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| Isotherm/Reference | Nonlinear form | Linear form | Plot | Characteristic parameters |
|
| One-parameter isotherm |
| Henry’s [28] | qe = KHECe | qe = KHECe | qe vs. Ce | KHE = Henry’s adsorption constant |
|
| Two-parameter isotherms |
| Freundlich [29] | qe = KFC1/n | ln qe = ln KF + 1/n lnCe | ln qe vs. lnCe | KF = adsorption capacity (mg/g)(L/mg)1/n |
| 1/n = adsorption intensity |
| Jovanovic [28] | | ln qe = ln qmax − KJCe | ln qe vs. Ce | qmax = maximum adsorbate uptake |
| KJ = Jovanovic constant |
| Langmuir-1 | [30] | = | vs. | qm = maximum adsorbate uptake |
| Langmuir-2 | | | b = Langmuir equilibrium constant (L/mg) |
| Langmuir-3 | qe = | qe vs. |
| Langmuir-4 | = −bqe + bqm | vs. qe |
| Langmuir-5 | = bqm − b | |
| Temkin [31] | qe = Bln AT.Ce | qe = Bln AT + Bln Ce | qe vs. ln Ce | AT: equilibrium binding constant (L/mg) bT = = adsorption energy (kJ/mol) |
| Elovich [32] | = KECeexp(−) | = ln KEqm − | vs. qe | qm = maximum adsorbate uptake |
| KE = Elovich equilibrium constant (L/mg) |
| Dubinin–Radushkevich (D-R) [28] | | | | Xm = adsorption capacity (mg/g) |
| K = constant related to the adsorption energy (mol2·kJ−2) |
| Fowler–Guggenheim [33] | KFGCe = | = −ln KFG + | vs. Ɵ | KFG = Fowler–Guggenheim equilibrium constant (L/mg) |
| W = is interaction energy between adsorbed molecules (KJmol−1) |
| Kiselev [34] | K1Ce = | = + k1kn | vs. | k1 = Kiselev equilibrium constant (L/mg) |
| kn = constant of complex formation between adsorbed molecules |
| Hill–de Boer [35, 36] | K1Ce = exp ( − ) | − = −ln K1 − | − vs. Ɵ | K1 = Hill–de Boer constant (L/mg) |
| K2 = energetic constant of the interaction between adsorbed molecules (kJmol−1) |
| Langmuir–Freundlich [37] | | ln( − 1) = ln KG − Nbln Ce | ln( − 1) vs. ln Ce | KG = saturation constant (mg/L) |
| Nb = cooperative binding constant |
| Flory–Huggins [28] | | ln = ln KFH + n ln(1 − θ) | ln vs. ln(1 − θ) | n = number of adsorbates occupying adsorption sites |
| KFH = Flory–Huggins equilibrium constant (L/mg) |
| Harkin–Jura [28] | | = – () ln Ce | vs. ln Ce | B and A are Harkin–Jura constants |
| Halsey [38] | qe = ()1/nH | ln qe = ln KH – 1/nHln Ce | ln qe vs. ln Ce | KH and nH are Halsey isotherm constants |
|
| Three-parameter isotherm |
| Redlich–Peterson [28] | qe = | ln(KR – 1) = bRln Ce + ln(aR) | ln(KR – 1) vs. ln Ce | KR, Redlich–Peterson isotherm constant (Lg−1) used to obtain the maximum value of the correlation coefficient aR = constant (L/mg) |
| bR = exponent that lies between 0 and 1 |
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