Effect of the adsorption pH and temperature on the parameters of the Brouers–Sotolongo models

  • Taher SelmiEmail author
  • Mongi Seffen
  • Alain Celzard
  • Vanessa Fierro
Advances in Water and Wastewater Pollutant Elimination


The goal of the present paper was to elucidate if—and how—the parameters of the Brouers–Sotolongo fractal (BSf) (n,α) kinetic model (α and τC) on the one hand, and of the generalised Brouers–Sotolongo (GBS) isotherm model (a and b) on the other hand, are correlated with adsorption pH and temperature. For that purpose, adsorption of aqueous solutions of two common dyes, methylene blue (MB) and methyl orange (MO) was carried out on four activated carbons (ACs) at three temperatures (25, 35 and 50 °C) and three pH (2.5, 5 and 8). Adsorption kinetics and isotherms were measured, and the corresponding curves were best fitted with specific forms of the aforementioned models, and corresponding to equations known as BSf (1,α) kinetic and Brouers–Gaspard isotherm models. Correlations between all model parameters and adsorption conditions were found, bringing some information about the adsorbate–adsorbent interaction.


Adsorption Activated carbon Dyes Fractal kinetics Brouers–Gaspard isotherm Heterogeneous surface 



The authors gratefully acknowledge the financial support from the EU-METALIC: Erasmus Mundus project and the Tunisian Ministry of Higher Education and Scientific Research.

Supplementary material

11356_2018_3835_MOESM1_ESM.docx (4.5 mb)
ESM 1 (DOCX 4573 kb)


