## 4 Discussion  
The experimental studies of DMT interaction with selected graphenes suggest that adsorbate binding is a cooperative process. The positive, cooperative binding is confirmed by [PERSON] and [PERSON] analysis of binding curves, which exert the characteristic sigmoid  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Surface Model**} & \multicolumn{2}{c}{**Geometry**} & \multicolumn{2}{c}{\(E_{ads}\)} & \multirow{2}{*}{**CT to DMT (e-)**} \\ \cline{2-2} \cline{5-6}  & Initial & Optimized & eV & kJ mol-1 & \\ \hline \hline \multirow{4}{*}{O-binding} & \multirow{4}{*}{O-binding} & \multirow{4}{*}{O-binding} & \multirow{4}{*}{O-binding} & \multirow{4}{*}{O-binding} & \multirow{4}{*}{O-binding} \\  & & & & & \\ \cline{1-1} \cline  
shape and Hill coefficient close to 2. This behavior indicates that once one ligand molecule is bound to the macromolecule, its affinity for other ligand molecules increases. It is also found previously by applying the same models on some dye nanoparticles composites [36; 37]. According to \(K_{ads}\) values, the interaction between DMT and GO surface yields a more stable associate. However, the maximum amount of adsorbed DMT per gram of adsorbate is higher for IG. This finding is to some extent corroborated by slightly larger Gibbs free energies (within the level of estimated uncertainty values) of adsorption obtained for GO, compared to IG. However, except for these indications, there is still no exact proof that GO is an intrinsically better adsorbent than IG.  
Moreover, DMT adsorption on both GO and IG surfaces is an exothermic process, with the Gibbs free energy of adsorption in the approximate range of \(-10\) to \(-30\) kJ mol\({}^{-1}\). Similar \(K_{g}\) and \(\Delta G\) values were obtained for both Langmuir and Liu models, and these values correspond to physisorption rather than chemisorption. The results are also well fitted with DR isotherm equation, confirming that physisorption with a specific distribution of energies might occur.  
The results of DFT model, in general, corroborate the experimental findings that physisorption mainly occurs. Based on the obtained results, efficient DMT adsorption on graphene is likely to originate from (1) dispersive interactions between surface and adsorbate and (2) chemical binding and dissociation on the unsaturated vacancy-type defects and edges (if any). Namely, adsorption of DMT on graphene can be significantly influenced by the introduction of vacancy-type defects. Thus, the structure of surface defects can decide between the chemical and physical nature of the adsorption. However, it should be kept in mind that such reactive vacancy-type defects are unstable in aqueous media and are easily oxidized by any oxygen species present in the solution [49; 50]. Corresponding oxydefect and N-defect models, describing such oxidized (and nitrogen-saturated) features on the surface, exhibited considerably lower reactivity in adsorption, similar to pristine graphene reactivity.  
Obtained results generally point to the fact that, despite some structural differences, the adsorption process of DMT on both IG and GO surfaces is determined by the same principles. The surface area of the adsorbent mainly determines the adsorption efficiency. Additionally, this study represents a successful step forward in ab initio modeling of adsorption of large adsorbates on carbonaceous materials. Obtained findings represent a basis for further development in this field: introducing more complex surface models, building the semiempirical models, evaluating the effects of solvent, etc.