Table 4 Different isotherm models that were investigated in this study.

From: Enhanced metal ion adsorption using ZnO-MXene nanocomposites with machine learning-based performance prediction

Type of Model

Equation

Plots

Parameters

Langmuir Model

\(\:\frac{{\text{C}}_{\text{e}}}{{\text{q}}_{\text{e}}}=\:\frac{1}{{\text{Q}}_{\text{m}}\text{b}}+\:\frac{1}{{\text{Q}}_{\text{m}}}{\text{C}}_{\text{e}}\)

\(\:\frac{1}{{q}_{f}}\:vs\:\frac{1}{{C}_{f}}\)

Qm = \(\:\frac{1}{\text{I}\text{n}\text{t}\text{e}\text{r}\text{c}\text{e}\text{p}\text{t}}\)

KL = \(\:\frac{\text{S}\text{l}\text{o}\text{p}\text{e}}{\text{I}\text{n}\text{t}\text{e}\text{r}\text{c}\text{e}\text{p}\text{t}}\)

Freundlich Model

\(\:\text{ln}{\text{q}}_{\text{f}}=\text{ln}{\text{K}}_{\text{f}}+\:\frac{1}{\text{n}}\text{ln}{\text{C}}_{\text{e}}\)

\(\:{ln\:q}_{f}vs\:{lnC}_{f}\)

n = \(\:\frac{1}{\text{S}\text{l}\text{o}\text{p}\text{e}}\)

\(\:{K}_{f}={e}^{Intercept}\)