Accurate Method for Calculating Mesopore Size Distributions from Argon Adsorption Data at 87 K Developed Using Model MCM-41 Materials

Argon adsorption isotherms were measured at 87 K for two macroporous silicas and a series of high-quality MCM-41 silicas with approximately cylindrical pores of average diameters from 2 to 6.5 nm. The pore sizes of the MCM-41 samples were accurately determined in earlier studies on the basis of powder X-ray diffraction and nitrogen adsorption using a geometrical relation between the pore volume, pore−center distance, and pore size in the honeycomb structure. Thus acquired model argon adsorption data for cylindrical mesopores were used to determine the statistical film thickness in the pores and the relation between the pore core radius and the capillary condensation/evaporation pressure. The statistical film thickness curve ( t -curve) was extrapolated over the entire pressure range by using data for suitable macroporous silicas. The t -curve is reported in forms of a simple empirical equation and tabulated data. The relation between the pore core radius and the capillary condensation pressure was interpolated and extrapolated over the range from about 2 to at least 50 nm using a suitable empirical equation, which is approximately equivalent to the Kelvin equation for large mesopore sizes. These relations were used in a standard procedure to calculate mesopore size distributions (PSDs). The obtained pore sizes were in excellent agreement with those evaluated on the basis of the geometrical method using X-ray diffraction (XRD) and primary mesopore volume data. Moreover, positions, heights, and widths of the PSD peaks in the primary mesopore range calculated from argon data were in remarkable agreement with those of the PSD data calculated from nitrogen adsorption data at 77 K using a properly calibrated method reported recently. The agreement extended also on the secondary mesopore range (above about 10 nm). The method also correctly reproduced MCM-41 total pore volumes obtained using a single-point method. Thus, an accurate and self-consistent method for calculating PSDs for silicas with cylindrical pores from argon adsorption data measured at 87 K was successfully developed. Moreover, the reported data for macroporous silicas can be used in comparative plot analysis to determine the external surface areas, primary mesopore volumes, and micropore volumes of microporous and mesoporous silicas.