Quantification of the confinement effect in microporous materials

Abstract

The confinement effect plays a key role in physisorption in microporous materials and many other systems. Confinement is related to the relationship between the pore geometry (pore size and topology) and the geometry of the adsorbed molecule. Geometric properties of the porous solid can be described using the concepts of Gaussian and mean curvatures. In this work we show that the Gaussian and mean curvatures are suited descriptors for mathematically quantifying the confinement of small molecules in porous solids. A method to determine these geometric parameters on microporous materials is presented. The new methodology is based on the reconstruction of the solid's accessible surface. Then, a numerical calculation of the Gaussian and mean curvatures is carried out over the reconstructed mesh. On the one hand, we show that the local curvature can be used to identify the most favourable adsorption sites. On the other hand, the global mean curvature of the solid is correlated to the heat of adsorption of CO2 and CH4 on several zeolites and MOFs. A theoretical justification for this empirical correlation is provided. In conclusion, our methodology allows for a semi-quantitative estimation of confinement, applicable to any pore geometry, independent of the chemical composition, and without the need for applying a force field.

High-throughput computational screening of metal–organic frameworks

“…Other descriptors have also been introduced and used to predict the isosteric heat of adsorption, such as the number of functional groups, dipole moment of the adsorbed gas, boiling temperature of the adsorbed gas and the mean curvature of the pore. 144,145 These descriptors are nice because they can be calculated more quickly than Q st . Another descriptor that has been introduced is the atomic property radial distribution function (AP-RDF), which is tailored for large scale QSPR.…”

Systematic Search of Suitable Metal–Organic Frameworks for Thermal Energy-Storage Applications with Low Global Warming Potential Refrigerants

“…Figure 6d shows that q st0 has a narrower distribution for MOFs with a large surface area than for smaller surface areas. At low porosity, low pore volume, low surface area, or high density, the topology (the curvature and shape of the pores) and the nature of the exposed atoms play an important role on q st0 , 78 which causes this large variation in q st0 . As observed from Figure 6a, the highest q st0 is obtained for ZIF-68 and ZIF-70 with R1234ze(E).…”

Modeling Adsorption Properties on the Basis of Microscopic, Molecular, and Structural Descriptors for Nonpolar Adsorbents

“…The link between simple and real pore geometries (i.e., between spheres and cylinders and arbitrary shapes) is established via the mean curvature of the real solid. Having evaluated the mean curvature of the accessible surface of the real solid, 33 one can calculate the characteristic length of the pore system by assuming cylindrical or spherical geometry. This characteristic length is then identified with the accessible pore radius and used in the descriptor-RSM model.…”

“…We therefore have to find a method to transpose the real pore geometry to a simplified shape (i.e., an assembly of spheres or cylindres) having an equivalent pore radius R that exerts the same confinement effect as the real solid. In a separate work, 33 we have developed a technique to calculate this equivalent pore diameter from the mean curvature of the accessible pore surface of the real solid. We will show here that if the equivalent spherical or cylindrical pore geometry is used within the framework of the RSM then experimental isotherms can be very well reproduced.…”

“…Because no analytical expression for the solid− fluid potential in hyperbolic geometries (consisting of saddle points) is available, we have therefore tested both the spherical and the cylindrical pore model for the case of MFI. The accessible pore radius R acc of the "equivalent" sphere or cylinder was identified with the mean curvature of the real pore system, calculated by the method described in ref 33.…”