NMR Study of Host Structure and Guest Dynamics Investigated with

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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

NMR Study of the Host Structure and Guest Dynamics Investigated with Alkane/Alkene Mixtures in Metal Organic Frameworks ZIF‑8 Dieter Freude,*,† Nina Dvoyashkina,† Sergei S. Arzumanov,‡,§ Daniil I. Kolokolov,‡,§ Alexander G. Stepanov,‡,§ Christian Chmelik,† Hua Jin,∥ Yanshuo Li,∥ Jörg Kärger,† and Jürgen Haase† †

Faculty for Physics and Earth Sciences, Leipzig University, Linnéstr. 5, Leipzig 04103, Germany Boreskov Institute of Catalysis, Siberian Branch of Russian Academy of Sciences, Prospekt Akademika Lavrentieva 5, Novosibirsk 630090, Russia § Novosibirsk State University, Pirogova Str. 2, Novosibirsk 630090, Russia ∥ School of Materials Science and Chemical Engineering, Ningbo University, 818 Fenghua Road, Ningbo 315211, P. R. China

J. Phys. Chem. C Downloaded from pubs.acs.org by UNITED ARAB EMIRATES UNIV on 01/12/19. For personal use only.

‡

ABSTRACT: Within the family of metal−organic frameworks, the zeolite− imidazolate framework (ZIF) of type ZIF-8 is among the most promising materials with potential application for hydrocarbon separation, notably of alkanes and alkenes. We have applied NMR spectroscopy for exploring the interaction of representative alkane/alkene mixtures with the host framework as well as the mobility of the various components in their mixture. Deviating from, for example, the separation patterns known for MFI-based membranes, the mobility of the faster molecules (alkenes) is found to remain essentially unaffected by the presence of more slowly diffusing molecules (alkanes). In addition, 2H and 67Zn magic-angle spinning NMR contributes to the characterization of ZIF-8 in search for guest-induced changes in the lattice structure.

1. INTRODUCTION Heterogeneously catalyzed and biocatalytic reactions are, together with separations, potential applications of metal− organic frameworks (MOFs). There has been remarkable progress in their research activities for 20 years. 1−3 Investigations include the exploration of mass transfer of alkane/alkene mixtures, notably in imidazolate framework 8 (ZIF-8),4,5 which has been proven to show particularly favorable features in this field of application. An investigation of the ethene/ethane mixture diffusion in ZIF-86 by magicangle spinning pulsed field gradient nuclear magnetic resonance (MAS PFG NMR) has shown that the selectivity of the self-diffusion coefficient D is determined as Dethene/ Dethane = 5.5 at a loading of four molecules per cavity. A similar ratio was reported by Mueller et al. for a somewhat smaller loading.7 This strong selectivity observed with ZIF-8 is in remarkable contrast with the behavior of alkane/alkene mixtures in the (non-polar) zeolite silicalite-1. Here, for carbon numbers between two and six, the coefficients of selfdiffusion for alkanes and alkenes did not show any substantial differences.8 This substantial difference in the diffusion patterns can be explained by the difference in the critical diameters of the considered host materials. Whilst, with values between 0.51 and 0.56 nm, the “window” sizes in silicalite-1 notably exceed the critical diameters of the alkanes and alkanes; these guest diameters do, in turn, even exceed the window diameter of 0.34 nm in ZIF-8 as indicated from X-ray diffraction analysis.5 © XXXX American Chemical Society

