Electronic structure–performance relationship in pyridine-based Schiff bases: a dual experimental–DFT study on corrosion inhibition

Abstract

Two pyridine-based Schiff bases, N-(4-bromobenzylidene)pyridin-3-amine (BBPA) and N-[4-(dimethylamino)benzylidene]pyridin-3-amine (DBPA), were synthesized and evaluated as corrosion inhibitors for carbon steel in 1.0 M HCl. Their inhibition performance was investigated using potentiodynamic polarization (PDP), electrochemical impedance spectroscopy (EIS), and electrochemical frequency modulation (EFM). Both compounds exhibited excellent corrosion protection, achieving inhibition efficiencies above 94% at 10 mM concentration. Adsorption studies revealed that the inhibitors obey the Langmuir isotherm and adsorb on the steel surface through a mixed physisorption–chemisorption mechanism. Density functional theory (DFT), Monte Carlo, molecular dynamics, and DFTB calculations were employed to elucidate the adsorption behavior and electronic properties of the inhibitors. Theoretical results demonstrated that DBPA possesses superior electron-donating ability, stronger adsorption affinity, and enhanced interaction with the Fe (110) surface compared with BBPA, consistent with the experimental findings. SEM analysis confirmed the formation of a protective adsorbed film on the steel surface. The combined experimental and computational results identify DBPA as the more effective inhibitor and highlight the crucial role of electronic substituent effects in governing corrosion inhibition performance.

Two pyridine-based Schiff bases, N-(4-bromobenzylidene)pyridin-3-amine (BBPA) and N-[4-(dimethylamino)benzylidene]pyridin-3-amine (DBPA), were synthesized and evaluated as corrosion inhibitors for carbon steel in 1.0 M HCl.

1. Introduction

Corrosion is one of the main causes of deterioration in the overall condition of critical metal components.^1,2 Although it cannot be completely and permanently eliminated, its negative effects and damage can be mitigated through the use of protective coatings and new alloys.³ Corrosion inhibitors and suitable coatings can be applied to the metal surface. Steel is one of the important materials which are required by different industries.^4–6 It can corrode in acidic as well as alkaline solutions.⁷ Sulfuric acid and hydrochloric acid are commonly used for acid descaling, pickling, cleaning and treatment in industrial and chemical applications.⁸ These processes usually involve dissolving large quantities of metal. Despite its high cost, carbon steel is used in large quantities for marine applications.⁹ Also, it is used in chemical processing, production, and refineries for petroleum, as well as in buildings and equipment for metal processing, etc.¹⁰ The equipment irons, and their alloy tubes and pipes are effectively exposed to severe corrosive effects characteristic of the applications of which they form a part.¹¹ Steel undergoes a chemical change when it reacts with non-oxidizing acids such as hydrochloric and sulfuric acids.¹² It forms iron(ii) salts, such as iron chloride and iron sulfate. The continuous removal of oxide layers leads to ongoing reactions between the metal surface and the acid solution.¹³ It is resulting in surface damage and severe corrosion.¹⁴ There are several methods available to protect carbon steel from corrosion under corrosive conditions.^15,16 Corrosion inhibitors¹⁷ are a cheap and efficient means to protect carbon steel against corrosion. They are generally added in small quantities to solutions susceptible to corrosion and act at the interface where the corrosion product forms between the metal and the aqueous solution.^18,19 Once they arrive at the corroded surface, they adsorb there, altering surface dynamics or electrochemical reactions in the electrical double layer.²⁰ These chemicals formed a thin protective film on the metal surface. It retards the inhibitive corrosion processes and reduces anodic and cathodic activities.²¹ There are many organic and inorganic corrosion inhibitors that can reduce corrosion of metal surfaces in acidic media.²² It has been reported that Schiff bases are useful in inhibiting acid corrosion of various metals and alloys.^23–25 Furthermore, research on corrosion inhibition is increasingly focusing on Schiff bases, which are easily synthesised from inexpensive precursors and are relatively non-toxic.^22,26 Generally, it contains imine groups and heteroatoms that influence the corrosion rate by interacting with the metal surface and forming a protective film.²⁷ The 4-bromobenzylidene and 4-(dimethylamino)benzylidene fragments are well known in organic and medicinal chemistry, and many hydrazone or heterocyclic Schiff bases incorporating these groups have been synthesized and structurally characterized.^28–33 The bromo group's strong electron-withdrawing nature and the dimethylamino group's strong electron-donating ability are expected to alter the electron density on the azomethine nitrogen and aromatic rings, thereby affecting the adsorption behaviour on the carbon steel surface. However, despite the extensive literature on Schiff base inhibitors, including studies on benzylidene–pyridine and benzylidene–imine systems,^34–38 no research has been found that evaluates N-(4-bromobenzylidene)pyridin-3-amine or N-[4-(dimethylamino)benzylidene]pyridin-3-amine as corrosion inhibitors. To the best of our knowledge, this work therefore explores these two simple pyridin-3-amine Schiff bases (BBPA and DBPA) as new inhibitors for carbon steel corrosion in hydrochloric acid solution. Accordingly, this work provides comparative insight into how substituent electronic effects within the same molecular framework govern the inhibition mechanism, employing electrochemical methods and theoretical approaches.

2. Experimental part

2.1. Corrosion inhibition approach

The carbon-steel samples used in the present work was obtained from an oil-sector facility in southern Iraq. The carbon steel's elemental composition was determined by spark optical emission spectroscopy as: Fe (91.30%), C (2.18%), Si (3.10%), Mn (1.36%), Cr (0.102%), Mo (0.127%), Ni (0.213%), Al (0.120%), Co (0.100%), Cu (0.596%), Nb (0.090%), Ti (0.060%), V (0.046%), W (0.050%), Pb (0.102%), Zr (0.027%).^22,39 To prepare the working electrode from it, the mechanical method was employed to produce uniform samples approximately 1 cm thick. A 1 cm² area was manually polished before applying epoxy to cover the entire region, with only one face exposed to the corrosive media. More details are provided in our peer-reviewed works.^16,40 The electrochemical cell comprised the working electrode (carbon steel), the reference electrode (mercury–mercury sulphate electrode), and the counter electrode (platinum plate), all fully immersed in 1 M hydrochloric acid. Electrochemical tests were conducted at 25 °C using a potentiostat, and the data were analyzed using the software provided with the potentiostat. The carbon-steel working electrode was allowed to spontaneously corrode for 30 minutes before testing to stabilize the open-circuit potential (OCP). Potentiodynamic polarization (PDP) is performed at a scan rate of 2 mV s⁻¹ over a potential range of ± 0.6 V. The inhibitory efficiency (η_p%) is evaluated using the equation:³⁹

1

where i_corr and i⁰_corr are corrosion current densities in the presence and absence of BBPA and DBPA, respectively. Thus, the frequency response range used for the impedance measurement was 1 Hz–100 kHz, with amplitude of ±10 mV. The inhibition efficiency (η_z%) was calculated using the equation:³⁹

2

The charge-transfer resistances R_ct for BBPA and DBPA inhibitors and for the inhibitor-free condition R⁰_ct are given. Moreover, a possible perturbation signal of 10 mV, which is the sum of two sine waves at frequencies 2 and 5 Hz, and containing a total of 16 cycles, satisfies the electrochemical frequency modulation (EFM) conditions. Principal parameters are deduced from the most prominent peaks. The efficiency η_EFM% was calculated using the equation:³⁹

3

2.2. Synthesis of BBPA and DBPA inhibitors

The BBPA and DBPA compounds were synthesized through a condensation reaction between 3-aminopyridine and substituted aromatic aldehyde compounds (4-bromobenzaldehyde and 4-dimethylaminobenzaldehyde), as shown in Scheme 1. The equimolar amounts of 3-aminopyridine (0.03 mol, 1.32 g, 99%, Sigma-Aldrich) and the respective aldehyde compound either 4-dimethylamino benzaldehyde (0.03 mol, 4.47 g, 98%) or 4-bromobenzaldehyde (0.03 mol, 5.56 g, 98%) were dissolved in 50 mL of absolute ethanol (add few drops of glacial acetic acid as a catalyst) in round-bottom flask that fitted with a reflux condenser. The reaction mixtures were stirred and heated under reflux for four hours and the progress of reaction was monitored by the thin-layer chromatography (TCL) using the hexane and the ethyl acetate (3 : 1). After completion, the mixtures were cooled to room temperature, and the solid products BBPA and DBPA were separated by filtration. The yields were rinsed multiple times with petroleum ether to remove any unreacted amine or impurities, and then purified by re-crystallization from hot ethanol. The final BBPA and DBPA were dried at about 70 °C for 3 hours and stored in a desiccator. The BBPA compound yielded of 87%, while the DBPA has yield 92% and the melting points ranging (116–121 °C).

Scheme 1. Synthesis of Schiff bases BBPA and DBPA through condensation of substituted benzaldehydes with 2-aminopyridine in ethanol under acidic conditions.

