) and a rigid coordination geometry
(Figure b). These
make ZnI an ideal candidate as a fully inorganic spin label.Indeed, the magnetic electron–electron dipole interaction
between pairs of ZnI ions enables the determination of
their spatial density distribution in the nanometer range by pulse
dipolar spectroscopy (PDS); see Figure d and Figure S3. The PDS
data are recorded as modulation that depends on the ZnI–ZnI, hence aluminum–aluminum, distance
distribution which can be derived with high resolution.[20,21] In the point dipole approximation, the dipolar frequency can be
written as , where g1 and g2 are the
characteristic isotropic g-values for the two spin
species (in the present case g1,2 = 1.998,
the average g-value of ZnI), and βe is the Bohr magneton. As an example
assuming a random distribution (spherical average), interspin distances
of 2 and 5 nm translate to dipolar frequencies
of 6.4771 and 0.4145 MHz, respectively. With a magnetic dipole moment
660 times larger than that of a proton (∼−9.285 ×
10–24 JT–1 as opposed to ∼1.411
× 10–26 JT–1), an electron
spin gives access to distances up to ∼15 nm, which are much
longer than those accessible through NMR.When, as in the present
case, multiple or distributed distances
are present, each contributes individually to the measured time trace
so that PDS may yield not only an average distance(s) but also their
relative distribution. Such an approach has found widespread use in
structural biology.[22,23] However, at variance with spin-labeled
biological systems where a sample is constituted by identical copies,
spin labeling in polycrystalline zeolites has a degree of variability
dependent on silicon-to-aluminum and aluminum-to-spin label ratios.
To take this into account, we developed tailored methods to interpret
the data based on a Monte Carlo approach.Among the available
PDS sequences,[20,21] for this work
we selected the Relaxation Induced Dipolar Modulation Enhancement
(RIDME) pulse sequence which exploits spontaneous relaxation events
to retrieve the dipolar coupling;[24] see Figure d and Figure S4. Figure a reports the room-temperature RIDME data after removal
of the background decay (form factor), which shows a pronounced damping
of the dipolar oscillations indicative of multiple or distributed
distances. As a first approximation, to obtain the relative distance
distribution, the RIDME trace was analyzed with DeerAnalysis,[25] which employs a model-free Tikhonov regularization
algorithm to derive a distance distribution without any prior knowledge
or assumptions (hereafter “model-free distribution”).
As shown in Figure b, the model-free distance distribution is not uniform over the entire
range, as it would be expected if no preferential sites were populated.
Rather, it displays maxima and minima compatible with specific siting.
Figure 2
Room-temperature
RIDME experimental data and extracted distance
distribution. (a) Background-divided time trace (black) with corresponding
fit (red) based on the model-free analysis (DeerAnalysis2018). The
primary data are reported in Figure S5,
whereas data on independent sample preparations are reported in Figure S6. (b) Model-free distance distributions
corresponding to the fitting in a obtained using Tikhonov regularization
in the DeerAnalysis toolbox. The region shaded in gray represent the
1.5 nm cutoff necessary to employ the point dipole approximation.
The experimental trace was recorded at room temperature.
Room-temperature
RIDME experimental data and extracted distance
distribution. (a) Background-divided time trace (black) with corresponding
fit (red) based on the model-free analysis (DeerAnalysis2018). The
primary data are reported in Figure S5,
whereas data on independent sample preparations are reported in Figure S6. (b) Model-free distance distributions
corresponding to the fitting in a obtained using Tikhonov regularization
in the DeerAnalysis toolbox. The region shaded in gray represent the
1.5 nm cutoff necessary to employ the point dipole approximation.
The experimental trace was recorded at room temperature.To assess the origin of such a discrete distribution and
whether
it allows the discrimination of specific siting sites among the 24
potentially available (named T1–T24), we turned to a Monte
Carlo approach. This step is necessary since in a sample no two crystallites
are exact copies. On the basis of the crystal structure for the dehydrated
H-ZSM5 at room temperature, we computed the expected ZnI···ZnI distances considering that each
ZnI randomly occupies either a single site (T7, T8, and
T10) or two sites (T7 and T10). These sites have been selected based
on previous diffraction and spectroscopic studies.[9,10,26] Moreover, as a point of reference, the expected
ZnI···ZnI distances for a completely
random distribution (all 24 sites populated with equal probability)
were evaluated (All Ts). The result of this analysis is presented
in Figure a as histograms.