Guest diffusion of alkanes and alkenes in ZIF-8 is, therefore, only possible in consequence of the lattice flexibility of MOFs quite in general9−11 and of ZIF-8 in particular.12−19 Increase in guest diameters is, therefore, expected to give rise to a dramatic decrease in molecular mobility and, hence, to a decrease in the flux rates through potential separation membranes. Simultaneously, small differences in the diameters of the molecules may give rise to an enhancement in the differences between their diffusivities. Exactly this is the situation when comparing ethene and ethane (with critical diameters of 0.39 and 0.42 nm, respectively)20 with propene and propane (with critical diameters of 0.40 and 0.48 nm, respectively),20 which is mainly considered in the present study. However, separation performance with propane/propene mixtures can be clearly expected to be enhanced in comparison with ethane/ethane mixtures as a consequence of the increasing molecular diameters and hence the differences in the diffusivities; this increase in diameter leads, simultaneously, to decreasing fluxes and hence to a reduction in the separation performance. The investigation of propane/propene mixtures in ZIF-8 has, correspondingly, been in the focus of numerous studies on kinetic uptake,14,21,22 by breakthrough,23 on membranes,24,25 and on mixed-matrix membranes.26,27 Applications of NMR spectroscopy28−31 concern structural investigations of ZIF-8 quite in general. Received: December 4, 2018 Revised: December 22, 2018 Published: December 28, 2018 A

DOI: 10.1021/acs.jpcc.8b11673 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

high-power Bruker probes. 1H MAS NMR spectroscopy was done using a Hahn echo, a 16-phase cycle and a delay of one rotation period (100 μs) between π/2- and π-pulses. 2H and 67 Zn MAS NMR experiments were performed with a single excitation pulse of 1 μs (0 dB attenuation) and 4 μs (6 dB attenuation) at 217.5 and 46.9 MHz, respectively. Chemical shift references correspond to ref 48. One 1H MAS PFG NMR experiment was performed by a stimulated spin-echo sequence with a 5 ms eddy current delay. The sequence consists of 7 radio frequency pulses, two sine-shaped bipolar gradient pulse pairs, and two gradient quench pulses. For details, see ref 8 and its Supporting Information. The same pulse program was used for 1H PFG NMR diffusometry on a spectrometer AVANCE 400. The field gradient was calibrated by a water sample for the MAS PFG NMR probe.8 The self-diffusion coefficient D of water at a temperature of 303 K is D = 2.594 × 10−9 m2 s−1.49 The gradient strength obtained at 100% gradient intensity is 0.54 T m−1 for the MAS PFG NMR probe (AVANCE 750, 10 A gradient current supply) and 21 T m−1 for the static PFG NMR probe PK350 on AVANCE 400 (60 A gradient current supply). PK350 is a low-power homemade probe with a nutation frequency of 20 kHz for 1H measurements. The repetition delay was always longer than the fivefold of the longitudinal relaxation time. We used 5 s for safety of the gradient coils in the case of PFG experiments. Up to 640 accumulations were used for 1H measurements. 2 H MAS NMR experiments request a very accurate setting

Most recent studies were devoted to the synthesis of a MOF with sharpened propene/propane separation32 and an ultramicroporous MOF for the ethylene/ethane separation.33 Recent developments also highlight the option of tuning of this separation by linker exchange,31,34,35 linker stiffening,32 or use of different metal centers.36,37 None of these studies, however, dealt with an investigation of the lattice-induced differences in propene and propane diffusion and, notably, with single-component diffusion measurements in the mixture. Such investigations are in the focus of this study. They have become possible by the application of PFG NMR in combination with “MAS” PFG NMR,38−42 followed by conventional PFG NMR studies43−46 with large field gradient pulses (notably exceeding those applicable under the conditions of MAS PFG NMR). These studies have been accompanied by NMR investigations, including the application of 2H and 67Zn NMR spectroscopy in search for guest-induced changes in the lattice structure.

2. EXPERIMENTAL SECTION 2.1. ZIF-8 Synthesis and Sample Preparation. Three ZIF-8 syntheses were performed following the procedure described in ref 4 but without microwave heating. In the present study, three different specimens of MOF ZIF-8 were under our disposal. They includeboth in small (hundreds of milligrams) quantitiesa deuterated specimen, specially synthesized47 by the use of perdeuterated 2-methylimidazole (2-mIM-d6), and larger-size (with diameters up to 20−50 μm) crystals, which are synthesized in Novosibirsk. These specimens have been applied for specific, spectroscopic measurements including 2H and 67Zn NMR and for 1H MAS PFG NMR. The major part of the measurements, notably all 1H PFG NMR self-diffusion measurements with propane/propene mixtures in ZIF-8, have been performed with crystallites with a size of about 5 μm, synthesized in Ningbo. A microimage of this material is shown in Figure 1.

