Scale-dependent nature of the surface fractal dimension for bi- and multi-disperse porous solids by mercury porosimetry

The surface fractal dimension was calculated by using a mathematical model and mercury intrusion data for a variety of bi- and multi-disperse porous solids including silica gels, alumina pellets, and building stones. The mathematical model was obtained by modifying the well-established scaling relation published previously [Ind. Eng. Chem. Res., 34 (1995) 1383-1386]. It was also verified by comparing with the theoretical surface fractal dimensions for regular fractal structures (Skerpinski tetrahedron and Menger sponge) and the calculated surface fractal dimensions for silica gel and alumina particles via the linear fitting method established previously. The calculation results for various bi- and multi-disperse porous solids have demonstrated that the scale-dependent nature of the surface fractal dimension is ubiquitous. The difference in the surface fractal dimension between pore size intervals usually exists. The estimation of the surface fractal dimension on an average stand may lead to erroneous results.