## 4 Conclusions  
From the n parameter of the Dubinin-Astakhov equation, it was found that the activated carbons are heterogeneous and that as the parameter of heterogeneity from this model moves away from 2, there are significant differences between the values of the micropores energy Eo and E obtained by the Dubinin-Radushkevich and Dubinin-Astakhov models, respectively.  
The determination of the pore size distribution calculated from the Quenched Solid Density Functional Theory (QSDFT) model showed that the impregnation and carbonisation processes modified the microporous structure of granular carbon, increasing it for the carbonised to 1073 K and decreasing it for the sample carbonised to 1273 K.  
The description of the phenol adsorption process on the surface of the activated carbons can be performed using the immersion calorimetric technique when is involves specific interactions that are given by enthalpy-driven processes, since a quantity of heat proportional to the interactions between the solid and the fluid is generated during the immersion, and it can be determined by this technique.  
The modified Langmuir model allows evaluation of the specific and non-specific interactions between the solute and the surface area and, therefore, the evaluation of changes in the interactions produced by the modifications.  
The sample impregnated with nitric acid and subsequently subjected to reflux in ammonium hydroxide solution, GNA, showed the highest values of phenol adsorption during the calorimetric process, while the activated carbon impregnated with nitric acid, GN, presented the lowest adsorption values. The treatment with nitric acid introduced acidic groups to the activated carbon surface, and the subsequent reflux in ammonium hydroxide solution allowed the formation of nitrogen groups, which increased interactions between phenol and activated carbon surface by hydrogen bonds.  
To compare the amount of phenol adsorbed on the monolayer on the activated carbon, GNA, during calorimetry with the equilibrium processes from Q\({}_{\rm o}\) of the Langmuir model, it was found that 97% of the adsorption was carried out in the first two hours of adsorption. Therefore, the heat transferred by interactions between the solute and the surface determined by calorimetry corresponds to almost all of the energy produced during the whole adsorption process.  
Figure 11: Relationship between the quantity of phenol adsorbed on the interface per unit of area and the immersion enthalpy per mole of phenol adsorbed on the interface for samples G, GN, GNA, and GC\({}_{1073}\).  
The immersion enthalpy values in phenol solutions showed that the oxygenated groups on the activated carbon surface increase the surface-water interactions; therefore, energy is required to move water from the surface and to adsorb phenol. This implies that the enthalpy values obtained during the phenol adsorption process would diminish when the activation has a greater number of oxygenated groups on the surface.  
A.M.C.-B.: experimental development and writing preparation L.G., F.G.-G. and J.C.M.-P.: experimental design, review of results and direction of the investigation.  
The authors thank the Framework Agreement between the Universidad de los Andes (Colombia) and the Universidad Nacional de Colombia and the act of agreement established between the Chemistry Departments of the two universities. The authors also appreciate the grant for the funding of research programs for Associate Professors, Full Professors, and Emeritus Professors, announced by the Faculty of Sciences of the Universidad de los Andes (Colombia), 28 November 2017, 2018-2019, according to the project \"Thermodynamic Characterization of the Adsorption of Contaminants on Porous Adsorbents\".  
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.