3 cos2 θmagic − 1

= 0 or of the magic-angle, which is defined as 2 θmagic = arc cos 3−1/2 ≈ 54.7356°. Figure 2 shows that the total

Figure 2. 2H MAS NMR spectra of ZIF-8. 1500 scans with a repetition time of 1 s were acquired for each spectrum. The spectrum consists of the centerband and 32 sidebands. Sidebands have a distance of 10 kHz (≈46 ppm). The upper inlet shows the centerband alone.

Figure 1. Scanning electron microscopy image of the small-crystallite ZIF-8 material applied in the PFG NMR self-diffusion studies.

Prior to NMR measurements, samples were activated at 393 K under high vacuum for 12 h before loading with propane/ propene at room temperature. 1H PFG NMR diffusion measurements were performed with 100 mm high glass tubes with a ZIF-8 bed 5 mm high and an outer diameter of 5 mm. Diffusion measurement via 1H MAS PFG NMR must be performed with notably smaller sample tubes of 12 mm height and an outer diameter of 3 mm. Sealing of such tubes necessitates special care.8 2.2. NMR Measurements. Multinuclear MAS NMR measurements were performed on a Bruker AVANCE 750 spectrometer at 17.6 T with a MAS frequency of 10 kHz and

side band spectrum width is 2785 ppm. The inlet in Figure 2 presents a spectrum width of each of the two signals of about 1.5 ppm. It means for the adjusted angle θ that −1.5 2785

3 cos2 θ − 1

1.5

≤ ≤ 2785 . From this, it follows that the setting 2 of the angle was equal to or better than two hundredths of a degree with respect to the theoretical value arc cos 3−1/2. 2.3. PFG NMR Signal Attenuation. For normal, isotropic diffusion, the self-diffusion coefficient, D, of molecules is obtained from the decay of the relative intensity, ψ(g = 0) = 1, in dependence on the squared field gradient intensity, g2, by the equation41 B


The Journal of Physical Chemistry C ÄÅ ÉÑ ÅÅ i 4δgγ y2 i yzÑÑÑÑ 2δ τ ÅÅ jj 2 z j z jΔ − − − pπ zzÑÑ ψ (g ) = expÅÅ−Dj ÅÅ k π z{ jk 2 3 {ÑÑÑÖ ÅÇ É ÅÄÅ 2 Ñ Ñ ÅÅÅ ijj 4δgγ yzz ÑÑÑ = expÅÅ−Dj Δ′ÑÑ z ÅÅ k π { ÑÑ (1) ÅÇ ÑÖ Here, we have considered the case of a stimulated spin-echo sequence with eddy current delay and two sine-shaped bipolar gradient pulse pairs with the duration δ for a single pulse and the intensity g. The delay τ denotes the time between gradient and radio frequency pulses. The observation time of the diffusion, Δ, is the time span between the start of the two gradient pairs. The corrected observation time, Δ′, is defined by eq 1. The values of Δ′ are only 0.5−1.5 ms shorter than the values Δ. The quantity γ stands for the magnetogyric ratio. In the case of 1H nuclei as considered in the present case, it amounts to γ = 26.7522128 × 107 s−1 T−1.48 The duration of a π pulse is denoted as pπ. Equation 1 is exactly correct only if all molecules contributing to the observed signal do indeed undergo normal diffusion. This is the case if the molecular root mean square displacement l2 during the observation time is sufficiently small in comparison with the mean crystal sizes. Under such conditions, the PFG NMR diffusion experiment may indeed be assumed to be performed in an essentially infinitely largely extended medium. For estimating the root mean square displacement we may, in the given case, make use of Einstein’s equation51−54 l2 =

6D

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3. RESULTS AND DISCUSSION 3.1. NMR Spectroscopy. ZIF-8 samples were characterized by multiple nuclear magnetic resonance spectroscopy. Our previous study6 included 1H MAS, 13C MAS, and 13 C[1H]CP MAS. CP stands for cross polarization. The CP results6 showed only a weak influence of the adsorbed molecule on the ZIF-8 signals, which was explained by a weak interaction between the MOF framework and the adsorbed molecules. The second-order quadrupole broadened 67Zn MAS NMR spectrum is shown in Figure 3. The experimentally obtained

