Abstract
Adsorption is a major basic and applied phenomenon in many scientific disciplines. In particular, the design of adsorbents to remove pollutants from wastewater requires advanced knowledge of adsorption isotherms, which are useful tools to identify physicochemical factors that control adsorption performance. Recent modeling of adsorption isotherms has focused on the use of statistical physics. Here, we review the major adsorption isotherm models based on statistical physics. We discuss steric, energetic, and thermodynamic parameters.
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References
Al Mardini F (2008) Etude de l’adsorption du pesticide Bromacil sur charbon actif en poudre en milieu aqueux : effet compétiteur des matières organiques naturelles. PhD thesis. Université de Poitiers. France
Al-Ghouti MA, Da’ana DA (2020) Guidelines for the use and interpretation of adsorption isotherm models: a review. J Hazard Mater 393:122383. https://doi.org/10.1016/j.jhazmat.2020.122383
Alyousef H, Aouaini F, Ben Yahia M (2020a) New insights on physico-chemical investigation of water adsorption isotherm into seed of dates using statistical physics treatment: pore size and energy distributions. J Mol Liq 298:112041. https://doi.org/10.1016/j.molliq.2019.112041
Alyousef H, Ben Yahia M, Aouaini F (2020b) Statistical physics modeling of water vapor adsorption isotherm into kernels of dates: experiments, microscopic interpretation and thermodynamic functions evaluation. Arab J Chem 13:4691–4702. https://doi.org/10.1016/j.arabjc.2019.11.004
Alyousef AH, Ben Yahia M, Aouaini F (2020c) New insights on microscopic interpretation of adsorption isotherms of ionophores (manganese–porphyrin complexes) using statistical physics formalism. AIP Adv 10:065210. https://doi.org/10.1063/5.0010970
Amrhar O, Nassali H, Elyoubi SM (2015) Application of nonlinear regression analysis to select the optimum absorption isotherm for Methylene Blue adsorption onto Natural Illitic Clay. Bull Soc Roy Sci Liège 84:116–130
Amrhar O, Berisha A, El Gana L, Nassali H, Elyoubi MS (2021) Removal of methylene blue dye by adsorption onto Natural Muscovite Clay: experimental, theoretical and computational investigation. Inter J Envon Anal Chem 1–26. https://doi.org/10.1080/03067319.2021.1897119
Ariga K, Lvov Y, Kunitake T (1997) Assembling alternate dye−polyion molecular films by electrostatic layer-by-layer adsorption. J Am Chem Soc 119:2224–2231. https://doi.org/10.1021/ja963442c
Atrous M, Sellaoui L, Bouzid M, Lima EC, Thue PS, Bonilla-Petriciolet A, Ben Lamine A (2019) Adsorption of dyes acid red 1 and acid green 25 on grafted clay: modeling and statistical physics interpretation. J Mol Liq 294:111610. https://doi.org/10.1016/j.molliq.2019.111610
Ayachi F, Nakbi A, Sakly A, Pinto LAA, Ben Lamine A (2019a) Application of statistical physics formalism for the modeling of adsorption isotherms of water molecules on the microalgae Spirulina platensis. Food Bioprod Process 114:103–112. https://doi.org/10.1016/j.fbp.2018.12.001
Ayachi FZ, Kyzas G, Aatrous M, Sakly A, Ben Lamine A (2019b) Evaluating the adsorption of Ni(II) and Cu(II) on spirulina biomass by statistical physics formalism. J Ind Eng Chem 80:461–470. https://doi.org/10.1016/j.jiec.2019.05.044
