## 2 Materials and Methods
### Methods of Investigations
#### 2.4.6 Adsorption Studies  
Adsorption isotherms of dyes from aqueous solutions were determined using a static method, but adsorption experiments were performed differently depending on the typeof adsorbent. In the case of carbon materials, the weighted amount of adsorbent (\(\sim\)0.02 g) was contacted with 5 mL of water and degassed under a vacuum. An adsorbent was then poured over with a dye solution (pH = 7), placed in an incubator shaker at 25 \({}^{\circ}\)C (Innova 40R, New Brunswick Scientific, Edison, NJ, USA), and kept there until adsorption equilibrium was reached. A sample of the dye solution was then taken, and its concentration was determined by using the Cary 100 UV/Vis spectrophotometer (Varian Inc., Melbourne, VIC, Australia). Then, a certain amount of the dye stock solution was added to an adsorption system. These activities were repeated several times to measure the adsorption isotherms over a wide concentration range (0.07-0.92 mmol/L for MB; 0.07-0.55 mmol/L for MG; 0.05-0.32 mmol/L for CV). For polymeric materials, the series of adsorbent samples (\(\sim\)0.1 g for MB; \(\sim\)0.08 g for CV) were contacted with water, degassed, and poured with dye solutions of different concentrations (0.02-0.42 mmol/L for MB; 0.01-0.20 mmol/L for CV) and placed in an incubator shaker at 25 \({}^{\circ}\)C. After attaining adsorption equilibrium, the solute concentrations were determined based on the spectrophotometric measurements. In order to keep the pH conditions of the adsorption experiments constant, solutions of all dyes were prepared using a buffer with pH = 7. The analysis of the equilibrium data was based on the Generalized Langmuir equation (GL) [62; 63; 64]:  
\[\theta=\left[\frac{\left(Kc_{eq}\right)^{n}}{1+\left(Kc_{eq}\right)^{n}} \right]^{\frac{m}{n}} \tag{1}\]  
where \(\theta\) = a\({}_{\text{eq}}\)/a\({}_{\text{m}}\) is the global adsorption isotherm; a\({}_{\text{m}}\) is the adsorption capacity; m, n are the heterogeneity parameters; and K is the equilibrium constant. Depending on the specific values of \(m\) and \(n\) parameters, the GL equation is simplified into four equations: Langmuir (L) (GL: \(m\) = \(n\) = 1), Langmuir-Freundlich (LF) (GL: \(0<m\) = \(n\) \(\leq\) 1), Generalized Freundlich (GF) (GL: \(n\) = 1, \(0<m\) \(\leq\) 1), and Toth (T) (GL: \(m\) = 1, \(0<n\) \(\leq\) 1). The Generalized Langmuir isotherm (GL) is usually applied for the analysis of localised physical adsorption on energetically heterogeneous solids and despite its relatively simple form, it describes most of the available experimental data quite well. The GL equation corresponds to an asymmetric quasi-Gaussian adsorption energy distribution function; the heterogeneity parameters m and n characterise the extension of this function towards higher (m \(<\) 1) and lower (n \(<\) 1) adsorption energies (the smaller m and n is, the greater the heterogeneity). The Toth equation corresponds to an asymmetric quasi-Gaussian adsorption energy distribution function extended towards low energies, while the GF isotherm corresponds to an exponential function with a characteristic minimum energy. The Langmuir-Freundlich (LF) equation conforms to a symmetric quasi-Gaussian adsorption energy distribution function, and equation (L) describes adsorption on a solid characterized by energetic homogeneity. Similar to the adsorption equilibrium experiments, the kinetic measurements were also carried out using a UV/Vis spectrophotometer. The dye solution of a certain concentration was brought into contact with the known amount of solid in a glass vessel. During the entire experiment, the suspension solution was stirred magnetically, and at a certain point in time, the solution samples were collected in a measuring cell and measured.