Microporous and Mesoporous Materials

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1 Microporous and Mesoporous Materials 147 (2012) Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: Ethene/ethane mixture diffusion in the MOF sieve ZIF-8 studied by MAS PFG NMR diffusometry Christian Chmelik a,, Dieter Freude a, Helge Bux b, Jürgen Haase a a Fakultät für Physik und Geowissenschaften der Universität Leipzig, Linnéstr. 5, Leipzig, Germany b Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, Hannover, Germany article info abstract Article history: Received 18 April 2011 Received in revised form 31 May 2011 Accepted 6 June 2011 Available online 13 June 2011 Keywords: NMR MAS PFG NMR Diffusion ZIF-8 Ethane The adsorption and diffusion of ethene/ethane mixtures is explored by 1 H and 13 C MAS NMR spectroscopy and by the combination of PFG NMR with magic-angle spinning (MAS PFG NMR). Some indication for a preferential adsorption of the molecules close to the methyl-groups of the imidazole-rings was found, however no evidence for structural changes upon adsorption of an ethene/ethane mixture. MAS PFG NMR allows an individual but simultaneous observation of both molecules in adsorbed state and as well as in the gas phase. The intracrystalline MAS PFG NMR diffusivities are in consistent agreement with our previous data obtained by IR microscopy. Our consideration includes the loading dependence and the correlation of self-diffusion with transport diffusion by accounting for the influence of the thermodynamic factor. The diffusion selectivity is determined to D ethene :D ethane = 5.5 at a loading of four molecules per cavity. The higher mobility of ethene can be rationalized by its smaller size compared to ethane. This conclusion is validated by the measured activation energies for diffusion which are considerably higher for ethane. On the other hand, differences in the guest host interaction between the saturated and non-saturated molecules can be excluded as possible reason for the different diffusivities. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction Potential applications in storage, separations, and catalysis caused a remarkable progress of research activities on metal organic frameworks (MOFs) [1 3]. The mass transfer of molecular mixtures inside the nanopores and through the outer surface is essential for the applicability of the particular system which is zeolitic imidazolate framework 8 (ZIF-8) [4 6] in the present study. Direct access to the transfer through the outer surface and the mobility in the framework was obtained by our previous IR and interference microscopic investigations [7]. It could be shown that the self-diffusivity exceeds the transport diffusivity if molecular clustering dominates the molecular mobility. For the understanding of the molecular transport detailed information about the self-diffusion of the adsorbed molecules are needed. An established experimental technique for measuring self-diffusivities in porous materials is the pulsed field gradient nuclear magnetic resonance (PFG NMR) [8,9]. Usually, the NMR signal of adsorbed molecules is broadened due to heterogeneities in the magnetic susceptibility of the host material and by the restricted molecular mobility which, in turn, Corresponding author. Tel.: ; fax: address: chmelik@physik.uni-leipzig.de (C. Chmelik). reduces the spectroscopic resolution of PFG NMR. This drawback can be overcome by the combination of PFG NMR with magic-angle spinning (MAS PFG NMR). The increase of the spectroscopic resolution by MAS narrowing allows to monitor the diffusion of different components of a mixture simultaneously, as we could demonstrate in previous studies with zeolites [10] and mesoporous materials [11]. Gratz et al. have recently used this technique to study the diffusion in a MOF system, viz. of n-hexane and benzene in MOF-5 [12]. One of the major differences of MOFs compared to classical nanoporous materials, such as zeolites, is the flexibility of the host lattice. Also for the new MOF subclass of ZIFs (zeolitic imidazolate frameworks) such effects were reported. Gücüyner et al. [13] found a gate-opening effect upon adsorption of an ethene/ethane mixture on ZIF-7. Although a similar effect was not observed in recent permeation measurements through a ZIF-8 membrane for this mixture, the existence of a structural change upon adsorption cannot be ruled out in general. Indeed, diffusion measurements with methane in giant ZIF-8 crystals revealed a particular strong increase in the molecular mobility which might be explained with structural transitions [14]. Recent studies using molecular simulations further emphasize the importance of framework flexibility for the adsorption and the transport of molecules in ZIF-8 [15,16]. Though not understood in detail, the occurrence of framework changes is closely related to the local distribution of adsorbed /$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi: /j.micromeso

