*3.2. Kinetic Analysis*

Information about the dynamics of the adsorption was obtained by investigating the kinetics of the process, applying pseudo first-order and pseudo second-order kinetic models (Equations (2) and (3)). By using the *qt* values reported in Figure 1B, the results shown in Figure 3A,B were obtained. Table 1 reports the calculated kinetic parameters.

**Figure 3.** Pseudo first-order (**A**) and second-order (**B**) kinetic models applied to experiments of adsorption in which the amount of the adsorbent was changed.

**Table 1.** Kinetic parameters obtained by applying the pseudo first-order and second-order kinetic models.


The best kinetic model to describe the experimental data was evaluated by comparing the *R2* values of the linear fitting, as well as the experimental adsorption capacities at equilibrium, qe,exp (contact time 120 min), with those obtained by applying the kinetic equations, qe,calc (calculated adsorption capacities) [13,14]. From Table 1, the *R<sup>2</sup>* values and the comparison between qe,exp and qe,calc suggest that the application of the pseudo second-order equation better described the experimental data, emphasizing the role of both Kp and chitosan amounts during the adsorption process [13,14,16]. Antunes et al. [31] reported that the use of this kinetic model indicates that the rate-controlling step depends on both physical and chemical interactions between the pollutant and adsorbent [31]. However, it is worth pointing out that, from the data reported in Table 1, when using the smallest CH amount, the pseudo first-order model is probably preferred. This suggests that, under this condition, the rate limiting step could be the Kp concentration, i.e., the diffusion of Kp mainly controls the removal of the NSAID [28].

Additional information was obtained by adopting the Weber–Morris model (W–M). The intra-particle diffusion model was used, as described by the following equation: qt = kint × t 1/2 + C, where *C* represents the thickness of the boundary layer, and kint is the kinetic constant related to the intra-particle diffusion rate in mg·g−1·min−1/<sup>2</sup> [32]. As reported by Lin et al. [32], if the plot of qt versus t1/<sup>2</sup> is represented by a straight line passing through the origin, the intra-particle diffusion is the limiting stage of the adsorption. On the other hand, if multiple linear segments are necessary to fit the experimental data, two or more steps could be involved during the NSAID adsorption process [31,32]. The W–M equation was, thus, applied (Figure 4A,B) to the qt values reported in Figures 1C and 2B, referring to experiments in which the amounts of both CH and Kp were changed.

**Figure 4.** Weber–Morris plot applied to experiments of adsorption in which the amounts of the adsorbent (**A**) and Kp (**B**) were changed.

As a whole, the findings suggested that, under our experimental conditions, the Kp adsorption process could be described by two steps: (i) diffusion from the solution to the external surface of the adsorbent, and (ii) intra-particle adsorption and diffusion. Indeed, the experimental points could be divided into these two stages (Figure 4A,B). Moreover, during the second stage, since the ΔC of Kp decreased, the adsorption process decreased, reaching an equilibrium state. Once again, the exception was represented by the condition in which the smallest amount of chitosan was used. In this case, the regression line of the first stage passed through the origin of the plot, suggesting that the intra-particle diffusion was the rate-limiting step [31]. In this latter case, the number of available free sites present on the CH surface was lowered, and the diffusion controlled the process as previously supposed.

## *3.3. E*ff*ect of pH*

To get insight into the nature of the adsorption process, the effect of pH during the adsorption of Kp onto CH was investigated, by adding either HCl or NaOH. To avoid changes in pH values during the adsorption process, due to the presence of acetic acid added during chitosan film preparation, the used adsorbent (150 mg) was neutralized with NaOH and washed several times with fresh water, until a neutral pH was achieved.

As reported in Figure 5A, the percentage of Kp adsorption was calculated at each pH value and contact time. The maximum adsorption occurred between pH 3 and pH 5, while it decreased after this pH value, with the lowest Kp removal at pH 12. Interestingly, at the beginning of the process, i.e., in the first 15 min, the Kp removal was approximately the same at pH 3 and 5, and it was reduced upon increasing the pH value. Instead, upon extending the contact time, the affinity at pH 3 was slightly reduced, and the results at pH 5 appeared the best. These findings were better evidenced by calculating the associated qt values (Figure 5B).

Clearly, at both pH 3 and pH 5, the adsorption capacities were good, having the highest values, and, at pH 3, the qt,max was reached quickly in the first minute. In order to better understand this behavior, the zero-point charge (ZPC) of CH was determined using the drift method [14] (Figure 5C). The observed cross-section region of the curves in Figure 5C indicated that the pHZPC of CH was around pH 7. This means that, below pH 7, the chitosan amino groups were positively charged, while they were deprotonated toward the pHZPC. After this pH value, chitosan became mainly negatively charged [33]. The negative charge on the surface of the chitosan film in alkaline medium could be mainly ascribed to the presence of negative ions (OH−) in solution, that would form a negative layer on the surface of chitosan. Moreover, in accordance with the carboxylic moieties present in the Kp chemical structure (see Figure 1A), the NSAID pKa is reported to be around 4 [34]. This means that, below this pH value, Kp was present as a neutral molecule (Kp-H), while, above this value, it was present as an anionic one (Kp−).

