Performance evaluation and assessment of the corrosion inhibition mechanism of carbon steel in HCl medium by a new hydrazone compound: Insights from experimental, DFT and first-principles DFT simulations

2.1.1 Synthesis of ethyl (5-methoxy-2-methyl-1H-indol-3-yl)acetate (2)

Access of absolute ethanol was added to 0.01 mol of indomethacin in the presence of 5 mL conc. H₂SO₄. The mixture was refluxed for 7 h. The mixture was poured into crushed ice and neutralized with NaHCO₃. The ester was separated as an oily layer, then washed with water three times and extracted with diethyl ether 2 × 50 mL and then recrystallized from cyclohexan to afford the title compound as silver crystals with m.p = 74–76 ^˚C.

IR(KBR): (C⚌O ester 1710), (NH3316), (C—H aliphatic 2832–2975), (⚌C—H aromatic 3002) cm⁻¹.

2.1.2 Synthesis of 2-(5-methoxy-2-methyl-1H-indol-3-yl)acetohydrazide (4)

To a solution of 0.01 mol from compound (2) in ethanol, 0.06 mol of hydrazine hydrate was added and the mixture was refluxed for 24 h. The reaction mixture was cooled and the precipitate was formed, collected, and recrystallized from ethanol to afford the title compound as pale yellow crystals with m.p = 166–168 ^˚C. IR(KBR): (C = O amide 1656), (NH-NH₂ 3288–3215), (C—H aliphatic 2835–2971) cm⁻¹.

2.1.3 Synthesis of (5) N'-[(Z)-(4-chlorophenyl)methylidene]-2-(5-methoxy-2-methyl-1H-indol-3-yl)acetohydrazide

An equimolar mixture of compound 4 and 4-chlorobenzaldehyde in absolute ethanol was refluxed with catalytic amounts of glacial acetic acid for 6 h. The mixture was cooled and the precipitate was formed, collected and recrystallized from ethanol to afford the title compound 5 with m.p = 188–190 ^˚C. IR(KBR): (C⚌O amide 1648), (—CH⚌N— 1609), (NH 3295), (C—H aliphatic 2851–2922) cm⁻¹.

¹H NMR (400 MHz, DMSO): δ = 3.8(s, 3H, OCH₃), 2.3(s, 3H, CH₃), 3.6(s,2H, —CH₂), 10.6(s, 1H, NH), 11.3(s,1H, NH), 8.2(s,1H, —CH⚌N—), 6.8–7.7 (m, 7H, aromatic protons in two phenyl rings). ¹³C NMR δ = 13.0(CH₃), 34(—CH₂), 55(—OCH₃),43 (2C, 103–155(fourteen aromatic carbons in two phenyl rings and pyrrol moiety), 146 (C⚌N), 173 (C⚌O amide).

2.5.1 DFT and MD details

The Dmol3 program in Material Studio Software was used to optimize the geometry of the hydrazone molecule according to the generalized gradient approximation (GGA) with the Perdew-Burke-Enzerhof (PBE) functional (Weston et al., 2012). The Conductor-like Screening Model (COSMO) was used to simulate the effect of water as a solvent during the calculations (Heidari et al., 2021). Full details are reported in the supplementary material.

To determine the best adsorption configuration of the hydrazone molecule, a molecular dynamics simulation was carried out using Forcite code implemented in Materials Studio. The unit cell of iron, exported from the database of Material studio software, was cleaved at the surface (1 1 0) and replicated 8 times in the × and y direction. To reduce the effect of periodic replicas, a space of 30 Å was inserted at the z-axis of the created super-cell. After adding 500 water molecules and the optimized hydrazone molecule into the super-cell, the adsorption system was geometrically optimized according to the Smart algorithm (Mehmeti and Podvorica, 2018) using the COMPASSIII force field (Han et al., 2016). MD simulations were carried out under the NVT ensemble (canonical, i.e., the number of particles N, the volume V, and the temperature T of the system were kept constant), room temperature, 1 fs time step, and 1000 ps simulation time. All other MD simulation details were “default” values of Ultra-fine quality of Forcite module.

