## 3 Results
### Dark Adsorption Experiments
#### 3.1.2 Adsorption Kinetics  
The adsorption kinetics for 2_4_-DCF-TiO\({}_{2}\)/stainless steel system for the four pH values of the working solution is presented in Figure 2 (non-linear fitting) and Figure 3 (linear fitting). It is observed that the adsorption process proceeds rapidly, the adsorption equilibrium being reached after about 30 min regardless of the initial concentration of 2_4_-DCF. The pH of the working solution influences the adsorption capacity of the photocatalytic membrane in the sense that for the same initial concentration of 2_4_-DCF there is an increase in the adsorption capacity of the catalyst as the pH of the working solution decreases with a maximum corresponding to pH 3. Thus, for an initial concentration of 2_4_-DCF of 84.9 mg/L the adsorption capacity of the catalyst increases from 5.311 mg 2_4_-DCF/g adsorbent at pH 7 to 8.413 mg 2_4_-DCF/g adsorbent at pH 3, for an initial concentration of 169.79 mg/L the adsorption capacity of the catalyst increases from 10.739 mg 2_4_-DCF/g adsorbent at pH 7 to 14.803 mg 2_4_-DCF/g adsorbent at pH 3, and for an initial concentration of 254.69 mg/L the adsorption capacity of the catalyst increases from 12.190 mg 2_4_-DCF/g adsorbent at pH 7 to 19.156 mg 2_4_-DCF/g adsorbent at pH 7 to 19.156 mg 2_4_-DCF/g adsorbent at pH 3. Figure 2: Adsorption kinetics of 2_4_-DCF (expressed as OC) from aqueous solutions under different pH conditions and different initial concentrations: (**a**) 37.50 mg OC/L; (**b**) 75.00 mg OC/L; (**c**) 112.50 mg OC/L. Second-order kinetics described by the equations presented below were used to estimate the kinetic parameters of the 2,4-DCF adsorption process [28]. The kinetic parameters and the correlation coefficients are presented in Table 3.  
\[\frac{\mathrm{d}\mathrm{q}_{\mathrm{t}}}{\mathrm{dt}}=\mathrm{k}\left(\mathrm{ q}_{\mathrm{e}}-\mathrm{q}_{\mathrm{t}}\right)^{2} \tag{5}\]  
where \(\mathrm{q}_{\mathrm{t}}\) is the adsorption capacity of the adsorbent at time t, \(\mathrm{q}_{\mathrm{e}}\) represents the adsorption capacity of the adsorbent at equilibrium, and \(\mathrm{k}\) represents the second order kinetic constant of the adsorption process, \(\mathrm{g}\cdot\mathrm{mg}^{-1}\cdot\mathrm{min}^{-1}\). The integrated form of the above equation (considering the boundary conditions t = 0, t = t and \(\mathrm{q}_{\mathrm{t}}\) = 0 \(\mathrm{q}_{\mathrm{t}}\) = \(\mathrm{q}_{\mathrm{e}}\)) is as follows:  
\[\frac{1}{\left(\mathrm{q}_{\mathrm{e}}-\mathrm{q}_{\mathrm{t}}\right)}=\frac {1}{\mathrm{q}_{\mathrm{e}}}+\mathrm{kt} \tag{6}\]  
Rearranging the above equation, its linearized form is obtained:  
\[\left(\frac{\mathrm{t}}{\mathrm{q}_{\mathrm{t}}}\right)=\frac{1}{\mathrm{k} \mathrm{q}_{\mathrm{e}}}^{2}+\frac{1}{\mathrm{q}_{\mathrm{e}}}(\mathrm{t}) \tag{7}\]  
\[\mathrm{h}=\mathrm{k}\mathrm{q}_{\mathrm{e}}{}^{2} \tag{8}\]  
\[\mathrm{t}_{1/2}=\frac{1}{\mathrm{k}\mathrm{q}_{\mathrm{e}}} \tag{9}\]  
where \(\mathrm{h}\) is the initial adsorption rate, \(\mathrm{mg}\cdot\mathrm{g}^{-1}\cdot\mathrm{min}^{-1}\), and \(\mathrm{t}_{1/2}\) represents the half-life, min. Representing graphically \(\mathrm{t}/\mathrm{q}_{\mathrm{m}}\) as a function of t, a line is obtained from which \(\mathrm{q}_{\mathrm{e}}\), \(\mathrm{k}\), \(\mathrm{h}\)  
Figure 3: Linear fitting of adsorption kinetics of 2,4-DCF (expressed as OC) from aqueous solutions under different \(\mathrm{pH}\) conditions and different initial concentrations: (**a**) 37.50 mg OC/L; (**b**) 75.00 mg OC/L; (**c**) 112.50 mg OC/L. and t\({}_{1/2}\) can be calculated from the slope, respectively, the line at its origin. Regarding the kinetic parameters of the adsorption process, namely the initial adsorption rate and the half-life, their values vary depending on the pH value of the working solution. Thus, the initial adsorption rate increases as the pH of the working solution decreases, and the half-life decreases as the pH of the working solution decreases.