A New Method of Calculating Pore Size Distribution: Analysis of Adsorption Isotherms of N2 and CCl4 for a Series of MCM-41 Mesoporous Silicas

Abstract

The adsorption isotherms of N2 gas at 77 K and CCl4 vapor at 283.15, 298.15, and 308.15 K were measured for six samples of the mesoporous silicas having uniform cylindrical pores (MCM-41). The pore radii of the six samples (rp), which were evaluated from the αs plots of the N2 isotherms, were 1.13, 1.29, 1.50, 1.65, 1.90, and 2.53 nm. The CCl4 adsorption isotherms show that the capillary condensation occurs at the very narrow P/P0 range. The core radii of the six adsorbents (rc), which were estimated from a comparison plot of the CCl4 isotherm, were 0.90, 1.01, 1.28, 1.37, 1.60, and 2.17 nm. In the comparison plot, the standard CCl4 isotherm for nonporous silica was used as the reference isotherm. It has been clarified that the Polanyi adsorption potential of capillary condensation is proportional to the reciprocal of the core radii: RT ln(P0/P)=5.37rc−1 nm−1, ln(P0/P)=2.17rc−1 nm−1 at 298.15 K, [A]. The statistical thickness of adsorbed CCl4 on the curved surface (t(pore)), which was estimated from the difference between the pore radii and the core radii, was given by Eq. [B]: t(pore)=0.188+0.336(P/P0)+0.382(P/P0)2 nm [B], (0.08<P/P0<0.60). The equations [A] and [B] give the fundamental information necessary to calculate the pore size distribution of mesoporous adsorbents in the range of rp=1.0–5 nm. Furthermore, it has been found that the pore size distribution up to rp=55 nm can be estimated from Eq. [A] and the adsorbed thickness of CCl4 up to P/P0=0.96 (cf. Table 5).