2.5.2 First-principles DFT simulations

First-principles DFT simulations were carried out within the framework of spin-polarized DFT using the CASTEP code (Kokalj et al., 2021). The exchange–correlation energy was described within the generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerh (PBE) (Perdew et al., 1996). The empirical dispersion correction was used to accurately describe the effect of van der Waals (vdW) interactions (Grimme, 2006). The energy cut-off for the plane-wave basis was set at 30 Ry. All convergence thresholds were default “Fine” quality values in the CASTEP module. Monkhorst–Pack Brillouin zone k-point grids of (8x8x8) and (2x2x1) were used for the optimization calculation of the bulk lattice parameters and adsorption models, respectively. The initial lattice parameter of iron was 2.862 Å while the optimized one is 2.858 Å, confirming that selected methods and models were reasonable.

The surface Fe(1 1 0) was built by constructing a periodic multi-slab model with a (5x5) supercell and a vacuum spacing of 20 Å along the z direction to account for spurious interactions between slabs. The hydrazone molecule was placed on the top side of the slab. The two bottom-most atomic layers were fixed to bulk positions whereas all other degrees of freedom were allowed to relax. A cubic box of 30 Å in size was created for first-principles DFT calculations of standalone molecules. Inkscape software was used for the post-processing of all figures. The total energies of isolated hydrazone (noted E_mol), Fe(1 1 0) iron surface (noted E_surf), and hydrazone/Fe(1 1 0) adsorption systems (noted E_mol/surf) were used to determine the interaction energy as:

3.3.1 Potentiodynamic polarization curves

Tafel curves have been used to understand the effect of temperature on the corrosion reaction of carbon steel in hydrochloric acid with and without inhibitor at an optimum concentration of 10^-3 mol/L. The experiment was conducted at different temperatures ranging from 303 to 333 K. Fig. 4 summarizes the obtained results.

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Fig. 4

Potentiodynamic polarization curves of carbon steel in 1.0 mol/L HCl without (a) and with 10^-3 mol/L of HTH (b) at different temperatures.

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Fig. 4 shows that the corrosion current density increases as the temperature rises from 303 K to 333 K, both in the presence and absence of the inhibitor. We also see that the cathodic curve is parallel, implying that the H⁺ reduction process follows the same activation mechanism. Table 4 summarizes the results of the effect of temperature on carbon steel in the presence and absence of the inhibitor at an optimum concentration of 10^-3 mol/L.

The table shows that the cathodic and anodic Tafel slopes (β_c, β_a) increase with increasing temperature for both the inhibited and uninhibited systems. Furthermore, the results suggest that when the hydrazone component is present, the values of i_corr (253 µA/cm²) increase slightly with increasing temperatures, as opposed to the acidic medium, which showed a noticeable increase (2250 µA/cm²). These data indicate that i_corr increased slightly in the presence of the hydrazone compound at high temperatures compared to its considerable increase in the acidic medium. The efficiency of hydrazone changes slightly towards low values, reaching 88% at 333 K. However, this performance is very high considering the experimental conditions and other organic corrosion inhibitors, which explain that the inhibitor molecules are stable at high temperatures (Chkirate et al., 2021; Dehri and Özcan, 2006). It can be said that despite the increase in temperature, the inhibitor efficiency decreases slightly due to the strong interaction of π-bonds and lone pair electrons on —NH, —N⚌N—, and —C⚌N— groups with the steel surface (Cordero et al., 2008).

3.3.2 Electrochemical impedance spectroscopy measurements

Fig. 5 represents the Nyquist diagrams and modulus of carbon steel in a 1 mol/L HCl solution in the presence of an optimum concentration of 10^-3 mol/L of the hydrazone at different temperatures ranging from 303 to 333 K. Fig. 5 shows that the diameter of the semicircle reduces as the temperature rises, indicating that the efficacy of the inhibition is influenced by temperature. Table 5 summarizes the results of parameters of carbon steel in inhibited and uninhibited acid solutions derived from EIS measurements at various temperatures ranging from 303 K to 333 K at a concentration of 10^-3 mol/L for the inhibited solution.

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Fig. 5

Electrochemical impedance spectra of carbon steel in 1.0 mol/L HCl without (a, c) and with 10^-3 mol/L of HTH (b, d) at different temperatures.

