Evaluation of pore size distribution in boundary region of micropore and mesopore using gas adsorption method

This paper discusses an accurate method of pore size distribution evaluation in boundary regions of micropores and mesopores using the gas adsorption process on the basis of the capillary condensation theory, which is liable to be underestimated with the existing BJH and DH methods. A typical nitrogen adsorption isotherm for highly ordered mesoporous silica, which has cylindrical pores with diameter smaller than 4 nm, is considered to be type IV and it is well known for the steep increase of the amount adsorbed through capillary condensation in the region of the relative pressure P/ P 0 smaller than 0.4. In calculating the distribution of the pore size from the change of the amount adsorbed due to capillary condensation, it is important to accurately predict both the multilayer thickness t of the adsorbed nitrogen molecules and the critical radius r c where capillary condensation occurs. It is necessary to consider the curvature of the adsorption layer–gas phase interface when predicting the multilayer thickness t of nitrogen adsorbed within the pore of highly ordered mesoporous silica. Revision of the Kelvin equation is also required when r c is to be predicted. While the predicted value of t based on the Broekhoff and de Boer theory is matched well with the value of t which is actually measured using highly ordered mesoporous silica, and the predicted value of r c based on the GTKB–Kelvin–cylindrical equation that has been revised considering the effect of the interfacial curvature on the interfacial tension of the adsorption layer–gas phase interface is matched with the value of r c which is actually measured using highly ordered mesoporous silica. A combination method of the Broekhoff and de Boer equation and the GTKB–Kelvin–cylindrical equation is proposed as a means of accurately evaluating, from the nitrogen adsorption isotherm, the pore size distribution in the highly ordered mesoporous silica in boundary region of micropore and mesopore. The proposed new method of pore size evaluation features high accuracy and offers the convenience of obtaining the pore size distribution without repeated calculations by employing the same algorithm as DH method. The pore size predicted by the Halsey equation and the Kelvin equation of the conventional DH method is about 20% smaller than the pore size predicted by the newly proposed evaluation method.