Table 4 Isotherm parameters of UiO-66 prepared for the removal of rifampicin from wastewater.

Two parameters

Langmuir isotherm

\(\:{q}_{e}={q}_{{max}}\left(\frac{{k}_{L}{C}_{e}}{1+{k}_{L}{C}_{e}}\right)\)

K_L

44,932

110.88

0.97

Freundlich isotherm

\(\:{q}_{e}={k}_{F}\:({{C}_{e})}^{\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{$n$}\right.}\)

1/n

0.217

–

0.995

K_F

46.38

–

0.997

Temkin isotherm

\(\:{q}_{e}=\frac{RT}{{A}_{T}}{ln}{A}_{T}+\frac{RT}{{A}_{T}}Ln\:{C}_{e}\)

RT

8.31

A_T

1.64

Dubinin‒Radushkevich isotherm

\(\:{q}_{e}=\left({q}_{max}\right){exp}\left(-{k}_{ad}{\epsilon\:}^{2}\right)\)

K_ad

0.0017

145.19

0.9997

Three parameters isotherm

Langmuir–Freundlich isotherm

\(\:{q}_{e}=\frac{{q}_{max}{\left({k}_{LF}\:{C}_{e}\right)}^{\text{M}\text{L}\text{F}}}{1+{\left({k}_{LF\:}{C}_{e}\right)}^{\text{M}\text{L}\text{F}}}\)

K_LF

0.086

139.188

0.999

M_LF

1.47

Sips isotherm

\(\:{q}_{e}=\frac{{\left({q}_{max}{k}_{s}\:{C}_{e}\right)}^{1/n}}{{\left(1+{k}_{s}\:{C}_{e}\right)}^{1/n}}\)

K_S

0.027

139.189

0.999

1/n

1.47

Redlich–Peterson isotherm

\(\:{q}_{e}=\frac{{k}_{R\:\:}{C}_{e}}{1+{a}_{R\:\:}{{C}_{e}}^{\beta}}\)

K_R

8.5

–

1

a_R

0.026

β

1.149

Toth isotherm

\(\:{q}_{e}=\frac{{k}_{e}\:{C}_{e}}{{\left(1+{\left({k}_{L}\:{C}_{e}\right)}^{n}\right)}^{1∕n}}\)

K_e

9.76

–

1

K_L

0.026

N

1.15

Kahn isotherm

\(\:{q}_{e}=\frac{{q}_{max}{\:b}_{k\:}{C}_{e}}{{\left(1+{b}_{k\:}{C}_{e}\right)}^{{a}_{k}}}\)

b_k

0.037

243.58

0.9999

a_k

1.218

Higher parameter isotherm

Baudu isotherm

\(\:{q}_{e}=\frac{{q}_{max}{\:b}_{0}{\:{C}_{e}}^{1+X+Y}}{1+{b}_{0}{\:{C}_{e}}^{1+X}}\)

b_o

0.01

49.9

0.998

X

0.012

Y

0.248

Fritz–Schlunder isotherm

\(\:{q}_{e}=\frac{{q}_{{max}_{Fss}}{k}_{1}{{C}_{e}}^{{m}_{1}}}{1+{k}_{2}{{C}_{e}}^{{m}_{2}}}\)

K₁

0.855

54.2

0.995

K₂

0

m₁

0.217

m₂

0