Figure 3. 67Zn MAS NMR spectra of ZIF-8. 25 000 scans with a repetition time of 1 s were acquired for each spectrum. The upper red spectrum shows the unloaded ZIF-8, whereas the lower blue spectrum shows the ethane/ethene-loaded sample in glass ampoules. The loaded sample has a lower signal-to-noise ratio because only about 20 mg ZIF-8 are in the fused glass ampoules, whereas a full rotor contains about 80 mg of the unloaded material.

(2)

where the small difference between Δ and Δ′ has been neglected. With Figure 1, the size of the crystallites applied in the PFG NMR diffusion studies with propane/propene mixtures is seen to be of the order of 5 μm. With the maximum value of D ≈ 2 × 10−12 m2 s−1 as attained in our measurements with propane/propene mixtures in ZIF-8 (namely for propene at 373 K, see Table 1) we end up, via

shift of the center of gravity of a signal, δcg, corresponds to the sum of isotropic chemical shift, δcs, and isotropic quadrupole shift, δiso quad. The latter is about the 0.85-fold of the full width at half-maximum (fwhm), see ref 56 p 1.4. In order to compare our shift values, δcg, with the chemical shift, δcs, in ref 57, we calculate δcs = δcg + fwhm × 0.85/46.9 and obtain δcs ≈ 297 and 294 ppm instead of the above given values for δcg. They are a few ppm higher than the reference value of 291 ppm.57 In conclusion, 67Zn MAS NMR confirmed the tetrahedral Zn coordination. The very small difference between the unloaded and loaded samples is a hint that loading with one molecule ethane plus one molecule ethene per cage does not remarkably influence the coordination of the Zn atoms. 2 H NMR spectroscopy of ZIF-8 was already applied in our (AGS’s) previous work.47 It could be shown that the 2-mIM linkers of the ZIF-8 are very mobile and their mobility is sensitive to the presence of benzene guest molecules. Simultaneously, all loaded and unloaded samples were found to be characterized by almost identical 2H NMR line shapes.47 Here, we present the (first, to the best of our knowledge) 2H MAS NMR spectrum of an unloaded sample ZIF-8. The static (i.e. recorded without MAS) 2H NMR line shape of the identical sample is shown in Figure 1b of ref 47. The 2H MAS NMR spectrum of ZIF-8 (inlet in Figure 2) consists of two well-separated lines at about 7.0 and 2.0 ppm, corresponding to the two CH-groups in the imidazole-ring and to the methylgroup, respectively. A similar 1H MAS NMR spectrum was observed for the unloaded ZIF-8,6 where the signal of the

Table 1. Self-Diffusion Coefficients for the Temperatures 303 and 373 K for a Gradient Pulse Durations of δ = 1 ms and a Diffusion Observation Time of Δ = 40 msa diffusion coefficients (m2 s−1) loading in molecules per cavity 1 1 1 1

propene propene + 1 propane propene + 2 propane propene + 4 propane

T = 303 K 6.02 6.63 7.16 7.04

× × × ×

10−13 10−13 10−13 10−13

T = 373 K 1.50 1.45 1.95 1.67

× × × ×

10−12 10−12 10−12 10−12

a

The accuracy of the values (standard deviation) is in the range between 5 and 10%.

eq 2, with a maximum mean displacement of l2 ≈ 0.7 μm for the maximum observation time Δ = 40 ms. Crystal diameters of about 5 μm are thus found to be completely sufficient for the measurement of genuine intracrystalline self-diffusion coefficients for propane/propene mixtures in ZIF-8. It is true, however, that for PFG NMR diffusion measurements with the much more mobile ethane/ethene mixtures in ZIF-86 and with three-component mixtures55 application of notably larger crystallites (with sizes of 20−50 μm) had been necessary. C


