Corrosion inhibition of aluminum in 1 M HCl by novel pyrimidine derivatives, EFM measurements, DFT calculations and MD simulation

3.4.1 Calculation of the main quantum parameters

The optimized geometries of the compounds are obtained using the B3LYB/6–311++G (p,d) level and are presented in Fig. 10. In this study, dihedral angles analysis was applied to determine the flatness of the studied geometrical structures. The analysis showed that; the most stable geometry of the studied compounds is planar structures which are favored in the inhibition reaction (Khaled and El-Maghraby, 2014). The frontier molecular orbital energy of the highest occupied molecular orbital and the lowest unoccupied molecular orbital denoted as E_HOMO and E_LUMO, respectively, energy gap ( $\mathrm{\Delta }E$ ), dipole moment ( $\mu$ ), ionization energy (I), electron affinity (A), absolute electronegativity ( $\chi$ ), absolute hardness ( $\eta$ ), absolute softness ( $\sigma$ ) , absolute electrophilicity parameter $(\omega )$ and fraction of electrons transferred $(\mathrm{\Delta }N)$ are determined for both neutral and protonated pyridine-pyrimidine derivatives are listed in Tables 5a and 5b. Fig. 11a shows the shape of the HOMO, LUMO orbitals, and electrostatic potential (ESP) distribution of the studied inhibitors. The electron density indicates that a negative charge in red is easily delocalized on the N, S, O and Cl atoms because of the lone pair. thus, we can consider that EMMD would reveal a more suitable affinity to the adsorption onto the aluminum surface through the lone pair electrons located on N, S and O atom to the vacant aluminum P-orbital. Generally, a high value of ${\mathrm{E}}_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ is often associated with a higher tendency of the molecule to donate electrons to an acceptor metal having an empty or vacant orbital molecular leading to stronger adsorption on the metal surface and better inhibition efficiency (Al-Mobarak et al., 2010). On the other hand, the lower the value of ${\mathrm{E}}_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$ , indicates that the molecule would accept electrons easily from the metal surface and thus lead to stronger adsorption and higher inhibition efficiency. Also, the energy difference between the HOMO and the LUMO, ${\mathrm{\Delta }\mathrm{E}}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ is the parameter that measures the chemical reactivity of the molecule towards adsorption on the metal surface (Zhang et al., 2021). As the ${\mathrm{\Delta }\mathrm{E}}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ decreases, the reactivity of the molecule increases leading to an increase in the inhibition efficiency of the molecule because the energy to remove an electron from the last occupied orbital will be low (Zhang et al., 2021). The calculated (ΔE) values listed in Tables 5a and 5b indicate that the EMMD display the smallest value of ΔE, meaning that the inhibitor EMMD molecule represent the highest reactivity, compared to the other molecules and, consequently, the better inhibition efficiency in accordance with the experimental results. The studied compounds are more prone to protonation on the pyridine-pyrimidine derivatives nitrogen (Fig. 11b). The trend for ΔE values have the order inhibitor > inhibitor H+ in the aqueous phase. These consequences mean the highest inhibition efficiency and reactivity of studied inhibitors in the protonated form (Fig. 11b). Furthermore, it has also been reported that the values of dipole moment (μ) of inhibitors follow the order of $\mathrm{P}\mathrm{D}<\mathrm{P}\mathrm{A}<\mathrm{A}\mathrm{D}\mathrm{T}<\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}$ which increases the polarizability and facilitate adsorption of EMMD on the aluminum surface. This may regarded to increase the opportunity of inhibitors molecules accumulation on the Al surface, consequently, increase the pyridine-pyrimidine derivatives adsorption on the Al surface and therefore inhibition efficiency enhanced (Mineva et al., 2001). In addition, the global properties as global hardness ( $\eta$ ), global softness ( $\sigma$ ) are important characteristics for measuring the molecular stability and reactivity. A soft molecule has a small energy gap and a hard molecule has a great energy gap (Djenane et al., 2019; Hasanov et al., 2007). Results in Table 5a showed that the value of ( $\mathrm{S}$ ) increases in order, $\mathrm{P}\mathrm{D}<\mathrm{P}\mathrm{A}<\mathrm{A}\mathrm{D}\mathrm{T}<\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}$ , this behaviour is attributed to chemical structure, where existing of the heteroatoms substituents leads to increase the electrons transfer between the studied inhibitors and the Al surface that forming a strong protective film. Furthermore, the global hardness ( $\eta$ ) of inhibitor H+ species in aqueous solution (Table 5b), is lower than that of inhibitor (Table 5a), which indicates stronger dipole–dipole interactions of the protonated form and Al interface in comparison to that of inhibitor. The fraction of electrons transferred $(\mathrm{\Delta }N)$ between the pyridine-pyrimidine derivatives inhibitors and Al surface atom were listed in Table 5a and showed that $\mathrm{\Delta }\mathrm{N}<3.6$ indicates that the investigated inhibitors contribute electrons to the aluminum interface implies a greater tendency of the inhibitors to adsorb on the metal surface by donor–acceptor interactions of non-bonding electron pairs of the heteroatoms and π-electrons with the vacant P-orbitals of the aluminum atom.

