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Quantitative Predictions of Molecular Diffusion in Binary MixedLinker Zeolitic Imidazolate Frameworks Using Molecular Simulations Ross J. Verploegh, Ying Wu, Salah Eddine Boulfelfel, and David S. Sholl J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00781 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 21, 2018

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The Journal of Physical Chemistry

Quantitative Predictions of Molecular Diffusion in Binary Mixed-Linker Zeolitic Imidazolate Frameworks Using Molecular Simulations

Ross J. Verploegh1,ǂ, Ying Wu1,2,ǂ, Salah Eddine Boulfelfel1, David S. Sholl1,* 1

2

School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100

The School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, Guangdong, People’s Republic of China 510641

*CORRESPONDING AUTHOR: [email protected]

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ABSTRACT Experimental studies have shown that adsorbate diffusion in zeolitic imidazolate frameworks (ZIFs) can be tuned by incorporating two different imidazolate linkers in the ZIF crystals. We demonstrate for the first time that atomistic simulations are capable of quantitatively predicting self-diffusion in binary mixed-linker ZIFs. Diffusion coefficients of various adsorbates for which prior experimental data exists are predicted in ZIF-8-90, ZIF-8/SALEM-2 materials comprised of imidazolate and 2-methylimidazolate linkers in the cubic SOD topology, and ZIF-7-90 materials over a composition range that is known experimentally to be in the SOD topology. A combination of conventional and biased molecular dynamics simulations as well as a previously developed lattice-diffusion model allows us to access the full range of diffusion time scales for adsorbates such as small hydrocarbons, alcohols, benzene, and water.


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1. INTRODUCTION Metal-organic frameworks (MOFs)1, a class of nanoporous materials formed through the linking of metal ions and organic linkers, will increasingly find themselves useful for molecular storage, delivery, catalytic, sieving, and sensing applications2 as enterprising researchers and engineers identify product/market fits3. Continually adding to an already expansive set of synthesized MOFs, researchers are engineering MOFs with heterogeneous building units, such combinations of metal nodes, organic linkers, and defects.4-8 One subset of MOFs exhibiting heterogeneity are mixed-linker MOFs, also termed hybrid, mixed-ligand, or multivariate MOFs. These mixed-linker MOFs have demonstrated enhanced adsorption properties over their parent MOFs.4 Synthesis protocols for controlling linker placement are being reported such as “programmed pores”9 and sequential linker installation (SLI)10. One challenge associated with mixed-linker MOFs is that they can potentially exhibit both long and short-range ordering of their linkers. The structure of mixed-linker MOFs exhibiting long-range order can be determined using single crystal X-ray diffraction (XRD) techniques.11 Various NMR methods can be used to determine the structure of MOFs exhibiting short-range order (SRO). Because these methods are demanding, however, there are only a handful of mixed-linker MOF families (ZIFs, MTVMOFs, DUT-5, UiO-66) for which the short-range ordering of organic linkers has been experimentally determined.12-15 In this work, we concentrate on zeolitic imidazolate frameworks (ZIFs)11, a well-studied family of MOFs compromised of Zn or Co metal centers and various functionalized imidazolate linkers. ZIFs have demonstrated potential as adsorbents or molecular sieves in both adsorption16 and membrane based separations17-19. ZIFs can form in a multitude of topologies while containing single or multiple types of imidazolate linkers (i.e. mixed-linker ZIFs).20-21 Mixedlinker ZIFs have been synthesized de novo with binary combinations of functionalized imidazolate linkers such as 2-methylimidazolate (mIm), benzimidazolate (BzIm), and carboxaldehyde-2-imidazolate (ImCA).22-23 Post-synthetic modifications such as solvent assisted linker exchange (SALE)24, thermal treatment25, solvent-assisted crystal redemption (SACRed)26, or chemical transformations27 on single-linker ZIFs can also be used to create mixed-linker ZIFs. These methods can create mixed-linker ZIFs exhibiting either long-range order (e.g. ZIF-68, ZIF-69)20 as determined through single crystal x-ray diffraction (XRD) or short-range order (e.g. ZIF-8-90)28. Methods using a combination of NMR techniques and computational modeling 3 ACS Paragon Plus Environment


have been developed to quantify the short-range ordering (SRO) of imidazolate linkers in binary mixed-linker ZIFs.14 The incorporation of multiple functionalized imidazolate linkers allows for tunability of properties such as adsorption and diffusion when compared to the parent singlelinker ZIF materials.22-23, 29 To our knowledge, only three experimental studies have thoroughly examined diffusion in binary mixed-linker ZIFs. Eum et al. demonstrated that varying the mixed-linker composition of ZIF-8x-90100-x allowed for continuous tuning of the diffusion and adsorption of water, alcohol, and C4 isomers.28