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signal of propene at about 5 ppm, two CH2 signals of propene at about 4 ppm with a difference of 0.1 ppm, a CH3 signal of propene at about 1 ppm, and the CH3 and CH2 signals of propane in the range between 0 and 1 ppm. Chemical shift values for propane and propene in different solvents can be found in ref 60. Signals of molecules adsorbed in ZIF-8 have a susceptibility shift of −0.55 ppm with respect to signals in the gas phase.6 Spinning sidebands are outside of the region displayed in Figure 4 and contain mainly signals of the CH and CH3 groups of ZIF-8. We expect for the 1:1 loading a signal intensity ratio of 8/6 due to the number of hydrogen atoms in the molecules. However, we see in the spectrum on the bottom that the signal intensity of propane is about half the intensity of echo propene signals. The transverse relaxation time TMAS , the 2 time constant of the Hahn echo decay under MAS conditions, is shorter for propane than for propene. This causes weaker propane signal for the spectrum on the bottom. However, the MAS PFG NMR signal of propane on the top decays within 10 ms (four gradient pulses of 2 ms duration and spacing in between) to 1/40. This is notably different from the decay of 1/5 as observed with propene. Therefore, the relative intensity of propane is about 1 order of magnitude lower than for propene in the MAS PFG NMR spectrum of Figure 4. In addition, even the maximum gradient intensity of 0.5 T m−1 as attainable in our MAS PFG NMR experiments is seen to be still too small to attain any signal attenuation, excluding the option of MAS NMR diffusion studies with propane/propene mixtures in ZIF-8. We continue with an estimate of the measuring conditions with “ordinary” PFG NMR, that is, without the application of MAS. Here, the increase in gradient intensity (from 0.5 up to 14.4 T m−1) has to be purchased by a decrease in the echo echo decay from TMAS to Techo and, hence, by a decrease in the 2 2 time over which the (notably stronger) PFGs may be applied. We start with a simple Techo measurement for propane in 2 ZIF-8 by means of a Hahn echo. From the spectra shown in Figure 5, a value of Techo ≈ 300 μs can be derived. A similar 2

methyl groups was slightly broader and the intensity ratio between two CH and three CH3 protons was 2/3, as expected. The residual hydrogen atoms of the present deuterated ZIF-8 yield a similar 1H MAS NMR spectrum (not shown here) with the expected ratio 2/3 between CH and CH3 protons. The upper inlet in Figure 2 shows, in the centerband, a ratio of about 1/5 between CD and CD3 deuterium atoms. The simulation of the whole sideband spectrum by the dmfit58 program yielded the following parameters for the two signals: the CD signal at about 7.0 ppm has a linewidth fwhm = 0.74 ppm, a quadrupole coupling constant CQ = 187 kHz and an asymmetry parameter of the electric field gradient of η = 0.07. The CD3 signal at about 2.0 ppm has a linewidth fwhm = 0.62 ppm, a quadrupole coupling constant CQ = 50 kHz, and an asymmetry parameter of the electric field gradient of η = 0.23. Different values of CQ explain why the CD signal is underrepresented in the centerband. The CD signal intensity is correspondingly overrepresented in the outer spinning sidebands. CQ = 187 kHz and η = 0.07 agree well with the values of 185 kHz and η = 0.08, which were obtained for the fit of the static (2H NMR) CD signal of the MeOH loaded ZIF-8 at ambient temperature, see Figure 2 in ref 47. There, the quadrupole parameters were discussed in dependence on the temperature,47 and results about the mobility of the 2-methylimidazolate linkers were obtained without application of MAS. The present study shows that the 2H MAS NMR spectrum of ZIF-8 allows the separate simulation of two well-resolved signals with a better signal-to-noise ratio. The latter comes from the fact that the signal intensity (area under the line) of a broad static spectrum is transferred into narrow signal peaks of the MAS sideband spectrum. 3.2. NMR Diffusometry. Figure 4 shows 1H MAS NMR and 1H MAS PFG NMR spectra of ZIF-8 loaded with a 1:1 mixture of propane and propene at an overall concentration of less than one molecule per cavity.59 The 1H MAS NMR spectrum consists of two broader signals of the CH and CH3 groups of ZIF-8 at about 7 and 2 ppm, respectively, a CH

