Physical meaning of the parameters used in fractal kinetic and generalised adsorption models of Brouers–Sotolongo

The aim of the present study was to clarify the physical meaning of the parameters used in fractal kinetic and generalised isotherm models of Brouers–Sotolongo. For this purpose, adsorption of methylene blue (MB) and methyl orange (MO) onto four activated carbons (ACs) was carried out. These ACs were characterised in terms of composition, surface area, pore volumes and pore size distributions, carbon nanotexture and surface chemistry. Adsorption isotherms were carried out at 25 °C, and at pH 2.5 and 8 for MO and MB, respectively, and fitted with Langmuir, Freundlich, Jovanovich, Hill–Sips, Brouers–Sotolongo, Brouers–Gaspard and General Brouers–Sotolongo (GBS) models. Adsorption kinetics were fitted by traditional pseudo-first and pseudo-second order models and compared to the Brouers–Sotolongo (BSf) fractal kinetic model. GBS and BSf were found to be the best models describing adsorption isotherms and kinetics, respectively. This finding suggests that MB and MO adsorption is probabilistic and closely correlated to the heterogeneous character of the adsorbent surface. Moreover, BSf and GBS parameters were correlated with surface area and amount of surface functional groups. In particular, higher surface area and amount of functional groups respectively decreased and increased the constants τc and α of the BSf stochastic model.