Skip to main content
. 2024 Mar 14;14(13):8752–8768. doi: 10.1039/d3ra08709c

The mathematical characteristics of the traditional isotherm models under consideration.

293 K 303 K 313 K
DI Langmuir model Q max (mg g−1) 190.2 164.2 137.7
b (L mg−1) 3.7 × 10−7 3.24 × 10−7 1.51 × 10−8
R 2 0.99 0.99 0.99
χ 2 0.05 0.13 0.17
Freundlich model 1/n 0.80 0.84 0.94
k F (mg g−1) 2.27 1.61 1.24
R 2 0.82 0.85 0.83
χ 2 4.92 3.17 3.59
D–R model β (mol2 kJ−2) 0.041 0.046 0.056
Q m (mg g−1) 201.7 174.3 147.9
R 2 0.999 0.99 0.99
χ 2 0.05 0.028 0.17
E (kJ mol−1) 3.49 3.29 2.98
ZD Langmuir model Q max (mg g−1) 258.6 219.8 178.3
b (L mg−1) 2.8 × 10−6 1.43 × 10−7 2.03 × 10−8
R 2 0.99 0.99 0.99
χ 2 0.35 0.71 0.38
Freundlich model 1/n 0.83 0.87 0.90
k F (mg g−1) 2.67 1.84 1.2
R 2 0.86 0.84 0.82
χ 2 4.43 5.71 6.99
D–R model β (mol2 kJ−2) 0.016 0.021 0.032
Q m (mg g−1) 265.6 229.3 190.6
R 2 0.99 0.99 0.99
χ 2 0.33 0.21 0.29
E (kJ mol−1) 5.6 4.9 3.95
CD/ZD Langmuir model Q max (mg g−1) 297.7 260.8 213.2
b (L mg−1) 7.7 × 10−7 3.4 × 10−7 6.1 × 10−7
R 2 0.99 0.99 0.99
χ 2 0.029 0.011 0.067
Freundlich model 1/n 0.81 0.87 0.84
k F (mg g−1) 3.53 2.21 2.03
R 2 0.84 0.85 0.86
χ 2 6.12 5.24 5.02
D–R model β (mol2 kJ−2) 0.0081 0.0088 0.011
Q m (mg g−1) 312.5 275.9 223.6
R 2 0.99 0.99 0.99
χ 2 0.19 0.31 0.087
E (kJ mol−1) 7.85 7.5 6.7