**4. Comparison of diffusivities from molecular dynamics with experiments**

Measuring diffusivities of gas molecules in nanoporous materials is a challenging process, therefore experimentally measured diffusion data for gases in the pores of MOFs is still very limited. Stallmach and co-workers(Stallmach et al., 2006) carried out the first experimental study in the literature for diffusivity of hydrocarbons in MOF-5. They measured diffusion of methane, ethane, n-hexane, benzene by pulsed field gradient-nuclear magnetic resonance (PFG-NMR) which is a well-established technique for intra-crystalline diffusion studies in nanoporous materials. Diffusion of methane and ethane in MOF-5 was found to be faster than in NaX which was attributed to the larger pores of the former. This study supplied the first experimental data points for gas diffusion in MOFs for direct comparison between experiments and MD simulations. The measured diffusivity of n-hexane, 3.2-4.1×10-9 m2/s, was found to be in a good agreement with the value of 2.2×10-9 m2/s predicted by earlier MD simulations(Sarkisov et al., 2004) for a slightly higher loading. However, the self diffusivity of CH4 measured by PFG-NMR was about one order of magnitude higher than the value of 3.1×10-8 m2/s reported in MD simulations.(Sarkisov et al., 2004; Skoulidas&Sholl, 2005) Stallmach and coworkers attributed this discrepancy to the imperfections that may exist in the MOF structure and loadings used in MD simulations which were lower than the ones considered in the experiments. Zhao and coworkers(Zhao et al., 2009) measured diffusivity of CO2 in MOF-5 and reported a value (8×10-13 m2/s) which is several orders of magnitude smaller than the one obtained by the MD simulations (4×10-9 m2/s)(Skoulidas&Sholl, 2005) and also significantly smaller than the diffusivity of larger adsorbates such as n-hexane, benzene measured by other groups. This large difference between experiments and simulations can be again attributed to the imperfections in the synthesized MOF structure.

The first experimental exploration of the H2 self diffusivity in MOFs was performed by quasielastic neutron scattering (QENS) measurements.(Salles et al., 2008) The QENS technique has proved to be very powerful to extract the loading dependence of the diffusivities for a wide range of adsorbates including H2 diffusivity in zeolites.(Jobic et al., 1999) Combining QENS technique with molecular simulations has been successful in the past to characterize the diffusion mechanism of various adsorbates in nanoporous materials.(Jobic&Theodorou, 2007) The self diffusivities of H2 in MOFs, MIL-47(V) and MIL-53(Cr) were extracted from QENS measurements and compared with the ones predicted by MD simulations performed in the NVT ensemble using the Evans isokinetic

Recent Advances in Molecular Dynamics

accurate for a wide variety of adsorbed mixtures.(Sholl, 2006)

CO2/CH4 in CuBTC.(Keskin&Sholl, 2009a; Keskin et al., 2009a)

the results of MD simulations for ZIF-68 and ZIF-70. (Liu et al., 2011)

**6. Conclusion and outlook** 

Simulations of Gas Diffusion in Metal Organic Frameworks 271

of gas mixtures in membranes mixture diffusivity data is required. However, at the time of that study there was no binary diffusion data available for MOF-5. Keskin and Sholl applied the SSK approach to quantify mixture diffusion of CO2/CH4 in MOF-5. This approach combines information from the loading dependence of the single component self diffusivities and corrected diffusivities (computed from MD simulations) with the binary adsorption isotherms (computed from GCMC simulations) to predict the loading and composition dependent matrix of binary diffusion coefficients. The SSK approach defines the mixture diffusivities for all loadings and compositions, an important feature of any description that will be used in examining a wide range of potential membrane operating conditions. Prior tests of this method by comparison with detailed atomic simulations of binary diffusion in silica zeolites and carbon nanotubes indicated that this approach is