2 136 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) molecules. The position of adsorbed molecules within a ZIF-8 cavity has already been discussed to some extend in the literature. Wu et al. [17] claim that at low temperatures the strongest adsorption sites of methane are directly associated with the organic linkers, instead of the ZnN 4 clusters of ZIF-8. Preferred locations in the surrounding of the linkers were also reported in several studies using molecular simulations [14 20]. In the present study we apply 1 H MAS PFG NMR to investigate mixture diffusion of ethene/ethane in MOF ZIF-8. In addition, we use 13 C MAS NMR spectroscopy to seek for a direct experimental evidence of framework flexibility or structural changes upon adsorption and for preferential adsorption sites. 2. Experimental 2.1. Synthesis Multiple batches of ZIF-8 crystals were typically prepared as following: g zinc chloride (>99% Merck), g 2-methylimidazole (>99%, Sigma Aldrich), and g sodium formate (>99%, Sigma Aldrich) were solved by ultra-sonic in 70 ml methanol (99.9%, Roth), respectively yielding in a molar ratio of 1:1:0.5:500. The solution then was heated within a steel mantled PFTE autoclave (Parr Instruments) to 413 K by convectional heating for 20 h. After cooling to ambient temperature, light yellowcolored, crystalline material was separated from solution by filtration. Additional crystals were carefully collected from the autoclave walls and combined with the bulk. The crystals were intensively washed with methanol, dried at 338 K under air for 12 h, and subsequently sieved by a steel mesh of 50 lm mesh width (Haver and Boecker). The retained crystals with sizes >50 lm were used for our experiments. The XRD pattern is shown in the Supplementary material Sample preparation One ZIF-8 sample was measured by 1 H and 13 C CP MAS NMR in the as-synthesized form. The mixture-loaded samples were prepared by heating 15 mg of ZIF-8 in glass tubes of 3 mm outer diameter. The temperature was increased under vacuum with a rate of 10 K h 1. The samples were maintained at 393 K for 24 h under vacuum (less than 10 2 Pa). Based on the sample weight and the atomic composition the number of the guest molecules to reach a certain loading was calculated. Then the crystals were volumetrically loaded (defined volume of adsorption gas at an adjusted pressure for a weighted mass of the MOF material) first with ethene then with ethane by freezing with liquid nitrogen. After that the glass tubes (8 mm length) were sealed off. Two loadings were prepared: two molecules ethene plus two molecules ethane and four molecules ethene plus four molecules ethane per cavity. The latter fills nearly 80% of the adsorption volume of the ZIF-8 cavities [21]. The loading of the sealed samples was verified by 1 H MAS NMR comparing the signals of the adsorbed molecules with the signals of the ZIF-8 framework and with a test sample. The mass per cavity (one unit cell consists of two cavities) needed for the determination of the amount to load was calculated as following. ZIF-8 is the ZIF-analog of the sodalite (SOD) structure. The truncated octahedron, as structure building unit (SBU) of the SOD structure, consists of 24 vertices and 36 edges. In the SOD structure every cage is connected with its neighbors by face-sharing, and accordingly each cavity consists of 6 Zn 2+ and 12 mim 1 (C 4 H 5 N 2 ) yielding in a mass of 1365 g per mole cavities. Fig. 1. Stimulated-echo sequence with bipolar sine-gradient pulses and eddy current delay before detection NMR measurements NMR measurements were performed on a Bruker AVANCE 750 spectrometer with wide-bore magnet (17.6 T). The MAS frequency was m rot = 10 khz, if not noted otherwise. The 10-kHz rotation of a 4-mm-rotor increases the temperature within the rotor by 10 with respect to the detected temperature of the air flow outside the rotor [22]. The temperatures of measurements given below are sample temperatures within the rotor. The external magnetic field was calibrated by means of the 1 H MAS NMR signal of highly viscose polydimethyl siloxane (PDMS) with a chemical shift of 0.07 ppm in a spinning rotor (external standard). 1 H MAS NMR spectroscopy was performed with a single-pulse excitation. 13 C MAS NMR spectroscopy was carried out with 1 H cross-polarization (CP) by a 1.5-db Hartman Hahn ramp (duration 5 ms) or without CP. Proton decoupling was done by spinal 64 [23]. A 4-mm-MAS-probe with pulsed field gradient capabilities (maximum gradient strength 0.54 T m 1 ) and a maximum radio frequency (rf) power of m rf = 100 khz was used for diffusion measurements on the 750-MHz-Spectrometer. A stimulated-echo sequence with bipolar sine-gradient pulses and eddy current delay [24,25] was applied, see Fig. 1. The signal attenuation for singlecomponent isotropic diffusion is given by [25] " W ¼ S ¼ exp D 4dgc 2 D s # 2d S o p 2 3 p p The sequence for alternating sine shaped gradient pulses and longitudinal eddy current delay (LED), see Fig. 1, consists of seven rf pulses, four magnetic field gradient pulses of duration d and intensity g, and two eddy current quench pulses. We used a gradient pulse duration of d = 2 ms and a p-pulse length p p =5ls, an observation time of D = 200 ms, a delay between gradient and rf pulses s = 0.5 ms, and an eddy current delay s ecd = 4.5 ms. The repetition delay was 5 s and much longer than the longitudinal relaxation time T 1, which has a length of about 1 s. The gradient pulse strength was varied between 0.05 and 0.5 T m 1. The duration of observation time, gradient pulse duration and the