Isothermal Modeling and MOORA-Based Model Selection for Chromium Ion Adsorption by Rhizopus nigricans
DOI:
https://doi.org/10.54987/ngcgsb21Keywords:
Rhizopus nigricans biomass, Chromium (VI) adsorption, Isothermal Modelling, MOORA ranking, Nonlinear regressionAbstract
Adsorption of hexavalent chromium (Cr(VI)) onto Rhizopus nigricans biomass. The Langmuir model yielded a physically justified maximum adsorption capacity, QmL, of 112.756 mg/g (95 percent confidence interval from 98.780 to 126.731 mg/g), which almost matched the experimental maximum. Despite this, the uptake capacity increases continuously with equilibrium concentration, with the final data points showing a steady upward trend rather than leveling off into a distinct plateau. This indicates that complete saturation of the binding sites has not yet been reached within the tested concentration range. Because heterogeneous isotherm models better reflected the overall equilibrium profile, model selection based just on Qm was insufficient. The isotherm equations were directly fitted using nonlinear regression, and the model’s performance was assessed using several error criteria. According to MOORA approach, Fritz-Schlunder III, Redlich-Peterson, and the Toth model are the best models overall, better than Langmuir. Despite this, all these best models failed to produce maximum adsorption capacity values near the experimental value. It is suggested that Cr(VI) biosorption by Rhizopus nigricans biomass included heterogeneous binding sites rather than ideal uniform monolayer adsorption. Thus, the Langmuir isotherm model initially suggested to describe this monolayer adsorption process may be inaccurate, because the uptake capacity is still actively increasing, the true maximum saturation capacity is likely higher than this maximum recorded value.This behavior is most likely impacted by the chemical variety of the fungal surface. More equilibrium points and resampling methods for parameter validation should be included in future studies.
References
1 Tumolo M, Ancona V, De Paola D, Losacco D, Campanale C, Massarelli C, et al. Chromium Pollution in European Water, Sources, Health Risk, and Remediation Strategies: An Overview. Int J Environ Res Public Health. 2020 Jan;17(15):5438. doi:10.3390/ijerph17155438
2 Mohammadpour A, Gharehchahi E, Gharaghani MA, Shahsavani E, Golaki M, Berndtsson R, et al. Assessment of drinking water quality and identifying pollution sources in a chromite mining region. J Hazard Mater. 2024 Dec 5;480:136050. doi:10.1016/j.jhazmat.2024.136050
3 Idriss AA, Ahmad AK. Heavy Metals Nickel and Chromium in Sediments in the Juru River, Penang, Malaysia. J Environ Prot. 2013 Nov 8;2013. doi:10.4236/jep.2013.411144
4 Madhavi V, Reddy AVB, Reddy KG, Madhavi G, Prasad TNVKV. An overview on research trends in remediation of chromium. Res J Recent Sci. 2013;2(1):71–83.
5 Chaudhuri M, Azizan NKB. Adsorptive Removal of Chromium(VI) from Aqueous Solution by an Agricultural Waste-Based Activated Carbon. Water Air Soil Pollut. 2012 May 1;223(4):1765–71. doi:10.1007/s11270-011-0981-8
6 Amir A, Rahim R, Abdul-Talib S. Removal of Chromium Hexavalent Using Agriculture Waste. Int J Environ Sci Dev. 2017 Jan 1;8:260–3. doi:10.18178/ijesd.2017.8.4.959
7 Hanafiah SFM, Salleh NFM, Ghafar NA, Shukri NM, Kamarudin NHN, Hapani M, et al. Efficiency of Coconut Husk as Agricultural Adsorbent in Removal of Chromium and Nickel Ions from Aqueous Solution. IOP Conf Ser Earth Environ Sci. 2020 Dec;596(1):012048. doi:10.1088/1755-1315/596/1/012048
8 Konradt N, Dillmann S, Becker J, Schroden D, Rohns HP, Wagner C, et al. Removal of Chromium Species from Low-Contaminated Raw Water by Different Drinking Water Treatment Processes. Water. 2023 Jan;15(3):3. doi:10.3390/w15030516
