Insights into Mass Transfer Barriers in Metal–Organic Frameworks

Abstract

Identifying mass transfer limitations is imperative for the practical application of nanoporous solids in adsorptive separations and catalysis. In particular, metal–organic frameworks (MOFs) with a staggering assortment of unique pore architectures and chemical binding sites are one class of materials where understanding structure–property relationships can facilitate material design. Here, we performed volumetric physisorption measurements and collected n-hexane adsorption isotherms of nine Zr-MOFs with unique pore architectures, textural properties, and crystal sizes. We collected measurements on a commercially available adsorption instrument and used a generalized mass transfer model that includes intracrystalline diffusion as well as a possible mass transfer resistance at the crystal boundary. The results indicate that uptake rates in all of the MOFs considered here are limited by mass transfer through crystallite surfaces. Moreover, the severity and guest concentration dependence of these surface resistances differ for each MOF. The identification of surface permeability as the rate-limiting mass transfer process within MOFs will aid the design of next-generation adsorbents and catalysts.

On the Origin of Interfacial Resistance in Ideal Nanomaterials

“…Thus, the interfacial resistance is essentially dependent on the fluid–solid interaction potential. In practice, the interfacial resistance is frequently represented in terms of a finite surface permeability used in a boundary condition for a diffusion model; , however, the use of such a boundary condition in finite systems has been questioned, as the entry length is not negligible in comparison to system size in such cases, and a model considering nonuniform transport coefficient considered more appropriate …”

“…Experimentally, interfacial resistance to fluid transport in nanomaterials, as determined by fitting of diffusion models with finite surface permeability to transient uptake data, is believed to arise from surface pore blockages and structural distortions. 6,9−11 On the contrary, it has also been observed that the low surface permeability is largely nonstructural in origin, and not entirely due to blockages and surface defects, 12 and that it may be a surface diffusion process occurring in a finite region in the vicinity of the pore mouth or external surface. 13−15 In support, molecular dynamics (MD) simulations have suggested the existence of interfacial resistance even in ideal materials, albeit putatively.…”

“…Experimentally, interfacial resistance to fluid transport in nanomaterials, as determined by fitting of diffusion models with finite surface permeability to transient uptake data, is believed to arise from surface pore blockages and structural distortions. ,− On the contrary, it has also been observed that the low surface permeability is largely nonstructural in origin, and not entirely due to blockages and surface defects, and that it may be a surface diffusion process occurring in a finite region in the vicinity of the pore mouth or external surface. − In support, molecular dynamics (MD) simulations have suggested the existence of interfacial resistance even in ideal materials, albeit putatively. − In such simulations, the excess resistance of a finite nanoscale material over that expected based on the diffusivity under periodic boundary conditions (i.e., in the absence of boundaries) is attributed to interfacial resistance, but without direct evidence for its existence or of the underlying mechanisms. These simulations and thermodynamic theories assume the interfacial resistance to reside in a very narrow zone in the solid in the vicinity of the external surface, whose length may be of the order of a nanometer, which is the distance over which the density profile develops, essentially resembling a sharp interface.…”

Influence of Pore Size on Hydrocarbon Transport in Isostructural Metal–Organic Framework Crystallites

“…These frameworks have one-dimensional channels that create a direct diffusional path, which simplified our analysis by eliminating the effect of tortuosity throughout multiple interconnected pathways. , Previous mass transport studies in MOFs have identified additional diffusional resistances at the surfaces of MOF particles, termed surface barriers. These features may result from structural defects on the particle surface, or the narrowing or blockage of pore mouths. ,− We sought to determine whether surface permeation or intracrystalline diffusion is rate limiting to overall mass transport, as well as quantify the mass transport coefficients of hydrocarbons into Co 2 Cl 2 BBTA and Co 2 Cl 2 BTDD. We used a recently reported volumetric method to measure the gas-phase diffusion of hydrocarbons in bulk MOF powders, which allowed us to quantify mass transport simultaneously while collecting adsorption isotherms.…”

Chemically routed interpore molecular diffusion in nanoporous thin films

“…The surface barrier phenomenon 22,23 is related to the steps A and B, while step C is usually the rate limiting factor. 6,24 As the permeation is directly proportional to the diffusivity and adsorbate solubility, managing the interpore diffusion is the key in case of nanoporous solids. Earlier studies revealed that the diffusion in the nanoporous solids, e.g.…”