## 3 Results and Discussion
### The Adsorption Properties of the Mesoporous Materials  
The adsorption properties towards cationic dyes, which are derivatives of thiazine (methylene blue; MB) and triarylmethane (crystal violet; CV), were investigated for selected materials: the mesoporous carbons C3 and C4 as well as the mesoporous polymers P1 and P2. For carbon materials, additional adsorption studies with another derivative of triarylmethane (malachite green, MG) were carried out. Figure 14A-E show the adsorption isotherms of the individual dyes on carbon and polymer materials in the standard form \(a\) vs. _c\({}_{eq}\)_ and the reduced form _a/S\({}_{BET}\)_ vs. _c\({}_{eq}\)_. Analysis of Figure 14A,B suggests that methylene blue is comparably adsorbed by the carbon C3 which is a material of mixed porosity (microporous and mesoporous) and the mesoporous carbon C4, in comparison to the mesoporous polymeric materials P2 and P1 for which the weakest adsorption is found. The values of a maximum adsorption capacity (a\({}_{\text{m}}\)) determined based on the Generalized Langmuir equation (GL) for these materials equal to 1.01; 0.88; 0.044 and 0.038 mmol/g,  
Figure 13: Dependences of surface charge density on pH for carbons (**A**) and polymer materials (**B**). respectively. Such a significant difference in the adsorption of methylene blue on different types of materials (carbon or polymer) is the result of several closely related factors, i.e., (i) affinity of the solid for the dye under given experimental conditions; (ii) surface charge of the adsorbent; (iii) chemical form of the adsorbate molecule; (iv) porosity of the adsorbent; and (v) molecular dimensions of the adsorbate and its three-dimensional structure. The high affinity of carbons for methylene blue is frequently observed [60; 69; 70; 71] and can be attributed to (i) strong attractive interactions between the deprotonated functional groups on the adsorbent surface and the ionized adsorbate; (ii) \(\pi\)-\(\pi\) interactions of the adsorbent graphene layers with the adsorbate aromatic polyring; (iii) free dispersion interactions (London forces); (iv) hydrogen bonds between nitrogen, sulphur, or hydrogen atoms (methyl groups) of the adsorbate molecule and hydrogen or oxygen atoms belonging to the adsorbent surface groups. In the case of polymers, their much lower affinity for methylene blue is due to (i) repulsive electrostatic forces between the weakly positively charged adsorbent particles and the adsorbate cation; (ii) lack of or slight interactions resulting from differences in the distribution of electron density in aromatic systems (X-ray diffraction studies). Due to the chemical structure of polymers and methylene blue, free dispersion interactions and hydrogen bonds are highly probable. The influence of the surface charge of polymers on the affinity towards ionisable dyes has been discussed in many works [72; 73; 74]. The slope of the adsorption isotherm in the range of low equilibrium concentrations is a measure of adsorbent-adsorbate affinity. This adsorption property is also expressed by the value of the equilibrium constant (log K) obtained by fitting the theoretical curve to  
Figure 14: Comparison of the adsorption isotherms for (**A**) methylene blue on C3 and C4, (**B**) methylene blue on P1 and P2, (**C**) malachite green on C3 and C4, (**D**) crystal violet on C3 and C4, and (**E**) crystal violet on P1 and P2. The lines correspond to the fitted Generalized Langmuir equation (Generalized Freundlich (GF) and Langmuir (L) equations). The inset figures show the adsorption isotherms in the reduced form _a/S\({}_{BET}\)_ vs. _c\({}_{\alpha}\)_.  
experimental data. For the adsorption systems discussed, this parameter is in the range of 1.12-1.62 which indicates high affinity adsorbents towards adsorbate. However, it should be noted that log K is significantly overestimated for systems with polymers due to the type of theoretical isotherm chosen (Langmuir isotherm).