## 2 Materials and Methods
### Batch Adsorption Test  
#### 3.4.1 Sorption Capacities  
The process of dye adsorption on the poly(DVB), DVB-VBCl, poly(EGDMA) and EGDMA-VBCl microspheres was carried out using a static method. It involves determining the difference in concentrations of the dye in the solutions before and after adsorption. For this purpose, a known amount of adsorbent was introduced into a defined volume of dye solution and mixed at a constant temperature until equilibrium of the process was reached. This allows the adsorption capacity to be determined. The experimental equilibrium data were modelled using linear forms of the [PERSON] (Equation (3)), [PERSON] (Equation (4)) and Temkin (Equation (5)) isotherm models [21; 22]:  
\[\frac{C_{e}}{q_{e}}=\frac{1}{Q_{0}k_{L}}+\frac{C_{e}}{Q_{0}} \tag{3}\]  
Figure 5: DSC curves of (**a**) poly(DVB) and DVB-VBCl as well as (**b**) poly(EGDMA) and EGDMA-VBCl. \[log\ q_{e}=log\ k_{F}+\frac{1}{n}log\ C_{e} \tag{4}\]  
\[q_{e}=\left(\frac{RT}{b_{T}}\right)lnA+\left(\frac{RT}{b_{T}}\right)lnC_{e} \tag{5}\]  
where \(q_{e}\)--the adsorption capacity (mg/g), \(C_{e}\)--the equilibrium concentration of solution (mg/L), \(Q_{0}\)--the monolayer adsorption capacity (mg/g), \(k_{L}\)--the Langmuir constant (related to the free energy of adsorption) (L/mg), \(k_{\rm F}\) (mg\({}^{1-1/n}\) L\({}^{1/n}\)/g), \(1/n\)--the Freundlich constants connected with adsorption capacity of adsorbent and the surface heterogeneity, respectively, \(R\)--the gas constant (8.314 J/mol K), \(T\)--the temperature (K), \(A\) (L/g) and \(b_{T}\) (J/mol)--the Temkin constants. The isotherm parameters were calculated from the slopes and intercepts of the \(C_{e}/q_{e}\) vs. \(C_{e}\), log \(q_{e}\) vs. log \(C_{e}\) and \(q_{e}\) vs. In\(C_{e}\) plots (\(Q_{0}\) = 1/slope, \(b\) = slope/intercept, \(1/n\) = slope, \(k_{\rm F}\) = 10\({}^{\rm intercept}\), \(b_{T}\) = \(RT\)/slope, \(A\) = exp(intercept/slope)) and are listed in Table 2.  
The adsorption isotherms of AO on the poly(DVB), DVB-VBCl, poly(EGDMA) and EGDMA-VBCl microspheres are shown in Figure 6. Fitting lines corresponding to the three adsorption isotherms indicate that the Freundlich model seems to be the best one. The Freundlich isotherm is an empirical model which is widely applied to describe heterogeneous systems, especially adsorption of organic compounds. The determination coefficients for the Freundlich model were found to be in the range 0.980-0.997. The \(k_{\rm F}\) values were ranged from 4.56 to 7.85 mg\({}^{1-1/n}\) L\({}^{1/n}\)/g. The 1/n parameters describing the intensity of adsorption were below in the investigated system and prove favorable uptake of AO by the poly(DVB), DVB-VBCl, poly(EGDMA) and EGDMA-VBCl microspheres (unfavorable adsorption 1/n > 1). The Langmuir isotherm assumes that an adsorbate (i.e., AO dye) can form a monolayer of molecules on the surface of an adsorbent (i.e., polymeric microspheres), interacting with adsorption sites and not interacting with each other. The Temkin isotherm equation, on the other hand, assumes that the heat of adsorption of all dye molecules in the layer would decrease linearly due to the adsorbent-adsorbate interaction; moreover, adsorption is characterized by a uniform distribution of binding energy. Considering AO adsorption on poly(DVB), DVB-VBCl, poly(EGDMA) and EGDMA-VBCl, it can be seen that the Langmuir and Temkin models provided an unsatisfactory description of experimental data. The values of the determination coefficients R\({}^{2}\) for the Langmuir model ranged from 0.149 to 0.669 and from 0.664 to 0.767 for the Temkin model. These values were smaller than those determined for the Freundlich model.