## 2 Results
### Determination of Kinetic Parameters  
The mechanism of dye adsorption generally can involve three steps, one or any combination of which can be the rate-controlling ones: (i) mass transfer through the external boundary layer of liquid surrounding the microspheres; (ii) adsorption on the surface (internal or external), the energy depending on the type of binding process (physical or chemical)--this step is often extremely rapid; (iii) diffusion of the dye molecules to the adsorption sites either by a pore diffusion process or by a solid surface diffusion mechanism. The contact time-dependent experiments in the dyes-DVB-co-GMA-TETA systems were conducted to evaluate the kinetic parameters of sorption. The amounts of acid dye uptake by microspheres were calculated from Equation (6) as follows:  
\[q_{t}=\ \frac{(C_{0}-\ C_{t})}{m}\ V \tag{6}\]  
where \(C_{0}\) and \(C_{t}\) (mg/L) are acid dye concentrations in the solution before adsorption and after sorption time \(t\), respectively; \(V\) (L) is volume of the dye solution and \(m\) (g) is mass of DVB-co-GMA-TETA. The kinetics of AV1, AG16 and AR18 adsorption on DVB-co-GMA-TETA were examined to explore the dye retention rate-controlling mechanism using the pseudo-first order (PFO), the pseudo-second order (PSO) and intraparticle diffusion (IPD) kinetic models [30; 31]. The equations of the above mentioned models (Equations (7)-(9)) are expressed as:  
\[\frac{dq_{t}}{dt}=k_{1}(q_{e}-q_{t}) \tag{7}\]  
\[\frac{dq_{t}}{dt}=\ k_{2}(q_{e}-q_{t})^{2} \tag{8}\]  
\[q_{t}=\ k_{i}t^{1/2} \tag{9}\]  
Figure 6: Suggested mechanism of dye interactions with DVB-co-GMA-TETA in aqueous solution. where \(q_{e}\) and \(q_{t}\) (mg/g) are dye amounts sorbed at the equilibrium and at any time \(t\), \(k_{1}\) (1/min) and \(k_{2}\) (g/mg min) are rate constants of sorption determined from PFO and PSO equations, respectively, and \(k_{i}\) is the intraparticle diffusion rate constant (mg/g min\({}^{0.5}\)). There are two essential steps in the adsorption of dyes onto DVB-_co_-GMA-TETA. The first one covers the time from 1 min to 120 min and is related to the visible increase in the amount of dyes adsorbed per unit mass of the resin. The second one covers the subsequent minutes (from 120 to 180 min), in which the adsorption progress is much slower and leads to the establishment of a dynamic equilibrium (Figure 7). After 180 min, the AV1, AG16 and AR18 adsorption reached equilibrium and the maximum dye adsorption was 85 mg/g, 59.9 mg/g and 88.7 mg/g, respectively. The non-linear plots (Figure 7a,b) showing the fit of the PFO and PSO models for the sorption of AV1, AG16 and AR18 on DVB-_co_-GMA-TETA were obtained and the calculated kinetic parameters are presented in Table 5.  
Figure 7: Influence of phase contact time on the acid dye uptake (\(C_{0}\) = 100 mg/L) by DVB-_co_-GMA-TETA with non-linear (Non-LR) fitting of PFO (**a**) and PSO (**b**) kinetic models to experimental data as well as IPD multilinear plot (**c**) and the linear fitting of IPD (**d**) model to experimental data. The determination coefficients \(R^{2}\) (and \(R^{2}_{adj}\)) of the PFO and PSO models were in the range of 0.916-0.991 (0.892-0.987) and 0.959-0.989 (0.947-0.986), respectively. Moreover, \(q_{e}\) calculated from the PFO and PSO equations are not in line with experimental values (\(q_{exp}\)). It can be concluded that neither PFO nor PSO models can be applied for description of kinetic sorption data of the acid dyes on DVB-\(co\)-GMA-TETA. However, these models are frequently used for calculation of kinetic parameters during dye removal technologies (Table 4). It was observed that the intraparticle diffusion may be a rate-limiting step, as the \(R^{2}\) and \(R^{2}_{adj}\) values were high and equaled 0.939 and 0.922, 0.991 and 0.990 as well as 0.989 and 0.986 for AV1, AR18 and AG16 sorption on DVB-\(co\)-GMA-TETA, respectively. The best fitting of experimental data to the IPD model was obtained as shown in Figure 7d.