## 2 Results and Discussion
### Equilibrium Studies--adsorption Isotherms
The model is suitable for describing adsorption on surfaces with a certain degree of heterogeneity, correcting for the limitation at the high adsorbate concentrations usually associated with the Freundlich model:  
\[q_{e}=q_{m}\frac{\left(K_{S}\cdot C_{e}\right)^{n}}{1+\left(K_{S}\cdot C_{e} \right)^{n}} \tag{7}\]  
where \(q_{e}\) is the equilibrium adsorption capacity, mM\(\cdot\)g\({}^{-1}\), \(C_{e}\) is the equilibrium molar concentration of the adsorbate in solution, mM\(\cdot\)L\({}^{-1}\), \(K_{S}\) is the Sips isotherm constant, L\(\cdot\)mM\({}^{-1}\), \(n\) is the heterogeneity parameter, with values between 0 and 1, and \(q_{m}\) is the maximum adsorption capacity, mM g\({}^{-1}\). The _Rellich-Peterson_ adsorption isotherm [50] is also a three-parameter isotherm, which takes into consideration a hybrid adsorption mechanism:  
\[q_{e}=\frac{K_{RP}\cdot C_{e}}{1+a\cdot C_{e}^{b}} \tag{8}\]  
where \(q_{e}\) is the equilibrium adsorption capacity, mM\(\cdot\)g\({}^{-1}\), \(C_{e}\) is the equilibrium molar concentration of the adsorbate in solution, mM\(\cdot\)L\({}^{-1}\), \(K_{RP}\) is the Redlich-Peterson isotherm constant, L\(\cdot\)mM\({}^{-1}\), \(a\) is the constant depending, on the nature of adsorption interactions, L\(\cdot\)mM\({}^{-1}\), and \(b\) is the exponent, with values between 0 and 1. The experimental equilibrium data at four initial adsorbate concentrations (3.0, 2.5, 2.0, and 1.0 mM/L) and at four temperatures (298 K, 308 K, 313 K, and 318 K) are presented in Table S2. The parameters of the adsorption isotherms were evaluated by non-linear regression analysis using the equilibrium data (see Table S2). Due to the repetitive nature of the calculations, the non-linear regression analysis graphs of the adsorbates on the best-performing adsorbent, PAB3, are presented in the following figures. Similar regression data were also obtained for the adsorbents PAB2 and PAB1. The data for the non-linear regression analysis using the Langmuir, Freundlich, Sips, and Redlich-Petersen adsorption isotherms are presented in Figures 11-14 for the adsorption of the studied adsorbates on the best-performing adsorbent, PAB3. Similar data were also obtained from the study of the adsorption on the adsorbents PAB1 and PAB2 and are not presented in detail. The isotherm parameters calculated for the adsorption of the sulfamethoxazole are presented in Table S3 and those for the adsorption of the tetracycline in Table S5. The data obtained by the non-linear regression analysis indicated an excellent fit with the experimental equilibrium data. The best correlations were obtained with the Sips and Redlich-Peterson adsorption isotherms (see the values of the coefficients of determination, R-Squared, \(R^{2}\)). The Sips and Freundlich isotherms indicated a rather high degree of heterogeneity of the adsorbent surface. These findings suggest that the adsorption mechanism is most likely hybrid. The calculated value of the separation factors \(R_{L}\) (see Table 3 and Supplementary Materials Table S4) clearly indicate that the adsorption process is _favorable_ for all the adsorbents studied: \(0<R_{L}<1\). In the absence of specific surface functional groups that can determine the interactions between an adsorbent and adsorbate molecules, adsorption over porous adsorbents primarily depends on the surface area and porosity of the material [51]. The interactions between functionalized S-DVB adsorbents and pharmaceuticals, including antibiotics such  
Figure 11: _Langmuir_ isotherm non-linear regression analysis. Left: Sulfamethoxazole on PAB3. Right: Tetracycline on PAB3. Figure 12: _Freundlich_ isotherm non-linear regression analysis. Left: Sulfamethoxazole on PAB3. Right: Tetracycline on PAB3. as sulfamethoxazole and tetracycline, in aqueous solutions, can be attributed to various interactions [5; 6; 7; 52].