A year later, Keskin and coworkers presented the validity of SSK approach in a MOF.(Keskin et al., 2008) They examined both KP and SSK approaches by comparing predictions of these methods with the results of MD simulations for mixture transport of H2/CH4 in CuBTC. In order to use SSK correlation, continuous functions describing the pure component self and corrected diffusivities were required. The self and corrected diffusivities of each species in H2/CH4 mixture were calculated by MD simulations. Based on these single component diffusivities, the SSK approach predicted the Fickian diffusivities. Mixture MD simulations in a Nosé-Hoover thermostat in the NVT ensemble calculated Onsager coefficients (Equation 4) for H2/CH4 mixture and these values were converted to Fickian diffusivities (Equations 5 and 6). The predictions of the SSK approach for the Fickian diffusivities were in good agreement with the direct MD simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. Mixture self diffusivities were predicted using KP correlations based on single component self diffusivities, corrected diffusivities and fractional loadings. Comparison between KP predictions and mixture MD simulations were also found to be in a good agreement. The SSK approach was also used to obtain Fickian diffusivities of CH4/H2, N2/H2, N2/CH4, CO2/H2, CO2/N2 mixtures in MOF-5 and CH4/H2,

Babarao and Jiang calculated self diffusivities of CH4 and CO2 in IRMOF-1 as a function of total loading based on the adsorption of an equimolar mixture using MD simulations and compared their results with the predictions of KP correlation.(Babarao&Jiang, 2008) Theory predictions were found to be in a fairly good agreement with MD simulations particularly for CH4 diffusivity in IRMOF-1 whereas the CO2 diffusivity was slightly overestimated by the theory. No certain reasoning was given for this overestimation. The predictions of KP correlations for mixture self diffusivities of CH4 and H2 were in reasonable agreement with

Because of the large number of different MOFs that exist, efforts to predict the performance of MOFs using molecular modeling play an important role in selecting materials for specific applications. The high number of publications on MOFs and the dense interest of academy and industry on these new nanoporous materials hint that MOFs have numerous potential applications. Since almost all of these applications require the knowledge of molecular

thermostat.(Frenkel&Smit, 2002) Simulated data was in a good agreement with the experimentally measured data for both MILs. Experiments measured a diffusivity of 9×10-8 m2/s (1.65×10-7 m2/s) and simulations predicted 4.5×10-8 m2/s (1.5×10-7 m2/s) at a loading of 0.5 H2 molecules per unit cell of MIL-53(Cr) (MIL-47(V)). In a similar study, QENS measurements were combined with MD simulations in NVT ensemble using either Berendsen or Evans thermostat to determine the self diffusivity of H2 in the same MILs.(Salles et al., 2008) Two different force fields, spherical one site model(Frost et al., 2006) and explicit two atoms model(Yang&Zhong, 2005) were used in MD simulations of H2. Comparisons between QENS data and MD simulations clearly showed that the two force fields lead to very similar diffusivity values that produce the experimental value. This observation suggests that H2 diffusion is not significantly affected by the potential model.

A combination of MD and QENS measurements were used to examine the diffusivity of water in MIL-53(Cr).(Salles et al., 2011) The breathing of this MOF upon water adsorption induces a structural transition between narrow pore (NP) and large pore (LP) forms. The self diffusivity of water was faster in LP form (8×10-10 m2/s) compared to the one in NP form (2.5×10-11 m2/s) since the confinement degree was much higher in NP structure. As an extension of this work, self, corrected and transport diffusivities of CO2 in MIL-47(V) were determined using MD and QENS.(Salles et al., 2010) While self and corrected diffusivities exhibited a decreasing profile with increased loading as expected, transport diffusivity presented an unexpected trend with a decrease at low loadings. This behavior was attributed to the unusual evolution of thermodynamic correction factor. This work was a good example of probing the transport diffusivity of gases in MOFs by combining MD and QENS.

Two experiments studied diffusion of alkanes in MOFs: The diffusivity of n-butane, isobutane, 2-methylbutane and 2,2-dimethylpropane in CuBTC was investigated using infrared microscopy and MD simulations.(Chmelik et al., 2009) In another work, intracrystalline self diffusivities of propane, propene, n-butane, 1-butene, n-pentane and n-hexane in CuBTC were assessed using PFG-NMR and MD simulations.(Wehring et al., 2010) For the nalkanes, measured diffusivities within the experimental uncertainty agreed with the values from the MD simulations. The different trends observed in diffusivities of alkanes remained as an unsolved issue.