Azha SF, Sellaoui L, Shamsudin MS, Ismail S, Bonilla-Petriciolet A, Ben Lamine A, Erto A (2018) Synthesis and characterization of a novel amphoteric adsorbent coating for anionic and cationic dyes adsorption: experimental investigation and statistical physics modelling. Chem Eng J 351:221–229. https://doi.org/10.1016/j.cej.2018.06.092
Ben Manaa M, Schmaltz B, Bouaziz N, Berton N, Van FT, Ben Lamine A (2018) Adsorption isotherms of N3 dye on TiO2 mesoporous for dye sensitized solar cells: their realization, their modeling and consequent interpretations using a statistical physics treatment. J Alloy Compd 765:385–395. https://doi.org/10.1016/j.jallcom.2018.06.234
Ben Torkia Y, Dotto GL, Ben Lamine A (2018) Statistical physics modeling of synthetic dyes adsorption onto Spirulina platensis nanoparticles. Environ Sci Pollut Res 25:28973–28984. https://doi.org/10.1007/s11356-018-2898-x
Ben Yahia M, Knani S, Dhaou H, Hachicha MA, Jemni A, Ben Lamine A (2013) Modeling and interpretations by the statistical physics formalism of hydrogen adsorption isotherm on LaNi4.75Fe0.25. Int J Hydrogen Energy 38:11536–11542. https://doi.org/10.1016/j.ijhydene.2013.03.083
Bergaoui M, Nakhli A, Al-Muhtaseb S, Khalfaoui M (2018a) Adsorption process of n-alkanes onto BAX-1100 activated carbon: Theoretical estimation of isosteric heat of adsorption and energy distribution of heterogeneous surfaces. J Mol Liq 252:399–407. https://doi.org/10.1016/j.molliq.2018.01.016
Bergaoui M, Nakhli A, Benguerba Y, Khalfaoui M, Erto A, Soetaredjo FE, Ismadji S, Ernst B (2018b) Novel insights into the adsorption mechanism of methylene blue onto organo-bentonite: Adsorption isotherms modeling and molecular simulation. J Mol Liq 272:697–707. https://doi.org/10.1016/j.molliq.2018.10.001
Briki C, Bouzid M, Dhaou MH, Jemni A, Lamine AB (2018) Experimental and theoretical study of hydrogen absorption by LaNi3.6Mn0.3Al0.4Co0.7 alloy using statistical physics modeling. Int J Hydrogen Energy 43:9722–9732. https://doi.org/10.1016/j.ijhydene.2018.02.201
Brown AM (2001) A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet. Comput Methods Programs Biomed 65:191–200. https://doi.org/10.1016/S0169-2607(00)00124-3
Carter MC, Kilduff JE, Weber WJ (1995) Site energy distribution analysis of preloaded adsorbents. Environ Sci Technol 29:1773–1780. https://doi.org/10.1021/es00007a013
Cerofolini GF (1974) Localized adsorption on heterogeneous surfaces. Thin Solid Films 23:129–152. https://doi.org/10.1016/0040-6090(74)90235-1
Chowdhury S, Mishra R, Saha P, Kushwaha P (2011) Adsorption thermodynamics, kinetics and isosteric heat of adsorption of malachite green onto chemically modified rice husk. Desalination 265:159–168. https://doi.org/10.1016/j.desal.2010.07.047
Crini G, Lichtfouse E, Wilson LD, Morin-Crini N (2019) Conventional and non-conventional adsorbents for wastewater treatment. Environ Chem Lett 17:195–213. https://doi.org/10.1007/s10311-018-0786-8
Diu B, Guthmann C, Lederer D, Roulet B (2001) Eléments de physique statistique. Enseignement des sciences, HERMANN
Dotto GL, Pinto LAA, Hachicha MA, Knani S (2015) New physicochemical interpretations for the adsorption of food dyes on chitosan films using statistical physics treatment. Food Chem 171:1–7. https://doi.org/10.1016/j.foodchem.2014.08.098