Figure 5. Fourier transform of the Hahn echo of a propane-loaded ZIF-8 (less than one molecule per cavity) at 373 K. The pulse distance of the echo sequence increases from 100 (top) to 200 μs, 500 ≈ 300 μs can be determined μs, and 1 ms (bottom). A value Techo 2 from the signal decay.59 Figure 4. 1H MAS NMR spectrum and 1H MAS PFG NMR spectrum (inlet) of ZIF-8 loaded with a 1:1 mixture of propane and propene at room temperature. The MAS frequency was 10 kHz. A Hahn-echo pulse sequence with 100 μs pulse distance was used for the 1H MAS NMR spectrum on the bottom. The 1H MAS PFG NMR spectrum (inlet on the top) was measured by a stimulated spin-echo sequence with eddy current delay, two sine-shaped bipolar gradient pulse pairs, and two gradient quench pulses. The gradient intensity varied linearly between 0.05 and 0.5 T m−1, the gradient pulse width was 2 ms, and the diffusion observation time was 100 ms.59 Below the spectrum, the origin of the various lines is indicated.

measurement for a propene-loaded sample of ZIF-8 yields = 7 ms.59 Our PFG NMR measurements are typically Techo 2 performed with alternating gradients of 1 ms duration, with included eddy current delays.41,55,61 This adds up to a total of 5 ms during which nuclear magnetization is oriented perpendicular to the external magnetic field. During this time, signal intensity is subject to attenuation with the time −5/0.3 constant Techo ≈ 10−7 for 2 , yielding an attenuation of e −5/7 propane and of e ≈ 0.5 for propene. The contribution of the propane molecules in propane/propene mixtures in ZIF-8 D


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The Journal of Physical Chemistry C to the signal of 1H PFG NMR is thus found to be far too small for being observable. Propene molecules in this mixture, however, are expected to be accessible by selective diffusion measurement. Figure 6 shows a typical 1H PFG NMR spectrum for propene in a propane/propene mixtures adsorbed in ZIF-8. In

both the table and the graphical representation, propene selfdiffusion is seen to be, within the given temperature and concentration range, essentially unaffected by the presence of co-adsorbed propane molecules. Similar findings have already been reported for ethane and ethene in ZIF-8, where a negligible difference between unary and mixture diffusivities was found.7,22,62 It is remarkable that now a similar trend was found for the C3-hydrocarbons despite an about 25 times higher difference in the olefin and paraffin diffusivities compared to ethene and ethane. Temperature enhancement from 303 to 373 K leads to diffusivity enhancement by about a factor of 3, once again essentially unaffected by the presence of propane molecules. The observed diffusivity enhancement with increasing temperature is in fair agreement with the predictions based on dynamically corrected transition state theory (TST)17 and corresponds with an activation energy of (11 ± 2) kJ mol−1. This value can be compared with an activation energy of about 30 kJ mol−1 (ref 63 and Figure 16.7 in ref 53) determined for propene in zeolite DDR whose critical pore size of 0.366 nm does even notably exceed that of ZIF-8 (0.34 nm).64 This “anomaly” in the trend of the activation energy nicely illustrates the flexibility-related reduction of the resistance during molecular passages between adjacent cavities in ZIF-8 in comparison with the much more rigid lattice of zeolite DDR. This finding, simultaneously, nicely confirms the suitability of the model of translational motion inherent to the application of TST, implying that the rate of molecular propagation is controlled by passages through the 6-membered rings connecting the big cavities. This influence notably exceeds any drag effects experienced by the interaction with the co-adsorbed molecules. The decisive role of molecular passages through the “windows” between adjacent cavities on overall mass transfer does appear in the observation that the propene diffusivities in ZIF-8 remain essentially independent of the presence of the co-adsorbed (and significantly less mobile) propane molecules. In fact, in numerous studies of multicomponent systems adsorbed in nanoporous materials, the diffusivity of the faster component was found to be reduced by the presence of a less mobile component, opposite to the behavior observed with propene and propane in ZIF-8. Examples include mixtures of n-heptane and benzene,66 ethane and ethene67 and CF4 and nbutane68 in NaX, of methane and ammonia/pyridine,69 methane and xenon,70 and n-butane and isobutane41 in MFI, excluding a sufficiently accurate prediction of membrane

