Two-parameters isotherm |
Langmuir76
|
|
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
|
|
qmax (mg/g) |
max. adsorption capacity |
217.81 |
0.93 |
KLF (L/mg) |
Equilibrium constant |
0.13 |
ns
|
Heterogeneity parameter |
3.87 |
Sips14
|
|
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
|
|
qmax (L/mg) |
Isotherm constant |
14.92 |
0.85 |
Ks (mg/g)g
|
Isotherm constant |
0.0028 |
βs (−) |
Isotherm constant |
1.73 |
Khan79
|
|
|
Isotherm constant |
5830.9 |
0.83 |
|
Isotherm constant |
0.0029 |
|
Isotherm constant |
9.83 |
Toth14
|
|
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
|
|
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
|
|
|
Fritz–Schlunder maxium adsorption capacity (mg/g) |
23.98 |
0.78 |
|
Model parameter |
0.057 |
|
Model exponent < 1 |
0.92 |
|
Model exponent < 1 |
0.99 |
Fritz–Schlunder (IV)(Unrestricted)80
|
|
|
Fritz–Schlunder maxium adsorption capacity (mg/g) |
0.1 |
0.93 |
|
Model parameter |
0.00046 |
|
Model exponent |
3.72 |
|
Model exponent |
3.73 |
Fritz–Schlunder (V)79
|
|
|
Fritz–Schlunder maximum adsorption capacity (mg/g) |
11.22 |
0.78 |
|
Model parameter |
2.14 |
|
Model parameter |
0.057 |
|
Model exponent < 1 |
0.92 |
|
Model exponent < 1 |
0.99 |
Fritz–Schlunder (V) (Unrestricted)79
|
|
|
Fritz–Schlunder maxium adsorption capacity (mg/g) |
0.74 |
0.93 |
|
Model parameter |
0.14 |
|
Model parameter |
0.00045 |
|
Model exponent |
3.72 |
|
Model exponent |
3.74 |