Dotto GL, Sellaoui L, Lima EC, Lamine AB (2016) Physicochemical and thermodynamic investigation of Ni(II) biosorption on various materials using the statistical physics modeling. J Mol Liq 220:129–135. https://doi.org/10.1016/j.molliq.2016.04.075
Duan S, Gu M, Tao M, Xian X (2020) Adsorption of methane on shale: statistical physics model and site energy distribution studies. Energy Fuels 34:304–318. https://doi.org/10.1021/acs.energyfuels.9b03746
Foo KY, Hameed BH (2010) Insights into the modeling of adsorption isotherm systems. Chem Eng J 156:2–10. https://doi.org/10.1016/j.cej.2009.09.013
Franco DSP, Piccin JS, Lima EC, Dotto GL (2015) Interpretations about methylene blue adsorption by surface modified chitin using the statistical physics treatment. Adsorption 21:557–564. https://doi.org/10.1007/s10450-015-9699-z
Gal S (1974) Recent advances in techniques for the determination of sorption isotherms. Water relations of foods. In: Duckworth RB (ed). pp 139-154
Giles CH, Smith D, Huitson A (1974) A general treatment and classification of the solute adsorption isotherm. I. Theoretical. J Colloid Interface Sci 47:755–765. https://doi.org/10.1016/0021-9797(74)90252-5
Gómez-Avilés A, Sellaoui L, Badawi M, Bonilla-Petriciolet A, Bedia J, Belver C (2021) Simultaneous adsorption of acetaminophen, diclofenac and tetracycline by organo-sepiolite: Experiments and statistical physics modelling. Chem Eng J 404:126601. https://doi.org/10.1016/j.cej.2020.126601
Gupta VK, Suhas (2009) Application of low-cost adsorbents for dye removal – A review. J Environ Manage 90:2313–2342. https://doi.org/10.1016/j.jenvman.2008.11.017
Gupta VK, Carrott PJM, Ribeiro Carrott MML, Suhas (2009) Low-cost adsorbents: growing approach to wastewater treatment—a review. Crit Rev Environ Sci Technol 39:783–842. https://doi.org/10.1080/10643380801977610
Hamid SA, Azha SF, Sellaoui L, Bonilla-Petriciolet A, Ismail S (2020) Adsorption of copper (II) cation on polysulfone/zeolite blend sheet membrane: Synthesis, characterization, experiments and adsorption modelling. Colloids Surf. A Physicochem. Eng. Asp. 601:124980. https://doi.org/10.1016/j.colsurfa.2020.124980
Hanafy H, Sellaoui L, Thue PS, Lima EC, Dotto GL, Alharbi T, Belmabrouk H, Bonilla-Petriciolet A, Lamine AB (2020) Statistical physics modeling and interpretation of the adsorption of dye remazol black B on natural and carbonized biomasses. J Mol Liq 299:112099. https://doi.org/10.1016/j.molliq.2019.112099
He J, Guo J, Zhou Q, Fang F (2019) Adsorption characteristics of nitrite on natural filter medium: kinetic, equilibrium, and site energy distribution studies. Ecotoxicol Environ Saf 169:435–441. https://doi.org/10.1016/j.ecoenv.2018.11.039
Ho Y-S (2004) Selection of optimum sorption isotherm. Carbon 42:2115–2116. https://doi.org/10.1016/j.carbon.2004.03.019
Ho YS, Porter JF, McKay G (2002) Equilibrium isotherm studies for the sorption of divalent metal ions onto peat: copper, nickel and lead single component systems. Water Air Soil Pollut 141:1–33. https://doi.org/10.1023/A:1021304828010
Jedli H, Briki C, Chrouda A, Brahmi J, Abassi A, Jbara A, Slimi K, Jemni A (2019) Experimental and theoretical study of CO 2 adsorption by activated clay using statistical physics modeling. RSC Adv 9:38454–38463. https://doi.org/10.1039/C9RA05904K