9 Singh VP, Godara P, Srivastava A. Sustainable microalgal bioremediation of heavy metals and dyes from synthetic wastewater: Progressing towards United Nations Sustainable Development Goals. Waste Manag Bull. 2024 Dec 1;2(4):123–35. doi:10.1016/j.wmb.2024.10.005
10 Meftah S, Meftah K, Drissi M, Radah I, Malous K, Amahrous A, et al. Heavy metal polluted water: Effects and sustainable treatment solutions using bio-adsorbents aligned with the SDGs. Discov Sustain. 2025 Feb 25;6(1):137. doi:10.1007/s43621-025-00895-6
11 Cervantes C, Campos-García J, Devars S, Gutiérrez-Corona F, Loza-Tavera H, Torres-Guzmán JC, et al. Interactions of chromium with microorganisms and plants. FEMS Microbiol Rev. 2001;25(3):335–47. doi:10.1016/S0168-6445(01)00057-2
12 Khambhaty Y, Mody K, Basha S, Jha B. Kinetics, equilibrium and thermodynamic studies on biosorption of hexavalent chromium by dead fungal biomass of marine Aspergillus niger. Chem Eng J. 2009 Jan 1;145(3):489–95. doi:10.1016/j.cej.2008.05.002
13 Zinicovscaia I, Safonov AV, Khijniak TV. Biosorption of hexavalent chromium and uranium by bacteria, microalga, and fungi [Internet]. 2017. 333–359 p. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058593571&doi=10.1201%2f9781315366029&partnerID=40&md5=867e0799806912213ce90b932df7caf9 doi:10.1201/9781315366029
14 Pandey K, Saharan B, Kumar R, Jabborova D, Duhan J. Modern-Day Green Strategies for the Removal of Chromium from Wastewater. J Xenobiotics. 2024 Nov 3;14. doi:https://doi.org/10.3390/jox14040089
15 Park D, Yun YS, Park JM. Use of dead fungal biomass for the detoxification of hexavalent chromium: screening and kinetics. Process Biochem. 2005 Jun 1;40(7):2559–65. doi:10.1016/j.procbio.2004.12.002
16 Mungasavalli DP, Viraraghavan T, Jin YC. Biosorption of chromium from aqueous solutions by pretreated Aspergillus niger: Batch and column studies. Colloids Surf Physicochem Eng Asp. 2007 Jul 5;301(1):214–23. doi:10.1016/j.colsurfa.2006.12.060
17 Beig SUR, Shah SA. Biosorption of Cr (VI) by acid-modified based-waste fungal biomass from Calocybe indica fruiting bodies production. Int J Phytoremediation. 2023 Aug 24;25(10):1269–88. doi:10.1080/15226514.2022.2147145 PubMed PMID: 36404648.
18 Bai RS, Abraham TE. Studies on chromium(VI) adsorption–desorption using immobilized fungal biomass. Bioresour Technol. 2003 Mar 1;87(1):17–26. doi:10.1016/S0960-8524(02)00222-5
19 Khare KS, Phelan FR. Quantitative Comparison of Atomistic Simulations with Experiment for a Cross-Linked Epoxy: A Specific Volume–Cooling Rate Analysis. Macromolecules. 2018 Jan 23;51(2):564–75. doi:10.1021/acs.macromol.7b01303
20 Ridha FN, Webley PA. Anomalous Henry’s law behavior of nitrogen and carbon dioxide adsorption on alkali-exchanged chabazite zeolites. Sep Purif Technol. 2009;67(3):336–43. doi:10.1016/j.seppur.2009.03.045
21 Langmuir I. THE ADSORPTION OF GASES ON PLANE SURFACES OF GLASS, MICA AND PLATINUM. J Am Chem Soc. 1918;40(2):1361–402. doi:10.1021/ja01269a066
22 Jovanović DS. Physical adsorption of gases - I: Isotherms for monolayer and multilayer adsorption. Kolloid-Z Amp Z Für Polym. 1969;235(1):1203–13. doi:10.1007/BF01542530
23 Carmo AM, Hundal LS, Thompson ML. Sorption of hydrophobic organic compounds by soil materials: Application of unit equivalent Freundlich coefficients. Environ Sci Technol. 2000;34(20):4363–9. doi:10.1021/es000968v
24 Radushkevich LV. Potential theory of sorption and structure of carbons. Zhurnal Fiz Khimii. 1949;23:1410–20.
25 Dubinin MM. Modern state of the theory of volume filling of micropore adsorbents during adsorption of gases and steams on carbon adsorbents. Zh Fiz Khim. 1965;39(6):1305–17.
