**3.7 Molecular dynamic simulations (MDS)**

Molecular dynamic simulations (MDS) are one of the most effective theoretical methods for elucidates and interprets at the molecular level the mode and configurations of the adsorbed inhibitory molecules on the metal surface. Also, the MDS method is principally used to calculate the adsorption energy of the inhibitive molecules. In this context, MDS are largely applied to analysis the adsorption modes of phosphonates and phosphonic acids on metal surfaces. The adsorption energies of phosphonate derivatives on metal surfaces can be also calculated using MDS.

Concerning the application of MDS to study the mechanism of adsorption of phosphonate molecules on metal surfaces, we can cite the results obtained by Moumeni et al. [23], where she studied the adsorption mode of three phosphonic derivatives on the carbon steel surface **(Figure 11**). Also, the calculated values of the adsorption energy for the investigated inhibitors indicate that adsorption affinity of the substituted phosphonate in *Para* position is higher than these of *Ortho* and *Meta* positions (**Table 2**).

#### **Figure 11.**

*AFM image of mild steel in the presence of 10<sup>3</sup> mol/L of ethyl hydrogen [(2-methoxyphenyl)(methylamino) methyl]phosphonate [23].*


**Table 2.**

*Calculated adsorption energies of DEPAMP, o-DEPAMP and p-DEPAMP using molecular dynamic simulations [23].*

*Phosphonates and Phosphonic Acids: New Promising Corrosion Inhibitors DOI: http://dx.doi.org/10.5772/intechopen.109499*

Furthermore, the adsorption energy of phosphonates and phosphonic acids increases with the increase in the number of phosphonate groups in the molecule (O]Pd(OH)2 or O]Pd(OR)2).

**Figure 11** shows the MDS results of Diethyl(phenyl(phenylamino)methyl) phosphonate (DEPAMP), Diethyl(((2methoxyphenyl)amino)(phenyl)methyl) phosphonate (o-DEPAMP) and Diethyl(((4methoxyphenyl)amino)(phenyl)methyl) phosphonate (p-DEPAMP) [23].