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Table 5 shows that as temperature increases, the polarization resistance decreases from 22.35 to 7.3 Ω cm² for the uninhibited solution and from 397 to 67 Ω cm² for the inhibited solution. At 333 K, the inhibitory efficiency decreases to a maximum value of 89%. It can be seen that the decrease is insignificant at high temperatures. This can be explained by the fact that the inhibitory molecules are stable and strongly adsorbed on the steel surface, forming a robust protective layer. In addition, as the corrosion inhibition process is strongly affected by temperature, it can be concluded that the adsorption of hydrazone molecules at high temperatures is significantly more important than their desorption, mostly because of chemical interactions between active sites of HTH molecules and vacant d-orbitals of iron.

From Bode representation in Fig. 5, it can be seen that the increase in temperature leads to a decrease in the phase angle values and the impedance modulus /Z/. This is consistent with the Nyquist plots and is explained by the fact that some molecules, especially physically interacting with the steel surface would desorb from the steel surface, therefore leading to an increased steel area exposed to the acidic solution.

Chaouiki et al. (Chaouiki et al., 2020b) have confirmed that the hydrazone as (E)‐Nʹ‐(2,4‐dimethoxybenzylidene)‐2‐(6‐methoxynaphthalen‐2‐yl),(E)-N'-(4-methoxybenzylidene)-2-(6-methoxynaphthalen 2-yl)propane hydrazide compound's adsorption on the surface of carbon steel in 1 mol/L HCl solution is stable in the temperature range of 303 K-333 K. They showed that the hydrazone inhibitor still can effectively protect the carbon steel at high temperatures.

The Arrhenius equation was used to analyze the effect of temperature on the corrosion of carbon steel in terms of activation energy. The results of the Tafel extrapolation were used to calculate the standard activation energy E_a. Fig. 6 illustrates Arrhenius diagrams of carbon steel in 1 mol/L HCl solution in the absence and presence of hydrazone at an optimal concentration of 10^-3 mol/L at temperatures ranging from 303 K to 333 K. The slope of the straight line produced by graphing 1000/T according to ln was used to calculate the value of the activation energy (E_a) according to the Arrhenius formula:

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Fig. 6

Arrhenius plots of the corrosion rate for carbon steel in 1.0 mol/L HCl in absence (a) and presence of 10^-3 mol/L of HTH (b). and (b)AAE.

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The carbon steel in inhibited solution has an activation energy value of 55.19 kJ mol⁻¹. The value of the non-inhibited solution is 45.24 kJ mol⁻¹. The inhibitor solution has high activation energy because it produces a protective layer that limits metal dissolution by raising the energy barrier for charge and mass transfer (Chafiq et al., 2020b). Consequently, the process of dissolving the inhibitory system is slow (Chaouiki et al., 2020a).

3.6.1 Quantum chemical calculations

Quantum chemical calculations (QCCs) are one of the most classical ways to assess the reactivity and electronic properties of organic compounds (Islam and Kaya, 2018). In corrosion inhibition studies, QCCs have been applied to investigate the adsorption characteristics and reactivity of corrosion inhibitors (Lgaz et al., 2021). Quantum chemical parameters have been also used to correlate the reactivity of corrosion inhibitors with their quantum chemical parameters; however, it has been shown that this approach has many limitations and cannot be used to make decisive conclusions about an inhibitor’s performance (Kokalj et al., 2021). It still can provide useful information about the reactivity of individual molecules such as potential adsorption sites. Herein, quantum chemical parameters are calculated for neutral and protonated HTH molecules to assess its global and local reactivity indices.

Frontier molecular orbitals, i.e., the highest occupied molecular orbital (HOMO) and lowest uncopied molecular orbital (LUMO) and their corresponding energies (E_HOMO and E_LUMO) are one of the well-known quantum chemical parameters that estimate the electron donating (in case of HOMO) and electron-accepting (in case of LUMO) power of a given molecule (Quadri et al., 2022). A widespread HOMO iso-surface on the entire molecule of the inhibitor or a particular part indicates that it can donate and share electrons with accepting chemical species (Olasunkanmi et al., 2016; Zaher et al., 2022). Likewise, a highly distributed LUMO iso-surface indicates that the corresponding molecule or part of it can accept electrons from electron-donating species (Olasunkanmi et al., 2016; Zaher et al., 2022). Inspection of Fig. 9, which shows the HOMO and LUMO iso-surfaces distributed on the optimized molecular structure of neutral and protonated THT molecules, indicates that 5-methoxyindole part is responsible for electron-donating while the chlorophenyl and hydrazone moieties are the main electron accepting parts.

