Skip to main content
. 2024 Jan 8;14:806. doi: 10.1038/s41598-023-48382-0

Table 2.

The non-linear isotherm models and the values of estimated parameters of MOX adsorption using Zn–Co–Fe LDH as adsorbent.

Isotherm models Equation Model parameters* Values R2
Two-parameters isotherm
 Langmuir76 qe=qmaxKLCe1+KLCe qmax (mg/g) Reflects monolayer formation 291.48 0.78
KL (L/mg) Adsorption equilibrium constant 0.077
 Freundlich77 qe = Kf Ce1/nf Kf (L/g) Reflects the relative adsorption capacity 0.399 0.68
1/nf (−) Constant for surface heterogeneity 49.13
 Temkin78 qe = (R*T/bT) Ln(AT * Ce)R is the universal gas constant and T is the absolute temperature bT Temkin constant 34.56 0.76
AT (L/g) Isotherm equilibrium binding constant 0.54
 Dubinin–Radushkevich77 qe = (qm) exp (− Kad ε2) ε = RT (1 + (1/Ce)) qm (mg/g) Theoretical adsorption capacity 271.32 0.83
Kad (mol2/KJ2) Related to adsorption energy 0.0016
Three-parameters isotherm
 Langmuir–Freundlich79 qe=qmax(KlfCe)ns1+(KlfCe)ns qmax (mg/g) max. adsorption capacity 217.81 0.93
KLF (L/mg) Equilibrium constant 0.13
ns Heterogeneity parameter 3.87
 Sips14 qe=qmaxKSCens1+KS(Ce)ns qmax (mg/g) Sips constant for maximum adsorption capacity 217.82 0.93
Ks (L/mg) Equilibrium constant 0.00036
1/ns (−) Sips' exponent 3.88
 Redlich–Peterson15 qe=qmaxCe1+KS(Ce)βs qmax (L/mg) Isotherm constant 14.92 0.85
Ks (mg/g)g Isotherm constant 0.0028
βs (−) Isotherm constant 1.73
 Khan79 qe=QmbKCe[1+bKCe]ak Qm Isotherm constant 5830.9 0.83
bK Isotherm constant 0.0029
ak Isotherm constant 9.83
 Toth14 qe=KeCe[1+(KLCe)n]1/n Ke (mol*L/mg*mg) Tóth max. adsorption capacity 25.78 0.85
KL (L/mg) Tóth equilibrium constant 0.0028
n (−) Tóth model exponent 1.73
Higher-parameters isotherm
 Baudu79 qe=qmaxbo(Ce)1+x+y1+bo(Ce)1+x qmax (mg/g) Baudu max. adsorption capacity 5357.67 0.85
bo(−) equilibrium constant 0.0028
X (−) Baudu parameter − 0.73
Y (−) Baudu parameter 0.73
 Fritz–Schlunder (IV)80 qe=qmFSS(Ce)m11+K1(Ce)m2 qmFSS Fritz–Schlunder maxium adsorption capacity (mg/g) 23.98 0.78
K1 Model parameter 0.057
m1 Model exponent < 1 0.92
m2 Model exponent < 1 0.99
 Fritz–Schlunder (IV)(Unrestricted)80 qe=qmFSS(Ce)m11+K1(Ce)m2 qmFSS Fritz–Schlunder maxium adsorption capacity (mg/g) 0.1 0.93
K1 Model parameter 0.00046
m1 Model exponent 3.72
m2 Model exponent 3.73
 Fritz–Schlunder (V)79 qe=qmFSSK1(Ce)m11+K2(Ce)m2 qmFSS Fritz–Schlunder maximum adsorption capacity (mg/g) 11.22 0.78
K1 Model parameter 2.14
K2 Model parameter 0.057
m1 Model exponent < 1 0.92
m2 Model exponent < 1 0.99
 Fritz–Schlunder (V) (Unrestricted)79 qe=qmFSSK1(Ce)m11+K2(Ce)m2 qmFSS Fritz–Schlunder maxium adsorption capacity (mg/g) 0.74 0.93
K1 Model parameter 0.14
K2 Model parameter 0.00045
m1 Model exponent 3.72
m2 Model exponent 3.74