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Fig. 10

Optimized geometry, numbering system, natural charges, bond lengths, bond angles, dihedral angle and vector of dipole moment for the studied compounds at the B3LYP/6–311++G(d,p).

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Fig. 11a

HOMO, LUMO maps, ESP and 3D-MEP for the studied compounds PD, PA, ADT and EMMD using B3LYP/6–311++G (d,p).

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Fig. 11b

HOMO and LUMO maps, for the protonated form of the studied compounds using B3LYP/6–311++G (d,p).

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Furthermore, the highest fraction of electrons transferred is associated with the best inhibitor EMMD, this correlates well with the trend of experimental corrosion inhibition efficiency. On the other hand, it has been found (Awad et al., 2010) that the anticorrosive molecule-metallic surface process is controlled by an electronic back-donation process. According this concept, the change of energy shows a direct proportionality to the global hardness of the molecule, as defined as ${\mathrm{\Delta }E}_{\mathit{Back}-donation}=-\frac{\eta }{4}$ , if $\eta >0$ and ${\mathrm{\Delta }E}_{\mathit{Back}-donation}<0$ this suggests that back-donation from the molecule to metal is energetically favored. The results reported in Tables 5a and 5b show that ${\mathrm{\Delta }E}_{\mathit{Back}-donation}<0$ for our inhibitors, thus the charge transfer from the pyridine-pyrimidine derivatives inhibitors to Al surface is energetically favorable meaning that the inhibition efficiency increases with inhibitor adsorption on the metallic surface (Abdallah et al., 2021), The estimated ${\mathrm{\Delta }E}_{\mathit{Back}-donation}$ values are in accordance with the experimental data in the following tendency $\mathrm{P}\mathrm{D}<\mathrm{P}\mathrm{A}<\mathrm{A}\mathrm{D}\mathrm{T}<\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}.$ Electrophilicity index measures the capacity of molecule to acquire electrons (Parr et al., 1999), the values of electrophilicity $(\omega )$ are in increasing order; $\mathrm{P}\mathrm{D}<\mathrm{P}\mathrm{A}<\mathrm{A}\mathrm{D}\mathrm{T}<\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}$ , in accordance with experimental techniques. The low ionization energy of studied inhibitors indicates that it is easy for an atom to remove its outer electrons and it is easy for electrons transfer between the metal and inhibitors, and hence, increases the inhibition efficiency of inhibitors. Finally, the quantum parameters presented in Tables 5a and 5b indicate that the studied pyridine-pyrimidine derivatives have excellent corrosion inhibition properties in the protonated form and this obtained quantum parameters agree completely with the experimental results.