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Fig. 9

Optimized molecular structure (a)-(a’) and frontier molecular orbital iso-surfaces HOMO (b)-(b’) and LUMO (c)-(c’) of neutral (a)-(c) and protonated (a’)-(c’) HTH molecules obtained by DFT at GGA/PBE level.

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The corresponding HOMO and LUMO energies of neutral and protonated HTH molecules are −5.052 and −2.74 eV, and −6.6.2 and −3.749 eV, respectively (Table 7). It can be noted that the electron-donating ability of the molecule decreased after protonation while its electron-accepting tendency increased, which is a highly expected result. The energy gap, which is defined as the difference between frontier molecular orbital energies is a key factor in investigating a molecule’s stability. A molecule with a high energy gap would have high stability and therefore be less reactive when interacting with other chemical species and vice versa (Lgaz et al., 2021). The quantum chemical parameters of HTH are listed in Table 7. From the data in Table 7, it can be seen that the neutral hydrazone has a lower energy gap value compared with the protonated one. It indicates that the neutral form would have more ability to interact with chemical species (Gece, 2008). On the other hand, the fraction of transferred electron (ΔN) of protonated molecule shows a negative value compared to the neutral one, which indicates that the protonated form of the HTH compound cannot participate in electron-donating upon interaction with other chemical species (Saha et al., 2016). Most of the other quantum chemical parameters follow the same trend as they are derived from HOMO and LUMO energies.

Global reactivity descriptors, as their name may imply, give general information about inhibitor’s reactivity without specifying the most potential adsorption sites. In contrast, local reactivity indices such as Fukui functions provide more precise information about the ability of each atom in the molecule to donate or accept electrons to/from interacting species. In other words, a molecule can have only a limited number of atoms or a functional group responsible for its corrosion inhibition performance. Knowing this detailed reactivity of each part of the molecule would be very helpful in designing new corrosion inhibitors with high performance. Table 8 lists the Fukui function indices of the investigated HTH molecule. The Fukui function can be used to identify the sites within the molecule that is available for nucleophilic and electrophilic attacks. Atomic sites, where the Fukui function is large, are softer and vice versa (Obot et al., 2015). The electrophilic Fukui index f⁺_k characterizes the sites for nucleophilic attacks. The nucleophilic Fukui index f^-_k describes preferred sites for attack by electrophiles (Bassey, 2014; Gómez et al., 2006). In Table 8, it is obvious that atoms C(14), N(16), C(17), O(19), C(34), C(36), and Cl(41) exhibit the highest electrophilic Fukui index f⁺_k, thus acting as preferred atomic sites to accept electrons during a nucleophilic attack (Pareek et al., 2019). On the other side, atoms C(1), C(2), C(5), N(7), C(9), and O(10) have the highest nucleophilic Fukui index f^-_k, suggesting that they are favorable sites for donating an electron to accepting species (Pareek et al., 2019). These results strengthen the previous conclusions from experimental tests that the molecule under investigation has several reactive atomic sites available for accepting and sharing electrons with vacant d-orbitals of iron, thus providing high protection against acid corrosion.

3.6.2 Molecular dynamics simulation

Classical molecular dynamics simulation has emerged as an excellent theoretical tool in corrosion inhibition research (Obot et al., 2018). In recent years, molecular dynamics simulation has become very popular in corrosion inhibition studies to investigate the adsorption configurations of inhibitor molecules on metal surfaces in the presence of a simulated corrosive solution. Even though in most MD studies of corrosion inhibition only classical forcefields are used to model the interaction between inhibitor molecules and metal surfaces, which cannot provide insights into the bond formation and breaking upon adsorption (Kokalj, 2021), it is still very useful in understanding the adsorption behavior of inhibitor molecules in presence of other particles such as water molecules and corrosive ions. Herein, MD simulation was performed for one inhibitor molecule interacting with Fe(1 1 0) surface in presence of 1450 water molecules, 10 chlorides, and 10 hydronium ions to mimic the corrosion inhibition process. Fig. 10 represents the adsorption configuration of HTH on Fe(1 1 0) equilibrated for 5000 ps MD simulation. It can be observed that the 5-methoxyindole of the THT molecule tends to exhibit a parallel disposition over the iron surface, with the carbonyl group also in close contact with iron atoms. Such disposition can maximize the interaction between HTH’s adsorption sites and iron atoms. It is well-documented that most large-size organic compounds tend to adopt a parallel adsorption mode when interacting with metal surfaces, forming strong covalent bonds with vacant d-orbitals of iron atoms. In presence of water and other particles, it would be very competitive for the HTH to get adsorbed on the Fe(1 1 0) surface. Therefore, it can be concluded from the adsorption configuration that HTH has a strong affinity to iron atoms. At this level, MD simulation is useful and helpful in understanding the adsorption characteristics of inhibitor molecules in presence of other particles, however, it overestimates the interaction energy of adsorbing molecules and thus this parameter is not considered (Kokalj, 2021). A more robust way to determine the interaction energy of HTH on Fe(1 1 0) surface is through the first-principles method.

