**1. Introduction**

Over approximately the last decade, metal organic framework (MOF) materials have attracted a great deal of attention as a new addition to the classes of nanoporous materials. MOFs, also known as porous coordination polymers (PCPs) or porous coordination networks (PCNs), are hybrid materials composed of single metal ions or polynuclear metal clusters linked by organic ligands through strong coordination bonds. Due to these strong coordination bonds, MOFs are crystallographically well defined structures that can keep their permanent porosity and crystal structure after the removal of the guest species used during synthesis.(Eddaoudi et al., 2000; Li et al., 1999; Rowsell et al., 2005; Yaghi et al., 2003) MOFs typically have low densities (0.2-1 g/cm3), high surface areas (500-4500 m2/g), high porosities and reasonable thermal and mechanical stabilities. This combination of properties has made MOFs interesting materials for a wide range of potential applications, including gas storage, gas separation, catalysis and biomedical applications.(Eddaoudi et al., 2002; Keskin&Kizilel, 2011; Millward&Yaghi, 2005; Mueller et al., 2006; Pan et al., 2004)

MOFs have become attractive alternatives to traditional nanoporous materials specifically in gas storage and gas separation since their synthesis can be readily adapted to control pore connectivity, structure and dimension by varying the linkers, ligands and metals in the material.(Düren et al., 2004; Eddaoudi et al., 2002; El-Kaderi et al., 2007) Hundreds of MOF materials with various physical and chemical characteristics have been synthesized to date.(James, 2003; Kitagawa et al., 2004; Uemura et al., 2005; Yaghi et al., 2003) Most of the studies in the literature have focused on a few specific MOF groups such as IRMOFs (isoreticular MOFs)(Eddaoudi et al., 2002), ZIFs (zeolite imidazolate frameworks)(Park et al., 2006), CPOs (coordination polymers of Oslo)(Dietzel et al., 2005; Dietzel et al., 2006), MILs (Materials of the Institute Lavoisier)(Loiseau et al., 2004), CuBTC (Copper 1,3,5 benzenetricarboxylate) (Chui et al., 1999) and Zn(bdc)(ted)0.5 (Zinc 1,4-benzenedicarboxylic acid-triethylenediamine) (Li et al., 1998). As an example Figure 1 shows the unit cell structure of one of the most widely studied MOFs, CuBTC (also known as HKUST-1). The figures from left to right represent an empty CuBTC structure, a CuBTC structure with CH4 molecules in the pores at 100 bar, 298 K and a CuBTC structure with adsorbed CH4 and H2 molecules in the pores at 100 bar, 298 K for a bulk gas composition of CH4/H2:5/95.

Recent Advances in Molecular Dynamics

**2. Molecular dynamics models** 

addressed in the next section in details.

**2.1 Models for gases** 

Simulations of Gas Diffusion in Metal Organic Frameworks 257

The objective of this chapter is to review the recent advances in MD simulations of gas diffusion in MOFs. In Section 2, the MD models used for gas molecules and MOFs will be introduced. Studies which computed single component and mixture gas diffusivities in MOFs will be reviewed in Section 3. The discussion of comparing results of MD simulations with the experimental measurements and with the predictions of theoretical correlations will be given in Sections 4 and 5, respectively. Finally, opportunities and challenges in using MD simulations for examining gas diffusion in MOFs will be summarized in Section 6.

Gas diffusion is an observable consequence of the motion of atoms and molecules as a response to external force such as temperature, pressure or concentration change. Molecular dynamics (MD) is a natural method to simulate the motion and dynamics of atoms and molecules. The main concept in an MD simulation is to generate successive configurations of a system by integrating Newton's law of motion.(Frenkel&Smit, 2002) Using MD simulations, various diffusion coefficients can be measured from the trajectories showing how the positions and velocities of the particles vary with time in the system. Several different types of gas diffusion coefficients and the methods to measure them will be

In accessing the gas diffusion in nanoporous materials, equilibrium MD simulations which model the behavior of the system in equilibrium have been very widely utilized. In equilibrium MD simulations, first a short grand canonical Monte Carlo (GCMC) simulation is applied to generate the initial configurations of the atoms in the nanopores. Initial velocities are generally randomly assigned to each particle (atom) based on Maxwell-Boltzmann velocity distribution.(Allen&Tildesley, 1987; Frenkel&Smit, 2002) An initial NVT-MD (NVT: constant number of molecules, constant volume, constant temperature) simulation is performed to equilibrate the system. After the equilibration, Newton's equation is integrated and the positions of each particle in the system are recorded at a pre-specified rate. Nosé-Hoover thermostat is very widely applied to keep the desired temperature and the integration of the system dynamics is based on the explicit N-V-T chain integrator by Martyna et al.(Martyna et al., 1992; Martyna et al., 1996) By keeping temperature constant, Newton's equations are integrated in a canonical ensemble (NVT) instead of a microcanonical ensemble (NVE: constant number of molecules, constant volume and constant energy). To describe the dynamics of rigid-linear molecules such as carbon dioxide the MD algorithm of Ciccotti et al.(Ciccotti et al., 1982) is widely used. The so-called order *N* algorithm(Frenkel&Smit, 2002) is

In order to perform classical MD simulations to measure gas diffusion in MOFs' pores, force fields defining interactions between gas molecules-gas molecules and gas molecules-MOF's atoms are required. Once these force fields are specified, dynamical properties of the gases in the simulated material can be probed. These force fields will be studied in two parts:

Diffusion of hydrogen, methane, argon, carbon dioxide and nitrogen are very widely studied in MOFs. For H2, three different types of fluid-fluid potential models have been

implemented to calculate the diffusivities from the saved trajectories.

models for gas molecules (adsorbates) and models for MOFs (adsorbents).

Fig. 1. Unit cell representation of a widely studied MOF, CuBTC. From left to right: Empty CuBTC, CuBTC with CH4 molecules (blue spheres) in the pores, CuBTC with CH4 and H2 (orange spheres) molecules in the pores. The atoms in the unit cell are copper (green), oxygen (red), carbon (gray) and hydrogen (white).

The enormous number of different possible MOFs indicates that purely experimental means for designing optimal MOFs for targeted applications is inefficient at best. Efforts to predict the performance of MOFs using molecular modeling play an important role in selecting materials for specific applications. In many applications that are envisioned for MOFs, diffusion behavior of gases is of paramount importance. Applications such as catalysis, membranes and sensors cannot be evaluated for MOFs without information on gas diffusion rates. Most of the information on gas diffusion in MOFs has been provided by molecular dynamics (MD) studies. Figure 2 indicates that the idea of using MD simulations to assess the diffusivity of gases in MOFs is a new area and there is a rapid growth in the number of publications featuring the terms 'MOFs', 'MD' and 'diffusion' over the past decade.

Fig. 2. Open bars represent the number of publications featuring the term 'metal organic framework', closed bars represent the number of publications featuring the terms 'metal organic framework' and 'molecular dynamics' and 'diffusion'. (Source: ISI Web of Science, retrieved August, 8 2011).

The objective of this chapter is to review the recent advances in MD simulations of gas diffusion in MOFs. In Section 2, the MD models used for gas molecules and MOFs will be introduced. Studies which computed single component and mixture gas diffusivities in MOFs will be reviewed in Section 3. The discussion of comparing results of MD simulations with the experimental measurements and with the predictions of theoretical correlations will be given in Sections 4 and 5, respectively. Finally, opportunities and challenges in using MD simulations for examining gas diffusion in MOFs will be summarized in Section 6.
