## 3 Results and Discussion
### Sorption Thermodynamics  
To describe the nature of the sorption process by determining thermodynamic parameters, experiments were performed at temperatures of 25, 30, and 35 \({}^{\circ}\)C (298; 303; 308 K). The pH of the solutions was adjusted to a neutral environment (pH 7). It was found that temperature has different influences on sorption to TiO\({}_{2}\) in different forms (Table 8). The sorption of IMT on the suspension decreased with increasing temperature. For the sorption of IMT on TiO\({}_{2}\)-GF, the effect of temperature was not noticeable due to a slight increase in active sites and \(K_{d}\) values. A similar temperature effect was found for the sorption of CRZ on all TiO\({}_{2}\) forms; increasing the temperature led to an increase in molecular diffusion to the surface of the photocatalyst and then promoted pharmaceutical binding [56]. Similar sorption thermodynamics depending on the type of sorbent used as for IMT was also reported for ciprofloxacin [37].  
Thermodynamic parameters, including Gibbs free energy, \(\Delta G^{\circ}\), enthalpy, \(\Delta H^{\circ}\), and entropy, \(\Delta S^{\circ}\), were calculated using the following equations [57]:  
\[\Delta G^{\circ}=-RTlnK_{d} \tag{7}\]  
Figure 4: Effect of sorbent dosage (1—suspended TiO\({}_{2}\), 2—TiO\({}_{2}\)-GF, 3—TiO\({}_{2}\)/CNT-GF. 1: min—0.5 g/L, average—1.0 g/L, max—1.5 g/L; mass layer of 2: min—2.3 g/L, average—3.7 g/L, max—5.2 g/L; mass layer of 3: min—47.8 g/L, average—73.2 g/L, max—107.6 g/L).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sample** & \multicolumn{3}{c}{\(K_{d}\), mL/g} & \multicolumn{3}{c}{\(\Delta G^{\circ}\), kJ/mol} & \multicolumn{3}{c}{\(\Delta H^{\circ}\),} \\ \hline
**IMT** & **298 K** & **303 K** & **308 K** & **298 K** & **303 K** & **308 K** & **kJ/mol** & **\(\Delta S^{\circ}\), J/mol** \\ \hline suspended & 213.8 & 61.9 & 49.7 & \(-\)13.3 & \(-\)10.4 & \(-\)10.0 & \(-\)57.9 & \(-\)151.0 \\ TiO\({}_{2}\)-GF & 36.4 & 40.3 & 47.4 & \(-\)8.8 & \(-\)9.3 & \(-\)9.5 & 10.4 & 64.6 \\ TiO\({}_{2}\)/CNT-GF & 82.3 & 82.5 & 88.7 & \(-\)10.9 & \(-\)11.1 & \(-\)1.8 & 2.9 & 46.4 \\ \hline
**CRZ** & & & & & & & & \\ \hline suspended & 233.8 & 268.8 & 271.7 & \(-\)13.5 & \(-\)14.3 & \(-\)14.8 & 16.7 & 101.7 \\ TiO\({}_{2}\)-GF & 179.2 & 180.9 & 197.6 & \(-\)10.1 & \(-\)11.6 & \(-\)11.9 & 3.82 & 55.8 \\ TiO\({}_{2}\)/CNT-GF & 234.1 & 325.2 & 357.0 & \(-\)8.1 & \(-\)8.7 & \(-\)9.7 & 5.97 & 65.6 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Thermodynamic parameters for IMT and CRZ sorption.  
\[lnK_{d}=-\frac{\Delta H^{\circ}}{RT}+\frac{\Delta S^{\circ}}{R} \tag{8}\]  
The sorption of IMT and CRZ on all sorbents is favorable and spontaneous physisorption process, which is confirmed by negative values of \(\Delta G^{\circ}\), ranging from \(-1.8\) to \(-14.8\) kJ/mol for both pharmaceuticals [58]. The more negative the \(\Delta G^{\circ}\) values, the higher sorption affinity of the pharmaceuticals, as a result of increased driving molecular forces such as Van der Waals forces [59]. The positive \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) values indicate that the sorption of CRZ onto three forms of TiO\({}_{2}\) and of IMT onto both types of immobilized TiO\({}_{2}\), is an endothermic reaction [60], where an increase in temperature leads to a higher sorption capacity. Based on the negative values of the thermodynamic parameters \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\), it can be assumed that IMT sorption in suspension is an exothermic reaction in which randomness at the interface of TiO\({}_{2}\) and IMT solution decreases [33; 59].