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Table 2 Adsorption isotherm parameters for removal of MG, MV, and MB

From: Alginate-coated perlite beads for the efficient removal of methylene blue, malachite green, and methyl violet from aqueous solutions: kinetic, thermodynamic, and equilibrium studies

Model Equation Eq. Ads. Dye Parameters for dye Reference
Modified Langmuir \( \frac{C_{\mathrm{e}}}{q_{\mathrm{e}}}=\frac{C_{\mathrm{s}}}{K_{\mathrm{ML}}{q}_{\mathrm{m}}}+\frac{\left({K}_{\mathrm{ML}}-1\right){C}_{\mathrm{e}}}{K_{\mathrm{ML}}{q}_{\mathrm{m}}} \) (3) AP
AP
AP
P
P
P
MB
MG
MV
MB
MG
MV
qm 104.1
74.6
149.2
6.64
3.86
4.97
KML 1100
1292
2381
3003
6089
4417
R 2
0.996
0.966
0.996
0.986
0.994
0.994
Azizian et al. 2018
Freundlich \( 1{nq}_{\mathrm{e}}=1{nK}_{\mathrm{f}}+\frac{1}{n}\;1{nC}_{\mathrm{e}} \) (4) AP
AP
AP
P
P
P
MB
MG
MV MB
MG
MV
K f
4.87
2.64
12.22
1.07
0.70
1.10
n
1.60
1.50
1.61
2.57
2.63
2.93
R 2
0.981
0.931
0.949
0.997
0.950
0.966
Freundlich 1906
D-R Inqe = lnqm− βε2 (5) AP
AP
AP
P
P
P
MB
MG
MV
MB
MG
MV
X m
*10−3
7.25
6.04
14.33
0.29
0.19
0.22
K
0.0073
0.0072
0.0058
0.0038
0.0039
0.0034
E
8.84
8.33
9.29
11.47
11.32
12.13
R 2
0.994
0.960
0.976
0.993
0.964
0.976
Dubinin and Radushkevich 1947
Temkin qe = BlnKT + BlnCe (6) AP
AP
AP
P
P
P
MB
MG
MV
MB
MG
MV
B
19.49
15.04
28.58
1.24
0.79
0.95
K t
0.41
0.28
1.05
1.14
1.13
1.72
R 2
0.959
0.971
0.966
0.969
0.953
0.961
Temkin and Pyzhev 1940
Scathard qe/Ce = QsKs − qeKs (7) AP
AP
AP
P
P
P
MB
MG
MV
MB
MG
MV
Q s
108.0
96.71
188.5
5.95
3.89
4.90
K s
0.03
0.017
0.059
0.118
0.101
0.150
R 2
0.936
0.744
0.956
0.783
0.872
0.843
Scatchard, 1949