spacing between gradient pulses were multiples of the rotation period of 100 ls. Diffusion measurements of the gas phase molecules in the inter-crystalline space were performed by a Hahn echo, two 500- ls gradient pulses and a 10-ms distance between the two rf pulses. The observation time, D, determines the diffusion path lengths. It should be shorter than the longitudinal relaxation time (about 1 s for the samples under study), but can be varied, in order to obtain a verification that the diffusion data are not distorted by unwanted effects related to susceptibility differences, small movements of particles under MAS conditions or diffusion barriers. We varied D from 20 to 200 ms and did not find a significant difference of the obtained diffusion coefficients. But the accuracy of the determination of D decreases with smaller values of D, since the signal attenuation by gradients becomes lower, e.g. only 15% for D = 20 ms. Therefore, we used D = 200 ms for our measurements. ð1þ

3 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) Fig H MAS NMR spectrum of the as-synthesized ZIF-8 sample measured at a Larmor frequency of 750 MHz, a MAS frequency of 17 khz and a sample temperature of 322 K. Asterisks denote spinning side bands. 3. Results Fig. 2 shows the 1 H MAS NMR spectrum of the as-synthesized ZIF-8 sample. We note only two signals from the ZIF-8 framework: The signals at 7.0 and 2.1 ppm correspond to the two CH-groups in the imidazole-ring and to the methyl-group, respectively. The signal of the methyl-groups is slightly broader and the intensity ratio between two CH and three CH 3 protons is 2/3 as expected. Three signals can be observed as expected in the 13 C CP MAS NMR spectra, see Fig. 3. The signal at about 150 ppm corresponds to the carbon atom between the two nitrogen atoms in the imidazole-ring. At 123 ppm we see the signal of the CH-groups, and at about 12 ppm appears the methyl-signal. For loaded MOFs no additional signals in the CP spectrum arise, since the cross-polarization is negligible for very mobile molecules. The inlet in Fig. 3 shows the changes between the non-loaded and fully loaded sample. The signal at 123 ppm does not change the chemical shift. (It is narrower in the loaded sample, since loading with mobile molecules increases the proton decoupling.) But the signal of the carbon atom in the ring between the nitrogen atoms and the signal of the connected methyl-group are slightly shifted upon loading: from 12.3 to 12.5 ppm and from to ppm for methyl-carbon and ring-carbon, respectively. Fig. 4 presents the 13 C MAS NMR spectrum of ZIF-8 loaded with four ethene and four ethane molecules per cavity. The absent cross-polarization reduces the signal-to-noise ratio compared to Fig. 3. However, signals of the adsorbed molecules are visible now. Similar to Fig. 3a we see in Fig. 4 signals at about 150 ppm ( ring-carbon atom between two nitrogen atoms), at about 123 ppm (CH-groups), and at about 12 ppm (methyl-groups). The signals of the adsorbed molecules appear at and 4.2 ppm Fig C MAS NMR proton decoupled spectrum of the ZIF-8 sample loaded with four ethene and four ethane molecules per cavity. The spectrum was measured at a Larmor frequency of 188 MHz, a MAS frequency of 10 khz and a sample temperature of 303 K. Asterisks denote spinning side bands. and contributions from the gas phase molecules arise at and 2.5 ppm for ethene and ethane, respectively. They have an intensity of about 10% with respect to the signals of the adsorbed molecules. Two well-resolved signals for both, ethene and ethane molecules, can be observed in the corresponding 1 H MAS NMR spectrum. Fig. 5 shows, like Fig. 2, the two very broad signals of the ZIF-8 framework at about 7 and 2 ppm. Two very narrow signals are observed at 5.0 and 0.6 ppm, which are related to ethene and ethane molecules in the gas phase. Broader signals with a line width of about 0.2 ppm appear at 4.5 and 0 ppm caused by adsorbed ethene and ethane molecules, respectively. The spectrum in Fig. 5 was measured by means of a Hahn-echo with a pulse delay of one MAS period (100 ls). The intensity of the broad lines is reduced in the echo-signal. Nevertheless, the intensities of the sig- Fig H MAS NMR spectrum of a ZIF-8 sample loaded with two ethene and two ethane molecules per cavity. The spectrum was measured at a Larmor frequency of about 750 MHz by means of a Hahn-echo pulse sequence with a pulse distance of 100 ls. The sample temperature was 303 K. Fig C CP MAS NMR spectrum of the non-loaded (dotted line) ZIF-8 sample and the sample loaded with four molecules ethene plus four molecules ethane per cavity (solid line). Spectra were measured at a Larmor frequency of 188 MHz, a MAS frequency of 10 khz and a sample temperature of 303 K. Asterisks denote spinning side bands. The inlets increase the chemical shift scale by a factor of 10. Fig H MAS NMR spectrum of a ZIF-8 sample (smaller filling of the glass tube) loaded with two ethene and two ethane molecules per cavity. The spectrum was measured at a Larmor frequency of about 750 MHz by means of a Hahn-echo pulse sequence with a pulse distance of 10 ms with two mono-polar gradient pulses (after the rf pulses) with a duration of 500 ls and different intensities. The sample temperature was 303 K.

