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Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX-XXX

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Monitoring the Diffusivity of Light Hydrocarbons in a Mixture by Magic Angle Spinning Pulsed Field Gradient NMR: Methane/Ethane/ Ethene in ZIF‑8 Nina Dvoyashkina,† Dieter Freude,*,† Sergei S. Arzumanov,‡,§ and Alexander G. Stepanov*,‡,§ †

Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnéstrasse 5, 04103 Leipzig, Germany Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Prospekt Akademika Lavrentieva 5, Novosibirsk 630090, Russia § Department of Physical Chemistry, Faculty of Natural Sciences, Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russia ‡

ABSTRACT: 1H magic angle spinning pulsed field gradient (MAS PFG) NMR was applied for the measurement of the diffusivities in a three-component mixture of the light hydrocarbons methane, ethane, and ethene, which were absorbed in the micropores of ZIF-8 metal− organic framework (MOF). It has been found that diffusivity in the mixture increases in the order ethane < ethene < methane with variance of self-diffusion coefficients D from 0.22 × 10−10 m2 s−1 for ethane to 1.96 × 10−10 m2 s−1 for methane at 313 K. This tendency in increasing of diffusivity from ethane to methane is similar to the tendency for individual hydrocarbons. It is concluded that the interaction of a hydrocarbon with the micropore wall of the ZIF-8 framework influences the mobility rather than the intermolecular hydrocarbon interaction. The latter plays no role for the molecules, when they overcome the energy barrier of the window connecting neighbor cages. The activation energies Ea for diffusivity of the hydrocarbons in mixture increases in the order methane (Ea = 2.4 kJ mol−1) < ethene (Ea = 7.2 kJ mol−1) < ethane (Ea = 11.5 kJ mol−1) . At the lowest studied temperature (273 K) D of methane is larger than D of ethane and ethene by 13.3 and 2.2 times, correspondingly, while the diffusivities of ethene and ethane differ by 5.8 times. This finding offers the possibility for separation of the three studied hydrocarbons on ZIF-8.

1. INTRODUCTION Pulsed field gradient (PFG) NMR spectroscopy is often used for the measurement of the diffusivity of hydrocarbons in microporous materials, zeolites, and metal−organic frameworks (MOFs).1−7 The investigation of mixture diffusion becomes difficult, if the broadening prevents the resolution of different signals of the components in the mixture. Magic angle spinning (MAS) PFG NMR has the evident advantage of allowing the resolution of signals from different hydrocarbons in a mixture,8,9 which allows measurement of the diffusivities of individual hydrocarbons in their mixture. The zeolitic imidazolate framework ZIF-810 has a potential application for separation of mixtures of hydrocarbons. ZIF-8 has the formula Zn(MeIM)2, where MeIM = 2-methylimidazolate, and crystallizes in a sodalite-related structure: cubic, space group I4̅3m; a0 = 16.9910 (1) Å; V = 4905.2 (6) Å3; R1 = 0.0314.10 The diameter of the largest sphere that will fit into the framework is 11.6 Å.10 The size of the pore windows seems to be flexible. From crystallographic data it is about 3.4 Å. It has been shown that ZIF-8 can be applied for separation of ethane and ethene, 11,12 methane and ethane, 13 propane and propene,12,14,15 and H2 from other gases.16,17 The development of membranes based on ZIF-8 which can be potentially applied for hydrocarbon separation should be based on the knowledge © XXXX American Chemical Society

of diffusivities of hydrocarbons in mixtures. However, information on diffusivities of hydrocarbons in the mixtures being separated is scarce. One can suggest that hydrocarbons different in nature (e.g., olefins and paraffins) influence each other in a mixture by specific intermolecular interactions, and, therefore, the diffusivities of individual hydrocarbons in a mixture could be essentially different from that when only a single hydrocarbon diffuses in the porous material intended to be used for separation. In this regard, the knowledge of the diffusivity of each of the hydrocarbons in the mixture is of particular importance. In this paper, MAS PFG NMR was applied to analyze the diffusivity of each of the compounds in a mixture of three hydrocarbonsmethane, ethane, and ethanein zeolitic imidazolate framework ZIF-8, as a potential microporous material that can be used for separation processes. Received: September 20, 2017 Revised: October 27, 2017 Published: October 30, 2017 A

DOI: 10.1021/acs.jpcc.7b09335 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

