Self-Diffusion of Chain Molecules in the Metal–Organic Framework

Letter pubs.acs.org/JPCL

Self-Diffusion of Chain Molecules in the Metal−Organic Framework IRMOF-1: Simulation and Experiment Denise C. Ford,† David Dubbeldam,†,⊥ Randall Q. Snurr,*,† Volker Künzel,‡ Markus Wehring,‡ Frank Stallmach,‡ Jörg Kar̈ ger,‡ and Ulrich Müller§ †

Chemical and Biological Engineering Department, Northwestern University, 2145 Sheridan Road, Evanston Illinois 60208, United States ‡ Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnèstrasse 5, 04103 Leipzig, Germany § BASF SE, GCC/PZ - M301, 67056 Ludwigshafen, Germany S Supporting Information *

ABSTRACT: Metal−organic frameworks (MOFs) possess characteristics, such as tunable pore size and chemical functionality, that make them attractive candidates for separations, catalysis, gas storage, and sensing applications. The rate of diffusion of guest molecules in the pores is an important property for all of these potential applications. In this work, the self-diffusion of hydrocarbons in IRMOF-1 was studied as a function of chain length with a combination of molecular dynamics simulations and pulsed field gradient NMR experiments. Excellent agreement is seen between the experiments and simulations, and the self-diffusion coefficients in IRMOF-1 are on the same order as those in the bulk liquid. Additionally, the effect of concentration on diffusivity was found to be very small for low to moderate loadings. Molecular dynamics simulations also provided insights about the preferential diffusion pathways of these guests in IRMOF-1.

SECTION: Surfaces, Interfaces, Catalysis

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in MIL-46(V) and MIL-53(Cr), intracrystalline diffusivities and surface permeabilities of methanol in a manganese formate MOF obtained from transient concentration profiles,7 and the measurement of ethane, n-propane, and n-butane diffusivities in Zn(tbip) from transient concentration profiles.8 The MIL studies demonstrated very good agreement between experiment and simulation at moderate to high loadings but poorer agreement at very low loading. Qualitative agreement between experiment and simulation was observed for many of the key features of the diffusive behavior of butane and pentane isomers in HKUST-1; however, a dip in the diffusivities around a loading indicative of a phase transition was observed experimentally but not predicted by the MD simulations, and the experiment and simulation results did not agree quantitatively. In this Letter, we report the self-diffusion coefficients determined from molecular dynamics (MD) simulations and pulsed field gradient (PFG) NMR measurements for methane, ethane, n-hexane, n-decane, n-dodecane, n-hexadecane, and benzene in a prototypical MOF, IRMOF-1, and compare the results with data from the literature for bulk liquids and in the zeolite NaX.9−11 In addition, we have used MD simulations to

etal−organic frameworks (MOFs) and related materials formed by the self-assembly of organic linkers via coordinating nodes are an exciting new development in the field of porous materials. Varying the nature of the linkers and the coordinating nodes allows for the synthesis of an immense number of materials, and their properties can be tailored by the choice of the constituent building blocks. These features have created great interest in MOFs for applications such as gas storage, chemical separations, sensing, and catalysis. In all of these applications, the rate of guest molecule diffusion through the pores plays an important role in determining the viability of the process. The equilibrium adsorption of various molecules has been studied experimentally and computationally in many MOFs, both as a means of characterization and to assess the potential of MOFs for gas storage and separations. Diffusion studies, however, are much scarcer, with the majority of the data coming from MD simulations. In fact, the first experimental study of diffusion in a MOF was reported by Stallmach et al.1 almost 2 years after the first MD results.2,3 Stallmach et al. used PFG NMR to measure the self-diffusion coefficients of methane, ethane, n-hexane, and benzene in IRMOF-1. Recently, additional experimental studies of diffusion in MOFs have been completed, including a study of the Maxwell− Stefan diffusivities of small linear and branched alkanes in HKUST-1 using infrared microscopy,4 quasi-elastic neutron scattering measurements of methane5 and hydrogen6 diffusion © 2012 American Chemical Society