These distance probability distributions were used to compute the
corresponding form factors considering the distances between 1.6 and
5 nm. The lower limit complies with the Löwenstein rule[27] and the point dipole approximation for the magnetic
dipolar coupling, whereas the upper limit is consistent with the length
of the experimental trace. In zeolites, distances <1.6 nm are in
principle possible but are not suitable for PDS because the dipolar
frequency would be contaminated by the exchange interaction. Such
distances are best assessed by considering the line broadening of
the EPR line. However, such an effect was found negligible on these
samples. The computed form factors were then analyzed in the same
way as the experimental data to yield the corresponding model-free
distance distribution. Figure b reports a comparison between the calculated (T7) and experimental
form factors, while Figure c compares the model-free distance distributions and shows
that the distribution broadens and becomes progressively less defined
the more sites are considered.
Figure 3
Comparison between the Monte Carlo statistics
and experimental
data. (a) Histograms reporting the normalized distribution of the
ZnI···ZnI distances in the range
0–6 nm as computed through the Monte Carlo approach for the
individual sites T7, T8, T10, for the pair of sites T7–T10,
and for all T sites. The bin size is 0.2 Å. (b) Overlay of the
calculated form factor for the site T7 (green line) and the experimental
form factor (black line) measured at room temperature. The calculated
form factor is based on the distance distribution reported in (a)
considering all distances between 1.5 and 5 nm. The apparent noise
in the calculated form factor is the result of the discrete number
of counts. (c) Calculated distance distributions obtained using Tikhonov
regularization for the sites T7, T8, T10, the pair of sites T7–T10,
and all T sites compared with the experimental result (red line).
For better visualization, the distance distributions have been vertically
offset. The calculated form factor is based on the distance distribution
reported in (a) considering all distances between 1.5 and 5 nm. The
region shaded in gray represents the 1.5 nm cutoff necessary to employ
the point dipole approximation.
Comparison between the Monte Carlo statistics
and experimental
data. (a) Histograms reporting the normalized distribution of the
ZnI···ZnI distances in the range
0–6 nm as computed through the Monte Carlo approach for the
individual sites T7, T8, T10, for the pair of sites T7–T10,
and for all T sites. The bin size is 0.2 Å. (b) Overlay of the
calculated form factor for the site T7 (green line) and the experimental
form factor (black line) measured at room temperature. The calculated
form factor is based on the distance distribution reported in (a)
considering all distances between 1.5 and 5 nm. The apparent noise
in the calculated form factor is the result of the discrete number
of counts. (c) Calculated distance distributions obtained using Tikhonov
regularization for the sites T7, T8, T10, the pair of sites T7–T10,
and all T sites compared with the experimental result (red line).
For better visualization, the distance distributions have been vertically
offset. The calculated form factor is based on the distance distribution
reported in (a) considering all distances between 1.5 and 5 nm. The
region shaded in gray represents the 1.5 nm cutoff necessary to employ
the point dipole approximation.This comparison provides evidence that ZnI ions, and
therefore aluminum ions, do not occupy random but preferred sites
within the ZSM-5 structure and that PDS is sensitive enough to pinpoint
such specific sites. In fact, the distance distributions computed
through the Monte Carlo approach show distinct patterns that, in principle,
allow one to distinguish between T sites; see Supporting Figure 7 for an extended comparison. Note that,
as a consequence of the crystalline nature of the zeolite framework,
the clearest differences manifest at short distances (<3 nm) and
effectively provide a unique “barcode” to identify each
T site. At longer distances, all distributions display a similar pattern
due to the average crystal structure rather than single-site behavior.
Even restricting to distances <2 nm, only sites T1, T4, T7, and
T11 show patterns compatible with the experimental results. Of these,
only T1[17] and T7[9,10,19] have been already implicated as probable
aluminum substitution sites. Considering the replicas reported in Supporting Figure 6, we estimate that the uncertainty
in the position of the maxima of the distance distribution (below
3 nm) is on the order of ±0.25 nm.Having established that
PDS provides meaningful data even in the
case of complex, disordered samples such as ZSM5 zeolites, we set
out to examine whether PDS is sensitive enough to detect how the aluminum
probability distance distribution varies upon chemical treatment.
To this end, we selected a steaming procedure that is known to cause
a rearrangement of the Al sites and a redistribution of Brønsted
and Lewis acid sites.[28]Figure reports a comparison of the
experimental form factor before and after steaming and the relative
model-free distance distributions. As is readily apparent, the distance
distribution varies considerably in the range 1.5–2.7 nm before
and after treatment, with the appearance of two discrete peaks at
1.91 and 2.48 nm for the steamed sample. Remarkably, all other distances
remain unchanged highlighting that the structural modification is
mostly short-range, at least as the active sites capable of stabilizing
ZnI are concerned. These results are in line with atom
probe tomography data, which revealed a nonrandomness for the Al distribution
even for highly crystalline materials and reported a most probable
Al–Al neighbor distance of 1.80 ± 0.6 nm for a pristine
ZSM-5 zeolite (Si/Al = 17) and of 0.9 ± 0.3 nm for the same ZSM-5
zeolite after severe steaming.[12]
Figure 4
Effect of chemical
stress (steaming) on the measured distance distribution.