2.3. Computational part

Gaussian 16 (ref. 41) was used to study the correlation between the effectiveness and chemical properties of BBPA and DBPA inhibitor molecules. The optimized structures of the neutral and protonated forms of BBPA and DBPA were computed at the DFT-B3LYP/6-311G (d,p) level. The effect of the solvent has been accounted for by the integral equation formalism polarizable continuum model (IEFPCM)⁴² using water as the solvent. Calculations were performed for the aqueous phase using the static dielectric constant of water (ε = 78.35) established in Gaussian 16 program.^41,43 The energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) and the molecular electrostatic potential (MEP) were visualized using GaussView 6 software.⁴⁴ Monte Carlo (MC) simulations in BIOVIA Materials Studio 2020 were employed to determine the most favourable conformation of BBPA and DBPA inhibitor on the Fe (110) surface. The COMPASS-II force field was used to optimize the configurations of inhibitor-corrosive media. The computational representation was constructed to simulate the interactions between BBPA and the DBPA inhibitor molecules, and between the corrosive species Cl⁻ anions, H₃O⁺ cations, and H₂O molecules. The simulation cell of the Fe (110) interface is 26.51 Å × 26.51 Å × 42.10 Å. MD simulations were performed on the selected Fe (110) surface, which is energetically more stable. The analysis of the system as a function of temperature control by the Andersen thermostat ensemble “NVT”, using the COMPASS-II force field, was performed over a 500 ps simulation with a time step of 1.0 fs. To clarify the mechanisms of adsorption and the role of the DBPA inhibitor at the interface between the iron surface and the inhibitor, a study was undertaken using the Density Functional Theory Tight Binding (DFTB) model. In this study, Koster's trans3d-DFTB parameters⁴⁵ were applied to all simulations of the DBPA inhibitor and in its protonated form. Structural optimizations of its molecules were performed using the Smart algorithm, which adhered to precise convergence criteria, including a maximum displacement of 0.001 Å, a force tolerance of 0.1 kcal mol⁻¹ Å⁻¹, and an energy tolerance of 0.02 kcal mol⁻¹. It is important to note that the BBPA, which contains bromine atoms, is not allowed, and the program failed to calculate because it lacks Slater–Koster parameters to describe the expected bonds. The self-consistent charge (SCC) method was used to treat the coulombic interactions between partial atomic charges.⁴⁶ To improve convergence was used Broyden mixing and a smearing factor of 0.03. The SCC tolerance was set to 10⁻⁸ atomic units. Also sets the convergence parameters to fine quality in DFTB. The iron crystal lattice was simulated using a Monkhorst–Pack 8 × 8 × 8 k-point grid in the Brillouin zone.⁴⁷ A 5 × 5 supercell configuration was built. The DBPA inhibitor molecules were placed 7 Å from the iron surface to estimate the partial density of states in the absence of DBPA adsorption. In contrast, for the DBPA inhibitor-Fe (110) complex, the DBPA inhibitor was located closer to the iron substrate with a parallel adsorption orientation to calculate the interaction energy of the DBPA inhibitor adsorption system on Fe (110). DFT and MC–MD results can identify BBPA and DBPA inhibitors with desired properties using the quantitative structure–activity relationship (QSAR) method. The correlation between the compounds' inhibition efficiencies indicated that the QSAR method⁴⁸ could be used to study the inhibitors. A quadratic model⁴⁹ was proposed to estimate inhibition efficiencies. According to this model, the regression analyses fit the experimental data well, and the calculated inhibition efficiencies of the BBPA and DBPA inhibitors were close to their experimental values. The simplest regression form was initially examined in Minitab version 20 as a preliminary verification of the proposed concentration-dependent relationship. Subsequently, a complete analysis was performed in MATLAB R2024a, from which the regression coefficients, IE_calc, R², and RMSE were obtained for the PDP, EFM, and EIS datasets of the BBPA and DBDA inhibitors. The coefficient of determination (R², [corr(IE_exp, IE_cal)]²) and root mean square error (RMSE where N is the number of experimental concentrations) were used to evaluate the agreement between the calculated inhibition efficiencies and the experimental data.^50–52

3. Results and discussion

3.1. Characterization of the BBPA and DBPA inhibitors

3.1.1. FT-IR analysis

Compound BBPA (Fig. S1) showed a significant spectrum: the absorption band at 1665 cm⁻¹ is due to the bending of the (C N imine group), which confirms the synthesis of the BBPA compound. The absorption band at 1585 cm⁻¹ is due to the stretching of the (C C) bond of aromatic ring mode, and an absorption band at 1489 cm⁻¹ is due to the bending of the (C–H in-plane) bond. It also displayed an absorption band at 806 cm⁻¹ due to the bending of the (C–H) out-of-plane aromatic bond. Additionally, it exhibited an absorption band at 524 cm⁻¹ due to the stretching of the (aryl–Br) bond. The adsorption band at 2368 cm⁻¹ caused by the stretching of (C–H) bond appears in a weak mode. The band at 2982 cm⁻¹ is due to the stretching of the (O–H) bond of the moisture. Alike, compound DBPA (Fig. S1) displayed an absorption band at 1697 cm⁻¹ due to the stretching of the imine (C N) bond, while the absorption band at 1620 cm⁻¹ results from the stretching of the aromatic (C C) bond. Additionally, the bands at 1195 and 1064 cm⁻¹ correspond to the stretches of the (C–N) bond in the aryl–N (CH₃)₂ groups. The absorption band at 1411 cm⁻¹ reflects the bending of the (CH₃) group in the N (CH₃)₂. The DBPA compound exhibits a band at 817 cm⁻¹ is caused by the out-of-plane bending of the aromatic (C–H) bond. Additionally, the adsorption band at 2361 cm⁻¹ is due to the stretching of the (C–H) bond in weak mode, and another band at 2304 cm⁻¹ arises from the stretching of the (O–H) bond of moisture, appearing as a broad weak band.

3.1.2. ¹H and ¹³C NMR analysis

The ¹H and ¹³C NMR spectra are shown in Fig. S2 and S3. The ¹H NMR spectrum of the BBPA molecule in DMSO-d₆ displayed clear signals at specific chemical shifts (δ) in parts per million (ppm). These signals appeared at δ = 9.97 (HC N, singlet), 8.72 (C–H1 and C–H6-pyridine, multiple), 8.51 (C-H4-pyridine, multiple), 7.53 (C-H5-pyridine, multiple), and 7.85 (p-Br-C6-H4-benzylidene, multiple). The DBPA molecule exhibits distinct signals at δ (ppm) = 9.67 (HC N, singlet), 8.76 (C-H2-pyridine, multiple), 8.54 (C-H6-pyridine, singlet), 8.38 (C-H4-pyridine, multiple), 7.59 (C-H5-pyridine, multiple), 7.78 (H-ortho to CH N, doublet) and 6.75 (H-ortho to NMe₂, doublet). Furthermore, as shown in Fig. S3, the ¹³C NMR spectra of BBPA and DBPA displayed distinct signals at δ (ppm) = 167.12 (C N), 162.17 (C N–CH), 159.45 (C2 and C6-pyridine), 147.31(C4-pyridine) and 135.31–124.52 (CH-aromatic rings) for BBPA. The DBPA shows chemical shifts of 164.15 for (C N), 154.12 (C–NMe₂), 147.15 (C3-pyridine), 145.16 (C4-pyridine), 126–142 (CH-aromatic “phenyl ring”), 123–138 (CH-aromatic “pyridine H-2, 4, 5, 6”) and 38–42 for (–N (CH₃)₂ methyl carbons).

3.1.3. UV-visible analysis

To determine the UV-visible spectra of BBPA and DBPA, a wavelength range of 200–800 nm was used for measurement. Quantification of the BBPA and DBPA compounds was performed in the lab at room temperature, with concentrations from 4 × 10⁻⁴ M. Fig. S4 shows the UV spectrum of compound BBPA. The strongest absorption occurs near 265 nm, while the weaker broad is at 384 nm. This is due to π–π* and n–π* electronic transitions. It is clear that para-Br is a weak electron-withdrawing substituent present in the ring, resulting in reduced electron density and causing hypsochromic shift.⁵³ Furthermore, the ketimine generally has slightly different orbital energies, so n–π* absorbs at a weaker and slightly lower wavelength. Additionally, the pentyl chain is not conjugated and has minimal electronic influence on the BBPA. Fig. S4 also displays the UV spectrum of compound DBPA. The peak maximum occurs at λ_max = 297.5 nm, with additional peaks at 349 nm and 361 nm. These peaks result from π–π* and n–π* electronic transitions in the conjugated aromatic/C N system, which appears as a strong, sharp peak. There is also a transition from the nonbonding (ion pair on the imine) to the π* system, which is assigned as symmetry-forbidden and appears as a weak peak, as shown in Fig. S4.

