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The current work deals with the applicability of the fractal version of the Frenkel−Halsey−Hill (FHH) theory of multilayer adsorption. The concept of the standard isotherm is introduced to examine the weakness of this equation when the solid−gas potential controls the adsorption process of gas on a given solid. The results of the determination of the fractal dimension of typical samples of carbon blacks, activated carbon, and aerogels (mixed SiO2−ZrO2 and pure silica) are given. They show that the fractal dimension depends critically of the coverage exponent s for a flat surface of the same chemical nature.

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The surface fractal dimension of commercial rubber-grade carbon blacks and of pyrolytic carbon blacks (CBp) was determined using nitrogen sorption data. The CBp were produced by vacuum pyrolysis of used tires at different temperatures and pressures. Commercial carbon blacks and CBp obtained at low pyrolysis pressures have a similar fractal dimension of the surface (Ds) or roughness. CBp produced at higher pyrolysis pressures have a smaller fractal dimension than commercial grades, suggesting a smoother surface. Complementary SIMS and ESCA investigations showed that the decreasing fractal dimension with increasing pyrolysis pressure is due to the formation of carbonaceous deposits on the CBp from the pyrolyzed organic material.