Received: February 3, 2012 Accepted: March 12, 2012 Published: March 12, 2012 930

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shown (see Figure 1 in ref 1). The significantly lower Ds from simulation for methane is consistent with the idea that the experimental results for methane are not a measure of pure intracrystalline self-diffusion. Additionally, the calculated selfdiffusion coefficient for methane is in excellent agreement with the simulations of Sarkisov et al.,2 Skoulidas and Sholl,19 and Babarao and Jiang.20 An exponential decrease in diffusivity with chain length is evident from both the simulation and the experimental results. The self-diffusivities up to n-decane are nearly identical to those reported for bulk liquid n-alkanes, which indicates that IRMOF1 creates minimal diffusion restrictions for short n-alkanes. Because IRMOF-1 has the smallest pores in the IRMOF family, the other IRMOFs should exhibit even lower restrictions to molecular diffusion. In contrast, the zeolite NaX shows the same trend in the diffusivities, but the values are about an order of magnitude lower than those in the bulk liquid. NaX and IRMOF-1 have similar pore sizes, but the much higher void fraction of IRMOF-1 leads to the higher diffusion coefficients seen in Figure 1. The simulated activation energies for diffusion are presented in Figure 2 along with the activation energies for methane and

examine the effect of loading on diffusion and to gain molecular-level insights into the diffusion process. MD simulations were performed in a single rigid unit cell using the NVT ensemble. In a previous study,12 we found that framework flexibility has only a mild effect on diffusion of nalkanes and benzene in IRMOF-1 but adds considerably to the simulation time. The Lennard-Jones parameters for IRMOF-1 were taken from the generic DREIDING force field13 for the alkane simulations. For the benzene simulations, the LennardJones parameters and framework atom charges were taken from a special force field developed for the IRMOFs.14 The LennardJones parameters for the guest species (and atomic charges for benzene) were taken from the TraPPE force field.15,16 The loading of molecules was set at 5−9 carbon atoms per cage, corresponding to 20−25% pore filling, to match the experimental conditions. Exact loadings are given in Table S2 (Supporting Information). The experimental diffusion measurements were performed by the PFG NMR technique at 400 MHz 1H resonance frequency using the 13-interval rf pulse sequence.17,18 Spinecho attenuations were measured at two observation times (10 and 80 ms) by successively increasing the intensity of the PFGs up to a maximum value of about 10 T/m. All measurements were carried out at 298 ± 1 K. The PFG NMR spin-echo attenuations were analyzed using a biexponential fitting routine with a constant (nondiffusing) background, which was described in detail previously.1 Additional simulation and experimental details are provided in the Supporting Information. The self-diffusion coefficients (Ds) for all species are presented in Figure 1. The diffusivities cover over 2 orders of

Figure 2. Activation energies for self-diffusion of n-alkanes and benzene in IRMOF-1 measured with PFG NMR and calculated from MD simulations. A least-squares regression line is drawn through the MD data. Results for the bulk liquid9,10 and in NaX (100−120 mg/ g)11 are shown for comparison. The curve drawn through the NaX data is a guide for the eye.

ethane from PFG NMR. Due to the exchange with the gas phase, the reported NMR data represent upper limits for the activation energies of intracrystalline self-diffusion. Therefore, they are both higher than the MD results. This comparison shows that the temperature-dependent MD simulations yield activation energies which, at least for methane and ethane, are consistent with those from PFG NMR. The MD data in IRMOF-1 fall remarkably near literature results for the bulk liquid. The dependence of the self-diffusivity on loading was studied for methane, n-hexane, and benzene by MD simulation, and the results are presented in Figure 3. For all three species, there is only a small dependence of the diffusivity on loading until very high loadings, where a substantial decrease occurs. Five distinct patterns for the concentration dependence of self-diffusivities are known from Kärger and Pfeifer’s review of data for

Figure 1. Self-diffusion coefficients of n-alkanes in IRMOF-1 measured with PFG NMR and calculated from MD simulations at 298 K. Leastsquares regression lines are drawn through these data series. Methane was excluded from the PFG NMR fit. Results for benzene are shown for comparison. Self-diffusion coefficients for the bulk liquid9,10 and in the zeolite NaX (100−120 mg/g)11 are also presented.