3.2. Electrochemical techniques

3.2.1. Potentiodynamic polarization (PDP) studies

In order to determine the mechanism of corrosion inhibition and evaluate the efficiency of the synthesized Schiff bases, BBPA and DBPA, potentiodynamic polarization experiments were performed for the carbon steel electrode in 1.0 M HCl at 25 °C. The parameters obtained from the Tafel extrapolation of the polarization curves are presented in Table 1, while the respective curves are shown in Fig. 1. As can be seen from Table 1, the presence of BBPA and DBPA inhibitors considerably affects the electrochemical activity of the metal electrode under consideration. In the case of the blank solution, i_corr is as high as 1043.0 µA cm⁻². When adding the inhibitors, a sharp decrease in i_corr value occurs regardless of the concentration (1–10 mM).³⁹ So, for example, in the case of the highest investigated concentration (10 mM), the i_corr value decreased to 57.9 µA cm⁻² for BBPA and to 57.6 µA cm⁻² for DBPA. This means that the corrosion rate considerably decreased as well, resulting in a high value of the inhibition efficiency (η_p). The increase in inhibitor concentration leads to the increase in η_p, achieving maximum values of 94.45% for BBPA and 94.48% for DBPA at 10 mM. This means that the inhibition effect is concentration-dependent, which is explained by higher surface coverage (θ) of the metal due to the rise in concentration of inhibitors in the bulk solution.⁵⁴ At the maximum concentration (10 mM), the surface coverage approached approximately 0.94 (for both compounds) and, consequently, around 94% of the active surface sites responsible for the occurrence of corrosion reactions became inaccessible due to blocking by the inhibitor molecules.⁵⁵ The value of E_corr characterizes the mode of inhibition (cathodic, anodic, or mixed). In the case of the blank solution, it amounts to −768.8 mV vs. MSE. For BBPA, E_corr shifts negatively, ranging from −785.7 mV to −865.4 mV (depending on the inhibitor concentration). Similarly, for DBPA, there is a negative shift, varying from −828.2 mV to −807.2 mV. Although the magnitude of potential shift is considerable (especially, for BBPA), the maximal value is still quite close to the typical values of the potential shift for mixed-type inhibitors.⁵⁶ Moreover, deviations in the values of β_a and β_c from those in the blank solution (β_a = 210.5 mV dec⁻¹, β_c = 174.8 mV dec⁻¹) are indicative of the inhibition of both anodic (metal dissolution) and cathodic (hydrogen evolution) reactions.⁵⁷ Thus, BBPA and DBPA are inhibitors of mixed type, inhibiting anodic and cathodic reactions simultaneously, although with a somewhat greater tendency towards inhibition of the cathodic reactions, which is confirmed by a negative shift in E_corr.⁵⁸ Comparison of these inhibitors suggests that DBPA has a higher efficiency at lower concentrations compared to BBPA. For example, at a concentration of 1 mM, the former had 91.36% of efficiency, while the latter one was 88.67%. This difference may be explained in terms of electronic influences of the substituents in the Schiff bases benzaldehyde fragment. Thus, DBPA has a dimethylamino group, which is a strong donor of electrons (+M group).⁷ Therefore, DBPA has a higher electron density on the benzene ring, which through conjugation increases the electron density on azomethine and pyridine nitrogen atoms. A higher electron density increases the efficiency of donation of electrons to d orbitals on the iron surface, thus increasing the efficiency of adsorption and inhibition of oxidation.⁵⁹ However, BBPA has a bromine atom, whose influence cannot be considered purely electron-donating due to its electronegativity (−I). Therefore, BBPA has lower electron density and hence lower adsorption capability and inhibition efficiency at lower concentrations. As seen from the potentiodynamic curves in Fig. 1, the curves obtained for solutions with inhibitors are shifted towards lower currents compared to the blank. Parallelism of the anodic and cathodic branches in the presence of inhibitors confirms that addition of BBPA and DBPA does not change the mechanism of hydrogen evolution or iron dissolution reaction but merely blocks active centers on the metal surface.⁶⁰ It is especially noticeable cathodic suppression, which conforms to the mixed inhibition effect with cathodic contribution.

Table 1. Electrochemical parameters^a for carbon steel dissolution in 1.0 M HCl solution containing different concentrations of the (BBPA and DBPA) inhibitors obtained from polarization measurements at 25 °C.

Inhibitor name	Conc. (mM)	E corr vs. MSE (mV)	i corr (µA cm−2) ± SD	β a (mV dec−1)	−βc (mV dec−1)	k (mpy)	θ	η p%
Blank	—	−768.8	1043.0 ± 9.25	210.5	174.8	549.30	—	—
BBPA	1	−785.7	118.2 ± 5.41	133.9	159.1	62.23	0.8867	88.67
	3	−847.6	86.4 ± 2.89	119.8	157.2	45.50	0.9172	91.72
	5	−837.2	75.9 ± 2.77	122.8	152.2	39.97	0.9272	92.72
	7	−861.5	60.7 ± 2.15	135.0	169.7	31.99	0.9418	94.18
	10	−865.4	57.9 ± 2.87	115.3	152.5	30.47	0.9445	94.45
DBPA	1	−828.2	90.1 ± 6.41	119.0	151.7	47.46	0.9136	91.36
	3	−834.9	76.8 ± 5.58	119.0	152.3	40.47	0.9263	92.63
	5	−828.1	61.2 ± 1.18	126.2	151.4	32.21	0.9414	94.14
	7	−832.8	60.0 ± 1.47	117.8	150.0	31.60	0.9425	94.25
	10	−807.2	57.6 ± 2.39	120.0	142.2	30.33	0.9448	94.48

^a E _corr, is the corrosion potential; i_corr, is the corrosion current density: β_a and β_c are Tafel constants for both anode and cathode; k, is the corrosion rate; θ, is the surface coverage; η_p, is the inhibition efficiency.

Fig. 1. Potentiodynamic polarization curves for the corrosion of carbon steel in 1.0 M HCl in absence and presence of different concentrations of BBPA (a) and DBPA (b) compounds at 25 °C.

3.2.2. Electrochemical frequency modulation (EFM) studies

The results obtained using the potentiodynamic polarization were confirmed by applying the Electrochemical Frequency Modulation (EFM) method, which allows calculating kinetic parameters of the corrosion process with minimum interference to the electrode system.⁵³ Unlike other approaches, EFM is a non-destructive testing method capable of providing information about corrosion rates and determining Tafel coefficients (β_a and β_c) from the current response to sinusoidally modulated voltages.⁶¹ The intermodulation spectra of steel dissolution in absence and presence of BBPA and DBPA molecules are shown in Fig. 2 and 3. The unique feature of the EFM method is the internal validation of the accuracy of obtained data through causality factors (CF-2 and CF-3). According to theory, valid values of causality factors are CF-2 = 2.0 and CF-3 = 3.0.⁶² It can be seen from Table 2 that causality factors in the blank acid solution and in the solutions containing BBPA and DBPA inhibitors are quite close to theoretical values. Thus, the current responses were provoked by a perturbation signal, and kinetic parameters (i_corr, β_a, β_c) are reliable. Kinetic parameters of the electrochemical corrosion process obtained through the EFM technique are presented in Table 2. In the blank solution (1.0 M HCl), i_corr and k values were relatively high. After adding BBPA and DBPA inhibitors, there was a significant drop in the corrosion current density and rate (k).⁶³ The decrease in the current density can be clearly seen in the values of inhibition efficiency (η_EFM). Inhibition efficiency increases with an increase in the inhibitor concentration. Maximum values were reached in the concentration range of 10 mM (93.20% and 93.78%, respectively). Surface coverage also increased from 0.82 to 0.94 depending on the concentration of inhibitors. Anodic and cathodic Tafel slopes (β_a and β_c) were determined after adding BBPA and DBPA inhibitors. Analysis of changes in Tafel slopes shows that both values oscillate and have no obvious trends towards anodic or cathodic inhibition, indicating that inhibitors affect the kinetics of both processes – iron dissolution and hydrogen evolution.⁶⁴ Based on the results of the EFM study, it can be concluded that BBPA and DBPA act as mixed-type inhibitors, which is consistent with the results of PDP experiments. The EFM method confirms the results obtained from PDP, proving that the tested compounds are efficient inhibitors of carbon steel corrosion in acidic environments, while DBPA is a better inhibitor because of its rich electron structure.

Fig. 2. Intermodulation spectra for carbon steel in 1.0 M HCl in absence and presence of different concentrations from BBPA compound at 25 °C.

Fig. 3. Intermodulation spectra for carbon steel in 1.0 M HCl in absence and presence of different concentrations from DBPA compound at 25 °C.

Table 2. Electrochemical kinetic parameters^a obtained by EFM technique for carbon steel in the absence and presence of various concentrations of (BBPA and DBPA) inhibitors in 1.0 M HCl at 25 °C.

