Table 4 Linear and nonlinear forms of adoption kinetics models

PFO

Qt = Qe(1 − \(e^{ - K1t}\))

\(\log \left( {Qe - {\text{Qt}}} \right)\) = \(\log Qe\) − \(\frac{K1t}{{2.303}}\)

[47, 50]

PSO

Qt = \(\frac{{Qe^{2} K_{2} t}}{{1 + QeK_{2} t}}\)

\(\frac{t}{Qt}\) = \(\left( \frac{1}{Qe} \right)\)t + \(\frac{1}{{K2Qe^{2} }}\)

[47, 50]

IPD

Qe = kd × t^0.5 + C

Qe = kd × t^0.5 + C

[32, 50]

Elovich

Qt = \(\frac{1}{\beta }\) ln(\(\alpha \beta t + 1\))

Qt = \(\frac{1}{\alpha }\) ln (αβ) + \(\frac{1}{ \uparrow \alpha }\) ln t

[45, 56]