4 138 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) D T or D / m 2 s ethene ethane Fig H MAS PFG NMR spectrum of ZIF-8 loaded with two ethene and two ethane molecules per cavity. The spectrum was measured at a Larmor frequency of about 750 MHz by means of the pulse sequence presented in Fig. 1. The gradient pulse duration and observation time were 2 ms and 200 ms, respectively. The gradient intensity was varied between 0.05 and 0.5 T m 1. The sample temperature was 363 K. Fig. 8. Decay of the ethene and ethane signals in one of the 1 H MAS PFG NMR spectra of the ZIF-8 loaded with two ethene and two ethane molecules per cavity measured at the temperature of 363 K. nals from both molecules can be compared: we find that about 15% of the molecules are located in the gas phase. Fig. 6 shows on the top a spectrum similar to Fig. 5. The rf pulse distance of the Hahn echo is now considerably longer (10 ms). Therefore, the broad framework signals disappeared. The amount of MOF in the glass tube is less, and thus the intensities of the gas phase signals increased. The ratio between ethene and ethane molecules in the sample is one, but about 40% of the ethene molecules and 30% of the ethane molecules are in the gas phase, respectively. The gas phase signals are decreasing under the influence of weak field gradients (with a duration of the mono-polar gradient pulses of 0.5 ms), whereas the intensities of the signals of the adsorbed molecules remain unaffected. An equation similar to Eq. (1) was utilized (2d was substituted by d for single mono-polar gradient pulses), in order to determine the self-diffusion coefficient D c / molecules per cage Fig. 9. Transport diffusion coefficients D T (triangles in the figure) which were derived in dependence on the concentration c of molecule mixtures ethene/ethane or single-component molecules from gas sorption uptake experiments by infra-red microscopy, IRM, on a large single crystal (300 lm size) at the temperature of 298 K [7,21]. Open and solid triangles denote the mixtures and single-components, respectively. Inverted and upright triangles denote ethene and ethane, respectively. The ethene/ethane ratios in the gas mixtures are 1/1.5 and 1.9/1. The latter ratio is denoted by upright bars in the open triangles. The concentration c corresponds to the sum of ethene plus ethane molecules per cage. Solid pentagons on the bottom denote the self-diffusion coefficient of ethane determined by tracer IR microscopy [7]. Solid asterisks (ethene) and solid spheres (ethane) at c = 4 and c = 8 mixture molecules per cage were taken from the MAS PFG NMR data in Table 1 for 283 and 303 K. See also the Supplementary material for more details. of the molecules in the gas phase. We obtain D = m 2 s 1 for both, the ethene and ethane, gas phase diffusivities. For the diffusion measurements of the adsorbed molecules we applied longer gradient pulse durations and longer observation times. Therefore, no gas phase signals are present in these spectra even for the weakest applied gradient of 0.05 T m 1. Fig. 7 shows a typical two-dimensional spectrum with the pulsed field gradient strength in the second dimension. The signal decay with increasing strength of the field gradient pulses is stronger for the ethene signal at 4.5 ppm than for the ethane signal at 0 ppm. Fig. 8 shows the decay w = S/S 0, see Eq. (1), for both signals. The self-diffusion coefficients were determined from the slope of the dotted lines in Fig. 8 to 1.21 and m 2 s 1 for ethene and ethane, respectively. Table 1 gives the values of the selfdiffusion coefficients in dependence on the temperature. Apparent activation energies, E a, can be determined from the values in Table 1 by means of an Arrhenius plot, D ¼ D 0 expð Ea Þ. RT In the range of 283 and 363 K we estimate E a to 6.6 and 4.9 kj mol 1 for lower and higher loading of ethene, respectively. The values for ethane are significantly higher, 9.6 and 8.6 kj mol 1 for lower and higher loading, respectively. The pre-exponential factor, D 0, is in the range m 2 s 1 for all molecules and loadings. In Fig. 9, the mixture MAS PFG NMR self-diffusivities of ethene (stars) and ethane (circles) at 283 K (black) and 303 K (gray) are compared to transport diffusivities by IR microscopy at 298 K (ethane: red upright triangles; ethene: blue inverted triangles). The IR data were obtained on large ZIF-8 single crystals (size ca. 300 lm) Table 1 Self-diffusion coefficients, D, of molecules in two mixtures of ethene and ethane molecules adsorbed in MOF ZIF-8 in dependence on the temperature. D is given in units of m 2 s 1 and has a variance of ±10%. Loading per cavityntemperature 283 K 303 K 323 K 343 K 363 K D (ethene) (10 10 m 2 s 1 ) 2 Ethene + 2 ethane D (ethane) (10 10 m 2 s 1 ) 2 Ethene + 2 ethane D (ethene) (10 10 m 2 s 1 ) 4 Ethene + 4 ethane D (ethane) (10 10 m 2 s 1 ) 4 Ethene + 4 ethane