3.4.2 Molecular electrostatic potential (MEP)

The electronic density is correlated to electrophilic and nucleophilic attack by the molecular electrostatic potential (MEP) for considerate the sites and the hydrogen-bonding interactions (Politzer and Murray, 2002). MEP is related to electronegativity, dipole moment, and chemical reactivity of molecules so, it is useful for visualizing the variable and defining how molecules interact with each other via charge distributions. Fig. 11a shows the 3D-MEP for studied inhibitors PD, PA, ADT and EMMD using DFT/B3LYP/6–311 ++ G (d,p). According to the MEP plots, the distribution of the lone-pair of the electrons of the oxygen and nitrogen atoms in the negative region is mainly above the atomic sites O and N and are represented in red, and thus the resulted in positive sites about hydrogen and carbon atoms (blue). The color diagram in possible rises for the electronegativity in the subsequent order: red < orange < yellow < green < blue for MEP surface was as follows: electron-rich red (partially negative charge); blue for electron affinity, (partially positive charge); light blue for the area of a little electron affinity, yellow for the little electron-rich region; and green represents neutral (zero potential). This elucidates that the EMMD is the most predominant toward electrophilic attack and so it has the highest capability of bonding to the Al surface, agreement well with experimental and theoretical investigations.

3.4.3 Natural charges and natural population analysis

The natural population analysis (Politzer and Murray, 2002), was performed on the electronic structures of pyridine-pyrimidine derivatives, are calculated by DFT/B3LYP method with 6–311++G (d, p) basis set in the gaseous phase. The natural population analysis obviously describes the distribution of electrons in various sub-shells of their atomic orbits. Table 6a depicts the natural charge, natural Population, natural population of the total electrons on the sub-shells, and natural electronic configuration of active sites for PD, PA, ADT and EMMD. In this study the most negative centers are N6, N10 and N11atoms in PD, N5, N8 and N12 atoms in PA, N5, N8 and N10 atoms in ADT, finally N17, N18, O22 and O23 atoms in EMMD. The values obtained indicated that the nitrogen atoms in studied compounds have the highest negative atomic charges, indicating that the inhibitors studied can effectively prevent corrosion of the aluminum by adsorption on its surface through its active sites. S19 and Cl16 atoms in EMMD inhibitor act mostly as electrophilic centers since these atoms possess excess of positive charge, which is actually necessary to balance and stabilize the accumulation of negative charges on the aluminum surface (Fouda et al., 2019). Additionally, the natural population analysis showed that 81 electrons in EMMD compound than the others compounds are distributed on the sub-shells as total-Lewis (effective core, core and valence Lewis) and total non-Lewis (valence non-Lewis and Rydberg non-Lewis). The computed values and percentage of each are presented in Table 6b.

3.4.4 Calculation of the atomic loads of Mulliken

In order to predict the possible adsorption centers of the pyridine-pyrimidine derivatives, the Mulliken charge can be utilized. It has been found that the more negative the atomic charges of the adsorbed center are, the easier it is for the atom to give up its electrons to the Metal's unoccupied orbital (El-Haddad et al., 2019). The distribution of the Mulliken charges and the orientation of the polar moment are shown schematically in Fig. 10. The values of the charge's distribution are also showed in Tables 7 and 8. The atoms have high charge densities, are the nitrogen, oxygen, and some carbon atoms. As a result, N, O, S, Cl, and some C atoms are the active adsorptive centers with the highest ability to bind to the metal's surface, so, these atoms act as an electronic donor. Some carbon atoms, on the other hand, have positive charges that nucleophiles will attack. Therefore, pyridine-pyrimidine derivatives can accept aluminum^'s electrons through these atoms, and these observations can be confirmed by the study of the Fukui indices.

3.4.5 Condensed Fukui indices

The Fukui indices evaluate and analyze the inhibitor molecules' local reactivity as well as their corresponding electrophilic and nucleophilic behavior. The electrophilic and nucleophilic attack is presented by the maximum values of $f_k^{-}$ and $f_k^{+}$ , respectively, (Contreras et al., 1999). Fukui functions for nucleophilic and electrophilic attacks of the inhibitor molecules have been determined by taking the finite difference approximations as introduced by Yang and Mortier (Yang and Mortier, 1986) as follows:

If $\mathrm{\Delta }{f}_k<0,$ the site may be preferred for an electrophilic attack, whereas, If $\mathrm{\Delta }{f}_k>0$ the s may be favored for a nucleophilic attack. The values of the $f_k^{-}$ , $f_k^{+}$ and $\mathrm{\Delta }{f}_k$ for the inhibitors (PD, PA, ADT and EMMD) and protonated form have been determined and tabulated in Tables 7 and 8. The preferred sites for electrophilic attack is preferably occur at N10 and N11 atoms in PD, at C3, C4 and N8 atoms in PA, at N5 and S9 in ADT, and at S19 and O22 atoms in EMMD, where they are shown by the highest value of $f_k^{-}$ and the more negative value of $\mathrm{\Delta }{f}_k$ . The preferred sites for nucleophilic attack would preferably occur at C4, C5 and N6 atoms in PD, at N5 and N12 atoms in PA, at C3, C4 and N8 and N10 atoms in ADT, and at C7, C12, C16, C17, C18 and O23 atoms in EMMD where the highest value of, $f_k^{+}$ and the more positive of $\mathrm{\Delta }{f}_k$ .

3.4.6 Thermodynamic properties

The standard thermodynamic functions, the heat capacity $C_{p,m}^0$ , entropy $S_m^0$ and enthalpy $H_m^0$ , for compounds (PD, PA, ADT and EMMD) were obtained at the DFT/B3LYP/6–311++G (d,p) level and are listed in Table 9.

Table 9 showed that the standard heat capacities, entropies, and enthalpies increase at all temperatures from 298 to 323 K, because the intensities of the molecular vibration increase with the increasing temperature and the efficiency of inhibitors increases in the order $\mathit{EMMD}>ADT>PA>PD$ . The correlations between these thermodynamic properties and temperatures T are shown in Fig. 12. The correlation equations will be helpful for the further studies for pyridine-pyrimidine derivatives inhibitors.

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Fig. 12

Correlation graphics of thermodynamic properties and temperatures for the studied Inhibitors at the B3LYP/6–311++G (d,p).

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3.4.7 Natural bond orbital (NBO) analysis

Natural Bond Orbital NBO analysis indicates the strength of the interaction between atoms, which involves the amount of charge transfer and affects molecular stability. Analysis of NBO as the second-order interaction energy E² can be used to determine the orbital filled with electrons or empty, which contributes to the delocalization of electrons from bonding (BD) or lone pair (LP) to anti-bonding (BD)* (Fouda et al., 2017b). Bonding BD shows the condition of the atom that is bonded to other atoms. The Lone Pair symbol LP shows a lone pair on the associated atom, and the Rydberg symbol RY indicates the type of atomic orbital with the highest quantum number and energy (Mert et al., 2014).

The NBO analysis by using the second-order perturbative energy results has been generally used to estimate the hybridization and non-covalent interactions, which provide information on the contribution to the lowering of the stabilization energy of a particular molecular system, including hyperconjugation, resonance, etc. (Guerrab et al., 2019; Guerrab et al., 2020). In this study, the second order perturbative energy results for PD, PA, ADT and EMMD compounds were determined and presented in Table 10. Accordingly, the highest contribution to the stabilization energy lowering for studied compounds has come from the LP (1) N11 → πC1-N6, LP (1) N8 → π*C4-N12, LP (1) N5 → π*C4-S9 and LP (1) C10 → σC7-C10 interactions: the resonance energy for this interactions has been calculated as 35.57 kcal mol⁻¹, 48.07 kcal mol⁻¹, 57.26 kcal mol⁻¹ and 89.48 kcal mol⁻¹ for PD, PA, ADT and EMMD compounds, respectively. The contribution to the lowering of the stabilization energy for EMMD is calculated for the electron delocalization from the lone pair of the N18 atom to antibonding orbital σ*C20-O23 is 35.00 kcal mol⁻¹. In addition to the stabilization energy of the LP (1) O22 → σ*C20-O23 is 27.95 kcal mol⁻¹. It is worth to mention that the stabilization energy of the LP (1) Cl16 → σ*C20-O23 interaction is calculated in 16.80 kcal mol⁻¹. In conclusion EMMD has the greatest effect on increasing corrosion inhibition efficiency compared to other inhibitors because it has the highest E².