Inhibitor name	Conc. (mM)	i corr (µA cm−2) ± SD	β a (mV dec−1)	β c (mV dec−1)	CF-2	CF-3	k (mpy)	θ	η EFM%
Blank	—	1288 ± 8.13	146.2	156.2	1.978	2.707	597.10	—	—
BBPA	1	220.5 ± 9.37	112.4	178.5	1.952	3.170	102.20	0.8288	82.88
	3	131.8 ± 7.56	142.7	193.0	1.485	2.798	61.08	0.8977	89.77
	5	104.1 ± 6.25	148.4	185.6	2.720	3.771	48.26	0.9192	91.92
	7	90.5 ± 4.44	114.7	130.8	1.775	3.278	41.93	0.9298	92.98
	10	87.6 ± 2.16	161.4	176.5	1.317	3.399	40.60	0.9320	93.20
DBPA	1	199.7 ± 10.52	148.7	219.1	1.981	3.008	92.56	0.8450	84.50
	3	104.8 ± 7.98	156.2	205.4	1.210	2.454	48.57	0.9186	91.86
	5	99.4 ± 5.32	175.7	333.8	2.548	2.909	46.08	0.9228	92.28
	7	88.8 ± 5.15	111.4	126.7	1.823	3.484	41.17	0.9310	93.10
	10	80.1 ± 6.01	154.9	187.0	1.970	3.393	37.10	0.9378	93.78

^a E _corr, is the corrosion potential; i_corr, is the corrosion current density: β_a and β_c are Tafel constants for both anode and cathode; k, is the corrosion rate; θ, is the surface coverage; η_EFM, is the inhibition efficiency.

3.2.3. Electrochemical impedance spectroscopy (EIS) studies

Electrochemical Impedance Spectroscopy (EIS) technique was employed to explain the corrosion inhibition effect of both BBPA and DBPA towards carbon steel in 1.0 M HCl. Fig. 4 shows the Nyquist plots and Bode diagrams acquired at different concentrations of the inhibitors, with the calculated electrochemical parameters based on the circuit fit being summarized in Table 3. The Nyquist plots (Fig. 4a and b) of the two types of inhibitors show only one capacitive loop characterized by a depressed semicircle.⁶⁵ The depression of the semicircles (centred below the real axis) results from the frequency dispersion and heterogeneity of the electrode surface, which is inherent to solid metal electrodes immersed in corrosion media.⁶⁶ As the concentrations of both BBPA and DBPA increase from 1 mM to 10 mM, the diameter of the capacitive loops significantly increases. This increase indicates that polarization resistance (R_p) increases due to the formation of the protective adsorbed film that hinders charge transfer reaction.⁶⁷ Comparing the two inhibitors, it can be noted that DBPA (Fig. 4b) presents a larger diameter semicircle compared to BBPA (Fig. 4a) at the same concentrations, meaning higher inhibitory efficiency.⁶⁸ Bode plots (Fig. 4c and d) confirm these observations, showing that at lower frequencies the impedance magnitude (|Z|) increases as the concentration of inhibitors increases, which reflects a higher resistance of the metal surface to corrosion. Moreover, phase angle plots show broadening of the capacitive peak and a move towards −90°, implying capacitive behavior (less reactivity) of the metal surface in the presence of inhibitors.⁶⁹ The parameters were extracted from the experimental data using equivalent circuit fitting as illustrated in the inset of Fig. 4. The capacitance was replaced by Constant Phase Element (CPE), since it represents an ideal capacitor taking into consideration roughness and inhomogeneity of the surface.⁷⁰ CPE impedance has the following formula:⁷¹

Z_CPE = Y₀⁻¹(jω)⁽⁻ⁿ⁾ 4

where Y₀ represents the magnitude of CPE while n (0 < n ≤ 1) is the exponent representing heterogeneity of the surface (n = 1 corresponds to an ideal capacitor). It can be observed from Table 3 that n₂ values for the double layers are within the range of 0.71 and 0.83, thus the heterogeneity of the steel surface is confirmed. Table 3 illustrates main parameters used for equivalent circuit fitting. Charge Transfer Resistance (R_ct): in the absence of any inhibitor, R_ct is very low (21.82 Ω cm²) implying quick corrosion. The introduction of inhibitors leads to a major increase in R_ct values.⁷² The R_ct value at 10 mM reaches 314.16 Ω cm² for BBPA while DBPA shows a value of 349.54 Ω cm². The substantial increase demonstrates that the inhibitors function as active site blockers which prevent charge transfer to iron during the dissolution process.⁴⁰ The presence of inhibitors causes C_dl values to decrease from the blank solution which has a value of 211.55 mF cm⁻².⁷³ The C_dl value at 10 mM drops to 35.12 mF cm⁻² with BBPA while DBPA shows a value of 38. The model explains this decrease through the equation C_dl =(εε₀A)/d.¹⁵ The equation defines C_dl through three components which include the dielectric constant of the medium, and the double layer thickness, as well as the actual surface area of the object. The metal surface sees water molecules with a high dielectric constant (ε ≈78) replaced by larger organic inhibitor molecules which have a lower dielectric constant (ε ≈2–10) through the addition of organic inhibitors. The electrical double layer thickness increases while dielectric constant (ε) decreases, which both lead to a decrease in C_dl.⁷⁴ According to Table 3, the inhibition efficiency (η_z) increases with inhibitor concentration, reaching maximum values of 95.78% for BBPA and 96.14% for DBPA at 10 mM. The two compounds achieve high efficiency which demonstrates their effectiveness as corrosion inhibitors for carbon steel in acidic environments.

Fig. 4. Nyquist plots, Bode and phase angle plots for steel in 1.0 M HCl solution without and with different concentrations of BBPA (a and c) and DBPA (b and d) compounds at 25 °C.

Table 3. EIS parameters for corrosion of steel in 1.0 M HCl in the absence and presence of different concentrations of (BBPA and DBPA) inhibitors at 25 °C^a.

Inhibitor	Conc. (mM)	R s (Ω cm2)	R f (Ω cm2)	CPEf		C f (mF cm−2)	R ct (Ω cm2) ± SD	CPEdl		C dl (µF cm−2)	Chi squared (χ2)	R p (Rf + Rct)	θ	η z%
				Y o1 (m Ω −1 sn cm−2)	n 1			Y o2 (µ Ω −1 sn cm−2)	n 2
Blank	—	2.1519					21.82 ± 3.15	515.46	0.8344	211.55	1.17 × 10−3	21.82	—	—
BBPA	1	2.283	50.5809	10.81	0.6096	7.35	93.10 ± 5.52	234.82	0.7145	50.97	2.31 × 10−3	143.69	0.8481	84.81
	3	2.181	99.1179	5.04	0.6477	3.46	217.04 ± 4.92	151.14	0.7553	49.95	1.46 × 10−3	316.15	0.9310	93.10
	5	1.9614	146.499	3.68	0.6881	2.78	246.20 ± 7.18	118.09	0.7898	46.06	1.50 × 10−3	392.70	0.9444	94.44
	7	2.9014	170.143	2.97	0.7107	2.25	288.44 ± 6.98	107.58	0.8017	45.57	1.03 × 10−3	458.58	0.9524	95.24
	10	2.1696	203.117	1.52	0.7687	1.07	314.16 ± 9.52	83.39	0.8081	35.12	5.83 × 10−4	517.28	0.9578	95.78
DBPA	1	2.2297	75.2186	8.52	0.614	6.44	150.71 ± 4.58	165.48	0.7542	49.69	7.39 × 10−4	225.93	0.9034	90.34
	3	2.2259	106.782	4.13	0.6588	2.70	222.77 ± 7.18	133.27	0.7719	47.14	9.11 × 10−4	329.55	0.9338	93.38
	5	1.208	151.583	3.23	0.6986	2.37	264.41 ± 5.97	108.58	0.7939	43.20	9.65 × 10−4	415.99	0.9475	94.75
	7	2.0998	176.111	2.68	0.7243	2.01	322.29 ± 6.39	88.40	0.8067	37.68	6.79 × 10−4	498.40	0.9562	95.62
	10	2.5789	216.230	0.13	0.7697	0.05	349.54 ± 8.18	81.31	0.8282	38.85	8.02 × 10−4	565.77	0.9614	96.14

^a R _s = solution resistance, R_ct = charge transfer resistant, Y₀, n = constant phase elements, C_dl = double layer capacitance, θ = surface coverage, η_z = inhibition efficiency.

3.3. Adsorption isotherm studies

The study examined how BBPA and DBPA adsorbed onto surfaces to understand corrosion inhibition mechanisms and how inhibitors interact with metal surfaces.⁷⁵ The electrochemical techniques of PDP, EIS, and EFM produced surface coverage measurements which researchers tested against the Freundlich, Langmuir, Temkin, Frumkin, Flory–Huggins, and El-Awady isotherm models. The statistical parameters for the fitted models, including the regression correlation coefficient (R²), slope, intercept, adsorption equilibrium constant (K_ads), and standard free energy of adsorption (ΔG_ads), are summarized in Table 4. The Langmuir adsorption isotherm provided the best match between experimental data and both inhibitors across all testing methods. The Langmuir isotherm shows its relationship through the linear equation:⁷⁶

C/θ = 1/K_ads + C 5

Table 4. Adsorption isotherms models of the inhibitors with values of R², slopes, intercepts, K_ads, and ΔG_ads obtained by using data from electrochemical measurements^a.

