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

Abstract

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 N 2 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 N 2 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.

Influence of Synthesis Parameters in Obtaining KIT-6 Mesoporous Material

“…Taking this into account, all discussion about the PSD and average pore diameter were carried out based on the VBS method applied in the desorption branch. This is because, according to the authors [24,44], the desorption branch reflects the transition of the equilibrium phase, which supports the macroscopic methods that use the Kelvin equation. From the data of the K0.012 and K0.022 samples obtained, there can be seen a similarity in the values of pore diameter when compared to the standard KIT-6.…”

“…From the N 2 adsorption-desorption experimental isotherm data at 77 K, it was possible to apply microscopic (based on molecular theories) and macroscopic (based on capillary condensation) methods. According to some [24,43,44], the most used microscopic method is the NLDFT, and the macroscopic methods are BJH and VBS, these last two based on the Kelvin equation.…”

Aminopropyl-modified mesoporous silica nanospheres for the adsorption of Cr(VI) from water

“…The isotherms of the pure and amino modified samples show the characteristic shape of type IV curves according to the IUPAC classification, associated with mesoporous materials. The absence of a hysteresis loop is associated with a reversible adsorptiondesorption process suggesting the presence of pores with diameters smaller than 4 nm [28,37]. The point corresponding to capillary condensation takes place at low values of relative pressure; besides, a slight shifting towards lower P/P 0 is observed for MSSP-APSw sample indicating a reduction in the pores size caused by the postsynthesis treatment.…”

“…The pore size distribution was determined by the Barrett-Joyner-Halenda/Kruk-Jaroniec-Sayari (BJH-KJS) method from the adsorption branch of the isotherm [28].…”

Incorporating Aluminum Into the Structure of SBA-15 by Adjusting the pH and Adding NaF

“…The aluminum insertion gradually fills the micropores present in the walls of the mesoporous channels, and the surface of these channels becomes more smooth and uniform without the presence of microporosity 20 . In fact, there are significant variations in the specific areas following the aluminum insertion, but the diameter of the mesopores does not vary significantly (BJH method underestimate the pore diameter, but for comparative purposes can be used 22 ), which is a strong evidence for a decrease in microporosity to maintain the diameter of the mesopores. Samples 15AlS61/pH2 and 15AlS120/pH2 presented higher values of specific area and volumes of micropores compared to samples 15AlS61/pH4 and 15AlS120/pH4, respectively (Table 2).…”