Jin Q, Yang Y, Dong X, Fang J (2016) Site energy distribution analysis of Cu (II) adsorption on sediments and residues by sequential extraction method. Environ Pollut 208:450–457. https://doi.org/10.1016/j.envpol.2015.10.014
Khalfaoui M, Nakhli A, Aguir Ch, Omri A, M’henni MF, Ben Lamine A (2014) Statistical thermodynamics of adsorption of dye DR75 onto natural materials and its modifications: double-layer model with two adsorption energies. Environ Sci Pollut Res 21:3134–3144. https://doi.org/10.1007/s11356-013-2263-z
Knani S, Mathlouthi M, Ben Lamine A (2007) Modeling of the psychophysical response curves using the grand canonical ensemble in statistical physics. Food Biophys 2:183–192. https://doi.org/10.1007/s11483-007-9042-7
Knani S, Khalifa N, Ben Yahia M, Aouaini F, Tounsi M (2020) Statistical physics study of the interaction of the 5, 10, 15, 20-tetrakis (4-tolylphenyl) porphyrin (H2TTPP) with magnesium ion: New microscopic interpretations. Arab J Chem 13:4374–4385. https://doi.org/10.1016/j.arabjc.2019.08.010
Krstić V, Urošević T, Pešovski B (2018) A review on adsorbents for treatment of water and wastewaters containing copper ions. Chem Eng Sci 192:273–287. https://doi.org/10.1016/j.ces.2018.07.022
Kumar KV, Monteiro de Castro M, Martinez-Escandell M, Molina-Sabio M, Rodriguez-Reinoso F (2011) A site energy distribution function from Toth isotherm for adsorption of gases on heterogeneous surfaces. Phys Chem Chem Phys 13:5753. https://doi.org/10.1039/c0cp00902d
Lamine AB, Bouazra Y (1997) Application of statistical thermodynamics to the olfaction mechanism. Chem Senses 22:67–75. https://doi.org/10.1093/chemse/22.1.67
Lebron YAR, Moreira VR, Drumond GP, Gomes GCF, da Silva MM, de Bernardes R, Jacob RSO, Viana MM, de Vasconcelos CKB, de Santos LVS (2020) Statistical physics modeling and optimization of norfloxacin adsorption onto graphene oxide. Colloids Surf, A 606:125534. https://doi.org/10.1016/j.colsurfa.2020.125534
Li Z, Gómez-Avilés A, Sellaoui L, Bedia J, Bonilla-Petriciolet A, Belver C (2019a) Adsorption of ibuprofen on organo-sepiolite and on zeolite/sepiolite heterostructure: Synthesis, characterization and statistical physics modeling. Chem Eng J 371:868–875. https://doi.org/10.1016/j.cej.2019.04.138
Li Z, Sellaoui L, Dotto GL, Lamine A, Bonilla-Petriciolet A, Hanafy H, Belmabrouk H, Netto MS, Erto A (2019b) Interpretation of the adsorption mechanism of Reactive Black 5 and Ponceau 4R dyes on chitosan/polyamide nanofibers via advanced statistical physics model. J Mol Liq 285:165–170. https://doi.org/10.1016/j.molliq.2019.04.091
Li Z, Hanafy H, Zhang L, Sellaoui L, Schadeck Netto M, Oliveira MLS, Seliem MK, Luiz Dotto G, Bonilla-Petriciolet A, Li Q (2020a) Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: experiments, characterization and physical interpretations. Chem Eng J 388:124263. https://doi.org/10.1016/j.cej.2020.124263
Li G, Wang Y, Bi J, Huang X, Mao Y, Luo L, Hao H (2020b) Partial oxidation strategy to synthesize WS2/WO3 heterostructure with enhanced pdsorption Performance for organic dyes: Synthesis, modelling, and mechanism. Nanomaterials 10:278. https://doi.org/10.3390/nano10020278
Lima DR, Sellaoui L, Klein L, Reis GS, Lima ÉC, Dotto GL (2018) Physicochemical and thermodynamic study of malachite green adsorption on raw and modified corn straw. Can J Chem Eng 96:779–787. https://doi.org/10.1002/cjce.22948