5 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) [7,21], grown in an optimized synthesis [21]. IR transport diffusivities of the single-components are represented by the solid triangles, whereas the open triangles and the ones with bar correspond to two different mixture compositions. In addition, IR single-component self-diffusivities of ethane from tracer-exchange measurements [7] are displayed in the graph (solid pentagons). All diffusivities are plotted over the total loading. 4. Discussion We can conclude from the solid-state NMR spectra in Figs. 2 and 3 that there are no by-products or compounds with different shortrange order in the synthesis products of ZIF-8. The spectra were obtained with very high signal-to-noise ratios. All observed signals correspond to the molecular components of ZIF-8. Signals which are caused by framework defects, different phases or by-products do not appear. The 1 H MAS NMR spectra of the ethene/ethane mixture on ZIF-8 show signals from the adsorbed molecules at 4.5 and 0.0 ppm and signals from the gas phase molecules at 5.0 and 0.6 ppm for ethene and ethane molecules, respectively. The values 5.28 and 0.86 ppm are given in the literature for CDCl3-diluted molecules ethene and ethane, respectively, see [26]. The shift difference between adsorbed and gas phase molecules amounts to 0.55 ± 0.05 ppm, see Fig. 5, and can be explained by a weak interaction of the molecular electron shell with the MOF framework. There is no significant difference in the resulting shielding effect for the hydrogen atoms in the ethene and ethane molecules. The exchange between gas phase and adsorbed molecules is relatively slow. The distance between the corresponding well-resolved signals is about 400 Hz. It means that the exchange rate between the two states of molecules is much smaller than 400 Hz. This fact is in agreement with the mean residence time s of a molecule in ZIF-8 particle with a diameter d >50lm, which can be estimated by the equation s ¼ d 2 =60D from the self-diffusion coefficient, see Eq. (13) in [8]. Using D =10 10 m 2 s 1 for the latter and 50 lm for the crystal diameter we obtain s corresponding to an exchange rate of 2.4 Hz. The latter rate is much smaller than 400 Hz, and well-resolved signals from the adsorbed component and the gas phase are hence expected. 13 C NMR spectra compared to 1 H spectra are more sensitive with respect to a change in the electronic structure. The signals of the adsorbed molecules have chemical shifts of and 4.2 ppm for ethene and ethane, respectively. The chemical shift of the gas phase signals are and 2.5 ppm for ethene and ethane, respectively. In the literature we find for CDCl 3 -diluted molecules for ethene and 7.0 ppm for ethane, see [26]. The shift difference between adsorbed and gas phase molecules amounts to +1.5 ppm and +1.7 ppm for ethene and ethane, respectively, see Fig. 4. This can again be explained by a weak interaction of the molecular electron shell with the MOF framework. The resulting shielding effect for the hydrogen atoms of the molecules is not significantly different for ethene and ethane. However, the shift sign is different compared to the corresponding effects in the 1 H NMR. This means that adsorption causes a shielding of the 1 H nuclei and a deshielding of the 13 C nuclei of the adsorbed molecules. Also between the carbon atoms of the ethene and ethane molecules no significant difference is detected. Therefore, one conclusion from the NMR spectra of the adsorbed molecules is that the adsorption interaction of the saturated molecules is similar to those of the unsaturated hydrocarbons. Two results can be obtained by comparing the 13 C spectra of the unloaded and loaded MOF s. The chemical shifts of the framework signals do not change, except a 0.2-ppm shift which can be traced back to a weak interaction between MOF-framework and the adsorbed molecules. Surprisingly the methyl-groups appear to be preferred adsorption sites, as shifts are not observed for the signal of the CH-groups close to the double bond of the imidazole-ring. This weak hint for a preferential adsorption of the guest molecules confirms the conclusion reported in the literature that the preferential sites are associated with the linker rather than the metalion [13,21,27]. However, in contrast