## 3 Results and Discussion
### DCF and PARX Adsorption Assays
#### 3.2.3 Adsorption Equilibrium Studies  
Figures 7 and 8 present the adsorption equilibrium curves of DCF and PARX for ACK and CC carbons. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**PARX**} \\ \hline  & **ACK** & **CC*** & **ACK** & **CC*** \\ \hline _PFO model_ & & & \\ R\({}^{2}\) & 0.972 & 0.976 & 0.989 & 0.980 \\ q\({}_{\rm e}\) (mg g\({}^{-1}\)) & 171 & 179 & 199 & 202 \\ k\({}_{1}\) (min\({}^{-1}\)) & 0.095 & 0.013 & 0.222 & 0.010 \\ \hline _PSO model_ & & & & \\ R\({}^{2}\) & 0.986 & 0.983 & 0.992 & 0.960 \\ q\({}_{\rm e}\) (mg g\({}^{-1}\)) & 175 & 201 & 204 & 227 \\ k\({}_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) & \(9\times 10^{-4}\) & \(1\times 10^{-4}\) & 0.002 & \(5\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Kinetic parameters obtained from the adjustment of the PFO and PSO models to the experimental kinetic data. Figure 7: Adsorption equilibrium curves of DCF and PARX for ACK carbon (Adsorbent mass = 10 mg: Contact time = 4 h; Solution volume = 25 mL; Solution initial pH = 6.0 (DCF) and 5.5 (PARX)). Dots—experimental data; Lines—isotherm models’ adjustment. The experimental data were modelled with the [PERSON], [PERSON], and Sips nonlinear models [48; 49; 50; 51] through the minimum of the least-squares method, and the best-fitting model was chosen through the highest determination coefficient, R\({}^{2}\). The model parameters obtained from the adjustments are presented in Table 7, observing that both the [PERSON] and Sips models were best-fitted. Several adsorbents, particularly carbon adsorbents, present heterogeneous surfaces with different types of binding sites with different binding energies; therefore, they are characterized by a binding affinity distribution function [52]. Thus, although the Langmuir model was a good fit to the data, Langmuir isotherm tends to overcompensate for the curvature in the isotherms, and it is unlikely that the carbon surfaces exhibit homogeneous adsorption of the target molecules on their surfaces. On the other hand, Freundlich isotherm tends to undercompensate the isotherm curvature, assuming an exponential distribution of active centers, which means that the number of available sites is infinite, but this is generally true for the systems where low adsorbate concentrations are involved [52]. The adsorbent/adsorbate systems reached saturation or are close to that. Thus, the Sips isotherm model is better to model the linear sub-saturation, as well as the curved saturation portions of the isotherms. Therefore, looking at the results obtained with Sips modeling, the Sips constants for DCF adsorption with both carbons present the same values, indicating a similar affinity of the molecule for the carbon surfaces; however, \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**PARX**} \\ \hline  & **ACK** & **CC*** ** & **ACK** & **CC*** ** & **ACK** & **CC*** ** \\ \hline
**Langmuir** & & & & \\ q\({}_{\text{m}}\) (mg g\({}^{-1}\)) & 217 & 239 & 276 & 330 \\ K\({}_{\text{L}}\) (L mg\({}^{-1}\)) & 0.2 & 0.2 & 0.2 & 0.03 \\ R\({}^{2}\) & 0.964 & 0.841 & 0.965 & 0.948 \\ \hline
**[PERSON]** & & & & \\ K\({}_{\text{F}}\) [mg g\({}^{-1}\) (mg L\({}^{-1}\))n] & 82.5 & 74.0 & 102 & 20.9 \\ n (dimensionless) & 5.0 & 3.9 & 0.23 & 1.75 \\ R\({}^{2}\) & 0.842 & 0.732 & 0.953 & 0.932 \\ \hline
**[PERSON]** & & & & \\ q\({}_{\text{m}}\) (mg g\({}^{-1}\)) & 217 & 214 & 275 & 260 \\ K\({}_{\text{S}}\) (L mg\({}^{-1}\)) & 0.099 & 0.097 & 0.043 & 0.024 \\ n\({}_{\text{s}}\) & 0.5 & 1.66 & 0.2 & 1.24 \\ R\({}^{2}\) & 0.964 & 0.861 & 0.965 & 0.950 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Estimated parameters of the isotherm models adjusted to the experimental data of DCF and PARX adsorption. Figure 8: Adsorption equilibrium curves of DCF and PARX for CC carbon (Adsorbent mass = 10 mg; Contact time = 8 h; Solution volume = 25 mL; Solution initial pH = 6.0 (DCF) and 5.5 (PARX)). Dots—experimental data; Lines—isotherm models’ adjustment.