Limousin G, Gaudet J-P, Charlet L, Szenknect S, Barthès V, Krimissa M (2007) Sorption isotherms: a review on physical bases, modeling and measurement. Appl Geochem 22:249–275. https://doi.org/10.1016/j.apgeochem.2006.09.010
Lvov Y, Ariga K, Ichinose I, Kunitake T (1995) Assembly of multicomponent protein films by means of electrostatic layer-by-layer adsorption. J Am Chem Soc 117:6117–6123. https://doi.org/10.1021/ja00127a026
Marwa BM, Bruno S, Mongi B, Van Tran F, Abdelmottaleb BL (2016) Modeling of adsorption isotherms of dye N719 on titanium oxide using the grand canonical ensemble in statistical physics for dye sensitized solar cells. Sol Energy 135:177–187. https://doi.org/10.1016/j.solener.2016.05.015
Mobarak M, Mohamed EA, Selim AQ, Eissa MF, Seliem MK (2019a) Experimental results and theoretical statistical modeling of malachite green adsorption onto MCM–41 silica/rice husk composite modified by beta radiation. J Mol Liq 273:68–82. https://doi.org/10.1016/j.molliq.2018.09.132
Mobarak M, Mohamed EA, Selim AQ, Mohamed FM, Sellaoui L, Bonilla-Petriciolet A, Seliem MK (2019b) Statistical physics modeling and interpretation of methyl orange adsorption on high–order mesoporous composite of MCM–48 silica with treated rice husk. J Mol Liq 285:678–687. https://doi.org/10.1016/j.molliq.2019.04.116
Nakhli A, Khalfaoui M, Aguir C, Bergaoui M, M’henni MF, Ben Lamine A (2014) Statistical physics studies of multilayer adsorption on solid surface: adsorption of basic blue 41 dye onto functionalized Posidonia Biomass. Sep Sci Technol 49:2525–2533. https://doi.org/10.1080/01496395.2014.929703
Nakhli A, Bergaoui M, Aguir C, Khalfaoui M, M’henni MF, Ben Lamine A (2016) Adsorption thermodynamics in the framework of the statistical physics formalism: basic blue 41 adsorption onto Posidonia biomass. Desalin Water Treat 57:12730–12742. https://doi.org/10.1080/19443994.2015.1052564
Nakhli A, Mbouga MGN, Bergaoui M, Khalfaoui M, Cretin M, Huguet P (2017) Non-linear analysis in estimating model parameters for thymol adsorption onto hydroxyiron-clays. J Mol Liq 244:201–210. https://doi.org/10.1016/j.molliq.2017.08.128
Nakhli A, Mbouga MGN, Bergaoui M, Khalfaoui M, Cretin M, Huguet P (2018) Modeling of essential oils adsorption onto clays towards a better understanding of their interactions. J Mol Liq 249:132–143. https://doi.org/10.1016/j.molliq.2017.11.012
Ng JCY, Cheung WH, McKay G (2002) Equilibrium studies of the sorption of Cu(II) ions onto chitosan. J Colloid Interface Sci 255:64–74. https://doi.org/10.1006/jcis.2002.8664
Pang X, Sellaoui L, Franco D, Dotto GL, Georgin J, Bajahzar A, Belmabrouk H, Ben Lamine A, Bonilla-Petriciolet A, Li Z (2019) Adsorption of crystal violet on biomasses from pecan nutshell, para chestnut husk, araucaria bark and palm cactus: Experimental study and theoretical modeling via monolayer and double layer statistical physics models. Chem Eng J 378:122101. https://doi.org/10.1016/j.cej.2019.122101
Rangabhashiyam S, Anu N, Giri Nandagopal MS, Selvaraju N (2014) Relevance of isotherm models in biosorption of pollutants by agricultural byproducts. J Environ Chem Eng 2:398–414. https://doi.org/10.1016/j.jece.2014.01.014