(a) Background-divided time traces (black) with corresponding fits
(red and purple) based on the model-free analysis. For better visualization,
the RIDME time traces have been vertically offset. Both traces were
recorded at room temperature. The primary data and the validation
analysis are reported in Figure S5. (b)
Distance distributions corresponding to the fitting in (a) obtained
using Tikhonov regularization in the DeerAnalysis toolbox. The double-headed
arrow marks the shift in the range 1.91–2.48 nm after steaming.
The region shaded in gray represents the 1.5 nm cutoff necessary to
employ the point dipole approximation.
Effect of chemical
stress (steaming) on the measured distance distribution.
(a) Background-divided time traces (black) with corresponding fits
(red and purple) based on the model-free analysis. For better visualization,
the RIDME time traces have been vertically offset. Both traces were
recorded at room temperature. The primary data and the validation
analysis are reported in Figure S5. (b)
Distance distributions corresponding to the fitting in (a) obtained
using Tikhonov regularization in the DeerAnalysis toolbox. The double-headed
arrow marks the shift in the range 1.91–2.48 nm after steaming.
The region shaded in gray represents the 1.5 nm cutoff necessary to
employ the point dipole approximation.In summary, we proved that PDS is an effective and accurate method
to derive distances in the nanometer range for disordered polycrystalline
inorganic materials and that ZnI is a convenient spin label
for the determination of the isomorphous aluminum distribution within
the zeolite framework. We showed that the dipolar time trace and relative
distance distribution are incompatible with a nonpreferential population
of all T sites, but rather that ZnI—and hence aluminum—preferentially
binds to a restricted number of T sites and that PDS is sensitive
enough to capture the redistribution of aluminum after chemical treatment.
To the best of our knowledge, this is the first method able to give
a nanometer-range distribution of active sites in complex solid-state
systems such as zeolites. As a word of caution, we note that the measured
distance distribution depends on the sample and on the paramagnetic
probe employed, as different probes may prefer different anchoring
sites, and the distribution of aluminum Brønsted sites is influenced
by the silicon-to-aluminum ratio and the synthetic protocol used.
Moreover, paramagnetic labeling of polycrystalline inorganic materials
invariably shows some degree of variability; this is because—at
odds with site-direct spin-labeling in biological samples—multiple
anchoring sites are present, and it is not possible to exert fine
control over the degree of occupancy. This is reflected in the variability
of the associated distance distributions, which, far from constituting
a limit, is a reporter of the intrinsic complexity of such systems.
We believe that PDS may become a powerful tool in the characterization
of inorganic systems especially in combination with local probe techniques
(e.g., NMR). We also anticipate that the approach could be extended
to other paramagnetic species on polycrystalline inorganic supports
lacking long-range order to probe their spatial density and proximity,
a crucial factor to tune catalytic pathways and turnover rates.[3]
Materials and
Methods
Sample Preparation
Zeolite Pretreatment
The H-ZSM-5 zeolite
(Si/Al = 40,
supplied by Haldor Topsøe) was dehydrated by thermal treatment
at 393 K under a dynamic vacuum (residual pressure < 10–4 mbar) for 2 h and calcinated at 773 K in an O2 atmosphere
(390 mbar) to remove spurious organic residues. Excess O2 was subsequently removed by a dynamic vacuum (residual pressure
<10–4 mbar).
Zeolite Steaming
The calcinated H-ZSM-5 zeolite was
exposed to 50 mbar of water vapor at room temperature before being
heated to 973 K (20 K min–1 ramp) for 0.5 h. Subsequently,
the sample was allowed to slowly cool to room temperature in the oven.
The cycle was repeated three times, and between each cycle the sample
was left at 373 K for 1 h. Lastly, the sample was dehydrated by thermal
treatment at 673 K under a dynamic vacuum (residual pressure <
10–4 mbar).
Zn
Evaporation/Illumination
The Zn/ZSM-5 samples were
prepared by sublimation of metallic zinc on the protonated ZSM-5 zeolite
either directly after pretreatment or after steaming. The activated
zeolite was exposed for 2 min to metallic zinc vapors generated in
situ by heating a zinc metal bead (approximately 1 mm in diameter)
at 673 K. The Zn vapor pressure at this temperature was 0.4 mbar.
