Incommensurability effects on the specific surface area of nanoporous bodies

The monolayer adsorption of spherical molecules of diameter d on the internal surface of an mth generation Menger sponge MSm of size a as a model substance for a porous body is considered. It is shown that the specific (internal) surface area S of MSm is a highly discontinuous function of the diameter–pore commensurability ratio r=d/am, where am=a/3m is the edge length of the smallest pore. This implies that the fractal dimension D of the sponge cannot be recovered from the usual log–log plot of S vs. r unequivocally.