3.5.1 Scanning electron microscope (SEM) analysis

SEM is used to study the surface morphology of the aluminum samples of size $2.00\times 2.50\times 0.04\mathrm{c}\mathrm{m}$ samples immersed in 1 M HCl for 24 h in the absence and presence of 10⁻³M pyridine-pyrimidine derivatives PD, PA, ADT and EMMD. Fig. 13 shows the scanning electron microphotographs of aluminum in HCl in the absence and presence of 10⁻³M of investigated compounds. The surface of the polished aluminum sample Fig. 13a is very smooth and shows no corrosion. After immersion in uninhibited 1 M HCl solution for 24 h, the aluminum surface is damaged and is very rough as a result of many cracks and scratches on the Al surface due to metal dissolution Fig. 13b (Zhang et al., 2019). The presence of 10⁻³ M of inhibitors effectively retarded the dissolution of Al in 1 M HCl and surface damage has been reduced significantly Fig. 13(c- f) as compared to the blank solution (Fig. 13b) by adsorption and formation of protective films of PD, PA, ADT and EMMD on the aluminum surface. Fig. 14 shows particle size in $\mu m$ of PD, PA, ADT, and EMMD, they are 5.94, 5.23, 2.80 and 0.475 $\mu m$ respectively. On comparing these microphotographs and particle size, it appears that smoothing of the surface of test materials has been observed in the following sequence $\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}>\mathrm{A}\mathrm{D}\mathrm{T}>\mathrm{P}\mathrm{A}>\mathrm{P}\mathrm{D}$ The SEM results are in good agreement with the observed inhibition efficiency values from electrochemical and computational methods.

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Fig. 13

SEM images of aluminum immersed in 1 M HCl for 24 h at 298 K: (a) polished Al, (b) uninhibited Al, and 10_–3 M of (c) PD, (d) PA, (e) ADT and (f) EMMD.

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Fig. 14

Particle size distribution of inhibited Al using SEM analysis with 10^–3 M of (a) PD, (b) PA, (c) ADT and (d) EMMD.

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3.5.2 Energy dispersive X-ray analysis

Energy dispersive X-ray analysis (EDX) technique was used to get more information about the composition of the surface of the polished, corroded and inhibited aluminum surface in the absence and presence of 10⁻³M of pyridine-pyrimidine inhibitors in 1 M HCl solution after immersion of 24 h. The results obtained from the EDX spectra are shown in Fig. 15. Fig. 15a shows that the polished aluminum surface contains a large aluminum peak, whereas after immersing in 1 M HCl in the absence of the inhibitors (Fig. 15b), the aluminum peak was suppressed and the oxygen and chloride peaks observed due to the formation of oxide, hydroxide, and chloride compounds on the aluminum surface (Amin et al., 2009). In the presence of the inhibitors, the intensity of the aluminum peak was improved which indicates the adsorption of inhibitor molecules on the surface of aluminum, as shows in Fig. 15(c-f) which clearly show a decrease in oxygen and chloride contents and the presence of sulfur, carbon and nitrogen signals in the inhibited samples indicates that the inhibitor molecules containing these elements are adsorbed on the aluminum surface.

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Fig. 15

EDX images of polished aluminum (a) immersed in 1 M HCl (b) and in 1 M HCl with 10^–3 M of PD (c), PA (d), ADT (e) and EMMD (f) for 24 h at 298 K.

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3.5.3 Atomic force microscopy

The surface analysis of aluminum metal dipped in 1 M HCl solution for 24 h at 298 K in the absence and presence of inhibitors were studied using AFM. SEM micrographs only provide qualitative information about metal surfaces. To get some quantitative information about metal surface morphology we need AFM (Sharma and Kumar, 2021). Fig. 16 shows typical AFM images of polished aluminum metal (Fig. 16a), after immersion in 1 M HCl solution without inhibitor (Fig. 16b), and with inhibitors PD (Fig. 16c) and EMMD (Fig. 16d). One of the texture profiles currently defined by the International Organization of Standardization (ISO) is the roughness profile (ISO 4287), which list certain parameters for the evaluation of surface roughness (Umoren et al., 2020) Some of them are Ra Arithmetical mean height indicates, Ra is referred to as the average surface roughness and Sm average peak spacing. Rp Maximum profile peak height, Rv Maximum profile valley depth, Ry The maximum height of the profile Ry = Rp + Rv, Rq root-mean-square roughness and Rm average peak spacing profile irregularities. The numerical values of these parameters for the studied aluminum metal surfaces are given in the introduced tables in Fig. 16. After polishing the metal, a relatively smooth surface was obtained (Fig. 16a), and the values of all the roughness profile parameters are less than unity. When the Al surface sample was exposed to 1 M HCl solution in the absence of inhibitors, the surface was damaged and corroded as can be seen form (Fig. 16b), because of the corrosive attack by acid solution.