Rashidi et al. synthesized ZIF-7x-90100-x materials and showed that by

increasing the mole fraction of benzimidazolate linkers, the transport diffusivities of n-butane and isobutane were decreased by seven and four orders of magnitude, respectively, relative to the diffusivities in parent ZIF-90.23 Zhang and Koros used thermal modifications to make a SALEM-2/ZIF-8 hybrid material.25 They found that upon conversion of 17% of 2methylimidazolate linkers to unfunctionalized imidazolate linkers, the transport diffusivities of SF6 and isobutane increased three orders of magnitude and those of n-butane increase two orders of magnitude relative to the parent material. It would be useful to be able to use computational methods to efficiently and quantitatively treat mixed-linker ZIF materials in order to predict tunable diffusion characteristics as well as to possibly identify hybrid materials that exhibit more favorable diffusion characteristics relative to the parent materials. We present in this work the first quantitative predictions of adsorbate diffusion in binary mixed-linker ZIFs using molecular simulations. We previously examined the qualitative impact of local imidazolate ordering on the self-diffusion of adsorbates using a lattice-based model.30 Here, we extend that work to make quantitative predictions by using detailed molecular simulations to assess local hopping rates. The molecular simulations we present here use the intraZIF force field (FF)31 to describe the kinetic flexibility of the imidazolate linkers. We show that the intraZIF-FF represents relative potential energies from Born-Oppenheimer molecular dynamics (BOMD) simulations of the ZIF-8-90 framework better than the traditional AMBER3233

force field. We also demonstrate that our previously reported lattice-diffusion (LD) model

accurately reproduces the self-diffusivities from conventional molecular dynamics (MD) simulations for methane in ZIF-8-90 materials and make direct comparisons to all existing experimental diffusion data measured using PFG NMR and macroscopic uptake methods for ZIF-8-90 materials. For adsorbates that diffuse on time scales inaccessible to conventional MD, 4 ACS Paragon Plus Environment

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we use local hopping rates from biased MD simulations in combination with our LD model to predict diffusion in the binary mixed-linker ZIFs. We then predict the kinetic separation performance of SALEM-2/ZIF-8 and ZIF-7-90 hybrid materials for several representative adsorbates.

2. THEORY 2.1 Creating Mixed-Linker ZIF Structures We refer to mixed-linker ZIFs with combinations of mIm and ImCA linkers as ZIF-8x90100-x materials and those with combinations of BzIm and ImCA linkers as ZIF-7x-90100-x materials. Since a common name for the SALEM-2/ZIF-8 structure does not exist, we will refer to this structure as ZIFSOD-Imx-mIm100-x since it contains both unfunctionalized imidazolate (Im) and 2-methylimidazolate (mIm) linkers and is in the SOD topology. When referencing nonspecific ZIFs, we will refer to the two imidazolate linkers as type A and type B. The structures of the single-linker parent ZIFs (structure codes VELVOY11 for ZIF-8, WOJGEI27 for ZIF-90, VELVIS11 for ZIF-7, and IMIDZB10 for SALEM-234) were obtained from the Cambridge Structural Database (CSD)35. These structures exist in the SOD topology with cubic unit cells, similar unit cell volumes of 4767, 4904, and 5159 Å3, and pore limiting diameters36 (PLDs) of 3.30, 3.43, and 3.45 Å for SALEM-2, ZIF-8, and ZIF-90 respectively. The SALEM-2, ZIF-8, and ZIF-90 unit cells each contain 24 imidazolate linkers and 12 Zn metal centers. Using the parent ZIFs as starting structures, fully atomistic mixed-linker ZIF structures were created with predetermined binary imidazolate compositions and short-range order (SRO) of the imidazolate linkers. We quantify SRO using the Warren-Cowley parameter37-39 α j =1−