Thus, below pH 5, Kp was present as Kp-H, and CH showed a positively charged surface. As a result, a reduced affinity between Kp-H and the adsorbent was expected due to the reduced contribution of electrostatic interactions. However, since adsorption at pH 3 was quite significant, other forces should probably be considered during the process, such as dipole–dipole interactions and H-bonds. At pH 5, Kp was mainly present as Kp− and, at the same time, chitosan was positively charged; thus, electrostatic interactions between the carboxylic moieties of Kp− and the chitosan's positively charged amino groups took place, favoring pollutant removal. At pH > 5, i.e., pH 6, the chitosan amino groups were mainly deprotonated, thereby reducing the affinity between the adsorbent and the NSAID, thus suggesting an electrostatic repulsion between the negative Kp and CH charges [35–38]. This effect was more evident at pH 12, at which the adsorption was completely blocked. Figure 5D reports the possible scheme of interaction between Kp and CH, considering mainly electrostatic forces.

**Figure 5.** Percentage of Kp adsorption from an aqueous solution (1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M) when 150 mg of chitosan was used at different pH values (**A**); drift method to determine the zero-point charge of the adsorbent (**B**); adsorption capacities, qt, referring to Kp adsorption from an aqueous solution (1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M) when 150 mg of chitosan was used at different pH values (**C**); cartoon depicting the interaction between Kp and the adsorbent (**D**).

## *3.4. E*ff*ect of Salts in Kp Solutions*

With the aim of assessing the role of the electrostatic interaction between the Kp− anion and chitosan, some experiments were performed, changing the ionic strength of Kp solutions by adding electrolytes. By selecting NaCl as a model electrolyte at different concentrations, the experiments were performed using 150 mg of chitosan and 1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M Kp.

Thus, the Kp adsorption was evaluated, and the results obtained at 60 min of contact time are reported in Figure 6A. By changing the salt concentration from 0.01 M to 0.05 M, Kp removal decreased from 85%, in the absence of salt, to 20% with 0.05 M NaCl (Figure 6A). By choosing 0.01 M as the salt reference concentration, the electrolyte nature was changed. In particular, upon fixing the type of anion (Cl−), the cation was changed by exploring the effects of Na+, K<sup>+</sup>, and Mg2<sup>+</sup>. As reported in Figure 6B, upon decreasing the cation size from K<sup>+</sup> to Na+, the Kp removal efficiency decreased and, upon changing the cation associated charge, using Mg2+, the effect became more pronounced.

**Figure 6.** Percentage of Kp adsorption from an aqueous solution (1 <sup>×</sup> 10−<sup>5</sup> M, pH 5) when 150 mg of chitosan was used at different concentrations of NaCl (**A**) and in the presence of different salts at 0.01 M (**B**).

These results suggested a cation-mediated shielding effect of the Kp negative charge, confirming the involvement of the Kp carboxylic moieties in its adsorption onto the chitosan film. Interestingly, by changing the type of anion, and choosing K<sup>+</sup> as the cation, the results reported in Figure 6B were obtained. The absence of significant changes in the removal of Kp indicated that the inorganic anions did not affect the adsorption. In fact, in general, if the anion affected the process, its effect would involve the shielding of CH positive charges onto the film surface, slowing down the Kp diffusion into the film, thus preventing adsorption. Instead, the cation effects occurred in solution, shielding the Kp negative charge, thereby reducing the adsorbate/adsorbent affinity.

#### *3.5. Thermodynamic Analysis*

The Kp adsorption process was investigated by adopting three temperature values, i.e., 278, 288, and 298 K, using 150 mg of chitosan and a 1 <sup>×</sup> 10−<sup>5</sup> M Kp solution at pH 5. Figure 7 shows the obtained results in term of adsorption capacities (Figure 7A) and percentage of Kp adsorption (Figure 7B) at different contact times. Upon increasing the temperature values, the qt values and the Kp adsorption percentage at the equilibrium increased, indicating the endothermic character of the process. With the aim of obtaining the thermodynamic parameters, the Keq values were calculated at each temperature and, by using Equations (4) and (5), the correspondent ΔG◦ values were inferred (Table 2). The negative ΔG◦ values indicated the spontaneity of the Kp adsorption process onto chitosan. Furthermore, by plotting ln Keq versus 1/T (Figure 7C) and applying Equation (6), ΔH◦ and ΔS◦ were also calculated (Table 2). In agreement with the literature [31], the positive values of ΔH◦

and ΔS◦ confirmed the endothermic character of the process and the increased randomness at the adsorbent–adsorbate interface, respectively.

**Figure 7.** Adsorption capacities, qt (**A**), and percentage of Kp adsorption (**B**) at different contact times, referring to a Kp aqueous solution (1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M, pH 5) when 150 mg of chitosan was used at different temperature values; plot of ln (Keq) versus 1/T (**C**).


**Table 2.** Thermodynamic parameters.
