## 4 Discussions
### Adsorption Isotherm  
As reported above, data indicate that a complex interaction mechanism takes place between the steel and the inhibitor, and a chemisorption might occur. Given this awareness, the analysis, reported in this paragraph, follows anyway the literature approach of applying isotherm adsorption models to verify the most experimental and realistic data. Adsorption isotherms are in fact used to understand the mechanism of metal-inhibitor interaction. The most frequently used isotherms are Langmuir, Frumkin, Temkin, and Parson [38; 39]. The type of adsorption isotherm provides information about the interaction among both the adsorbed molecules themselves and their interactions with the metal surface. The most widely used isotherm employs the Langmuir model, whose primary assumptions are: (i) Adsorbate molecules attach to the active sites of the adsorbent surface, (ii) the Langmuir equation assumes that adsorption is monolayer, and (iii) all the sites on the solid surface are equal in size and shape and have equal affinity for adsorbate molecules [40]. However, the last two conditions are hard to fulfill in the corrosion studies, and this is the main weak point in terms of using the Langmuir model, as already evidenced by the literature [8]. Many practical cases, in fact, cannot be described the Langmuir model. The more complex adsorption models take into consideration factors such as the surface heterogeneity and the presence of areas having different adsorption energy or interactions between the adsorbed molecules.  
The Freundlich isotherm is empirical and very widely used to describe the adsorption characteristics when the energy of adsorption on a homogeneous surface is independent of surface coverage. Its linearized form is described by the following Equation (10):  
\[\ln\ \theta=\ln\ K+\frac{1}{n}\ln\ C_{e} \tag{10}\]  
where \(\theta\) is the surface coverage (calculated as \(E_{\text{{\tiny{{0}}}}}\)/100), \(C_{e}\) is the adsorbate concentration in solution at equilibrium (in mg L\({}^{-1}\)), Kis the equilibrium constant, and 1/\(n\) is a measure of intensity of adsorption. If the plotn \(\theta\) vs. ln \(C_{e}\) displays a linear trend, it means that the adsorption process can be described by the Freundlich model [41].  
If \(\Delta G_{\text{{\tiny{{ads}}}}}\) is lessthan \(-10.40\) kJmol\({}^{-1}\), it can be inferred that the inhibitor interacts on the C-Mn steel surface by electrostatic effect.  
The negative values of \(\Delta G^{\circ}_{\text{{\tiny{{ads}}}}}\), displayed in Table 8, confirmed the spontaneity of the process and stability of the adsorbed layer on the steel surface [42; 43]. The obtained values of \(\Delta G^{\circ}_{\text{{\tiny{{ads}}}}}\) show the dependence of \(\Delta G^{\circ}_{\text{{\tiny{{ads}}}}}\) on temperature (Table 10), indicating a strong interaction between the bio-polymer molecules and the metal surface.  
Thermodynamically, \(\Delta G^{\circ}_{\text{{\tiny{{ads}}}}}\) is related to the standard enthalpy and entropy of the adsorption process, \(\Delta H^{\circ}_{\text{{\tiny{{ads}}}}}\) and \(\Delta S^{\circ}_{\text{{\tiny{{ads}}}}}\), respectively, via the Equation (11):  
\[\Delta G^{\circ}_{\text{{\tiny{{ads}}}}}=\Delta H^{\circ}_{\text{{\tiny{{ads}} }}}-T\Delta S^{\circ}_{\text{{\tiny{{ads}}}}} \tag{11}\]  
Figure 11: \(E_{a}\) and \(\Delta H^{\circ}\) variation depending on the corrosion inhibitor concentration.  
The positive value of \(\Delta H^{\circ}\) suggests an endothermic nature of the metal dissolution process in the presence of the inhibitor. The positive value of \(\Delta S^{\circ}\) indicates that the adsorption process is accompanied by an increase in entropy, which is the driving force for the adsorption of the inhibitor onto the metal surface [31].