PjA ( B )

xB

(1)

where PjA(B) is the conditional probability of selecting a linker of type B at the jth neighbor site of a linker of type A, and xB is the fractional composition of linker type B. With this definition, a SRO α>0, α=0, or α isobutane and that diffusion of all three adsorbates is slower in ZIF-8 than in ZIF-90. Our calculations predict faster diffusion coefficients of n-butane and 1-butanol and slower diffusion of isobutane than the experimental diffusivities. Eum et al.28 and Zhang et al.55 independently measured n-butane and isobutane corrected diffusivities in ZIF-8 using the same kinetic uptake methodology and found two and three orders of magnitude difference in the diffusivities for nbutane and isobutane respectively. This experimental uncertainty is shown in the upper panel of Figure 7. Measuring slow adsorbate diffusion experimentally has the potential for significant uncertainties, possibly from external heat86 or mass transfer87 effects. For example, Tanaka et al. reported that 1-butanol diffusion in ZIF-8 crystals measured with macroscopic uptake measurements was significantly influenced by surface barriers.88 Similar observations have been made by Remi et al. for 1-butanol diffusion in zeolite SAPO-34.89 Overall, we quantitatively predict self-diffusion of adsorbates when comparing to PFG NMR measurements and provide the same qualitative trends of diffusion as revealed experimentally with macroscopic measurements of adsorbate diffusion in binary mixed-linker ZIF-8-90.


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Figure 7. Comparison of predicted (upper panel) and experimental28 (lower panel) self-diffusivities of nbutane, 1-butanol, and isobutane in ZIF-8x-90100-x. The upper panel features experimentally measured nbutane and isobutane diffusivities by (1) Eum et al.28 and (2) Zhang et al.55 to indicate the experimental uncertainties that exist for these materials. Rates used in the lattice-diffusion model are reported in the Supporting Information (Figure S2).



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4.2 ZIF-8/SALEM-2 in the SOD Topology Zhang and Koros measured transport diffusivities of n-butane, isobutane, and SF6 in hybrid SALEM-2/ZIF-8 materials created through thermal modification of the parent ZIF-8 material.25

They report two significant findings as the mole fraction of unfunctionalized

imidazolate linker increases from 0% to 17%: (1) the transport diffusivities of n-butane, isobutane, and SF6 increase by ~28, 400, and 432 times respectively and (2) the ideal diffusion selectivity of n-butane/isobutane decreases by over an order of magnitude. As a further test of our modeling approach, we attempted to predict these observed trends separate from any experimental input. Since the short-range order of the hybrid SALEM-2/ZIF-8 materials used in these experiments has not been experimentally measured, we used structures with random SRO (α=0).

As discussed above, diffusion is typically a weak function of SRO unless severe

clustering of linkers is occurring.30 Karagiaridi et al. synthesized SALEM-2 through solvent assisted linker exchange (SALE) and determined through XRD refinement that, in a structure containing 15% mIm linkers, these linkers were randomly dispersed.34 Figure 8a shows the rates of N2, methane, n-butane, isobutane, SF6, and benzene hopping through the four window types present in ZIFSOD-Imx-mIm100-x materials. Windows labeled type 1, 2, 3, and 4 have 3 Im, 2 Im/1 mIm, 1 Im/2 mIm, and 3 mIm linkers lining the plane of the window. The rates are calculated using the same procedure as described for the ZIF-8-90 materials. The molecules studied were chosen not only based on the original experimental study but also for their molecular diameters, shape, and charge characteristics. As observed in Figure 8a, the hopping rates for each of adsorbates monotonically decrease from type 1 to type 4 windows. The rate behavior for small molecules such as N2 and CH4 decreases monotonically from type 1 to type 4 windows. One surprising feature of these results is that the type 3 window hopping rate for benzene, which has a molecular diameter of 5.8 Å, is almost two orders of magnitude faster than SF6, which has a molecular diameter of 5.13 Å. Figure 8b shows the self-diffusivities for N2, methane, n-butane, isobutane, SF6, and benzene in ZIFSOD-Imx-mIm100-x at 308 K and infinite dilution. In order to directly compare the experimental transport diffusion coefficients of Zhang and Koros25 to our predicted selfdiffusivities, we calculated corrected diffusivities using single-component thermodynamic correction factors at an equilibrium bulk pressure of 0.03 bar28. 20 ACS Paragon Plus Environment

Since the experimental

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adsorption isotherms in the SALEM-2/ZIF-8 hybrids were not reported by Zhang and Koros, we performed Grand Canonical Monte Carlo (GCMC) simulations of n-butane, isobutane, and SF6 in SALEM-2/ZIF-8 hybrids (SRO α=0.0) under the rigid framework approximation using RASPA-2.090. The simulated isotherms and resulting thermodynamic correction factors as a function of bulk pressure are reported in the Supporting Information (Figures S.5a-S.5f) along with the GCMC simulation details. The open diamonds in Figure 8b show the corrected diffusivities. Our calculations predict that n-butane, isobutane, and SF6 diffuse faster than measured experimentally and that SF6 diffuses more quickly than isobutane over most of the composition range whereas the experimental measurements predict the reverse behavior for SF6 and isobutane.