to the neutron powder-diffraction measurements of Wu et al. [17] on methane adsorption at low temperatures we note a weak interaction with the methyl-groups instead a position near the double-bond of the imidazolate-ring. This difference might either be related to the different sorbate molecules or to the notably higher temperature in our experiments. Alternatively, it may be explained by rotated linker molecules. However, the shift differences of the framework carbon atoms between unloaded and fully loaded MOF are very small. This means that there are no detectable structural changes in the framework upon loading and, therefore, 13 C NMR gives no evidence of a gate opening effect [13,28] upon adsorption of an ethene/ethane mixture at room temperature. As already mentioned in Section 1, this conclusion might not hold for methane adsorption. Experiments addressing this question will be in the focus of our ongoing work. Our diffusion experiments with IRM bear a particularly remarkable result. Within the uncertainty of the measurements no difference between single-component and mixture diffusivities was found. As two molar ethene:ethane mixture compositions were studied (1:1.5 and 1.9:1) this means in turn that the diffusion occurs independent from the molar composition. Usually, in the mixture one notes a slow-down of the faster component and a mild speed-up of the tardier component. Exactly this trend was found in our previous study on methane and carbon dioxide in ZIF-8 [14]. Obviously, for an ethene or ethane molecule being in the position to jump to the next cavity it makes no difference, what species the nearest neighbors belong to. Also, it means only a negligible hindrance to ethene if one or two of the eight connections to neighboring cavities are occupied by the slower diffusing ethane molecules. Apart from this discussion we note that the mobility of the molecules remains nearly constant until a loading of up to four molecules per cavity. Thus we omitted, in the present study, single-component measurements and focused only on a 1:1 mixture at total loadings of four and eight molecules per cavity. The accuracy of loading for the NMR samples is ±10% and a similar error is expected for the calibration of the concentration scale for the IRM results. The accuracy of the determination of the diffusion coefficients is also not better than ±10%. Let us first focus on the low to intermediate loading side. For the loading of four molecules per cavity we note an excellent agreement between the transport diffusion coefficients and the 1 H MAS PFG NMR self-diffusion coefficients (see Fig. 9). Consequently, also the diffusion selectivity D ethene :D ethane = 5.5 determined by both techniques shows excellent agreement. The single-component tracer self-diffusivities obtained by IR microscopy are slightly lower than the values of the 1 H MAS PFG NMR self-diffusion coefficient. It should be noted that the scale of the diffusion path is different for different techniques. The diffusivity of m 2 s 1 translates within the observation time t ¼ D ¼ 200 ms (MAS PFG NMR) into molecular displacements k (root of the mean squared displacement) of 6 lm, as it can be obtained from the Einstein relation [29] for a three-dimensional Brownian motion D ¼hk 2 i=6t. The diffusivities from IR microscopy were obtained from displacements through the whole crystal, which is larger by a factor of 50. There has been extensive work on comparing diffusivities obtained by different microscopic, mesoscopic and macroscopic measuring techniques [30]. It is commonly observed that the measured mobilities are the larger the shorter the distances covered by the guest molecules are. This finding can be rationalized by the exis-

6 140 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) tence of defects. Molecules can move through a basically perfect lattice for short displacements. But their mobility experiences a reduction as the path lengths come close to the mean defect distance. Depending on the type of defects the reduction in the mobility can amount to several orders of magnitude. The almost perfect agreement between the MAS PFG NMR and IRM diffusivity serves, thus, as one of the rare cases where the consistent agreement of different diffusion techniques could be demonstrated. Although the high loading of eight molecules per cavity was not reached in the IRM experiments we can anticipate that the self-diffusivities are at this concentrations notably smaller than the transport diffusivities. This is in fact the expected trend and is easily understood if one considers the