magnitude from methane to n-hexadecane. Overall, excellent agreement is observed between simulation and experiment. Methane presents the greatest discrepancy; however, the lightest hydrocarbons methane and ethane easily exchange between the intra- and intercrystalline space on the NMR time scale, and the methane and high-temperature ethane measurements strongly depend on the observation time, as previously 931

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Figure 3. Self-diffusivity versus loading for methane, n-hexane, and benzene in IRMOF-1 determined from MD simulations. The IRMOF1 unit cell contains four large and four small cages. Figure 4. Slices through the position density plots of methane, nhexane, benzene, and n-hexadecane in IRMOF-1. The methane simulation was run for 2 ns, n-hexane for 7 ns, benzene for 8 ns, and nhexadecane for 20 ns to allow the guests to fully sample the periodic IRMOF-1 space.

adsorbate−zeolite systems.21 Methane and benzene in IRMOF1 display type-II behavior, where little or no decrease in diffusivity occurs until a loading where the guest species become crowded enough to hinder each other’s motion. Skoulidas and Sholl19 and Babarao and Jiang20 studied the loading dependence of methane in IRMOF-1 at low to moderate loadings and found only a small decrease in diffusivity, in agreement with our findings. The effect of loading on benzene self-diffusivity in IRMOF-1 was recently examined by Amirjalayer and Schmid.22 They calculated the self-diffusivity of benzene at 10, 20, 32, and 56 molecules/unit cell and found a minor increase in diffusivity at 20 molecules/ unit cell, followed by a small decrease at the higher loadings. We see this as well; however, overall, the trend is representative of type-II behavior. n-Hexane exhibits type-IV behavior, in agreement with the simulations of Xue and Zhong.23 This type of behavior is common among molecules that interact more strongly with host frameworks. At low loadings, each hexane molecule is able to find a favorable adsorption site; thus, the diffusion is rather slow. As the loading is increased, some hexane molecules are forced into less favorable locations, and more low-barrier hops between sites occur; therefore, the overall diffusivity is increased. Eventually, the overall diffusivity decreases as the molecules become packed tightly enough to hinder each other’s motion. To gain insight into the diffusion pathways taken by molecules of various sizes, the positions of each segment of methane, n-hexane, benzene, and n-hexadecane molecules within the IRMOF-1 framework were tracked during MD runs, and the three-dimensional position density histograms were examined. Two-dimensional slices through the cage centers, the cage corners, and the window region are shown in Figure 4. IRMOF-1 has two alternating types of cages, a cage with a 14.3 Å diameter and linker faces pointed toward the cage centers and a cage with a 10.9 Å diameter and linker edges pointed toward the cage centers. A preference for the corner regions of the large cages is exhibited by all species, while the centers of the small cages are avoided. Other adsorption sites are present in the window and the center of the large cage, especially for the longer alkanes. Methane is less localized than the other species, but it is studied at the highest molecule/cage loading and at the highest temperature relative to its critical temperature. These observations are in accordance with

detailed X-ray diffraction24 and Monte Carlo25 studies performed for Ar and N2 in IRMOF-1. Molecular diffusion often occurs as a series of hops from one adsorption site to another.21 On the basis of images similar to Figure 4, Amirjalayer et al.26 proposed that benzene diffuses in IRMOF-1 by hopping from one large cage to the next, without thermalizing in the small cages at low loading. Figure 4 suggests similar pathways for the n-alkanes, although the picture is less straightforward for methane and the long molecules. In summary, we have demonstrated excellent agreement between molecular simulation and experiment for diffusion of n-alkanes in IRMOF-1. It should be noted that this strategy of using the TraPPE force field for the guest molecules and DREIDING for the MOF has also yielded good predictions of adsorption isotherms for small molecules in a variety of MOFs.27 Here, we see that the same model also predicts transport properties in good agreement with experiment. The self-diffusion coefficients in IRMOF-1 are similar to those in the bulk liquid phase and roughly an order of magnitude higher than those in NaX, indicating that IRMOF-1, and consequently other IRMOFs, restrict diffusion less severely than a zeolite with a similar pore size. The loading of guest molecules was shown to have very little effect on the diffusivity of methane, nhexane, and benzene except at very high loadings, and visualization of the preferred adsorption sites provides microscopic insight into the diffusion pathways for chain molecules in IRMOFs.