Rouquerol F, Rouquerol J, Sing K (1999) General conclusions and recommendations. Adsorption by Powders and Porous Solids. Elsevier, pp 439–447
Selim AQ, Sellaoui L, Ahmed SA, Mobarak M, Mohamed EA, Lamine AB, Erto A, Bonilla-Petriciolet A, Seliem MK (2019a) Statistical physics-based analysis of the adsorption of Cu2+ and Zn2+ onto synthetic cancrinite in single-compound and binary systems. J Environ Chem Eng 7:103217. https://doi.org/10.1016/j.jece.2019.103217
Selim AQ, Sellaoui L, Mobarak M (2019b) Statistical physics modeling of phosphate adsorption onto chemically modified carbonaceous clay. J Mol Liq 279:94–107. https://doi.org/10.1016/j.molliq.2019.01.100
Sellaoui L, Guedidi H, Knani S, Reinert L, Duclaux L, Ben Lamine A (2015) Application of statistical physics formalism to the modeling of adsorption isotherms of ibuprofen on activated carbon. Fluid Phase Equilib 387:103–110. https://doi.org/10.1016/j.fluid.2014.12.018
Sellaoui L, Depci T, Kul AR, Knani S, Ben Lamine A (2016a) A new statistical physics model to interpret the binary adsorption isotherms of lead and zinc on activated carbon. J Mol Liq 214:220–230. https://doi.org/10.1016/j.molliq.2015.12.080
Sellaoui L, Dotto GL, Gonçalves JO, Pinto LAA, Knani S, Lamine AB (2016b) Equilibrium modeling of single and binary adsorption of Food Yellow 4 and Food Blue 2 on modified chitosan using a statistical physics theory: new microscopic interpretations. J Mol Liq 222:151–158. https://doi.org/10.1016/j.molliq.2016.07.005
Sellaoui L, Guedidi H, SarraWjihi S, Reinert L, Knani S, Duclaux L, Ben Lamine A (2016c) Experimental and theoretical studies of adsorption of ibuprofen on raw and two chemically modified activated carbons: new physicochemical interpretations. RSC Adv 6:12363–12373. https://doi.org/10.1039/C5RA22302D
Sellaoui L, Dotto GL, Lamine AB, Erto A (2017a) Interpretation of single and competitive adsorption of cadmium and zinc on activated carbon using monolayer and exclusive extended monolayer models. Environ Sci Pollut Res 24:19902–19908. https://doi.org/10.1007/s11356-017-9562-8
Sellaoui L, Edi Soetaredjo F, Ismadji S, Lima CE, Dotto GL, Ben Lamine A, Erto A (2017b) New insights into single-compound and binary adsorption of copper and lead ions on a treated sea mango shell: experimental and theoretical studies. Phys Chem Chem Phys 19:25927–25937. https://doi.org/10.1039/C7CP03770H
Sellaoui L, Mechi N, Lima ÉC, Dotto GL, Ben Lamine A (2017c) Adsorption of diclofenac and nimesulide on activated carbon: Statistical physics modeling and effect of adsorbate size. J Phys Chem Solids 109:117–123. https://doi.org/10.1016/j.jpcs.2017.05.019
Sellaoui L, Mendoza-Castillo DI, Reynel-Ávila HE, Bonilla-Petriciolet A, Ben Lamine A, Erto A (2018a) A new statistical physics model for the ternary adsorption of Cu2+, Cd2+ and Zn2+ ions on bone char: experimental investigation and simulations. Chem Eng J 343:544–553. https://doi.org/10.1016/j.cej.2018.03.033
Sellaoui L, Soetaredjo FE, Ismadji S, Bonilla-Petriciolet A, Belver C, Bedia J, Ben Lamine A, Erto A (2018b) Insights on the statistical physics modeling of the adsorption of Cd2+ and Pb2+ ions on bentonite-chitosan composite in single and binary systems. Chem Eng J 354:569–576. https://doi.org/10.1016/j.cej.2018.08.073