26 Mahanty B, Behera SK, Sahoo NK. Misinterpretation of Dubinin–Radushkevich isotherm and its implications on adsorption parameter estimates. Sep Sci Technol. 2023 May 3;58(7):1275–82. doi:10.1080/01496395.2023.2189050
27 Mudhoo A, Pittman CU. The Dubinin-Radushkevich models: Dissecting the ps/p to cs/ce replacement in solid-aqueous interfacial adsorption and tracking the validity of E = 8 kJ mol–1 for assigning sorption type. Chem Eng Res Des. 2023 Oct 1;198:370–402. doi:10.1016/j.cherd.2023.09.020
28 Koble RA, Corrigan TE. Adsorption isotherms for pure hydrocarbons. Ind Eng Chem. 1952 Feb 1;44(2):383–7. doi:10.1021/ie50506a049
29 Temkin MI, Pyzhev V. Kinetics of ammonia synthesis on promoted iron catalysts. Acta Physicochim USSR. 1940;12(3):327–56.
30 Chu KH. Revisiting the Temkin Isotherm: Dimensional Inconsistency and Approximate Forms. Ind Eng Chem Res. 2021 Aug 16. Located at: world. doi:10.1021/acs.iecr.1c01788
31 Redlich O, Peterson DL. A Useful Adsorption Isotherm. Shell Dev Co Emeryv Calif. 1958;63:1024.
32 Sips R. On the structure of a catalyst surface. J Chem Phys. 1948;16(5):490–5. doi:10.1063/1.1746922
33 Tóth J. Uniform interpretation of gas/solid adsorption. Adv Colloid Interface Sci. 1995;55(C):1–239. doi:10.1016/0001-8686(94)00226-3
34 Hill AV. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol. 1910;40:iv–vii. doi:https://doi.org/10.1098/rspb.1936.0046
35 Brunauer S, Emmett PH, Teller E. Adsorption of Gases in Multimolecular Layers. J Am Chem Soc. 1938;60(2):309–19. doi:10.1021/ja01269a023
36 Vieth WR, Sladek KJ. A model for diffusion in a glassy polymer. J Colloid Sci. 1965;20(9):1014–33. doi:10.1016/0095-8522(65)90071-1
37 Brouers F, Sotolongo O, Marquez F, Pirard JP. Microporous and heterogeneous surface adsorption isotherms arising from Levy distributions. Phys Stat Mech Its Appl. 2005 Apr 1;349(1):271–82. doi:10.1016/j.physa.2004.10.032
38 Hamissa AMB, Brouers F, Mahjoub B, Seffen M. Adsorption of Textile Dyes Using Agave Americana (L.) Fibres: Equilibrium and Kinetics Modelling. Adsorpt Sci Technol. 2007 Jun 1;25(5):311–25. doi:10.1260/026361707783432533
39 Brouers F, Al-Musawi TJ. Brouers-Sotolongo fractal kinetics versus fractional derivative kinetics: A new strategy to analyze the pollutants sorption kinetics in porous materials. J Hazard Mater. 2018 May 15;350:162–8. doi:10.1016/j.jhazmat.2018.02.015
40 Fritz W, Schluender EU. Simultaneous adsorption equilibria of organic solutes in dilute aqueous solutions on activated carbon. Chem Eng Sci. 1974;29(5):1279–82. doi:10.1016/0009-2509(74)80128-4
41 Chu KH, Tan B. Is the Frumkin (Fowler–Guggenheim) adsorption isotherm a two- or three-parameter equation? Colloid Interface Sci Commun. 2021 Nov 1;45:100519. doi:10.1016/j.colcom.2021.100519
42 Martucci A, Braschi I, Bisio C, Sarti E, Rodeghero E, Bagatin R, et al. Influence of water on the retention of methyl tertiary-butyl ether by high silica ZSM-5 and Y zeolites: A multidisciplinary study on the adsorption from liquid and gas phase. RSC Adv. 2015;5(106):86997–7006.
43 Chu KH, Debord J, Harel M, Bollinger JC. Mirror, Mirror on the Wall, Which Is the Fairest of Them All? Comparing the Hill, Sips, Koble–Corrigan, and Liu Adsorption Isotherms. Ind Eng Chem Res. 2022 May 18;61(19):6781–90. doi:10.1021/acs.iecr.2c00507
44 Shukor MY. Chitosan–Silica Composite Aerogel for the Adsorption of Cupric Ions: Isothermal Remodeling and MOORA-Based Model Selection. J Environ Microbiol Toxicol. 2024 Dec 26;12(2):2. doi:10.54987/jemat.v12i2.1026
45 Akaike H. Factor analysis and AIC. Psychometrika. 1987;52(3):317–32. doi:10.1007/BF02294359
46 Burnham KP, Anderson DR. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer Science & Business Media; 2002. 528 p.