Adsorption isotherm model	Linear form equation	Technique	Inhibitor	Slope	Intercept	R 2	K ads (M−1)	ΔGads (kJ mol−1)
Freundlich	log θ = log K + 1/n log C	EFM	BBPA	0.05299	0.08150	0.94538	1.2064	−10.59
			DBPA	0.04474	0.06641	0.89143	1.1652	−10.50
Langmuir		EFM	BBPA	1.05627	0.00016	0.99998	6385	−32.19
			DBPA	1.05489	0.00012	0.99998	8032	−32.77
		EIS	BBPA	1.02960	0.00014	1.00000	6976	−32.41
			DBPA	1.03139	0.00010	0.99997	9948	−33.31
		PDP	BBPA	1.04894	0.00011	0.99994	9277	−33.13
			DBPA	1.05304	0.00006	0.99998	18 072	−34.81
Frumkin		EFM	BBPA	−4.52523	7.46389	0.88178	2.9100 × 107	−53.41
			DBPA	−5.18024	8.15016	0.75300	1.4130 × 108	−57.39
Temkin		EFM	BBPA	20.37135	−23.88121	0.95035	0.3097	−7.16
			DBPA	22.51540	−26.02887	0.89647	0.3147	−7.21
Flory–Huggins		EFM	BBPA	2.20565	4.63113	0.97782	4.2769 × 104	−36.98
			DBPA	2.31087	4.84093	0.93472	6.9331 × 104	−38.20
El-Awady		EFM	BBPA	0.47359	2.12325	0.97878	30 428.17	−36.12
			DBPA	0.43278	2.07182	0.93796	61 272.80	−37.89

^a R ² = regression correlation coefficient, K = binding constant, θ = surface coverage, c = concentration.

Table 4 and Fig. 5 demonstrate that C/θ versus C produced straight line graphs which had R² values that approached perfect correlation because their values ranged between 0.99987 and 0.99998.⁷⁷ The slopes of these lines were very close to 1 (e.g., 1.0489 for BBPA and 1.0530 for DBPA using PDP data). The results show that BBPA and DBPA adsorbed onto carbon steel surfaces according to Langmuir isotherm patterns. The adsorption process results in inhibitor molecules establishing a monolayer on metal surfaces, while there exists no major lateral interaction among the molecules that have adsorbed onto the surface.¹⁹ The Langmuir plots intercepts enabled us to calculate the adsorption equilibrium constant (K_ads) and standard free energy of adsorption (ΔG_ads). These parameters give numerical data about how stable the inhibitor film remains on the steel surface.⁵⁸ The K_ads values reach extremely high levels which range between approximately 4500 M⁻¹ and 18 000 M⁻¹ based on different measurement methods because the inhibitor molecules establish powerful bonds with the steel surface.⁷⁸ The K_ads value increases because of stronger adhesion which results in better inhibition performance.⁷⁹ The electrochemical results show that DBPA exhibits higher K_ads values than BBPA according to the PDP data with DBPA showing 18 072 M⁻¹ and BBPA showing 9277 M⁻¹ which confirms that DBPA creates a more effective protective barrier. The ΔG_ads values were calculated using the equation:⁸⁰

ΔG_ads = −RT ln(55.5K_ads) 6

Fig. 5. The Langmuir adsorption model for BBPA and DBPA compounds on the steel.

The ΔG_ads values around −20 kJ mol⁻¹ show that physisorption occurs through electrostatic interaction between charged inhibitor molecules and the charged metal surface.⁸¹ The values that reach −40 kJ mol⁻¹ or below this point show that chemisorption occurs through coordinate covalent bonding which involves charge transfer from the inhibitor to the metal surface.⁸² The ΔG_ads values for BBPA and DBPA range between −31.34 and −34.81 kJ mol⁻¹ which exists between these two thresholds. The adsorption process involves both physisorption and chemisorption methods based on this evidence.⁸³ The molecules start to adsorb through electrostatic attraction which represents physisorption and then they develop coordinate bonds by nitrogen and oxygen atoms donating their lone pair electrons and aromatic rings giving π-electrons to the vacant d-orbitals of the iron surface through chemisorption.⁸⁴

3.4. DFT-electronic properties

The BBPA and DBPA compounds were optimized as illustrated in Fig. 6. Both compounds achieve acceptable convergence, with optimized electronic energies of −85619.7 eV and −19236.8 eV for BBPA and DBPA, respectively. It provides reasonable geometric stability and improves the fine behaviour on the potential energy surface (PES) through successful geometry optimization at the “B3LYP/6-311G (d,p) – DFT” level. As shown in Fig. 6, both compounds reached lower energy in their final structures relative to their initial geometries, with energetically favourable configurations that confirm the electronic bonding and the atoms' rearrangement. Thus, the optimized geometry of the BBPA compound shows carbon–carbon bonds of about 1.4 Å, carbon–hydrogen bonds of 1.08 Å, and an imine bond length of 1.27 Å. Bond lengths reflect a stable aromatic system with greater molecular co-planarity, as well as the stable imine bond.⁸⁵ Besides, the DBPA compound also has the same carbon–carbon bond lengths as the BBPA, with its aromatic characteristics. However, there are changes in the imine bond length to be about 1.28 Å, as well as the single bond length of carbon–nitrogen about 1.39 Å and rotation to be 118°, which loses the planarity of the benzene ring. The aromatic bonds' attributes confirmed π-conjugation and structural stability,⁸⁶ thereby enhancing strong interactions with the carbon steel surface via π–d orbital overlap.

Fig. 6. Optimized structures, ESP mapping and Mulliken atomic charges of BBPA and DBPA compounds.

It is important to assess the electronic properties of the BBPA and DBPA corrosion inhibitors to primarily determine their efficiency. Based on the FMO's analysis and Koopman's theorem,⁸⁷ document all the electronic parameters in Table 5. The DBPA/DBPA-aqueous phase/DBPAH inhibitor possesses higher HOMO energies than BBPA/BBPA-aqueous phase/BBPAH. In particular, the DBPA inhibitor in the gas phase exhibits a HOMO value of −5.451 eV, compared with −6.493 eV for BBPA, indicating a greater tendency to donate electrons to the carbon steel surface and, hence, to form a stronger protective adsorbed film.³⁹ Besides, the DBPA/DBPA-aqueous phase/DBPAH inhibitor exhibits lower LUMO energies than the BBPA/BBPA-aqueous phase/BBPAH, suggesting stronger feedback interaction with the carbon steel surface. This behaviour enhances the adsorption process and then contributes to improved inhibition performance to retard the corrosion process. Fig. 7 represents the HOMO and LUMO distributions of the BBPA and DBPA corrosion inhibitors, as well as the density of states (DOS) spectra. It is obvious from the frontier orbital distributions of HOMO that the electron densities are localized over the aromatic π-benzene ring⁸⁸ and the nitrogen active centres that act as immediate adsorption sites. Likewise, the LUMO distribution extends across the conjugated inhibitor molecule. This behaviour facilitates the back-donation of electrons⁸⁹ from the carbon steel surface, particularly from iron atoms, to the BBPA and DBPA corrosion inhibitors. Furthermore, DOS spectra confirm the electronic behaviour,⁹⁰ clearly indicating that the occupied molecular orbitals are distributed in the negative-energy region. In contrast, the virtual orbitals are located in the positive-energy region. The DBPA inhibitor molecule exhibits denser electronic states in the distribution near the frontier orbital region⁹¹ of the Fermi level than the BBPA inhibitor molecule. This behaviour enhances electronic mobility, leading to stronger interactions with the carbon steel surface via charge transfer.⁹² The DBPA inhibitor molecule exhibits extensive delocalization of the frontier orbitals compared with the BBPA molecule, owing to multiple nitrogen atoms and conjugated aromatic systems, thereby increasing the push of electron density towards the d-orbitals.

Table 5. Global descriptor parameters for compounds BBPA and DBDA at the neutral and the protonated form^a.

Inhibitors	HOMO (eV)	LUMO (eV)	E g (eV)	χ (eV)	µ (eV)	η (eV)	σ (eV−1)	ω (eV)	µ (D)	ΔEback-donation (eV)	ΔN
BBPA	−6.493	−2.378	4.114	4.436	−4.436	2.057	0.243	4.782	3.253	−0.514	0.623
Gas phase
BBPA	−6.508	−2.351	4.157	4.430	−4.430	2.078	0.240	4.721	4.726	−0.520	0.618
Aqueous phase
BBPAH	−7.775	−4567	3.207	6.171	−6.171	1.603	0.311	11.87	9.702	−0.401	0.259
DBDA	−5.451	−1.537	3.914	3.494	−4.94	1.957	0.255	3.119	6.972	−0.489	0.526
Gas phase
DBDA	−5.456	−1.753	3.703	3.604	−3.604	1.851	0.270	3.509	9.645	−0.463	0.917
Aqueous phase
DBDAH	−6.608	−4226	2.382	5.417	−5.417	1.191	0.419	12.318	14.57	−0.298	0.665

^a E _g = E_LUMO − E_HOMO, χ = −(E_LUMO − E_HOMO)/2, µ = −χ, η = (E_LUMO − E_HOMO)/2, σ = 1/η, ω = µ²/2η, ΔE_{back-donation} = −η/4, ΔN = (χ_Fe − χ_inh)/2(η_Fe + η_inh).

Fig. 7. Frontier molecular orbitals, energy gap and density of states of BBPA and DBPA compounds.