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ASSOCIATED CONTENT

S Supporting Information *

Calculation and experimental details; Arrhenius plots. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 1-847-467-1018. 932

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Present Address

(15) Martin, M. G.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 1. United-Atom Description of n-Alkanes. J. Phys. Chem. B 1998, 102, 2569−2577. (16) Rai, N.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 9. Explicit Hydrogen Description of Benzene and FiveMembered and Six-Membered Heterocyclic Aromatic Compounds. J. Phys. Chem. B 2007, 111, 10790−10799. (17) Cotts, R. M.; Hoch, M. J. R.; Sun, T.; Markert, J. T. Pulsed Field Gradient Stimulated Echo Methods for Improved NMR Diffusion Measurements in Heterogeneous Systems. J. Magn. Reson. 1989, 83, 252−266. (18) Stallmach, F.; Galvosas, P. Spin Echo NMR Diffusion Studies. Annual Reports on NMR Spectroscopy, Vol 61; Elsevier Academic Press Inc: San Diego, CA, 2007; Vol. 61, pp 51−131. (19) Skoulidas, A. I.; Sholl, D. S. Self-Diffusion and Transport Diffusion of Light Gases in Metal−Organic Framework Materials Assessed Using Molecular Dynamics Simulations. J. Phys. Chem. B 2005, 109, 15760−15768. (20) Babarao, R.; Jiang, J. W. Diffusion and Separation of CO2 and CH4 in Silicalite, C-168 Schwarzite, and IRMOF-1: A Comparative Study from Molecular Dynamics Simulation. Langmuir 2008, 24, 5474−5484. (21) Kärger, J.; Pfeifer, H. NMR Self-Diffusion Studies in Zeolite Science and Technology. Zeolites 1987, 7, 90−107. (22) Amirjalayer, S.; Schmid, R. Mechanism of Benzene Diffusion in MOF-5: A Molecular Dynamics Investigation. Microporous Mesoporous Mater. 2009, 125, 90−96. (23) Xue, C.; Zhong, C. Molecular Simulation Study of Hexane Diffusion in Dynamic Metal−Organic Frameworks. Chin. J. Chem. 2009, 27, 472−478. (24) Rowsell, J. L. C.; Spencer, E. C.; Eckert, J.; Howard, J. A. K.; Yaghi, O. M. Gas Adsorption Sites in a Large-Pore Metal−Organic Framework. Science 2005, 309, 1350−1354. (25) Dubbeldam, D.; Frost, H.; Walton, K. S.; Snurr, R. Q. Molecular Simulation of Adsorption Sites of Light Gases in the Metal−Organic Framework IRMOF-1. Fluid Phase Equilib. 2007, 261, 152−161. (26) Amirjalayer, S.; Tafipolsky, M.; Schmid, R. Molecular Dynamics Simulation of Benzene Diffusion in MOF-5: Importance of Lattice Dynamics. Angew. Chem., Int. Ed. 2007, 46, 463−466. (27) Snurr, R. Q.; Yazaydin, A. Ö .; Dubbeldam, D.; Frost, H., Molecular Modeling of Adsorption and Diffusion in Metal−Organic Frameworks. In Metal−Organic Frameworks: Design and Application, MacGillivray, L. R., Ed.; Wiley: Hoboken, NJ; 2010; pp 313−339.

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Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe achtergracht 166, 1018 WV Amsterdam, The Netherlands. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the Defense Threat Reduction Agency, the National Science Foundation (CTS-0507013), and the German Science Foundation (DFG) via the International Research Traning Group “Diffusion in porous materials” and Grant STA 648/1-2.

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