Adsorption and Dynamics in Hierarchical Metal–Organic Frameworks

Adsorption and dynamics in hierarchical metal–organic frameworks are investigated by means of molecular simulation. The models of hierarchical porous solids are obtained by carving mesopores of different diameters out of a crystal of Cu-BTC (model A) or by inserting a microporous particle of Cu-BTC in an amorphous silica mesopore (model B). We show that the nitrogen adsorption isotherms at 77 K for the solids corresponding to model A can be described as a linear combination of reference adsorption isotherms for pure microporous and mesoporous solids. In contrast, the adsorption isotherms for model B cannot be described accurately as a sum of reference microporous and mesoporous adsorption isotherms. The inserted particle acts as a constriction which helps nucleate the liquid phase within the mesopore so that no capillary condensation hysteresis is observed. The dynamics of nitrogen adsorbed at 77 K inside the porosity of the hierarchical solids is also investigated. The Fickian regime is reached at long times which are not attainable with molecular dynamics simulations. At higher temperature, the faster self-diffusion makes it possible to obtain the diffusivity of the adsorbate. Nitrogen adsorbed in the microporosity of the hierarchical porous solids has a self-diffusion coefficient close to that of nitrogen adsorbed in pure Cu-BTC. In contrast, diffusion in the mesoporosity is faster than in the microporosity so that the overall diffusivity is faster than in pure Cu-BTC

Molecular Simulation of Adsorption and Transport in Hierarchical Porous Materials

Adsorption and transport in hierarchical porous solids with micro- (∼1 nm) and mesoporosities (>2 nm) are investigated by molecular simulation. Two models of hierarchical solids are considered: microporous materials in which mesopores are carved out (model A) and mesoporous materials in which microporous nanoparticles are inserted (model B). Adsorption isotherms for model A can be described as a linear combination of the adsorption isotherms for pure mesoporous and microporous solids. In contrast, adsorption in model B departs from adsorption in pure microporous and mesoporous solids; the inserted microporous particles act as defects, which help nucleate the liquid phase within the mesopore and shift capillary condensation toward lower pressures. As far as transport under a pressure gradient is concerned, the flux in hierarchical materials consisting of microporous solids in which mesopores are carved out obeys the Navier–Stokes equation so that Darcy’s law is verified within the mesopore. Moreover, the flow in such materials is larger than in a single mesopore, due to the transfer between micropores and mesopores. This nonzero velocity at the mesopore surface implies that transport in such hierarchical materials involves slippage at the mesopore surface, although the adsorbate has a strong affinity for the surface. In contrast to model A, flux in model B is smaller than in a single mesopore, as the nanoparticles act as constrictions that hinder transport. By a subtle effect arising from fast transport in the mesopores, the presence of mesopores increases the number of molecules in the microporosity in hierarchical materials and, hence, decreases the flow in the micropores (due to mass conservation). As a result, we do not observe faster diffusion in the micropores of hierarchical materials upon flow but slower diffusion, which increases the contact time between the adsorbate and the surface of the microporosity

Validity of the <i>t‑plot</i> Method to Assess Microporosity in Hierarchical Micro/Mesoporous Materials

The <i>t-plot</i> method is a well-known technique which allows determining the micro- and/or mesoporous volumes and the specific surface area of a sample by comparison with a reference adsorption isotherm of a nonporous material having the same surface chemistry. In this paper, the validity of the <i>t-plot</i> method is discussed in the case of hierarchical porous materials exhibiting both micro- and mesoporosities. Different hierarchical zeolites with MCM-41 type ordered mesoporosity are prepared using pseudomorphic transformation. For comparison, we also consider simple mechanical mixtures of microporous and mesoporous materials. We first show an intrinsic failure of the <i>t-plot</i> method; this method does not describe the fact that, for a given surface chemistry and pressure, the thickness of the film adsorbed in micropores or small mesopores (< 10σ, σ being the diameter of the adsorbate) increases with decreasing the pore size (curvature effect). We further show that such an effect, which arises from the fact that the surface area and, hence, the free energy of the curved gas/liquid interface decreases with increasing the film thickness, is captured using the simple thermodynamical model by Derjaguin. The effect of such a drawback on the ability of the <i>t-plot</i> method to estimate the micro- and mesoporous volumes of hierarchical samples is then discussed, and an abacus is given to correct the underestimated microporous volume by the <i>t-plot</i> method