Sellaoui L, Soetaredjo FE, Ismadji S, Benguerba Y, Dotto GL, Bonilla-Petriciolet A, Rodrigues AE, Lamine AB, Erto A (2018c) Equilibrium study of single and binary adsorption of lead and mercury on bentonite-alginate composite: experiments and application of two theoretical approaches. J Mol Liq 253:160–168. https://doi.org/10.1016/j.molliq.2018.01.056
Sellaoui L, Mendoza-Castillo DI, Reynel-Ávila HE, Ávila-Camacho BA, Díaz-Muñoz LL, Ghalla H, Bonilla-Petriciolet A, Lamine AB (2019) Understanding the adsorption of Pb2+, Hg2+ and Zn2+ from aqueous solution on a lignocellulosic biomass char using advanced statistical physics models and density functional theory simulations. Chem Eng J 365:305–316. https://doi.org/10.1016/j.cej.2019.02.052
Sellaoui L, Franco D, Ghalla H, Georgin J, Netto M, Dotto GL, Bonilla-Petriciolet A, Belmabrouk H, Bajahzar A (2020) Insights of the adsorption mechanism of methylene blue on brazilian berries seeds: Experiments, phenomenological modelling and DFT calculations. Chem Eng J 394:125011. https://doi.org/10.1016/j.cej.2020.125011
Shen X, Guo X, Zhang M, Tao S, Wang X (2015) Sorption mechanisms of organic compounds by carbonaceous materials: site energy distribution consideration. Environ Sci Technol 49:4894–4902. https://doi.org/10.1021/es506034e
Singh NB, Nagpal G, Agrawal S, Rachna (2018) Water purification by using adsorbents: a review. Environ Technol Innov 11:187–240. https://doi.org/10.1016/j.eti.2018.05.006
Sircar S (1991) Isosteric heats of multicomponent gas adsorption on heterogeneous adsorbents. Langmuir 7:3065–3069. https://doi.org/10.1021/la00060a027
Sivarajasekar N, Baskar R (2014) Adsorption of basic red 9 onto activated carbon derived from immature cotton seeds: isotherm studies and error analysis. Desalin Water Treat 52:7743–7765. https://doi.org/10.1080/19443994.2013.834518
Souissi H, Ben Yahia M (2021) Application of innovative analytical modeling for the physicochemical analysis of adsorption isotherms of silver nitrate on helicenes: phenomenological study of the complexation process. Adsorpt Sci Technol 2021:1–14. https://doi.org/10.1155/2021/6619389
Toumi KH, Benguerba Y, Erto A, Dotto GL, Khalfaoui M, Tiar C, Nacef S, Amrane A (2018) Molecular modeling of cationic dyes adsorption on agricultural Algerian olive cake waste. J Mol Liq 264:127–133. https://doi.org/10.1016/j.molliq.2018.05.045
Wjihi S, Peres EC, Dotto GL, Lamine AB (2019) Physicochemical assessment of crystal violet adsorption on nanosilica through the infinity multilayer model and sites energy distribution. J Mol Liq 280:58–63. https://doi.org/10.1016/j.molliq.2018.12.064
Yagub MT, Sen TK, Afroze S, Ang HM (2014) Dye and its removal from aqueous solution by adsorption: a review. Adv Coll Interface Sci 209:172–184. https://doi.org/10.1016/j.cis.2014.04.002
Yahia MB, Manel BY (2020a) New insights in the physicochemical investigation of the vitamin B 12 nucleus using statistical physics treatment: interpretation of experiments and surface properties. RSC Adv 10:21724–21735. https://doi.org/10.1039/D0RA03077E
Yahia MB, Manel BY (2020b) Physico-chemical study of complexation of silver ion (Ag+) by macrocyclic molecules (hexa-Helicenes) based on statistical physics theory: new description of a cancer drug. Sci Rep 10:10328. https://doi.org/10.1038/s41598-020-67120-4
