Estimating pore size distribution from the differential curves of comparison plots

Abstract

Comparison plots, t- or alpha (s)-plot were constructed from the data of nitrogen adsorption on porous solids and on a nonporous reference. The variations in adsorption amount V with respect to t or alpha (s), represented by the tangent of the plots, dV/dt (or dV/d alpha (s)), are indicatives of the pore filling and thickening of the adsorbed layer. The shape of the differential plots, dV/dt (or dV/d alpha (s)), versus t (or alpha (s)) thus provide reliable information of the pore size distribution (PSD) of the adsorbents. Sharp peaks were observed on the differential plots for the samples of a uniform pore structure, such as alumina pillared clay and MCM-41 samples, because the filling of the uniform pores occurs in a very narrow range of relative pressure, and thus a very narrow range of t or alpha (s). For the samples of irregular pores, a broad peak on the differential curve is observed, reflecting a wide PSD. Besides, the position of the peak on t axis is intrinsically correlated to the pore size. An empirical expression for such a relation is suggested to be D = 6.347t, using experimental data of MCM-41 samples of various pore sizes. With this simple relation we can convert the differential curve to a PSD curve for microporous and mesoporous solids. This approach involves no mechanism of adsorption, concerning only the phenomenal process of adsorption by porous solids. It avoids theoretical assumption land thus the accompanying limitations), and complicated calculations. For the purpose of deriving PSD information from adsorption isotherm it is reliable and ready to be applied over a wide range of pore sizes.