47 Ezekiel M. The Sampling Variability of Linear and Curvilinear Regressions: A First Approximation to the Reliability of the Results Secured by the Graphic “Successive Approximation” Method. Ann Math Stat. 1930;1(4):275–333. doi:https://doi.org/10.1214/aoms/1177733062
48 Ross T. Indices for performance evaluation of predictive models in food microbiology. J Appl Bacteriol. 1996;81(5):501–8.
49 Marquardt DW. An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math. 1963;11(2):431–41.
50 Seidel A, Gelbin D. On applying the ideal adsorbed solution theory to multicomponent adsorption equilibria of dissolved organic components on activated carbon. Chem Eng Sci. 1988 Jan 1;43(1):79–88. doi:10.1016/0009-2509(88)87128-8
51 Porter JF, McKay G, Choy KH. The prediction of sorption from a binary mixture of acidic dyes using single- and mixed-isotherm variants of the ideal adsorbed solute theory. Chem Eng Sci. 1999;54(24):5863–85. doi:10.1016/S0009-2509(99)00178-5
52 Schwarz G. Estimating the Dimension of a Model. Ann Stat. 1978;6(2):461–4.
53 Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J Off Publ Fed Am Soc Exp Biol. 1987;1(5):365–74. doi:https://doi.org/10.1096/fasebj.1.5.3315805
54 Karel W, Brauers W, Zavadskas E. The MOORA method and its application to privatization in a transition economy. Control Cybern. 2006 Jan 1;35.
55 Brauers W. Multi-objective seaport planning by MOORA decision making. Ann Oper Res. 2013 Jul 1;206. doi:10.1007/s10479-013-1314-7
56 Gupta A, Gupta N, Garg R, Kumar R. Evaluation, Selection and Ranking of Software Reliability Growth Models using Multi criteria Decision making Approach. In: 2018 4th International Conference on Computing Communication and Automation (ICCCA) [Internet]. 2018 [cited 2025 Feb 18]. p. 1–8. Available from: https://ieeexplore.ieee.org/abstract/document/8777644 doi:10.1109/CCAA.2018.8777644
57 Lambert RJW, Mytilinaios I, Maitland L, Brown AM. Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel. Comput Methods Programs Biomed. 2012 Aug 1;107(2):155–63. doi:10.1016/j.cmpb.2011.05.009
58 Wu Z, Joo H, Ahn IS, Haam S, Kim JH, Lee K. Organic dye adsorption on mesoporous hybrid gels. Chem Eng J. 2004 Sep 15;102(3):277–82. doi:10.1016/j.cej.2004.05.008
59 Chandra IK, Ju YH, Ayucitra A, Ismadji S. Evans blue removal from wastewater by rarasaponin-bentonite. Int J Environ Sci Technol. 2013;10(2):359–70. doi:10.1007/s13762-012-0114-y
60 Vijayaraghavan K, Yun YS. Biosorption of C.I. Reactive Black 5 from aqueous solution using acid-treated biomass of brown seaweed Laminaria sp. Dyes Pigments. 2008 Jan 1;76(3):726–32. doi:10.1016/j.dyepig.2007.01.013
61 Foo KY, Hameed BH. Insights into the modeling of adsorption isotherm systems. Chem Eng J. 2010;156(1):2–10. doi:10.1016/j.cej.2009.09.013
62 Belhachemi M, Addoun F. Comparative adsorption isotherms and modeling of methylene blue onto activated carbons. Appl Water Sci. 2011 Dec 1;1(3):111–7. doi:10.1007/s13201-011-0014-1
63 Sivarajasekar N, Baskar R. Adsorption of basic red 9 onto activated carbon derived from immature cotton seeds: isotherm studies and error analysis. Desalination Water Treat. 2014 Dec 6;52(40–42):7743–65. doi:10.1080/19443994.2013.834518
64 Ayawei N, Ebelegi AN, Wankasi D. Modelling and Interpretation of Adsorption Isotherms. J Chem. 2017 Sep 5;2017:e3039817. doi:10.1155/2017/3039817
65 Maaloul N, Oulego P, Rendueles M, Ghorbal A, Díaz M. Cu(II) Ions Removal on Functionalized Cellulose Beads from Tunisian Almond (Prunus dulcis) Shell. Environ Sci Eng. 2021;65–71. doi:10.1007/978-3-030-51210-1_11
66 Chu KH, Hashim M, Santos YTDC, Debord J, Harel M, Bollinger JC. The Redlich–Peterson isotherm for aqueous phase adsorption: Pitfalls in data analysis and interpretation. Chem Eng Sci. 2023 Nov 28;285:119573. doi:10.1016/j.ces.2023.119573
