Improvement in the Pore Size Distribution for Ordered Mesoporous Materials with Cylindrical and Spherical Pores Using the Kelvin Equation

摘要

Ordered mesoporous materials such as MCM-41 and SBA-15, which exhibit cylindrical pores open at both ends and SBA-16 with spherical pores, show a strong influence on adsorption and catalytic processes, basically due to their defined pore sizes. In general, the textural characteristics of these materials are obtained by N₂ adsorption–desorption isotherms at 77 K where, for the calculus of the mesopores size, the “Kelvin equation” is used. Thus, several authors have conducted studies on the pore size distribution (PSD) for these materials, applying diverse methods such as: Barret, Joyner and Halenda (BJH); Dollimore and Heal (DH); and Kruk, Jaroniec and Sayari (BJH-KJS) methods. To obtain the PSD, the BJH and DH methods were proposed for cylindrical pores, using the desorption branch data of the isotherm, meanwhile the BJH-KJS method uses the adsorption branch data, but assumes the mechanism corresponding to the desorption branch for cylindrical pores. Due to the diversity of methods to evaluate the PSD, all of them with different considerations, it is difficult to determine the most suitable. In this work, with the aim to improve the analysis, the PSD was evaluated from the N₂ adsorption–desorption isotherms at 77 K for a series of materials, MCM-41, SBA-15 and SBA-16 type, synthesized in our laboratory. By a modification in the Kelvin equation with the addition of a correction term (f _c ) and assuming appropriate mechanisms of capillary condensation and capillary evaporation, an improved method is proposed to be used for cylindrical as well as spherical pore geometries based on the BJH algorithm. This term was obtained adjusting simulated isotherms with different values of f _c to the experimental isotherm. The results were compared to those obtained by traditional methods and by the Non-Local Density Functional Theory (NLDFT) model.