All samples were sealed under a vacuum and proved to be stable for
several months.The formation of ZnI strictly requires
the presence of a single Brønsted site. The formation of oxidized
Zn species by the reaction of metallic Zn with surface silanols or
extra-framework aluminum cannot be ruled out; however, these are expected
to be diamagnetic ZnII species that are EPR silent. XANES
data reported on the same system in ref (18) show that metallic Zn and ZnO particles, if
at all present, are not formed in appreciable yield.
Zn/Al Quantification
Total content determination
of
Al, Si, and Zn were performed by inductively coupled plasma–optical
emission spectroscopy (ICP-OES – Optima 7000 DV PerkinElmer)
equipped with a Cross Flow nebulizer, a Scott spray chamber, and an
Echelle monochromator. The wavelengths employed for the quantification
were 396.153 nm (Al), 212.412 nm (Si), and 206.412 nm (Zn). The dissolution
procedure consisted of an acid digestion in a microwave oven (milestone
MLS-1200 MEGA). Twenty milligram sample aliquots were treated with
a mixture of 5 mL of aqua regia and 2 mL of hydrofluoridic acid in
tetrafluoromethoxyl (TMF) bombs. Four 5 min heating steps (250, 400,
600, 250 W microwave power, respectively) were each followed by a
25 min ventilation step. Subsequently, 0.7 g of boric acid were added,
and the bombs were further heated at 250 W for 5 min and then cooled
by a ventilation step of 15 min. At the end of the treatment, the
samples appeared fully dissolved. Finally, the resulting solutions
were diluted to 25 mL with HPW. Each sample was analyzed in duplicate,
and each reported concentration was averaged on the basis of three
instrumental measurements. ICP analysis yielded a Si/Al content in
line with the nominal value and a Zn/Al content on the order of 1.00–1.40.
EPR Spectroscopy
Spectrometer Description
Q-band pulse
EPR experiments
were performed at 298 K on a Bruker ELEXYS 580 EPR spectrometer (microwave
frequency ≈ 33.7 GHz) equipped with a Bruker EN 5107D2 resonator
and an Oxford Instruments CF935 liquid-helium cryostat. The magnetic
field was measured by means of a Bruker ER035 M NMR gaussmeter. All
EPR measurements were performed at room temperature.
Echo-Detected Field Sweep (EDFS) EPR Spectrum
The EDFS
EPR spectrum was recorded with the standard Hahn echo sequence π/2−τ–π-echo
at 33.7658 GHz at room temperature with π/2 = 16 ns, π
= 32 ns, and τ = 200 ns.
Determination
of Relaxation Times
(Tand T. The phase memory time
(Tm) was measured
using the standard two-pulse echo sequence π/2−τ–π–τ–echo
where the interpulse delay τ had an initial value of 200 ns
and was incremented in steps of 16 ns. The longitudinal relaxation
time (T1) was measured with the standard
inversion recovery pulse sequence π–T−π/2−τ–π–τ–echo;
the time delay T had an initial value of 1000 ns
and was varied in steps of 500 ns. In both sets of measurements, tπ/2 = 16 ns and tπ = 32 ns. The shot repetition rate was 0.5 and 2 kHz
for Tm and T1, respectively.
Both Tm and T1 time traces
were fitted with a stretch exponential decay function, yielding for
the pristine ZSM-5 T1 = 15.644 μs
(0.94), Tm = 1.721 μs (0.73), and T1/Tm = 9.09 and
for the steamed ZSM-5 T1 = 15.897 μs (0.95), Tm = 1.894 μs (0.80), and T1/Tm = 8.39. The numbers in
parentheses represent the stretching factors. A relative long Tm is needed for sensitivity and to access long
distances (up to ∼6 nm), while a short T1 is desirable for fast signal averaging. A ratio 3 < T1/Tm < 10 was
determined desirable for RIDME sensitivity.
RIDME Pulse Sequence
The dead time free, five-pulse
RIDME introduced by Milikisyants et al.[24] sequence was used: π/2-τ1-π–τ2-π/2-tmix-π/2-τ3-π–τ4-echo, also shown in Figure S4. The experimental values were as follows: π/2 = 16 ns, π = 32 ns, τ1 =
400 ns. The initial position of the mixing block (π/2-tmix-π/2) was
140 ns before the primary echo, and the length of the RIMDE time trace
was 4000 ns. The delay τ2 was incremented in steps
of 16 ns, while τ3 was decremented by the same amount.
