## 3 Results and Discussion
### DCF and PARX Adsorption Assays
#### 3.2.2 Kinetic Study  
The effect of time (kinetic assay) was studied for the adsorption of both drugs (Figures 5 and 6).  
Figure 4: Effect of solution pH on the uptake capacity of DCF and PARX for ACK and CC carbons. (Adsorbent mass = 10 mg; DCF and PARX initial concentration = 100 mg L\({}^{-1}\); solution volume = 25 mL; contact time = 24 h).  
DCF and PARX uptake by ACK carbon achieved equilibrium at 240 min (4 h), with adsorption capacities of 182 mg g\({}^{-1}\) and 212 mg g\({}^{-1}\), respectively. On the other hand, the adsorption of both molecules by CC carbon reached equilibrium at around 480 min (8 h), indicating a slower adsorption rate. The adsorption capacities of DCF and PARX at equilibrium with CC carbon were 167 mg g\({}^{-1}\) and 205 mg g\({}^{-1}\), respectively, quite comparable to the values obtained at equilibrium for ANS-derived carbon. Thus, despite the higher surface area and micropore volume of ACK carbon (Table 2), its uptake capacity was not significantly higher than the one obtained for the commercial adsorbent.  
Experimental data were adjusted to the pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic nonlinear models [44; 45] (Table S1, Supplementary Materials) through the minimum of the least-squares method. The best-fitting model was chosen based on the determination coefficient, R\({}^{2}\). The kinetic parameters obtained from the models are presented in Table 6.  
Figure 5: Kinetic curves of DCF adsorption for ACK and CC carbons (Adsorbent mass = 10 mg; DCF initial concentration = 100 mg L\({}^{-1}\); Solution volume = 25 mL; Solution initial pH = 6.00). Dots—experimental data; Lines—kinetic model adjustments.  
Figure 6: Kinetic curves of PARX adsorption for ACK and CC carbons (Adsorbent mass = 10 mg; PARX initial concentration = 100 mg L\({}^{-1}\); Solution volume = 25 mL; Solution initial pH = 5.5). Dots—experimental data; Lines—kinetic models’ adjustment.  
Both kinetic models were well-fitted to the experimental data (R\({}^{2}>0.900\)), although the PSO kinetic model presented the best fit to most of the drug-carbon systems, with an exception for the PARX-CC system that presented a slightly better adjustment for the PFO model. Although these kinetic models are essentially mathematical and constituted by empirical equations, some authors mentioned that a good fit to the PFO model indicates that the surface reaction acts as the rate-limiting step, while the PSO model generally implies that the rate of adsorption is limited by the process of diffusion into a network of small pores [46; 47].  
It can be observed that the kinetic constant values are higher for the systems with the ACK sample, confirming the faster uptake of the molecules by this carbon due to its higher mesopore volume (Table 2). The uptake of PARX onto ACK carbon is the fastest, probably due to a higher affinity of the molecule to the adsorption sites of this carbon, as discussed further ahead (Section 3.2.4).  
Based on these results, an equilibrium time of 4 h has been chosen to complete the adsorption studies with ACK carbon for both drugs. For CC carbon, the equilibrium time chosen for both pharmaceutical compounds was 8 h.