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Fig. 16

Three dimension AFM images of polished Al, uninhibited Al and with 10⁻³M PD and EMMD.

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The calculated average surface roughness for uninhibited corroding surface was 105.16 nm.

However, the AFM images in the presence of PD and EMMD Fig. 16 (c and d) showed that the surface becomes smoother and the average roughness was reduced 28.28 and 22.78 nm in the existence of inhibitors PD and EMMD, respectively. Increased surface smoothness in the presence of the inhibitors indicates the adsorption of the inhibitors on the surface of Al. In fact, all parameters are almost smaller than those in (Fig. 16b) justified the development of a consistent inhibitor protective layer on the aluminum surface. The lower values of parameters roughness for EMMD than PD reveals that EMMD protects the Al surface more efficiently than PD in 1 M HCl solution. These roughness values confirm the inhibition efficiency data observed in the EFM measurements. The AFM results were in good agreement with SEM and EDX results.

3.6.1 Binding energy

Molecular dynamics simulations is a useful and new tool to investigate the interaction between inhibitors and metal surface. The adsorption progress of pyridine-pyrimidine derivatives on aluminum surface was investigated by performing molecular dynamics simulations, Fig. 17. In this study, (MD) simulation studies are performed to predict the binding energies $E_{\mathit{bind}}$ of these pyridine-pyrimidine inhibitors on aluminum surface and to display whether there is a significant correlation between experimental inhibition efficiencies and binding energies for inhibitors included in this study. Interaction energies between Al surface and inhibitor molecules was estimated using molecular dynamic simulation as follows (Madkour et al., 2018; Zuo et al., 2021):

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Fig. 17

Top views of the most stable low energy configurations for the adsorption of pyridine-pyrimidine inhibitors on Al (1 1 1) surface obtained using molecular dynamic (MD) simulations.

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Table 11 shows that EMMD has the highest adsorption energy on Al (1 1 1) surface, suggesting that EMMD is the best inhibitor between the investigated compounds which agrees well with the experimental results. The values of binding energy was calculated using Eq. (28). The values indicating that the interactions between pyridine-pyrimidine inhibitors and aluminum surface are very high. It is important to note that, the higher the value of binding energy, the easier the inhibitor adsorbs on the metal surface and the higher the inhibition efficiency. The binding energies obtained are observed to increase in the order $:\mathrm{P}\mathrm{D}<\mathrm{P}\mathrm{A}<\mathrm{A}\mathrm{D}\mathrm{T}<\mathrm{E}\mathrm{M}\mathrm{M}\mathrm{D}$ , this is in good accordance with the experimental data and DFT calculations.

3.6.2 Radial distribution function

For determining the type of pyridine-pyrimidine derivatives – Al interaction, radial distribution functions (RDFs) (or pair correlation function) $g_{(r)}$ were used as a useful method to evaluate the bond lengths. The lowest bond length from 1 Å up to 3.5 Å, indicates that the adsorption is chemisorption (Hsissou et al., 2019). While the highest bond length (greater than 3.5 Å) reflects that the adsorption is physisorption (Chafiq et al., 2021). RDFs were calculated using Molecular dynamics simulation. It is known that, there is a relationship during the mechanism of corrosion inhibition between the adsorption potential and bonding length (Chugh et al., 2020). Hansen and McDonald proposed and explained RDFs as the following (Chugh et al., 2020).

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Fig. 18

RDFs analysis of the pyridine-pyrimidine derivatives adsorbed on the Al₂O₃ surface.

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