As mentioned previously, macroscopic measurements of such low diffusion

coefficients are subject to order-of-magnitude uncertainties making an accurate assessment of the diffusion ranking for isobutane and SF6 impossible. We do correctly predict the two trends observed from the experimental single-component n-butane, isobutane, and SF6 transport diffusion data presented by Zhang and Koros. We determine that as the fraction of Im linkers increases from 0% to 20%, that the self-diffusivities of n-butane, isobutane, and SF6 increase by ~5, 476, and 59 times respectively and the ideal diffusion selectivity of n-butane/isobutane decreases by almost two orders of magnitude (Figure S3). While these experimental studies clearly demonstrate the tunable diffusion properties of binary mixed-linker ZIFs, the conclusion may be drawn from ideal diffusion selectivities that one or the other parent ZIF has the highest potential for molecular sieving, not the hybrid material. The self-diffusivities in Figure 8b also show interesting behavior when considering benzene. SALEM-2/ZIF-8 hybrids with mIm mole fractions between 0.4-0.9 have larger ideal diffusion selectivies for binary combinations of isobutane, SF6, and benzene than the parent ZIF materials (Figure S4). Even though the separations shown in the data have little practical interest, they illustrate the possibility that properties of a hybrid ZIF may improve upon the separation capability of the single-linker ZIFs.



(b)


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Figure 8. (a) Hopping rates of N2, methane, n-butane, isobutane, SF6, and benzene through the four window types in SALEM-2/ZIF-8 hybrids at 308 K, and (b) corresponding self-diffusion coefficients predicted using the lattice-diffusion model.

4.3 ZIF-7-90: Window Blocking By a Bulky Imidazolate Linker Rashidi et al. extensively characterized ZIF-7-90 and measured n-butane and isobutane transport diffusivities in these materials.23 They determined that ZIF-7-90 forms in a different topology than the parent ZIF-90 SOD materials for compositions exceeding 40% of benzimidazolate (BzIm) linkers. We have therefore only examined diffusion over the composition range 0-0.4 BzIm mole fraction in the cubic SOD topology.23 In our previous work, we presented a conceptually simple case for which adsorbate diffusion is “blocked” by a bulky imidazolate linker.30 The ZIF-7-90 material has the most potential for this type of behavior among the examples we have studied since benzimidazolate is a large linker that can block the aperture. The experimental data presented by Rashidi et al. indirectly supports this claim as transport diffusivities of n-butane and isobutane decreased by several orders of magnitude relative to the parent material when 40% mole fraction of BzIm linker was added.

Figure 9a

shows the hopping rates for N2, methane, propane, and n-butane as a function of window type in ZIF-7-90 where windows of type 1, 2, 3, and 4 contain 3 ImCA, 2 ImCA/1 BzIm, 1 ImCA/2 BzIm, and 3 BzIm linkers respectively. The hopping rates through the hybrid windows are measured in ZIF-740-9060. The type 4 window hopping rate is also measured in the ZIF-740-9060 structure rather than the parent ZIF-7 structure, since the hybrid structure maintains a rhombohedral unit cell and not the cubic SOD topology.11 A surprising outcome from these calculations is that the hopping rate decreases significantly from a window of type 1 to a window of type 2 but then increases for all four adsorbates in windows of type 3 and 4. Using the hopping rates in Figure 9a, we have predicted the self-diffusion coefficients for N2, methane, propane, and n-butane in ZIF-7x-90100-x as shown in Figure 9b. The self-diffusivities calculated with our standard LD model are in the filled circles. We find that even with hopping rates increasing for windows of type 3 and 4, the self-diffusion monotonically decreases over the entire composition range. One possible explanation for the sharp decrease in transport diffusivities reported by Rashidi et al. could be that, during crystallization of the hybrid material, BzIm linkers located themselves preferentially within “empty” windows. The probability of selecting a window of type 2 at a composition of 0.33 BzIm mole fraction and SRO α=0.0 is ~50% when using our 23 ACS Paragon Plus Environment


