, Volume 24, Issue 1, pp 11–27 | Cite as

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

  • Taher Selmi
  • Mongi Seffen
  • Habib Sammouda
  • Sandrine Mathieu
  • Jacek Jagiello
  • Alain Celzard
  • Vanessa Fierro


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.


Dyes adsorption Activated carbon Fractal kinetics Stochastic isotherm Surface heterogeneity Adsorption isotherms 



The Tunisian group gratefully acknowledges the financial support of the EU-METALIC Erasmus Mundus project, and of the Tunisian Ministry of Higher Education and Scientific Research. The French group gratefully acknowledges the financial support of the CPER 2007-2013 “Structuring the Competitiveness Fibre Cluster”, through local (Conseil Général des Vosges), regional (Région Lorraine), national (DRRT and FNADT) and European (FEDER) funds.

Supplementary material

10450_2017_9927_MOESM1_ESM.docx (1.1 mb)
Supplementary material 1 (DOCX 1139 KB)


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Energy and Materials (LabEM), High School of Sciences and Technology of Hammam SousseSousse UniversityHammam SousseTunisia
  2. 2.Institut Jean LamourUMR Université de Lorraine, CNRS 7198Nancy CedexFrance
  3. 3.Micromeritics Instrument CorporationNorcrossUSA
  4. 4.Institut Jean LamourUMR Université de Lorraine, CNRS 7198Epinal Cedex 9France

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