## 3 Results  
### Dimethoate Interaction with IG and GO Surfaces  
#### 3.1.1 Hill and Scatchard Analysis  
Several experiments were performed to elucidate the reaction mechanism of DMT interaction with IG and GO surfaces. Here, we used the approximation of the bimolecular interaction between biological macromolecules and the ligand, considering DMT as the ligand and adsorbents as macromolecules (receptors) with several binding sites [36; 37]. The DMT molecule was regarded as the box with the dimensions 10 \(\times\) 3 \(\times\) 3 nm. Its flat position on graphene surfaces was considered the energetically preferred orientation on the covers, as confirmed by DFT calculations (Section 3.2.1). The theoretical maximal concentration of binding sites (BS) for DMT on macromolecules (\(C_{BS-total}\)) corresponds to the complete monolayer covering with the ligand and is expressed as the molar concentration of BS per g of graphene material. It was calculated from the specific surface of the adsorbent [27; 28] and estimated the maximal surface of a single DMT binding site according to Equation (2):  
\[C_{BS-total}=\frac{\Sigma\gamma}{\sigma\cdot N_{A}} \tag{2}\]  
Here, \(\Sigma\) represents the specific surface of the graphene material obtained by the producer [38; 39], \(\sigma\)--maximal estimated surface of a single adsorption site (10 \(\times\) 3 A for a DMT molecule in the flat orientation), \(\gamma\)--mass concentration of graphene in g dm\({}^{-3}\), and \(N_{A}\) is the Avogadro number. Using Equation (2), the calculated values of \(C_{BS-total}\) for GO and IG are 300 mol g\({}^{-1}\) and 2.4 \(\times\) 10\({}^{4}\) mol g\({}^{-1}\), respectively. The first set of experiments in a water suspension of IG and GO was performed by keeping DMT concentration fixed (5 \(\times\) 10\({}^{-4}\) mol dm\({}^{-3}\)) at 25 \({}^{\circ}\)C and pH 6, while the surfactant concentration varied in the range from 0.05-2 g dm\({}^{-3}\). In the second series of experiments, adsorbent concentrations were constant (0.25 and 2 g dm\({}^{-3}\)), and the adsorption of DMT was dependent on its concentration in the mixture. In all cases, the water solutions were stirred for 24 h to achieve equilibrium in the homogeneous suspension. The equilibrium-free pesticide concentration was measured from the supernatant after separation of adsorbent by centrifugation and filtration. Finally, the concentration of adsorbed DMT was calculated as the difference between the initial and equilibrium values. The results presented in Figure 2 indicate that sigmoid-shaped dependences of adsorbed DMT on its equilibrium concentration were obtained in all cases. This reaction mechanism can be described by Hill and Scatchard models [26; 40; 41; 42], which provide information about the type of the ligand-macromolecule interaction and discriminates between the random and cooperative process of DMT binding mode on a graphene surface. Moreover, these models enable us to determine if there was an interaction between the BS where the ligands' subsequent binding depended on the BS number. Experimental values were fitted with Equation (3):  
\[C_{ads}=C_{max}\frac{C_{eq}^{n}}{K_{diss}^{n}+C_{eq}^{n}} \tag{3}\]Here, \(C_{ads}\) is the concentration of bounded DMT molecules on the active sites of a receptor, i.e., the occupied BS, \(C_{max}\) is yielding to the maximal number of occupied BS, \(C_{eq}\) is the free concentration of adsorbate, which is in equilibrium with bound ligands, \(K_{diss}\) is the apparent microscopic dissociation constant of adsorbent-adsorbate composite, and \(n_{H}\) is the Hill coefficient describing cooperativity of ligand-macromolecule interaction.