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Fig. 10

Snapshots of the optimized adsorption configuration of HTH on Fe(1 1 0) surface by molecular dynamics simulation; (a) Side view and (b) top view.

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3.6.3 First-principles DFT simulation

Opposite to quantum chemical calculations and molecular dynamics simulation, first-principles DFT simulation provides very significant physical insights into the adsorption of inhibitor molecules on metal surfaces (Damej et al., 2023). In addition to the most stable adsorption geometry, first-principles DFT can simulate the bond formation and breaking upon adsorption, which makes it more beneficial in comparison with other theoretical tools. Further, this approach exhibits similar accuracy to first principles DFT methods but does with a significant reduction in computational cost. To find the most stable adsorption geometries, three different adsorption modes are simulated by the first-principles DFT method, and their corresponding interaction energies and projected density of states (PDOS) are analyzed. Fig. 11 shows the optimized adsorption configuration of the three adsorption modes and their PDOS plots. It can be observed that adsorption configurations in Fig. 11a and b show no bonding with iron atoms. In Fig. 11a (Conf I), the HTH molecule is initially placed parallel to the top layer of Fe(1 1 0) surface so the 5-Methoxyindole part is close to the iron layer. In this configuration, distances between HTH atoms and iron atoms are within 3 Å, without forming any bond, which mostly suggests that only physical interactions can occur. The same conclusions can be made in the case of the second configuration in Fig. 11b (Conf II), where hydrazone and chlorophenyl moieties are initially placed parallel to the iron top layer. In contrast, when the HTH molecule is placed entirely parallel to the top layer of the iron surface (Conf III), it shows the formation of 4 bonds between C and O atoms with the iron surface. The formed bonds have bond distances of 2.25–2.29 and 1.97 Å for C-Fe and O-Fe, respectively. It has been reported that the sum of the covalent radii value for Fe-C (r_C + r_Fe) and Fe-O (r_O + r_Fe) are 2.08 and 1.98 Å, respectively (Cordero et al., 2008). Compared with all bond distances mentioned above, it can be said that all length distances are within the sum of covalent radii values of Fe-C and Fe-O, thus indicating the formation of covalent bonds. In terms of interactive force, the absolute values of interaction energy show the following trend: Conf III (-2.14 eV) > Conf II (-0.08 eV) > Conf I (-0.03 eV). The Conf III exhibits a significantly higher negative interaction energy value compared to other configurations. It strengthens the known fact that parallel adsorption mode is the most stable adsorption configuration of large-size organic compounds (Guo et al., 2017).

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Fig. 11

The optimized adsorption geometries and projected density of states of different configurations of HTH molecule on Fe(1 1 0) surface by SCC-DFTB method; Conf I (a), Conf II (b), and Conf III (c), and PDOSs (d). Bond lengths are in Å.

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To get further information about the nature of binding of the inhibitor molecule with iron atoms, PDOSs are analyzed as shown in Fig. 11d-I, 11d-II, and 11d-III for Conf I, Conf II, and Conf III, respectively. Fig. 11d shows the PDOS of the HTH molecule before adsorption for comparison. By comparison, it can be seen that most of the peaks related to the chemical states of Conf I and Conf II keep relatively similar shapes and intensities to those before adsorption. However, significant changes to peaks contributed by s- and p-orbitals of Conf III are observed, which is mainly attributed to orbital mixing between molecules' orbitals, especially p-orbitals and Fe d orbitals. It indicates that bonds formed between HTH’s molecule and iron atoms are covalent bonds (Kumar et al., 2022, 2020).