## 3 Results and Discussion
### The Adsorption Properties of the Mesoporous Materials
Based on these observations, one can indicate diffusion from a bulk solution and intramolecular diffusion as critical stages for the kinetics of malachite green and crystal violet adsorption. The differentiated adsorption rate on the mesoporous carbon C4 and the mixed type (micro- and mesoporous) carbon C3 is revealed by the values of the half-time t\({}_{1/2}\) determined in the optimisation procedure using the multi-exponential equation (this equation among all ones turned out to best describe the adsorption kinetics of tested systems; the results are collected in Table S1 in Supplementary Materials). The t\({}_{1/2}\) parameter is the time needed to achieve a 50% change in solution concentration and for the systems with C4 and C3, it is 99 and 416 min, respectively (the methylene blue adsorption); 116 and 710 min, respectively (the malachite green adsorption); and 406 and 1311 min, respectively (the crystal violet adsorption). One can also notice a huge difference in the times needed to reach the equilibrium state, which is related to the porosity characteristics of the adsorbents. The carbon C4 with wider pores enables it to reach equilibrium 9.4 times (the methylene blue adsorption), 4.5 times (the malachite green adsorption), and 2.5 times (the crystal violet adsorption) faster compared to the carbon C3. The adsorption kinetics of dyes in the polymer group show a similar trend as in the carbon group. The polymer P1 with larger pore sizes enables a faster process of pollutant removing from an aqueous solution than the polymer P2. The half-time t\({}_{1/2}\) values in the systems with P1 and P2 are 87 and 570 min, respectively (the methylene blue adsorption); and 92 and 337 min, respectively (the crystal violet adsorption). During the methylene blue adsorption on P1, a state close to equilibrium is reached after approx. 4500 min, while in the case of P2, the experiment time is insufficient to determine its value. For the crystal violet--P1 system and the crystal violet--P2 system adsorption remains at the same level after approx. 2100 and 7100 min, respectively, which corresponds to a difference of 3.4 times. By analysing the concentration profiles for two groups of materials, a correlation between the dye adsorption rate, the affinity of the adsorbent for the dye, and the adsorbent porosity can be seen. The use of a polymer weight 7.5 times higher than that of activated carbon compensates for a weak affinity of the adsorbent for methylene blue to such an extent that the kinetic profiles on the polymer P1 and the carbon C4 have very similar course. However, some of the adsorbate remains in the solution in an unbound form. The situation is slightly different during the crystal violet adsorption towards which the polymer has a higher affinity. Even though the crystal violet molecule is larger than the methylene blue molecule and is additionally spatially expanded, the adsorption rate is higher on the polymer P1 than on the carbon C4. For both systems, the equilibrium uptake u\({}_{\text{eq}}\) equals unity. One can see the similarity in the kinetics of crystal violet on the carbon C4 and the polymer P2, with a smaller share of larger pores than the polymer P1. The observations described above are confirmed by the kinetic profiles of dyes adsorption on the selected carbon and the polymer materials (Figure 17A,B). There is a clear change in the trend of the dye adsorption rate when changing adsorbent, i.e., for the carbon C3 there is an increase in the adsorption rate consistent with the decrease in the adsorbate size and shape, and for P2 there is an opposite situation, due to the difference in adsorbent-adsorbate affinity. The adsorption kinetics of tested systems was analysed by applying the classical equations e.g., first-order (FOE), second-order (SOE), and less popular equations, e.g., mixed 1,2-order (MOE), multi-exponential (m-exp), fractal-like MOE (f-MOE). The values of the parameters of various kinetic equations are collected in Table S1 in the Supplementary Materials.