Figure 6. 1H PFG NMR spectrum of ZIF-8 loaded with one molecule propene and four molecules propane per cavity. The measurement was performed at 373 K with gradient pulse durations of δ = 1 ms and a diffusion observation time of Δ = 40 ms. The gradient intensity varied linearly between 0.04 and 14.4 T m−1.

complete agreement with the estimate given in the previous paragraph, propane is seen to give no contribution to the signal. Only two signals, with a mutual distance of 3.5 ppm, can be observed. This is the inevitable consequence of the decrease in resolution in comparison with MAS NMR where, in Figure 4, for the CH2 signal a resolution of 0.1 ppm has been shown to be attained. The signal at about 1 ppm corresponds to the CH3 groups, whereas the signal at about 4.5 ppm is the superposition of the CH2 and the CH signals. In Figure 6, the total intensity of the two lines (area under the lines) is found to decay from 100% at 0.04 T m−1 to 21.5% at 14.4 T m−1. There is no substantial difference in the attenuation patterns of the two lines. This is the behavior expected following the prediction given by eq 1. Both lines belong to one and the same molecule, namely, to propene, and are, thus, subject to also one and the same diffusivity. A summary of the self-diffusion coefficients obtained in this study is provided in Table 1. Figure 7 compares these results with the outcome of recent single-component measurements with propene in ZIF-8 by single-crystal microimaging.22 In

Figure 7. (a) Self-diffusivities D of propene (at a loading of one molecule per cage) at 298 K with varying concentrations of co-adsorbed propane in ZIF-8 as determined via PFG NMR. All data are presented as a function of overall loading, that is, of the number of propene and (if present) propane molecules. (b) Coefficients of transport diffusion DT and the “corrected” diffusivity D0 of propene determined in single-component uptake measurements by IR imaging at 298 K. The measured diffusivities are compared with the prediction of their concentration dependences via TST (full lines).65 One molecule per cage corresponds to two molecules per u.c. or to 31 and 32 mg loading per g ZIF-8 for propene and propane, respectively. E


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this order of magnitude is relatively small in comparison with the usual outcome of comparative studies with seemingly identical systems under application of different measuring techniques and different samples.78,79 They are, commonly, referred to the differences in the investigated samples (caused by differences in their synthesis and/or pretreatment) which, quite often, appear much more distinctly in their transport patterns than in their structural properties.80 In the present case, on comparing the results of PFG NMR investigations of intracrystalline diffusion with uptake measurements, one has to be aware that the latter process may, additionally, be retarded by the influence of surface resistances. In such cases, “diffusivities” as deduced from uptake measurements must indeed be expected to be exceeded by the intracrystalline diffusivities determined by PFG NMR. If such surface resistances are caused by the formation of an essentially impermeable outer layer with dispersed holes,81−83 overall uptake and release may indeed be found to scale with the genuine intracrystalline diffusivity, reduced by a factor exclusively determined by the relative density and the extension of the “holes” within the surface layer.

selectivities on the basis of only the single-component permeabilities.71−73 However, in all these systems the pore space diameter as “perceived” by the diffusing molecules is only smoothly varying. As a consequence, more slowly diffusing molecules may in fact be expected to impede the diffusivity of the faster ones. The existence of “narrow windows” to be overcome by the propene and propane molecules in ZIF-8 gives rise to a completely different situation, where the passage through these windows is easily recognized as the decisive step in the overall mass transfer. For such a situation, following the reasoning of the classical conception of TST,74,75 the concentration dependence of the self-diffusivity has been suggested65 to be given, as a first-order estimate, by the relation D(c) = D(c = 0) ×

kp(c) c

(3)

with p(c) denoting the partial pressure of the molecule under study in the surrounding atmosphere for keeping its intracrystalline concentration at c and with k denoting the Henry constant, that is, the value of c for vanishing concentration c. p(c)