As seen from Table 5, the energy gap of the DBPA/DBPA-aqueous phase/DBPAH inhibitor exhibits lower values than the BBPA/BBPA-aqueous phase/BBPAH. The DBPAH shows the lowest energy gap of 2.38 eV, whereas BBPA exhibits a higher energy gap of about 4.11 eV. This indicates that DBPA/DBPA-aqueous phase/DBPAH inhibitors are more reactive and possess the best adsorption ability toward the carbon steel surface. Moreover, as is evident, the DBPA inhibitor exhibits lower electronegativity values than BBPA, confirming a stronger electron-donating ability and, hence, improved interactions that lead to bond formation with d-orbitals with iron atoms. Generally, the DBPA/DBPA-aqueous phase/DBPAH inhibitor exhibits lower hardness and higher softness values than the BBPA/BBPA-aqueous phase/BBPAH. In particular, DBPAH possesses the highest softness value (0.41 eV⁻¹) and the lowest hardness value (1.19 eV), indicating the greatest adsorption ability on the carbon steel surface. The DBPA/DBPA-aqueous phase/DBPAH inhibitors have much larger dipole moments than the BBPA derivatives. This suggests stronger polarity and enhances the adsorption tendency of the DBPA inhibitor molecules. Likewise, the protonated species DBPAH and BBPAH exhibit high dipole moments due to charge separation induced by protonation in acidic solution, thereby further promoting electrostatic forces that form before the inhibitor – carbon steel linkage bond. Thus, as shown in Table 5, all of the ΔN values are positive, which indicates the electron density transfer from the BBPA/DBPA inhibitor molecules to the d-orbital in Fe-atoms. The highest observed for DBPA in the aqueous phase is approximately 0.91. This indicates strong electron donation, enhancing adsorption and confirming its inhibitory efficiency. Besides, the ΔE_{back-donation} values are negative, indicating favorable back-donation interactions between the carbon steel surface and the BBPA/DBPA inhibitor molecules. Thus, the over-range between −0.29 and −0.51 for the BBPA and DBPA inhibitors at the high indicates a strong stabilization between the carbon steel surface and the BBPA/DBPA inhibitor molecules. This behavior supports the formation of a protective film. Generally, these findings are consistent with the electrochemical results, which enhance the effectiveness of the adsorption process for BBPA/DBPA inhibitors and provide suitable corrosion protection through electron transfer, forming a protective film; DBPA performs slightly better.

3.5. DFT-MAC/ESP and NBO

Mulliken atomic charge (MAC) analysis was performed to identify the active adsorption center atoms⁹³ that are responsible for the interaction between the electron donation of BBPA/DBPA inhibitor molecules and the vacant d-orbitals in the Fe-atoms. As seen from Table S1 as well as the charge distribution maps in Fig. 6, the nitrogen atoms have the highest negative charge densities. It indicates the presence of suitable adsorption-active centers for optimal adsorption performance. The nitrogen atoms N6 and N7 display meaningful negative charges for BBPA in both the gas and aqueous phases. In the BBPA aqueous phase, the atoms of (N6 and N7) have charges of −0.32 and −0.36, respectively, whereas in the BBPAH, the charge values become −0.31 and −0.39. Additionally, the greater negative charge density at N7 suggests it is the most favorable adsorption site on the BBPA molecule and the one that promotes chemisorption by forming a protective adsorbed layer. The DDBPA/DBPA-aqueous phase/DBPAH molecules display greater localization of negative charge on the N15 atom. The highest values were observed in the gas phase (−0.478) and the aqueous phase (−0.471). The DBPAH exhibits a value of about −0.44. Furthermore, N6 and N7 also show significant negative charges. Thus, several negatively charged sites provide multiple adsorption centers⁹⁴ on the carbon steel surface. Also, it is essential to note that the carbon atoms that are adjacent to the N-atoms exhibit intermediate negative charge densities, which indicates that the π-electron in the aromatic ring contributes to adsorption via π–d orbital interactions. The delocalized electron density across the BBPA/DBPA inhibitor molecules enhances their stability by increasing surface coverage. The DBPA inhibitor exhibits a stronger electron-donating ability than the BBPA inhibitor. Furthermore, as shown in Table S1, protonation of the BBPA/DBPA inhibitors in acidic solution slightly redistributes electron density but maintains its localization on the N atoms. In this manner, it initiates electrostatic attraction and enhances interaction between the BBPAH/DBPAH molecules and the carbon steel surface. Moreover, to identify the reactive adsorption sites of BBPA and DBPA on the carbon steel surface, electrostatic potential (ESP) maps were generated, as illustrated in Fig. 8. It reveals the distributions of negative electrostatic potential around the N atoms and the aromatic ring. It mainly refers to the localization of electron-rich sites that act as active centers and exhibit a stronger tendency to adsorb on the carbon steel surface. Thus, DBPA displays more widely and intensely distributed negative ESP regions than BBPA. Similarly, regions with positive values concentrate around the lower-electronegativity atoms of the terminal hydrogen. It is compatible with higher (−5.91 × 10⁻²) and lower (−4.94 × 10⁻²) values for the DBPA and PBPE inhibitors, respectively. These findings align with the electrochemical techniques results.

Fig. 8. Monte Carlo (MC) simulation snapshots and corresponding energy distributions for the neutral species (BBPA and DBDA) and the protonated species (BBPAH and DBDAH).

It is significant to analyze the natural bond orbital (NBO) to identify donor–acceptor interactions⁹⁵ and charge delocalization between BBPA and DBPA inhibitors and the carbon steel surface. It is governing the interaction strength and adsorption behaviour that affects the inhibition performance. The calculated occupancies, orbital energies, and hybridization states are presented in Tables S2–S7 for both BBPA/BBPA-aqueous phase/BBPAH and DDBPA/DBPA-aqueous phase/DBPAH inhibitors. It is clear from Table S2 that the two nitrogen atoms, N₆ and N₇, are the dominant donor sites and extend to the conjugated aromatic π-ring within the molecule. The LP (1) N₆ and LP (1) N₇, which denote to lone-pair orbitals, have occupancies of 1.918 and 1.905e, respectively, and orbital energies of −9.181 and −9.364 eV. It appears that corresponding hybridizations as (sp^{2.54 “}N₆” and sp^2.81 “N₇”), which reveal the p-character contributions to be as 71.72% and 73.71%, respectively. These indicate strong electron delocalization and, hence, enhanced electron-donating ability⁹⁶ of the lone pairs toward the vacant metallic d-orbitals of iron atoms. Furthermore, BD (2) C₉–C₁₄, BD (2) C₁₀–C₁₁, and BD (2) C₁₂–C₁₃ of π-bonding orbitals exhibits occupancies ranging from 1.623 to 1.674. It has π-character donations exceeding 99%, ensuring the comprehensive π-conjugation within the aromatic system. It is the π → Fe interactions³⁹ that contribute significantly to the adsorption. Besides, the bonding orbitals at BD (1) C₅–N₆ and BD (1) N₇–C₈ display highly stabilized energies of −22.443 and −24.422 eV, respectively, which are responsible for σ-bond orbitals and are associated with the nitrogen atoms. These reflect the strong electronic⁹⁷ stabilization and enhance the adsorption of active sites. As shown in Table S3, the occupancies of LP (1) N₆ and LP (1) N₇ increase marginally to 1.910, while the bonding orbitals, which correspond, become energetically more stabilized. Besides that, the high p-character in lone-pair orbitals and the π-bonding aromatic system are continuous. It is evident that the inhibitor's electron-donating capability, as a result of the electronic structure of the BBPA inhibitor, becomes slightly more stabilized due to solvent polarization effects. It is noticed from Table S4 that occupancies of the π-bonding orbitals decrease markedly, especially for BD (2) C₁₀–C₁₁ (0.831) and BD (2) C₁₂–C₁₃ (0.804), due to the protonation form, which induces substantial redistribution of electron density and leads to a partial disruption of the conjugated π-system. Further, the anti-bonding lone-pair orbitals LP* (1) C₁₄, LP* (1) C₉, LP* (1) C₄, and LP* (1) C₃ appear and reflect significant charge polarization for the BBPAH. Strong stabilization is related to nitrogen-containing σ-bonds, notably BD (1) N₇–C₈ (−26.187 eV) and BD (1) C₅–N₆ (−25.307 eV). These suggest that the protonated species strongly adsorb on the carbon steel surface via donor–acceptor⁹⁸ interactions and the electrostatic. Correspondingly, to inspect the BD (1) C₁₂–Br₁₅ orbital form Tables S2–S4 to show the significant stabilization and possess the occupancies as follows: 1.982e, 1.982e, and 0.991e, consistent with orbital energies of −18.120, −18.067, and −18.993 eV for the BBPA-gas phase/BBPA-aqueous phase/BBPAH, respectively. These values reveal an influential electronic interaction between the π-conjugated aromatic system and Br₁₅ atom, which enhances charge redistribution over the BBPA molecule and facilitates stronger donor–acceptor interactions. For the DBPA – gas phase (Tables S5), the lone-pair orbitals LP (1) N₆ and LP (1) N₇ correspond to occupancies of 1.917e and 1.879e, with orbital energies of −8.760 and −8.942 eV, respectively. These are the adsorption-active sites, together with N₁₅ and the π-aromatic system on the carbon steel surface. The contributions are limited to about 73%, associated with the sp^2.66 (N₆) and sp^2.73 (N₇) hybridizations, indicating dominant p-character orbitals that favor efficient electron donation to the d-orbital. Similarly, the BD (2) C₉–C₁₄, BD (2) C₁₂–C₁₃, and BD (2) C₁₀–C₁₁ as π-bonding orbitals have occupancies in the range between 1.608e and 1.731e, including p-character contributions of more than 99%. This depicts the extensive π-aromatic electron delocalization over the DBPA molecule. It is also significant to check the N₁₅ tertiary nitrogen center, which is related to σ-bonds, especially at BD (1) N₁₅–C₁₆ and BD (1) N₁₅–C₁₇, which possess admiringly stabilized orbital energies⁹⁹ of −20.230 and −20.243 eV. Thus, as evident from the presence of N₁₅, DBPA has higher electron density and donor capability than BBPA and a greater positive effect on desorption tendency. The lone-pair orbitals of N₆ and N₇ retain high occupancies and p-character contributions, with the π-conjugated system remaining stabilized, as evidenced by the related values in Table S6. Also, it includes σ-bonds (N₁₅), which support the formation of a stable adsorbed layer, after providing strong electronic stabilization and charge delocalization. The π-bonding orbitals (Table S7) BD (2) C₁₃–C₁₄ and BD (2) C₁₀–C₁₁ maintain occupancies of 0.883e and 0.889e for the DBPAH, respectively, which are slightly higher than those observed for BBPAH, as seen in Table S4. Further, the BD (1) N₇–H₃₃ and BD (1) N₆–H₃₄ orbitals affirm the protonation of its nitrogen centers. This enhances the strength of the stabilized bonding interactions that persist for BD (1) N₇–C₈ (−24.796 eV), BD (1) C₅–N₆ (−25.064 eV), and BD (1) C₁–N₆ (−25.217 eV) and improves the adsorption ability of DBPAH under acidic solution conditions. The nitrogen atoms primarily govern the adsorption behavior of the BBPA/DBPA inhibitor molecules. It acts as a donor centers, and this influence extends throughout the entire conjugated aromatic π-bonding system. Thus, DBPA shows stronger interactions with the d-orbital and hence exhibits better corrosion-inhibition efficiency than the BBPA inhibitor.

