Improvement to the Fractal Adsorption Isotherms of Porous Surfaces

Abstract

The theoretical and experimental Adsorption Isotherms (AI) are essential for the study of surface area and porous structure in solid materials. Also, the fractal dimension characterizes the roughness of a surface which means that a smooth surface has dimension two, whereas that of a highly rugged surface approaches to three. So, although there are several methods to evaluate fractal adsorption isotherms the Fripiat proposal can be considered as the generalization of the Brunauer-Emmett-Teller (BET) formulation for homogeneous surfaces because it contains, as particular case, the classical BET relationship for fractal dimension D=2. However, in the fitting of experimental Nitrogen adsorption data with the Fripiat approach is compulsory to use the BET classical formula for the calculation of the C constant and the monolayer volume. Thus, in order to overcome such constraint, in this work is presented an alternative treatment of fractal adsorption isotherms as applied to porous surfaces. The proposal is based on a relationship between the physical adsorption in homogeneous and inhomogeneous surfaces followed to the assumption that the emerging series are well correlated with polynomials. i.e. we propose an improved formulation to the fractal dimension which is solved by lineal regression avoiding the use of classical parameters. As expected, our proposition contains as particular cases the BET and Fripiat’s formulas. As an example of the usefulness of our proposal, we consider the experimental data of isothermal adsorption obtained with Al₂O₃ that were synthesized via sol-gel at various temperatures; the results are in good agreement with the fractal dimension evolution and with the microporous and mesoporous structure of the materials under consideration.