4. CONCLUSIONS NMR spectroscopy was applied for investigating the intracrystalline diffusivity of propene with co-adsorbed propane in MOFs of type ZIF-8. Propene diffusivities were found to be essentially independent of the presence of the propane molecules, providing ideal conditions for estimating the performance of propane/propene separation by ZIF-8 membranes on the basis of single-component permeation measurements. The activation energy of propene diffusion in ZIF-8 is found to be by a factor of about 3 smaller than in zeolite DDR, though the “window” diameters in ZIF-8 (0.34) as indicated from X-ray diffraction structure analysis are notably below those in zeolite DDR (0.366 nm). This “anomaly” nicely illustrates the effect of the flexibility of the host lattice for enhancement of the guest mobility in MOF ZIF-8. Accompanying 2H and 67Zn MAS NMR measurements gave little information about the influence of the presence of guest molecules on structural features of the host lattice, notably on the imidazolate linkers and the transition metal in their coordination center. Measurements of this type have, to the best of our knowledge, never been performed before. The 2H MAS NMR spectrum is superior to the static 2H NMR spectrum because the deconvolution into two signals is simpler and the signal-to-noise ratio is higher. However, we do not expect more information than the previous static 2H NMR studies.47 The strong deuteration can also change the nature of the ZIF-8. 67Zn MAS NMR spectra compare an unloaded ZIF8 and a loading with one molecule ethane plus one molecule ethene per cage. Result of the comparison of the noisy spectra is that the presence of the guest molecules does not give rise to a remarkable change of the tetrahedral structure.

This equation could indeed be shown to reproduce the concentration dependence of the diffusivities obtained via microimaging for a series of short-chain-length hydrocarbons in ZIF-8 under the conditions of single-component adsorption.22 In ref 76, eq 3 was shown to even correctly predict the concentration dependence of the diffusivities of the individual components during two-component adsorption of CO2/ethane and ethane/propene mixtures in zeolite DDR. Figure 7 shows, in addition to the self-diffusivities determined in this study, the transport diffusivity (DT, defined by Fick’s first law as the factor of proportionality between diffusive flux and concentration dln c gradient) and the “corrected diffusivities”, D0 ≡ DT dln p . The value D0 coincides with the self-diffusivities under TST conditions54,65 obtained in ref 22 for propene in ZIF-8 by uptake measurement via IR microimaging, jointly with their predictions based on TST. Furthermore, molecular simulations with dynamically corrected TST while maintaining full flexibility of the MOF framework have been successfully applied to predict diffusivities in ZIF-8 for various molecules at different temperatures.17 We note that, within the frame of TST, it is not unexpected that the presence of co-adsorbed propane molecules (if, as a first-order estimate, their influence is implied to be similar to that of propene) does not notably affect the propene diffusivities as investigated in our PFG NMR diffusion studies. A notable deviation from the predicted trend is only observable for the highest overall loading, with four propane molecules in total, where the measured propene self-diffusivity remains below their estimate. This, however, might be related to the severe simplifications inherent to the TST model here used in its simplest form. Because the window passages are well-known to be affected by the presence of linkers whose mobility is affected by molecules in their vicinity,11,17,31,32,37,47,77 it cannot be excluded that the increase in diffusivity with further increasing loading following eq 3 is compensated by a linkerinduced decrease in the transition rate.17,18 On comparing the results of the present investigations shown in Figure 7a with those of previous measurements in Figure 7b, we are, moreover, confronted with a difference in the absolute values by about a factor of three. A difference of

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone +49 341 97 32503. ORCID

Dieter Freude: 0000-0002-1814-3486 Sergei S. Arzumanov: 0000-0001-7358-3364 Daniil I. Kolokolov: 0000-0002-1434-095X F


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Alexander G. Stepanov: 0000-0003-2754-5273 Hua Jin: 0000-0001-5814-9607 Yanshuo Li: 0000-0002-7722-7962 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Deutsche Forschungsgemeinschaft (grant HA 1893/16), and S.S.A., D.I.K., and A.G.S. were supported by the Russian Academy of Science within the framework of budget project no. AAAA-A17-117041710084-2 for Boreskov Institute of Catalysis.

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