2. EXPERIMENTAL SECTION 2.1. Material Preparation. ZIF-8 crystals were synthesized similar to the procedures described earlier in refs 6, 16, and 18. ZnCl2, 2-methylimidazole (2-mIM), and NaHCO2 were dissolved in 70 mL of methanol. A clear solution was prepared with a molar ratio ZnCl 2 /2-mIM/NaHCO 2 /MeOH = 1:2:2:250. The solution was kept at 373 K for 24 h in a sealed glass tube under heating in an oven. After cooling to ambient temperature, crystalline material was separated from solution by filtration. The crystals were intensively washed with methanol and dried at 350 K under air for 10 h. X-ray diffraction analysis (XRD) proved that it was pure ZIF-8. The scanning electron microscopy (SEM) analysis showed that the dimensions of zeolite crystallites were in the range 20−50 μm. The relatively large size is necessary for the PFG NMR investigation, since the root-mean-square displacement of the molecules within the crystallites amounts about 24 μm for the largest measured value in the present study of D = 5 × 10−10 m2 s−1 and a diffusion observation time of 200 ms. Methane (≥99.0% purity), ethane (≥99.0% purity), and ethene (≥99.0% purity) were purchased from Aldrich Chemical Co. Inc. (ACC inc.) and were used without further purification. 2.2. Sample Preparation for NMR Experiments. About 30 mg of ZIF-8 powder was loaded into a 3.0 mm (o.d.) glass tube, in order to prepare samples for the NMR experiments. The tube was connected to a vacuum system and heated at 423 K for 8 h under vacuum to a final pressure above the sample of 10−2 Pa. After cooling of the sample to room temperature, the material was exposed to a gaseous hydrocarbon (10 mbar) (or a mixture of them, methane:ethane:ethene = 1:1:1) in the calibrated volume (38.7 mL) and finally adsorbed at the temperature of liquid nitrogen within a few minutes. The quantity of adsorbed hydrocarbon corresponded to six molecules per cavity of ZIF-8. In the case of adsorption of a mixture of hydrocarbons, the quantity corresponded to two molecules of each hydrocarbon per cavity of ZIF-8. After adsorption, the neck of the tube was sealed off at a distance of about 12 mm from the bottom, while the bottom was maintained in liquid nitrogen in order to prevent the sample heating by the flame. The sample was inserted into a MAS zirconia rotor of 4 mm outer diameter for the NMR experiments. 2.3. NMR Measurements. 1H MAS NMR spectra were recorded at 9.4 T on a Bruker Avance 400 spectrometer equipped with a broad-band double-resonance-MAS probe at 7.4 T and νrot = 10 kHz. The Hahn-echo pulse sequence (π/ 2−τ−π−τ−acquisition) was applied, where τ equals one rotor period (100 μs). The excitation pulse length was 5 μs (π/2), and typically 16 scans were accumulated with a 4−10 s delay. Magic angle spinning pulsed field gradient (MAS PFG) NMR diffusion measurements were performed on a Bruker AVANCE 750 spectrometer with wide-bore magnet at the field of 17.6 T and νrot = 10 kHz. The calibration of the temperature (273−373 K) inside the rotor was performed (accuracy of ±1 K) by using lead nitrate, located inside the rotor, as a 207Pb MAS NMR chemical shift thermometer.19 The 10 kHz rotation of a 4 mm rotor increases the temperature within the rotor by 10 K with respect to the detected temperature of the air flow outside the rotor.20 The temperature of measurements given below is the sample temperature within the rotor. The external magnetic field was calibrated by means of the 1H MAS NMR signal of highly

viscose polydimethylsiloxane (PDMS) with a chemical shift of 0.07 ppm in a spinning rotor (external standard). 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 νrf = 100 kHz was used for diffusion measurements. A stimulated-echo sequence with bipolar sine gradient pulses and eddy current delay21,22 was applied. The sequence for alternating sine shaped gradient pulses and longitudinal eddy current delay consists of seven rf pulses, four magnetic field gradient pulses of duration δ and intensity g, and two field gradient quench pulses.8,9 We used a gradient pulse duration of δ = 2 ms and a π-pulse length pπ = 5 μs, an observation time of Δ = 40−200 ms, a delay between gradient and rf pulses τ = 0.5 ms, and an eddy current delay τecd = 4.5 ms. The repetition delay was 5 s and much longer than the longitudinal relaxation time T1, which has a length of about 0.1 s. The gradient pulse strength was varied between 0.01 and 0.50 T m−1. The duration of the observation time, the gradient pulse duration, and the spacing between gradient pulses were multiples of the rotation period of 100 μs. The self-diffusion coefficient, D, of molecules was obtained from the analysis of the signal attenuation ψ = S/S0 in dependence of the field gradient intensity, g: ψ=

⎡ ⎛ 4δgγ ⎞2 ⎛ ⎞⎤ τ 2δ S ⎟ ⎜Δ − − = exp⎢ −D⎜ − pπ ⎟⎥ ⎠⎥⎦ ⎢⎣ ⎝ π ⎠ ⎝ S0 2 3

(1)

where γ denotes the gyromagnetic ratio, and other values are explained above.