3.6. MC/MD interactions

MC simulations were used to investigate how inhibitor molecules interact with the metal surface in an acidic corrosive medium. Fig. 8 shows the most stable configuration of DBPA, BBPA inhibitors, and their protonated forms on the cleaved Fe (110) surface. The low-energy configurations of the Fe (110)-DBPA, BBPA, DBPAH, and BBPAH inhibitors in aqueous solution are examined in this study. The simulation was conducted in an aqueous environment of water molecules to replicate corrosion in a real-world setting. The adsorption configuration is nearly parallel due to the inhibitor molecule's relaxation on the Fe (110) surface, as shown in Fig. 8. The molecular images for the inhibitors demonstrate how the aromatic ring system and the nitrogen atom align to interact directly with surface sites. This means that the imine nitrogen directionally binds to surface iron¹⁰⁰ centers. The phenyl ring is primarily parallel to the terrace, thereby enhancing interaction with the π-orbitals of iron in carbon steel. These interactions favor the formation of compact, adherent films that inhibit corrosion by the inhibitor molecules, as illustrated by the energy distribution (Fig. 8) of the corrosion system. It is clear from the energy distribution profiles that the water molecules are displaced far from the surface, as indicated by less negative values on the energy axis, and these values are also tabulated in Table 6 as the dE_ads/dN_i parameters. Moreover, the interactions of aggressive species (Cl⁻ and H₃O⁺) occur at different positions, owing to strong competitive adsorption and the ability of inhibitors to displace aggressive ions¹⁰¹ from the surface, as evidenced by DBPA and DBPAH compared with BBPA and BBPAH.

Table 6. Adsorption energy parameters obtained from Monte Carlo simulations for DBDA, DBDAH, BBPA, and BBDAH corrosion inhibitors on Fe (110) surface in aqueous acidic solution (200H₂O/10Cl⁻/10H₃O⁺).

Corrosion system	Adsorption energy (kcal mol−1)	Rigid adsorption energy (kcal mol−1)	Deformation energy (kcal mol−1)	dEads/dNi: inhibitor (kcal mol−1)	dEads/dNi: water (kcal mol−1)	dEads/dNi: H3O+ ions (kcal mol−1)	dEads/dNi: Cl− ions (kcal mol−1)
Fe (110) + (DBDA)/200H2O/10Cl− and 10H3O+	−3586.25	−3725.32	139.07	−78.67	−14.05	−142.07	−139.18
Fe (110) + (DBDAH)/200H2O/10Cl− and 10H3O+	−3700.04	−3648.22	−51.820	−279.51	−13.21	−139.67	−136.23
Fe (110) + (BBPA)/200H2O/10Cl− and 10H3O+	−3594.21	−3738.88	144.67	−142.10	−11.96	−152.73	−144.41
Fe (110) + (BBPAH)/200H2O/10Cl− and 10H3O+	−3607.56	−3735.40	127.84	−146.17	−7.510	−145.96	−152.77

Table 6 displays the descriptors calculated from MC stimulation. In general, the negative values of adsorption energies for all structures indicate that inhibitors are effective adsorptive inhibitors, with DBPAH being the superior inhibitor. This suggests a strong interaction with the metal surface, likely involving chemisorption, which exhibits the highest inhibitory effect due to its stronger adsorption. It is clear that protonated inhibitors (DBPAH, BBPAH) interact electrostatically with negatively charged metal surfaces and can also compete with H₃O⁺ and Cl⁻ ions; hence, protonation enhances inhibitor effectiveness in acidic corrosion systems. The DBPAH shows lesser values for all the parameters, i.e., rigid adsorption energy, deformation energy, and dE_ads/dN_i (−3648.22, −51.82, −279.51 kcal mol⁻¹) than DBPA, BBPA, and BBPAH, thus showing a stronger inhibition effect. Because of its little molecular distortion, the adsorption stability and corrosion protection are improved. DBPAH is a highly effective corrosion inhibitor. Table 6 shows that inhibitor molecules replace water molecules because their dE_ad/dN_i ratios are much lower. This is because dE_ads/dN_i shows whether metal adsorbents are absorbed or ignored. The inhibitors in this work are potent carbon steel inhibitors, as evidenced by theoretical modelling and experimental and spectral investigations. According to η%, the inhibitors are ranked as DBPA > BBPA. MD has helped clarify interactions among inhibition mechanisms, the behavior of DBPA and BBPA inhibitor molecules and their protonated forms, and corrosive ions in aqueous solution under controlled, simulated conditions, providing a clear view of their inhibitory performance. Fig. 9 shows the system after the MD simulation. The entire system reaches equilibrium, with temperature and energy stabilized. It is clear that the active DBPA, BBPA, and PBDE inhibitor molecules align parallel to the Fe (110) surface, except for the DBPAH configuration. This parallel alignment leads to the contact area and surface coverage under controlled temperature and in the presence of imine bond sites. The DBPAH form shows that the pendant is on the Fe (110) surface via the benzene ring. This behavior restricts the adsorption pattern,³⁹ thereby reducing the contact area. The preferred binding site was identified by E_binding = −E_interaction, with values in Table 7. A more negative E_interaction indicates that inhibitor molecules are highly reactive toward Fe (110) systems, consistent with the positive binding energy. The strongest adsorption is reflected by the most negative E_interaction value for 160.05 kcal mol⁻¹ in the DBPA form. Additionally, the BBPAH form, with its protonation, slightly enhances this interaction. Conversely, protonation markedly weakens the interaction in DBPAH, suggesting that the DBPA form is more compatible with the Fe (110) surface. The surface diffusion coefficient (D) in Table 7 shows that the low diffusion coefficients¹⁰² with the DBPA inhibitor are lower than others, indicating limited molecular mobility. This suggests restricted lateral motion on Fe (110), consistent with strong adsorption and a dense inhibitor film,¹⁰³ as indicated by the binding energy. The RDF profiles for Fe–N bonds show a first maximum around 3 Ź⁰⁴ for DBPA and protonated BBPA, as in Fig. 10. The value exceeds 2.3 Å,¹⁰⁵ typical for chemisorption. This aligns with previous quantum chemical and MD studies,^106,107 of imine inhibitors on iron (110) surfaces. Furthermore, it has been reported that when these bonds exceed 3.5 Å, physisorption becomes the only option, as observed for DBPAH. The values indicated a physisorption-dominated interaction, primarily driven by van der Waals forces and electrostatic attraction,¹⁰⁸ rather than by covalent bonds between iron and nitrogen in coordination. Furthermore, Fig. 10 shows that g(r) ≅ 5.01 for the DBPA inhibitor when compared with other structures. This effectively regulates the electron density distribution near the metal surface and enhances its stability.¹⁰⁹ These findings suggest that the adsorption process occurred efficiently and stably.

