Fractal analysis of physical adsorption on material surfaces

In order to find the fractal dimension of rough surfaces, adsorption isotherms are studied. Fripiat Gatineau and Van Damme ‘Langmuir 2 (1986) 562’ extended the BET-Formula ‘J. Am. Chem. Soc. 60 (1938) 309’ which was originally designed for flat surfaces. As far as we are aware, this method has never been practically applied. This is mainly due to a term in the formula not expressible in mathematically closed form. Besides, this isotherm displays an inconsistent behavior in the case of surface fractal dimension d=3 ‘Langmuir 4 (1988) 781’. In this paper we present a new modified BET-formula which does not exhibit the inconsistency for d=3 and yields an easy to use algorithm to determine the fractal dimension of a surface from one adsorption isotherm. The fractal dimension of a TiO2–ceramic ultrafiltration membrane is determined according to this method from a N2 adsorption isotherm. The result is compared with the fractal dimension estimated according to a method described by Neimark and Russ ‘J. Phys. Chem. (Transl. Zh. Fiz. Khim.) 64 (1990) 1397’, which uses fractal versions of Kelvin- and Kiselev-equation.