67 Langmuir I. The constitution and fundamental properties of solids and liquids. Part I. Solids. J Am Chem Soc. 1916;38(11):2221–95. doi:10.1021/ja02268a002
68 Hyder AHMG, Begum SA, Egiebor NO. Adsorption isotherm and kinetic studies of hexavalent chromium removal from aqueous solution onto bone char. J Environ Chem Eng. 2015;3(2):1329–36. doi:10.1016/j.jece.2014.12.005
69 Divband Hafshejani L, Mortazavi P, Sabz ALiPour S, Brooman Nasab S. Isotherm and Kinetics Study of The Adsorption of Chromium (VI) From Aqueous Solution by Zizyphus Spina-christi Leaves Ash Nanoparticles. Irrig Sci Eng. 2016 Dec 21;39(4):97–110. doi:10.22055/jise.2016.12499
70 Taha AA, Shreadah MA, Ahmed AM, Heiba HF. Multi-component adsorption of Pb(II), Cd(II), and Ni(II) onto Egyptian Na-activated bentonite; Equilibrium, kinetics, thermodynamics, and application for seawater desalination. J Environ Chem Eng. 2016;4(1):1166–80. doi:10.1016/j.jece.2016.01.025
71 Nag S, Mondal A, Bar N, Das SK. Biosorption of chromium (VI) from aqueous solutions and ANN modelling. Environ Sci Pollut Res. 2017 Aug 1;24(23):18817–35. doi:10.1007/s11356-017-9325-6
72 Srivastava S, Agrawal SB, Mondal MK. Synthesis, characterization and application of Lagerstroemia speciosa embedded magnetic nanoparticle for Cr(VI) adsorption from aqueous solution. J Environ Sci China. 2017 May;55:283–93. doi:10.1016/j.jes.2016.08.012 PubMed PMID: 28477823.
73 Ahsan MdA, Jabbari V, Islam MdT, Kim H, Hernandez-Viezcas JA, Lin Y, et al. Green synthesis of a highly efficient biosorbent for organic, pharmaceutical, and heavy metal pollutants removal: Engineering surface chemistry of polymeric biomass of spent coffee waste. J Water Process Eng. 2018 Oct 1;25:309–19. doi:10.1016/j.jwpe.2018.08.005
74 Boeykens SP, Saralegui A, Caracciolo N, Piol MN. Agroindustrial waste for lead and chromium biosorption. J Sustain Dev Energy Water Environ Syst. 2018;6(2):341–50. doi:10.13044/j.sdewes.d5.0184
75 Mahmood-Ul-Hassan M, Suthar V, Ahmad R, Yousra M. Biosorption of metal ions on lignocellulosic materials: batch and continuous-flow process studies. Environ Monit Assess. 2018;190(5). doi:10.1007/s10661-018-6674-7
76 Mortazavian S, An H, Chun D, Moon J. Activated carbon impregnated by zero-valent iron nanoparticles (AC/nZVI) optimized for simultaneous adsorption and reduction of aqueous hexavalent chromium: Material characterizations and kinetic studies. Chem Eng J. 2018 Jul 1;353. doi:10.1016/j.cej.2018.07.170
77 Sadiq A, Choubey A, Bajpai AK, Sadiq A, Choubey A, Bajpai AK. Biosorption of chromium ions by calcium alginate nanoparticles. J Chil Chem Soc. 2018;63(3):4077–81. doi:10.4067/s0717-97072018000304077
78 Abilio TE, Soares BC, José JC, Milani PA, Labuto G, Carrilho ENVM. Hexavalent chromium removal from water: adsorption properties of in natura and magnetic nanomodified sugarcane bagasse. Environ Sci Pollut Res. 2021;28(19):24816–29. doi:10.1007/s11356-020-11726-8
79 Dan-Iya BI, Shukor MY. Isothermal modelling of the adsorption of chromium onto calcium alginate nanoparticles. J Environ Microbiol Toxicol. 2021 Dec 31;9(2):2. doi:10.54987/jemat.v9i2.607
80 Mahmoud ME, El-Said GF, Ibrahim GAA, Elnashar AAS. Effective removal of hexavalent chromium from water by sustainable nano-scaled waste avocado seeds: adsorption isotherm, thermodynamics, kinetics, and error function. Biomass Convers Biorefinery. 2022;14(13):14725–43. doi:https://doi.org/10.1007/s13399-022-03619-2
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Ismail, Mohd Ezuan Khayat, Nur Adeela Yasid, Mohd Izuan Effendi Halmi, Ain Aqilah Basirun, M.Y. Shukor
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