Yahia MB, Sellaoui L (2020) Adsorptive removal of sunset yellow dye by biopolymers functionalized with (3–aminopropyltriethoxysilane): Analytical investigation via advanced model. J Mol Liq 312:113395. https://doi.org/10.1016/j.molliq.2020.113395
Yahia MB, Hsan LBH, Knani S, Yahia MB, Nasri H, Lamine AB (2016) Modeling of adsorption isotherms of zinc nitrate on a thin layer of porphyrin. J Mol Liq 222:576–585. https://doi.org/10.1016/j.molliq.2016.07.011
Yahia MB, Tounsi M, Aouaini F, Knani S, Yahia MB, Ben Lamine A (2017a) A statistical physics study of the interaction of [7]-helicene with alkali cations (K + and Cs + ): new insights on microscopic adsorption behavior. RSC Adv 7:44712–44723. https://doi.org/10.1039/C7RA08387D
Yahia MB, Knani S, Hsan LBH, Yahia MB, Nasri H, Ben Lamine A (2017b) Statistical studies of adsorption isotherms of iron nitrate and iron chloride on a thin layer of porphyrin. J Mol Liq 248:235–245. https://doi.org/10.1016/j.molliq.2017.10.073
Yahia MB, Aouaini F, Yahia MB, Almogait ES, Al-Ghamdi H (2019a) Theoretical investigation of the chlorophyll nucleus adsorption monitored with Quartz Crystal Microbalance technique: new insights on physicochemical properties. J Mol Liq 289:111188. https://doi.org/10.1016/j.molliq.2019.111188
Yahia MB, Yahia MB, Aouaini F, Knani S, Al-Ghamdi H, Almogait ES, Lamine AB (2019b) Adsorption of sodium and lithium ions onto helicenes molecules: experiments and phenomenological modeling. J Mol Liq 288:110998. https://doi.org/10.1016/j.molliq.2019.110998
Yahia MB, AlZahrani HYS, Yahia MB (2021) Application of advanced statistical physics modeling for the physicochemical analysis of adsorption isotherms of manganese (II) on porphyrins H2TPP and H2TTP. Braz J Chem Eng 38:373–388. https://doi.org/10.1007/s43153-021-00090-w
Yan B, Niu CH (2017) Modeling and site energy distribution analysis of levofloxacin sorption by biosorbents. Chem Eng J 307:631–642. https://doi.org/10.1016/j.cej.2016.08.065
Yazidi A, Sellaoui L, Dotto GL, Bonilla-Petriciolet A, Fröhlich AC, Lamine AB (2019) Monolayer and multilayer adsorption of pharmaceuticals on activated carbon: application of advanced statistical physics models. J Mol Liq 283:276–286. https://doi.org/10.1016/j.molliq.2019.03.101
Yazidi A, Atrous M, Edi Soetaredjo F, Sellaoui L, Ismadji S, Erto A, Bonilla-Petriciolet A, Luiz Dotto G, Ben Lamine A (2020) Adsorption of amoxicillin and tetracycline on activated carbon prepared from durian shell in single and binary systems: experimental study and modeling analysis. Chem Eng J 379:122320. https://doi.org/10.1016/j.cej.2019.122320
Zhang L, Sellaoui L, Franco D, Dotto GL, Bajahzar A, Belmabrouk H, Bonilla-Petriciolet A, Oliveira MLS, Li Z (2020) Adsorption of dyes brilliant blue, sunset yellow and tartrazine from aqueous solution on chitosan: analytical interpretation via multilayer statistical physics model. Chem Eng J 382:122952. https://doi.org/10.1016/j.cej.2019.122952
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Amrhar, O., El Gana, L. & Mobarak, M. Calculation of adsorption isotherms by statistical physics models: a review. Environ Chem Lett 19, 4519–4547 (2021). https://doi.org/10.1007/s10311-021-01279-8
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DOI: https://doi.org/10.1007/s10311-021-01279-8