  1. Al-Musawi TJ, Brouers F, Zarrabi M (2017) Kinetic modeling of antibiotic adsorption onto different nanomaterials using the Brouers–Sotolongo fractal equation. Environ Sci Pollut Res 24:4048–4057. CrossRefGoogle Scholar
  2. Ben Hamissa AM, Brouers F, Ncibi MC, Seffen M (2013) Kinetic modeling study on methylene blue sorption onto Agave americana fibers: fractal kinetics and regeneration studies. Sep Sci Technol 48:2834–2842. CrossRefGoogle Scholar
  3. Bouhamed F, Elouear Z, Bouzid J, Ouddane B (2016) Multi-component adsorption of copper, nickel and zinc from aqueous solutions onto activated carbon prepared from date stones. Environ Sci Pollut Res 23:15801–15806. CrossRefGoogle Scholar
  4. Brouers F (2014a) The fractal (BSf) kinetics equation and its approximations. J Mod Phys 5:1594–1601. CrossRefGoogle Scholar
  5. Brouers F (2014b) Statistical foundation of empirical isotherms. Open J Stat 4:687–701. CrossRefGoogle Scholar
  6. Brouers F, Al-Musawi TJ (2015) On the optimal use of isotherm models for the characterization of biosorption of lead onto algae. J Mol Liq 212:46–51. CrossRefGoogle Scholar
  7. Brouers F, Francisco M-M (2016) Dubinin isotherms versus the Brouers–Sotolongo family isotherms: A case study. Adsorpt Sci Technol 34:552–564. CrossRefGoogle Scholar
  8. Brouers F, Sotolongo-Costa O (2006) Generalized fractal kinetics in complex systems (application to biophysics and biotechnology). Phys A: Stat Mech Appl 368:165–175. CrossRefGoogle Scholar
  9. Brouers F, Sotolongo O, Marquez F, Pirard JP (2005) Microporous and heterogeneous surface adsorption isotherms arising from Levy distributions. Phys A: Stat Mech Appl 349:271–282. CrossRefGoogle Scholar
  10. Enaime G, Ennaciri K, Ounas A, Baçaoui A, Seffen M, Selmi T, Yaacoubi A (2017) Preparation and characterization of activated carbons from olive wastes by physical and chemical activation: application to Indigo carmine adsorption. J Mater Environ Sci 8:4125–4137Google Scholar
  11. Freundlich H (1906) Over the adsorption in solution. J Phys Chem 57:385–471Google Scholar
  12. Gaspard S, Altenor S, Passe-Coutrin N, Ouensanga A, Brouers F (2006) Parameters from a new kinetic equation to evaluate activated carbons efficiency for water treatment. Water Res 40:3467–3477. CrossRefGoogle Scholar
  13. Ho YS, McKay G (1999) Pseudo-second order model for sorption processes. Process Biochem 34:451–465. CrossRefGoogle Scholar
  14. Burr IW (1942) Cumulative frequency functions. Ann Math Stat 13:215–232. CrossRefGoogle Scholar
  15. Jones LB, Secomb TW, Dewhirst MW, El-Kareh AW (2014) The additive damage model: a mathematical model for cellular responses to drug combinations. J Theor Biol 357:10–20. CrossRefGoogle Scholar
  16. Kesraoui A, Moussa A, Ben Ali G, Seffen M (2016) Biosorption of alpacide blue from aqueous solution by lignocellulosic biomass: Luffa cylindrica fibers. Environ Sci Pollut Res 23:15832–15840. CrossRefGoogle Scholar
  17. Kesraoui A, Selmi T, Seffen M, Brouers F (2017) Influence of alternating current on the adsorption of indigo carmine. Environ Sci Pollut Res 24:9940–9950. CrossRefGoogle Scholar
  18. Klymko PW, Kopelman R (1982) Heterogeneous exciton kinetics: triplet naphthalene homofusion in an isotopic mixed crystal. J Phys Chem 86:3686–3688. CrossRefGoogle Scholar
  19. Kopelman R (1986) Rate processes on fractals: theory, simulations, and experiments. J Stat Phys 42:185–200. CrossRefGoogle Scholar
  20. Kopelman R (1988) Fractal reaction kinetics. Science 241:1620–1626. CrossRefGoogle Scholar
  21. Lagergren S (1898) Zur Theorie der Sogenannten Adsorption Gelöster Stoffe. Kungliga Svenska Vetenskapsakade- miens Handlingar 24:1–39Google Scholar
  22. Langmuir I (1918) The adsorption of gases on plane surfaces of glass, mica, and platinum. J Am Chem Soc 40:1361–1403CrossRefGoogle Scholar
  23. Meilanov RP, Sveshnikova DA, Shabanov OM (2002) Fractal nature of sorption kinetics. J Phys Chem A 106:11771–11774. CrossRefGoogle Scholar
  24. Mohan DP, Headrick TC (2013) A method for simulating burr type iii and type xii distributions through l-moments and l-correlations. Hindawi Publ Corp ISRN Appl Math 2013:14. CrossRefGoogle Scholar
  25. Naidoo R, Singh A, Arya SK, Beadle B, Glass N, Tanha J, Szymanski CM, Evoy S (2012) Surface-immobilization of chromatographically purified bacteriophages for the optimized capture of bacteria. Bacteriophage 2:15–24. CrossRefGoogle Scholar
  26. Ncibi M, Altenor S, Seffen M, Brouers F, Gaspard S (2008) Modelling single compound adsorption onto porous and non-porous sorbents using a deformed Weibull exponential isotherm. Chem Eng J 145:196–202CrossRefGoogle Scholar
  27. Ncibi MC, Mika S (2015) Optimized removal of antibiotic drugs from aqueous solutions usingsingle, double and multi-walled carbon nanotubes. J Hazard Mater 298:102–110. CrossRefGoogle Scholar
  28. Pereira LM (2010) Fractal pharmacokinetics. Comput Math Methods in Med 11:161–184. CrossRefGoogle Scholar
  29. Robledo A, Moyano LG (2008) q-deformed statistical-mechanical property in the dynamics of trajectories en route to the Feigenbaum attractor. Phys Rev E 77:036213. CrossRefGoogle Scholar
  30. Sandro A, Carene B, Evens E, Lambert J, Ehrhardt J-J, Gaspard S (2009) Adsorption studies of methylene blue and phenol onto vetiver roots activated carbon prepared by chemical activation. J Hazard Mater 165:1029–1039. CrossRefGoogle Scholar
  31. Selmi T, Sanchez-Sanchez A, Gadonneix P, Jagiello J, Seffen M, Sammouda H, Celzard A, Fierro V (2018a) Tetracycline removal with activated carbons produced by hydrothermal carbonisation of Agave americana fibres and mimosa tannin. Ind Crop Prod 115:146–157. CrossRefGoogle Scholar
  32. Selmi T, Seffen M, Brouers F, Fierro V, Sammouda H (2018b) Adsorption of model dyes onto porous materials: effect of ph and temperature on the parameters of Brouers-Sotolongo kinetic fractal and generalized isotherm. In: Kallel A, Ksibi M, Ben Dhia H, Khélifi N (eds) Recent advances in environmental science from the Euro-Mediterranean and surrounding regions: Proceedings of Euro-Mediterranean Conference for Environmental Integration (EMCEI-1), Tunisia 2017. Springer International Publishing, Cham, pp 1039–1041. doi:
  33. Selmi T, Seffen M, Sammouda H, Sandrine M, Jagiello J, Celzard A, Fierro V (2018c) Physical meaning of the parameters used in fractal kinetic and generalised adsorption models of Brouers–Sotolongo. Adsorption 24:11–27. CrossRefGoogle Scholar
  34. Sips R (1948) The structure of a catalyst surface. J Chem Phys 16:490–495. CrossRefGoogle Scholar
  35. Sotolongo-Grau O, Rodríguez-Pérez D, Antoranz JC, Sotolongo-Costa O (2010) Tissue radiation response with maximum tsallis entropy. Phys Rev Lett 105:158105CrossRefGoogle Scholar
  36. Sotolongo-Grau O, Rodriguez-Perez D, Sotolongo-Costa O, Antoranz JC (2013) Tsallis entropy approach to radiotherapy treatments. Phys A: Stat Mech Appl 392:2007–2015. CrossRefGoogle Scholar
  37. Stanislavsky A, Weron K (2013) Is there a motivation for a universal behaviour in molecular populations undergoing chemical reactions? Phys Chem Chem Phys 15:15595–15601. CrossRefGoogle Scholar
  38. Temkin MI (1941) Adsorption equilibriumand kinetics of process on non homogeneous surfaces and in the interaction between adsorbed molecules. J Phys Chem 15:296–233Google Scholar
  39. Tonkin JA, Shamsudeen S, Martyn RB, Rita ES, Paul R, Huw DS (2014) Optical tracking of drug release from porous silicon delivery vectors. Insti Eng Technol Optoelectron 8:113–116. CrossRefGoogle Scholar
  40. Tsallis C (2009) Nonadditive entropy and nonextensive statistical mechanics—an overview after 20 years. Braz J Phys 39:337–356. CrossRefGoogle Scholar
  41. Volesky B (2007) Biosorption and me. Water Res 41:4017–4029. CrossRefGoogle Scholar
  42. Weber WJ, Morris JC (1963) Kinetics of adsorption on carbonfrom solution. J Sanit Eng Div 89:31–60Google Scholar
  43. Wu F-C, Tseng R-L, Juang R-S (2009) Characteristics of Elovich equation used for the analysis of adsorption kinetics in dye-chitosan systems. Chem Eng J 150:366–373. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Energy and Materials (LabEM)Higher School of Science and Technology of Hammam Sousse, BP 4011 Hammam Sousse (Sousse University-Tunisia)SousseTunisia
  2. 2.UMR CNRS 7198Institut Jean LamourEpinal Cedex 9France

Personalised recommendations