different situations under which both diffusivities are measured. Self-diffusion is recorded under equilibrium. One limitation for the mobility of the individual molecules is related to the available vacancies and, hence, it will ultimately drop down at high pore fillings. Transport diffusion is introduced in Fick s law as constant which relates the flux density with a gradient in concentration. High pore fillings do not prevent a fast transport of mass (change in the local density). Diffusion theory even allows for a quantitative verification by a commonly used approach, which is often referred to as Darken correction. It is based on the calculation of corrected (or Maxwell Stefan) diffusivities which are obtained by dividing transport diffusivities by the thermodynamic factor (slope of the invers equilibrium isotherm in logarithmic coordinates). For porous structures of larger cavities with narrow windows like ZIF-8 we expect that self- and corrected diffusivity coincide over a wide loading range, see [7,30]. This is due to the absence of correlation effects which in general slowdown self-diffusion compared to corrected diffusion [31]. Indeed, for the present case we find good agreement between NMR and IRM diffusivities including the by eye extrapolation of the corrected IRM diffusivity to eight molecules per cavity (see Supplementary material). Although practically covered by the uncertainty of the measurements one might speculate that the diffusivities obtained by IRM tend to be somewhat smaller than expected based on the NMR data. Indeed, the existence of a mild surface barrier which might not be revealed by IR micro-imaging cannot be excluded [7]. Molecular clustering is another mechanism which may lead to self-diffusivities exceeding transport diffusivities [7,32]. However, for short alkanes at room temperature molecular clustering is usually of minor importance. As a particular advantage, MAS PFG NMR is able to measure simultaneously the signals of molecules in the gas phase and in the sorbed phase. In this way, the two factors establishing the long-range diffusivity D l.r.=p inter D inter [8] may be determined separately. 1 H MAS NMR spectroscopy yields the relative concentration of the molecules in the gas phase p inter, which is between 10% and 40% in the samples under study. For equal mixture loading it depends less on the type of molecule but more on the amount of MOF in the MAS glass tube (10% for the maximum amount of MOF). The self-diffusion coefficient D inter was determined as D inter = m 2 s 1 for ethene and ethane as well. The value p inter D inter, however, gives little information about adsorption. But it must be ensured that it is, as in our case, not included into the observation of the molecular displacement, since the simple addition of both diffusivities shows that the inter-effect is dominating. Early IRM studies were performed at ambient temperature, whereas the present studies of diffusivity were carried out in the temperature range K. Apparent activation energies are obtained as 6.6 and 4.9 kj mol 1 for lower and higher loading of ethene, respectively. The values for ethane are significantly higher, 9.6 and 8.6 kj mol 1 for lower and higher loading, respectively. At - room temperature we find D ethene :D ethane = 5.5. The faster self-diffusion of ethene can be rationalized by the smaller size of the methylene-groups compared to the methyl-groups. A smaller size means less hindering for crossing the windows of a cavity and hence a smaller apparent activation energy for ethene is observed. The pre-exponential factor is in the range m 2 s 1 and can be discussed in terms of the partition function. They are almost equal for both molecules, since vibrations are not activated at the used temperatures. In conclusion, the different diffusivities can be explained by the different size of molecules and a possible difference in the guest host interaction between the saturated and non-saturated molecule has no importance for the mobility of the molecules. 