Unified Maxwell–Stefan description of binary mixture diffusion in micro- and meso-porous materials

The Maxwell–Stefan (M–S) formulation for binary mixture diffusion in micro-porous materials such as zeolites, metal organic frameworks (MOFs), and covalent organic frameworks (COFs), that have pore sizes typically smaller than 2 nm, is formulated in a manner that is consistent with corresponding description for meso-porous systems. The M–S equations are set up in terms of species concentrations, ci  , defined in terms of accessible pore volume space. Molecular dynamics simulations were carried out to determine the exchange coefficients Đ12Đ12 for a large variety of binary mixtures in zeolites (MFI, AFI, BEA, FAU, LTA, CHA, and DDR), MOFs (CuBTC, IRMOF-1, Zn(bdc)dabco, Co(bdc)dabco, MIL-47, Co-FA, Mn-FA, and Zn(tbip)), COFs (COF-102, COF-103, and COF-108), and cylindrical silica pores of varying diameters. The exchange coefficients Đ12Đ12 in all structures were found to be related by a constant factor, F, with the corresponding M–S diffusivity for binary fluid   mixture, Đ12,flĐ12,fl, at the same total mixture concentration, ct, as within the pores. The factor F is primarily dictated by the degree of confinement of the guest molecules within the channels, defined as the ratio of the characteristic sizes of the guest molecules to that of the host channels. For meso-porous cylindrical silica pores: F  =1, and Đ12=Đ12,flĐ12=Đ12,fl. For CuBTC, MIL-47, IRMOF-1, and COFs, that have structures with a high fractional open space and channel dimensions of 0.8–1.85 nm, the factor F is found to be in the range 0.55–0.85. For structures such as MFI, BEA, Co-FA, Mn-FA, and Zn(tbip) that have smaller fractional open space, and channels smaller than 0.6 nm, the factor F   has values <0.2. The major conclusion of this study is that fluid mixture diffusivity Đ12,flĐ12,fl provides a good starting point for an engineering estimate of the exchange coefficient Đ12Đ12 in porous materials.