## 3 Results
### Dimethoate Interaction with IG and GO Surfaces
#### 3.1.2 Adsorption Isotherms and Standard Gibbs Free Energy
Additionally, \(\left|E_{ads,\ mean}\right|\) from DR isotherm is considerably lower compared to DFT calculated \(E_{ads}\). The latter comparison with DR isotherm, however, should be taken with reserve, as \(\left|E_{ads,\ mean}\right|\) is not the exact thermodynamic quantity, but rather a parameter related to adsorption strength. In the independent experiment, 0.250 mg/mL GO was used for adsorption of \(5\times 10^{-4}\) mol dm\({}^{-3}\) DMT as the model system to assess the temperature effect on the adsorption process. A slight increase of sorbed DMT concentration (5.90 \(\times\) 10\({}^{-6}\) mol dm\({}^{-3}\), 6.53 \(\times\) 10\({}^{-6}\) mol dm\({}^{-3}\), and 7.98 \(\times\) 10\({}^{-6}\) mol dm\({}^{-3}\) at 298, 303, and 308 K, respectively) was observed. It is worth noticing that DMT adsorption's temperature effects some similar commercial graphene materials (SM GO and GNA GO), indicating the same temperature-dependent trend (to be published). This behavior is characteristic for chemical adsorption due to the high energy of activation when the extent of adsorption rate increases initially and could decrease as the temperature increased further. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**adsorption Isotherm Models** & **adsorption Isotherm Parameters** & **IG** & **GO** \\ \hline \multirow{4}{*}{Langmuir} & \(q_{max}/\mathrm{mol\,dm^{-3}g^{-1}}\) & \(4.38\times 10^{-4}\) & \(3.04\times 10^{-5}\) \\  & \(K_{L}/\mathrm{dm^{-3}mol^{-1}}\) & \((1.3\pm 0.3)\times 10^{4}\) & \((5.0\pm 2.3)\times 10^{3}\) \\  & \(R^{2}\) & \(0.9985\) & \(0.9620\) \\  & \(\Delta G/\mathrm{M}\) mol\({}^{-1}\) & \(-27\pm 6\) & \(-31\pm 14\) \\ \hline \multirow{4}{*}{Liu} & \(q_{max}/\mathrm{mol\,dm^{-3}g^{-1}}\) & \(6.36\times 10^{-4}\) & \(2.81\times 10^{-5}\) \\  & \(R_{g}/\mathrm{dm^{-3}mol^{-1}}\) & \(380\pm 184\) & \((5.8\pm 0.6)\times 10^{3}\) \\  & \(n_{g}\) & \(1.60\pm 0.14\) & \(0.61\pm 0.05\) \\  & \(R^{2}\) & \(0.9993\) & \(0.9979\) \\  & \(\Delta G/\mathrm{M}\) mol\({}^{-1}\) & \(-24\pm 12\) & \(-31\pm 4\) \\ \hline \multirow{4}{*}{Dubinin-Raduschevich} & \(q_{max}/\mathrm{mol\,dm^{-3}g^{-1}}\) & \(8.51\times 10^{-4}\) & \(5.19\times 10^{-5}\) \\  & \(K_{DR}/\mathrm{dm^{-3}g^{-1}}\) & \(-4.63\times 10^{-3}\) & \(-3.11\times 10^{-3}\) \\ \cline{1-1}  & \(R^{2}\) & \(0.9997\) & \(0.9793\) \\ \cline{1-1}  & \(\left|E_{ads,\ mean}\right|/\mathrm{M}\) mol\({}^{-1}\) & \(1039\) & \(1269\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean values of fitting parameters of Langmuir, Liu, and Dubinin-Raduschevich models for two datasets with a constant graphene concentration (0.25 and 2 g dm\({}^{-3}\)). Moreover, higher adsorption strength in a smaller (3 \(\times\) 3) supercell implies that the adsorption energy depends on the surface coverage in the investigated range. Despite negative adsorption energies, optimized geometries are characterized by remarkably large closest substrate-to-adsorbate distances (2-3 A), independently of the input geometry, and quite a small charge transfer--not exceeding 0.01 electron per adsorbate molecule. These results point to the dispersive interactions included in this model indirectly, through Van der Waals corrections, as the main factor determining DMT adsorption on pristine graphene. The total electronic density of states (DOS) of pristine graphene, and graphene with adsorbed DMT in preferential adsorption geometry, is represented in Figure 5.  
This graph represents the energy distribution of electronic density--every peak, in essence, represents an electronic energy band. In this manner, the possible chemical bond formation would be reflected through novel bands' appearance upon adsorption. Simultaneously, the downshift of bands on the graph would point to the system's energy stabilization. As evident from Figure 5, in the case of a 6 \(\times\) 6 graphene supercell, there is no significant modification of graphene band structure upon adsorption of dimethoate.