original LD model.14 We term our original LD model as having “equal” window probabilities. We also considered a “weighted” LD model where BzIm linkers are placed randomly in windows that do not already contain a BzIm linker. This idea is somewhat analogous to Lowenstein’s rule, which is often invoked in aluminosilicate zeolites as prohibiting occupation of neighboring tetrahedral sites by Al atoms.91-92 Our weighted model produces structures between 0.0 and 0.33 BzIm mole fraction where every window is either a type 1 (i.e. zero BzIm linkers per window) or type 2 (i.e. one BzIm linker per window) window. Structures with compositions between 0.33 and 0.4 BzIm mole fraction are allowed to form windows of type 3 and type 4 only after all windows are initially type 2. ZIF-7-90 structures formed with compositions between 0.0 and 0.33 BzIm mole fraction are constrained to have SRO α exactly equal to 0.0. The SRO α values for structures with compositions between 0.33 and 0.4 BzIm mole fraction are not exactly zero and are slightly positive. For example, a structure containing 35% BzIm yields α=+0.02 and a structure containing 40% BzIm yields α=+0.08. Figure 9b shows the self-diffusivities predicted by the equal and weighted LD models. For BzIm mole fractions larger than 0.2, diffusion is predicted to be orders of magnitude different between the two LD models. This decrease in diffusivity cannot be attributed to a different short-range order because, as noted above, the weighted and equal LD models generated structures with very similar SRO. This is an example in which knowledge of the SRO is insufficient to completely describe the resulting diffusion properties of a mixed linker material. The methods that are currently available for measuring SRO in these materials experimentally are unfortunately not sufficient to assess the kind of local ordering that distinguishes the two models we have considered here.14


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(a)

(b)

Figure 9. (a) Hopping rates of N2, methane, propane and n-butane through the four window types in ZIF7-90 hybrids, and (b) corresponding self-diffusion coefficients predicted through the lattice-diffusion model for ZIF-7-90 structures with SRO α=0. Dashed lines represent the region where the probability of choosing a type one window drops from 52-44% for the “equal” LD model and from 40-25% for the “weighted” diffusion model. The percolation threshold (0.18 for body centered cubic lattice with SRO α=0) is approached much more quickly with the “weighted” LD model.30 25 ACS Paragon Plus Environment


5. SUMMARY In this work, we presented for the first time quantitative diffusion predictions in binary mixed-linker ZIF materials. We accomplished this by first introducing a hybrid intraZIF force field that is capable of representing the configurational potential energies observed in BornOppenheimer molecular dynamics simulations. We used this force field to self-consistently demonstrate that our previously developed lattice-diffusion model yields the same selfdiffusivities as fully detailed NPT-MD simulations for methane in ZIF-8-90 materials. We showed that it is possible to quantitatively predict diffusion of several adsorbates through ZIF-890 by comparison to experimental data taken using PFG NMR and macroscopic kinetic uptake methods. We qualitatively predicted diffusion trends in SALEM-2/ZIF-8 and ZIF-7-90 hybrids. In the SALEM-2/ZIF-8 materials, we correctly predicted diffusion trends seen experimentally. We also determined that a hybrid of this material is capable of higher ideal diffusion selectivities than the parent materials for adsorbates with similar molecular diameters. For ZIF-7-90 materials, we demonstrated that the preferential formation of certain window types can lead to large differences in diffusion predictions. The methods we introduced can be used to identify mixed-linker MOFs that can be used as the selective layer in single-layer membranes. Our simulated diffusivities can further be used to design multilayer membranes such as the ones proposed by Restrepo and Maldovan to manipulate mass flow of two-component gas streams.9394

Their membrane designs utilize metamaterials, engineered composite polymeric materials with

tailored spatial anisotropy; instead of using different polymers, it may be advantageous to use mixed-linker ZIFs. Overall, this suite of methods and conclusions demonstrates that atomistic simulations can quantitatively predict diffusion in mixed-linker MOFs and can be used to identify hybrid MOFs suitable for molecular sieving applications.

6. ASSOCIATED CONTENT Supporting Information Details on the relative potential energy comparisons between PBE-D3(BJ) and the AMBER and intraZIF force fields, mean squared displacement plots from NPT-MD simulations of methane in ZIF-8-90, hopping rates of n-butane, 1-butanol, and isobutane in ZIF-8-90, ideal diffusion selectivities in SALEM-2/ZIF-8 hybrids, and GCMC simulations for SALEM-2/ZIF-8 hybrids. 26 ACS Paragon Plus Environment

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7. AUTHOR INFORMATION Corresponding Author *[email protected] Author Contributions ǂ

These authors contributed equally.

Notes These authors declare no competing financial interest.

8. ACKNOWLEDGEMENTS R.J.V and D.S.S. gratefully acknowledge support from the National Science Foundation grant number 1604375. YW thanks the China Scholarship Council (CSC) (No. 201506150058) for a fellowship to visit the Georgia Institute of Technology.

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