In order to try and optimize the sensitivity, experiments were conducted
for three values of tmix, namely, 12,
16, and 20 μs. Since no significant improvement was found for
longer tmix, 12 μs was chosen as
the optimal value. In order to reduce nuclear modulation (ESSEM) effects
due to 27Al, a series of experiments employing a suppression
cycle was conducted in which τ1 was incremented 8
times in steps of 22 or 100 ns;[29] however,
no visible difference was observed. An eight-step phase cycle was
applied to remove phase offsets and echo crossing effects. The shot
repetition time was 500 μs. Each time trace consists of 250
points. The background decay was fitted to a stretched exponential
function I(t) = e–, with dimensionality 4.7791 and 3.6468 for the pristine and steamed
samples, respectively. This is common for RIDME experiments to account
for spectra diffusion processes.[30,31]
4p-DEER (PELDOR) Pulse Sequence
DEER (PELDOR)
experiments
were performed at room temperature on a Bruker ELEXSYS E580 spectrometer
operating at 33.846 GHz equipped with a Bruker EN 5107D2 resonator
housed in an Oxford Instruments continuous flow cryostat (CF935),
at the University of Padova (Italy). The four-pulse DEER sequence
used was π/2(νobs)−τ–π(νobs)–t′–π(νpump)–(τ + τ2–t′)−π(νobs)−τ2–echo, where the observer pulse length was 24 ns for
π/2 and 48 ns for π pulses; see Supporting Figure 9. The pump pulse length was also 48 ns. The first interpulse
delay (τ) was 300 ns, whereas the
long interpulse delay (τ2) was 2500 ns. The pump
and observer pulses were set on the high-field and low-field shoulder
of the EPR spectrum, respectively. The background was corrected by
a homogeneous three-dimensional exponential, and the distance distributions
were evaluated by either Tikhonov regularization; see Supporting Figure 10.
Data Analysis and Theoretical Prediction of Zn–Zn
Distances
Model-Free Analysis
As a starting point, data were
analyzed using the DeerAnalysis[25] program
developed by Gunnar Jeschke. This program allows the computation of
a model-free distance distribution. The sample is considered as a
collection of nanoobjects, each containing one or two electron spins.
The advantage of DeerAnalysis is that it has been extensively tested
by the EPR community on a large number of real (mostly biological)
samples and is therefore very reliable. The best witting was chosen
on the basis of the L curve criterion.
Monte Carlo Analysis
As opposed to biological samples
where site-directed mutagenesis allows one to precisely and reproducibly
introduce a spin label at specific sites, generating identical copies
of the same protein, the ZSM-5 sample is constituted by a large number
of particles, in which the ZnI ion occupies randomly the
available lattice positions. Therefore, to analyze the experimental
data, we apply a Monte Carlo approach. As a starting point, we used
the X-ray CIF file “ZSM-5, Calcinated” downloaded from
the Database of Zeolite Structures.We considered a ZSM-5 particle
that comprises 4 by 4 by 4 elementary unit cells. This cubic particle
has a maximum dimension, along the diagonal, of ∼25 nm and
is therefore significantly larger than the largest distance detectable
with the experiment, ∼7 nm. We then isolate the spatial coordinates
of the aluminum sites of interest to generate individual data sets
for single sites (T1 through T24), pairs of sites (e.g., T7–T10),
as well as a single data set containing all sites (all Ts). In this
approach, the ZnI···ZnI distances
are considered as the Si···Si distances. Each data
set is treated in the same way to generate a probability distribution
and the corresponding dipolar form factor. Namely, of all sites available
within a data set, we randomly selected a subset which represents
the ZnI occupancy. For the selected sites, we computed
the Euclidean distance between all possible pairs and used these distances
to generate a probability histogram (with an edge resolution of 0.2
Å = 0.02 nm). In order to account for the random distribution
of ZnI sites, the procedure was repeated a large number
of times (20 000) to generate replicas of the system and all
probability distributions summed together to generate a global distribution.
Because of the low occupancy, large distances are overrepresented,
and therefore the computed distance distribution is normalized to
the volume.The form factor is computed by multiplying the relevant
dipolar
trace by the number of counts determined through the Monte Carlo approach
and summing up the individual dipolar traces. This last approximation
holds as the low occupancy and randomness in ZnI distribution
allow one to consider the experimental time trace as the sum of pairwise
dipolar oscillations, not as the product of all possible dipolar traces.Data were analyzed and processed with a home-written MATLAB (The
MathWorks Inc., Natick, MA, USA) script. See also Supporting Figures 11 and 12.
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