3. RESULTS AND DISCUSSION The 1H MAS NMR spectrum of a mixture of methane, ethane, and ethene shows three well-resolved groups of signals (Figure 1). Methane exhibits a signal from the gaseous state at −0.1 ppm and two signals from the adsorbed states at −0.4 and −0.55 ppm. Ethane shows a small intensity signal from the gaseous state at 0.7 ppm and an intense signal at 0.2 ppm from the adsorbed state. Gaseous and adsorbed ethene shows signals at 5.1 and 4.5 ppm. Two signals of adsorbed methane belong to

Figure 1. 1H MAS NMR spectrum at 306 K of a mixture of methane, ethene, and ethane coadsorbed on ZIF-8 with loading of two molecules per cage of each hydrocarbon and total loading of all hydrocarbons of six molecules per cage. B


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obtained values of D coincide in the limit of ±20% with diffusivity measured earlier by 1H MAS PFG NMR.9 The diffusion coefficients for the gases in mixture increase in the order ethane (D = 0.22 × 10−10 m2 s−1 at 313 K) < ethene (D = 0.99 × 10−10 m2 s−1 at 313 K) < methane (D = 1.96 × 10−10 m2 s−1 at 313 K). The activation energies Ea for the diffusion of the individual components and for each of them in the mixture derived from the Arrhenius plots (Figure 3) are

methane molecules directly associated with the organic linkers (at −0.4 ppm) and those presumably located in the center of the cavity (the signal at −0.55 ppm).23 Three major wellresolved signals in the spectrum open the possibility for measurement of diffusivity simultaneously for three adsorbed gases: methane, ethene, and ethane. The two-dimensional spectrum with the pulsed field gradient strength in the second dimension for a mixture of adsorbed gases (Figure 2) shows that the signal decay with increasing

Figure 3. Arrhenius plots for diffusion coefficients of methane, ethane, and ethene as single components and in their mixture adsorbed in ZIF8. Methane (○); methane in mixture (●); ethene (▽); ethene in mixure (▲); ethane (□); ethane in mixture (■).

Figure 2. Two-dimensional (2D) presentation of signal decay with linearly increasing strength of gradient pulses for ZIF-8 sample loaded with methane/ethane/ethane mixture and measured at 373 K.

represented in Table 1. Ea’s for diffusivities of the hydrocarbons in the mixture increase in the order methane (Ea = 2.4 kJ mol−1) < ethene (Ea = 7.2 kJ mol−1) < ethane (Ea = 11.5 kJ mol−1). Ea values measured by us for ethene and ethane in a mixture of three gases are similar to the values measured earlier by Chmelik et al. for a mixture of ethane and ethene.9 Among the three studied hydrocarbons in the mixture, methane exhibits the largest diffusivity, D, while ethane shows the lowest diffusivity. At the lowest studied temperature (273 K), D of methane is larger than D’s of ethane and ethene by 13.3 and 2.2 times, correspondingly, while the diffusivities of ethene and ethane differ by 5.8 times. This finding offers the possibility for separation of the three studied hydrocarbons on ZIF-8. The difference in diffusivity is accepted to be strongly related to the size of the molecules and the intercage aperture,14,26,27 which is experimentally defined as 3.4 Å.10 We do not find any correlation between the diffusivity of the studied gases and the

strength of the field gradient pulses is stronger for the ethene and methane signals at 4.5 and −0.55 ppm than for the ethane signal at 0.2 ppm. This indicates that diffusion of methane and ethene occurs faster than diffusion of ethane. The detected faster diffusion of ethene with regard to ethane in ZIF-8 is in good accordance with earlier measurements of diffusivity of an ethene and ethane mixture in ZIF-8.9 A plot of the signal attenuation ψ = S/S0 in dependence of g2, eq 1, allows the determination of self-diffusion coefficients, D, for each of hydrocarbons in their mixture. Also, D values were measured for each individual hydrocarbon for a loading of six molecules per cage (Table 1). The diffusion coefficients are in accordance with earlier measured D values for methane by IRM,24 PFG NMR,6,7 and neutron scattering.25 For ethene and ethane most of the