5. Conclusions 1 H and 13 C MAS NMR spectroscopy show that there are no byproducts or compounds with different short-range order in the synthesis products of ZIF C NMR spectroscopy gives a weak hint for a preferential adsorption of the molecules close to the methyl-groups of the imidazole-rings. However, no direct evidence for a gate-opening effect or another structural change upon adsorption of an ethene/ ethane mixture is found. Four well-resolved signals were assigned to ethene and ethane molecules, which are adsorbed in the ZIF-8 crystals or non-adsorbed in the gas phase. The corresponding self-diffusion coefficients could be determined separately. The microscopic MAS PFG NMR diffusivities are in consistent agreement with the mesoscopic diffusivities of IR microscopy. The diffusion selectivity is determined to D ethene :D ethane = 5.5 at a loading of four molecules per cavity by both techniques. By accounting for the influence of the thermodynamic factor IRM transport diffusivities and NMR self-diffusivities could be directly transferred into each other. The latter is expected only for porous structures consisting of large cavities with narrow windows. The agreement between the results from both techniques is exceptionally good, if we consider the uncertainties in the determination of the absolute concentration and the diffusivities and the fact that crystals from different batches were investigated. The different diffusivities of ethene and ethane can be rationalized by the different size of molecules. This conclusion is supported by the higher activation energies of ethane diffusion compared to ethene. A possible difference in the guest host interaction between the saturated and non-saturated molecule has no impact on the mobility of the molecules. MAS PFG NMR gives access to a multitude of different aspects of guest diffusion and adsorption. In particular if combined with nonequilibrium methods as IR microscopy a most detailed picture on molecular transport can be obtained which facilitates its understanding on a molecular level. Acknowledgements The authors are grateful to Jörg Kärger and Jürgen Caro for valuable advice and thank the DFG for providing the spectrometer Avance 750. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi: /j.micromeso References [1] U. Mueller, M. Schubert, F. Teich, H. Puetter, K. Schierle-Arndt, J. Pastre, J. Mater. Chem. 16 (2006)

7 C. Chmelik et al. / Microporous and Mesoporous Materials 147 (2012) [2] G. Feréy, C. Serre, Chem. Soc. Rev. 38 (2009) [3] A.U. Czaja, N. Trukhan, U. Müller, Chem. Soc. Rev. 38 (2009) [4] H. Bux, F.Y. Liang, Y.S. Li, J. Cravillon, M. Wiebcke, J. Caro, J. Am. Chem. Soc. 131 (2009) [5] X.C. Huang, Y.Y. Lin, J.P. Zhang, X.M. Chen, Angew. Chem., Int. Ed. 45 (2006) [6] K.S. Park, Z. Ni, A.P. Cote, J.Y. Choi, R.D. Huang, F.J. Uribe-Romo, H.K. Chae, M. O Keeffe, O.M. Yaghi, PNAS 103 (2006) [7] C. Chmelik, H. Bux, J. Caro, L. Heinke, F. Hibbe, T. Titze, J. Kärger, Phys. Rev. Lett. 104 (2010) [8] J. Kärger, in: H.G. Karge, J. Weitkamp (Eds.), Science and Technology Molecular Sieves Adsorption and Diffusion, vol. 7, Springer, Berlin, Heidelberg, 2008, pp [9] F. Stallmach, P. Galvosas, Ann. Rep. NMR Spectrosc. 61 (2007) [10] M. Fernandez, J. Kärger, D. Freude, A. Pampel, J.M. van Baten, R. Krishna, Microporous Mesoporous Mater. 105 (2007) [11] M. Fernandez, A. Pampel, R. Takahashi, S. Sato, D. Freude, J. Kärger, Phys. Chem. Chem. Phys. 10 (2008) [12] M. Gratz, S. Hertel, M. Wehring, F. Stallmach, P. Galvosas, New J. Phys. 13 (2011) [13] C. Gücüyener, J. van den Bergh, J. Gascon, F. Kapteijn, J. Am. Chem. Soc. 132 (2010) [14] H. Bux, C. Chmelik, J.M. van Baten, R. Krishna, J. Caro, Adv. Mater. 22 (2010) [15] L. Hertäg, H. Bux, J. Caro, C. Chmelik, T. Remsungnen, M. Knauth, S. Fritzsche, J. Membr. Sci. 377 (2011) [16] D. Fairen-Jimenez, S.A. Moggach, M.T. Wharmby, P.A. Wright, S. Parsons, T. Düren, J. Am. Chem. Soc. 133 (2011) [17] H. Wu, W. Zhou, T. Yildirim, J. Phys. Chem. C 113 (2009) [18] M. Zhou, Q. Wang, L. Zhang, Y.C. Liu, Y. Kang, J. Phys. Chem. B 113 (2009) [19] E. Pantatosaki, F.G. Pazzona, G. Megariotis, G.K. Papadopoulos, J. Phys. Chem. B 114 (2010) [20] H.C. Guo, F. Shi, Z.F. Ma, X.Q. Liu, J. Phys. Chem. C 114 (2010) [21] H. Bux, C. Chmelik, R. Krishna, J. Caro, J. Membr. Sci. 369 (2011) [22] T. Mildner, H. Ernst, D. Freude, Solid State Nucl. Magn. Reson. 5 (1995) [23] B.M. Fung, A.K. Khitrin, K. Ermolaev, J. Magn. Reson. 142 (2000) [24] R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Markert, J. Magn. Reson. 83 (1989) [25] D.H. Wu, A.D. Chen, C.S. Johnson, J. Magn. Reson. A 115 (1995) [26] M. Hesse, H. Meier, B. Zeeh, Spectroscopic Methods in Organic Chemistry, Thieme, Stuttgart, New York, [27] H. Wu, W. Zhou, T. Yildirim, J. Am. Chem. Soc. 129 (2007) [28] K. Seehamart, T. Nanok, J. Kärger, C. Chmelik, R. Krishna, S. Fritzsche, Microporous Mesoporous Mater. 130 (2010) [29] A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, Mineola, 1926 (edited with notes by R. Fürth). [30] C. Chmelik, J. Kärger, Chem. Soc. Rev. 39 (2010) [31] R. Krishna, J. Phys. Chem. C 113 (2009) [32] R. Krishna, J.M. van Baten, Langmuir 26 (2010)