Determination of the Surface Fractal Dimension for Porous Media by Capillary Condensation

We describe several methods of evaluating the surface fractal dimension of porous media. These include the thermodynamic method and the fractal version of Frenkel−Halsey−Hill theory. Neither method yields accurate estimates of the fractal dimensions of porous solids under the whole range of experimental scales. We propose a modified thermodynamic method that is relatively simple but is significantly more accurate than Neimark's relation from the adsorption experiments. Then we use these methods to estimate the surface fractal dimension of several kinds of porous media. After a concrete analysis of the properties of topology and mercury porosimetry, N2 adsorption, and N2 desorption processes for porous media, we conclude that the real surface fractal dimension should be determined by Dabs (from the adsorption isotherm), Ddes (from the desorption isotherm), and Dm (from the mercury porosimetry) jointly as Dreal = Dabs + (Dm − Ddes).