Table 1. Self-Diffusion Coefficients, D, of Light Hydrocarbons Adsorbed in MOF ZIF-8 as Single Components and as Mixture of Three Gasesa D (×1010/m2 s−1) loading (molecules/cage) methane methane in mixtureb ethene ethene in mixtureb ethane ethane in mixtureb a

6 2 6 2 6 2

273 K

293 K

1.59

1.8

0.70 0.095 0.12

0.81 0.145

313 K

343 K

373 K

Ea (kJ mol−1)

1.76 1.96 1.06 0.99 0.26 0.22

2.84 2.06 1.22 1.24 0.30 0.325

5.35 2.13 1.51 1.63 0.37 0.43

18 ± 2 2.4 ± 0.4 6±1 7.2 ± 0.4 11 ± 2 11.5 ± 0.7

D has a variance of ±10%. bTotal loading of three components in mixture was six molecules per cage. C



■

kinetic diameter of the corresponding molecules. Both methane and ethane exhibit a kinetic diameter of 3.8 Å, while the kinetic diameter of ethene is only a bit larger, 3.9 Å. For all three gases their kinetic diameters are larger than the intercage aperture, 3.4 Å. Despite this, all three gases diffuse through the intercage aperture.11−15,25 While the diffusivities of methane and ethene are not essentially different, the diffusivities of methane and ethene differ essentially from that of ethane. One can suggest that some “effective” size of the ethane molecule while diffusing is larger than its kinetic diameter due to fast rotation of the methyl groups and random reorientations of the molecule located in the ZIF-8 β-cage. One can also suggest different effects of specific interactions of either olefin or paraffin with methylimidazolate linkers on torsional and librational motions of the linkers in ZIF-8.28 The different effects of specific interactions on linker mobility might influence the gate-opening mechanism, which could result in notably faster diffusivities of methane and ethene against ethane.27 Our measurements show for the studied mixture of gases that the diffusivities of individual ethene and ethane are similar to the diffusivity of these gases in a mixture. The activation energies of diffusivity for ethene and ethane are also similar for individual components and in the mixture. Note, however, while the diffusivities of individual methane and in a mixture are of the same magnitude, the activation energy for diffusivity of individual methane is essentially larger (18 kJ mol−1) compared to the Ea for methane in a mixture (2.4 kJ mol−1). We do not have an evident explanation of this fact. One can assume that this can be presumably related to the peculiarity of localization of methane in the pores of ZIF-8: in the vicinity of methylimidazolate linkers and in the center of the cavity.23 Localization of methane molecules in the vicinity of the intercage aperture makes the molecule jumps difficult into the neighboring cage for another methane molecule located in the center of the cavity. When in a mixture, ethene and ethane molecules located in the cavity affect the disposition of methane in the cavity pushing methane apart from the intercage site localization. This may decrease the energetic barrier for methane diffusion in a mixture with ethene and ethane.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel.: +49 3419732503. Fax: +49 3419739349 (D.F.). *E-mail: [email protected]. Tel.: +7 9529059559. Fax: +7 383 330 8056 (A.G.S.). ORCID

Alexander G. Stepanov: 0000-0003-2754-5273 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Russian Academy of Sciences within the framework of Budget Project No. 0303-2016-0003 for the Boreskov Institute of Catalysis and by the Deutsche Forschungsgemeinschaft, Grant HA 1893/16.

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REFERENCES

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4. CONCLUSION A mixture of three hydrocarbons, methane, ethane, and ethene, which were adsorbed in the zeolitic imidazolate framework ZIF8 was monitored by 1H MAS PFG NMR diffusometry. For comparison with the individual diffusivities of the molecules in the mixture, the single-component diffusivities in ZIF-8 were measured as well. The diffusivity in the mixture increases in the order ethane (D = 0.22 × 10−10 m2 s−1 at 313 K) < ethene (D = 0.99 × 10−10 m2 s−1 at 313 K) < methane (D = 1.96 × 10−10 m2 s−1 at 313 K), and the same tendency was observed for the single hydrocarbons. Activation energies for ethene and ethane in the mixture of the three gases are similar to the values measured earlier by Chmelik et al. for a mixture of ethane and ethene.9 The values of the present study are methane (Ea = 2.4 kJ mol−1) < ethene (Ea = 7.2 kJ mol−1) < ethane (Ea = 11.5 kJ mol−1). As expected, methane exhibits the largest diffusivity, D, while ethane shows the lowest diffusivity in the mixture. A separation of the three studied light hydrocarbons seems to be possible on ZIF-8, because at the lowest studied temperature (273 K) D of methane is larger than D’s of ethane and ethene by 13.3 and 2.2 times, correspondingly, while the diffusivities of ethene and ethane differ by 5.8 times. D


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