Fig. 9. Molecular dynamic (MD) simulation snapshots and corresponding energy distributions for the neutral species (BBPA and DBDA) and the protonated species (BBPAH and DBDAH).

Table 7. MD simulation results: interaction and binding energies (kcal mol⁻¹) and diffusion parameters (D and R²) for DBDA, DBDAH, BBPA, and BBPAH inhibitors on the Fe (110) surface in a simulated acidic solution (200H₂O/10Cl⁻/10H₃O⁺).

Corrosion system	Interaction energy (kcal mol−1)	Binding energy (kcal mol−1)	(D) m2 s−1 and R2
Fe (110) + (DBDA)/200H2O/10Cl− and 10H3O+	−160.05	160.05	0.171 (0.981)
Fe (110) + (DBDAH)/200H2O/10Cl− and 10H3O+	−51.750	51.750	0.604 (0.993)
Fe (110) + (BBPA)/200H2O/10Cl− and 10H3O+	−137.86	137.86	0.339 (0.999)
Fe (110) + (BBPAH)/200H2O/10Cl− and 10H3O+	−139.26	139.26	0.351 (0.989)

Fig. 10. Radial distribution function (RDF) g(r) for the Fe–N interaction in the adsorption of neutral species (BBPA and DBDA) and the protonated species (BBPAH and DBDAH) on an Fe (110) surface in simulated 1 M HCl.

3.7. DFT-tight-binding (TB) interactions

It is essential to explore the adsorption strength and active sites of DBPA and DBPAH inhibitor molecules and to understand them well. Thus, DFTB simulations were conducted for DBPA inhibitor molecules in their neutral and charged forms, since the DBPA molecule with a nitrogen atom is readily protonated in acidic solution, particularly under strongly acidic conditions. Fig. 11 depicts the projected density of states (PDOS) spectra before and after adsorption of DBPA in neutral and protonated forms on Fe (110). It demonstrates the stable adsorption geometries of the DBPA and DBPAH inhibitor molecules on the Fe (110) surface. The quantum-chemical analysis revealed that both include several active sites¹¹⁰ capable of interacting with iron atoms. The adsorption behaviour of both DBPA and DBPAH molecules shows a parallel arrangement on the iron surface. It suggests strong adsorption affinities at the iron surface and the ability to bind to iron atoms via carbon atoms. It can be noted that the DBPA molecule (Fig. 11) forms three single carbon–iron bonds with lengths ranging from 2.27 Å to 2.30 Å. In addition, the DBPAH molecule forms five carbon–iron (Fe–C) bonds, each with a length of 2.25–2.30 Å. To gain deeper insights into the nature of these interactions, it is important to compare these bond lengths to the sum of the corresponding covalent radii.⁴⁷ The carbon atom is known for its ability to form strong covalent bonds. It has a covalent radius of approximately 0.77 Å. For that, the covalent radii sum for Fe–C bonds is⁴⁶ approximately 2.03 Å. In our study, the bond lengths are very close to theoretical values, suggesting predominantly covalent character in the interactions between DBPA-based inhibitors and the Fe (110) surface. This indicates that the DBPA and DBPAH molecules are chemisorbed on the iron surface. It forms strong chemical bonds. To confirm the improved ability to interact with iron atoms, the interaction energy between the DBPA-Fe (110) surface and the DBPAH-Fe (110) surface can be calculated by using the following equation (E_interaction = E_total − (E_inhibitor − E_surface)).^111,112 For DBPA and protonated (DBPAH), the values are −604.64 kcal mol⁻¹ (−26.22 eV) and −617.32 kcal mol⁻¹ (−26.78 eV), respectively. A more negative DBPAH value indicates a slightly stronger interaction than that of DBPA, probably due to its electronic structure that enhances its bonding to the Fe (110) surface. However, the negative interaction for the DBPA and DBPAH molecules is a strong contributor to surface bonding, forming a protective layer that prevents corrosion of the carbon steel. Accordingly, the protonated molecule (DBPAH) has a strong tendency to adsorb onto the metal surface. The projected density of states (PDOS) method was employed to¹¹³ analyze charge transfer and the nature of the binding of the DBPA and DBPAH molecules on the Fe (110) surface. Fig. 11 illustrates the PDOS spectra before and after adsorption of DBPA in neutral and protonated forms. The analysis indicates that DBPA and DBPAH exhibit molecular states over the range (±6), which signify all 3d iron states and reflect their complete localization.¹¹³ The peaks indicate a significant interaction between DBPA molecules and the surface, confirming that the electronic contributions from the s and p orbitals decrease after adsorption. It accounted for the decrease in PDOS levels after adsorption of DBPA/DBPA forms on the outer layer of the steel, which was attributed to the system's thermodynamic stability. Also, there are changes in peak shape and a reduction in peak intensity for the adsorbed DBPA and DBPAH molecules, due to hybridization of activated sites¹¹⁴ during adsorption. DFTB results indicated the formation of bonds via chemisorption at the interface between iron and the DBPA inhibitor.

Fig. 11. DFTB analysis of the adsorption mechanism of DBPA and DBPAH on an iron (Fe) surface. (Top) Optimized adsorption configurations showing the most stable orientation of DBPA and DBPAH molecules on the Fe slab. (Middle) Projected Density of States (PDOS) spectra for the isolated systems before adsorption. (Bottom) PDOS spectra after adsorption.

3.8. Surface investigation (SEM-EDS)

The carbon steel samples were immersed in a 1 M hydrochloric acid solution for 24 hours. Afterwards, the surface was analyzed using SEM-EDS before and after applying the corrosion inhibitors as shown in Fig. 12. In the absence of BBPA and DBDA inhibitors (Fig. 12A), the corrosion damages the surface and shows visible voids of different sizes and depths. This indicates material loss and a rough surface, with dense corrosion products from the porous layer, including iron oxides that clearly appear on the surface, making it appear more damaged. In the presence of 10 mM BBPA and DBDA inhibitors, surface damage decreases, and fewer pits appear. Fig. 12B shows a surface morphology with relatively fewer defects and a smoother surface. This indicates the formation of a protective layer with dense compaction that minimises surface damage. In contrast, Fig. 12C shows that the protected carbon steel surface is slightly more heterogeneous. It demonstrates that both inhibitors BBPA and DBDA are good protectors of the carbon steel surface. The corresponding EDS spectrum (Fig. 13A) was dominated by iron (83.9 wt%), together with oxygen (10.2 wt%), chloride (3.3 wt%), and C (2.6 wt%). These elements in the corrosion residues result from exposure to a 1 M hydrochloric acid solution. EDS analysis (Fig. 13B) showed high carbon and nitrogen percentages. The carbon content increased from 2.6 wt% in the uninhibited carbon steel to 9.7 wt%, and nitrogen reached 4.4 wt%. No nitrogen was detected on the uninhibited steel carbon surface. Simultaneously, the detected iron contribution decreased from 83.9 to 70.0 wt%. The surface shows increased carbon and clear evidence of nitrogen consistent with adsorption of the DBDA inhibitor. The diminished relative intensity in the iron signal corresponds to surface coverage by a DBDA inhibitor layer. The effect was even more evident in the EDS spectrum (Fig. 13C) obtained in the presence of the BBPA inhibitor. It shows that the surface held 21.0 wt% carbon, 7.6 wt% nitrogen, and 1.1 wt% bromine, while the relative iron contribution dropped significantly to 33.3 wt%. The simultaneous detection of carbon and nitrogen, together with the appearance of bromine, provides evidence that the BBPA inhibitor adsorbed on the carbon steel surface. The significant increase in carbon and nitrogen, along with the reduced iron signal, suggests the formation of a BBPA inhibitor layer in the analyzed area. Importantly, EDS establishes elemental composition, and the present results support both inhibitor adsorption and surface film formation. Moreover, EDS elemental mapping reinforces the compositional findings by showing how the elements are distributed across the analyzed surface, as shown in Fig. 13. For the uninhibited carbon steel, the elemental maps indicate a heterogeneous distribution of iron, along with oxygen and chloride, over the severely affected carbon steel surface. In contrast, specimens with BBPA and DBDA inhibition show more uniform elemental distribution.

Fig. 12. SEM micrographs of steel: (A) after 24 h in 1.0 M HCl; (B) in 1.0 M HCl + 10 mM DBDA; (C) in 1.0 M HCl + 10 mM BBPA.

Fig. 13. EDX spectra of steel: (A) after 24 h in 1.0 M HCl; (B) in 1.0 M HCl + 10 mM DBDA; (C) in 1.0 M HCl + 10 mM BBPA.

3.9. QSAR analysis

The QSAR method has been used to correlate the inhibition efficiencies of BBPA and DBPsA with their molecular configurations in the gas and aqueous phases, as well as with their protonated forms in the aqueous phase. An attempt was made to correlate the experimental corrosion inhibition efficiencies obtained from PDP, EFM, and EIS with the calculated quantum chemical parameters from the DFT approach, as well as from MC and MD methods. Eqn (7) was proposed to calculate and derive equations for predicting inhibition efficiency (IE_cal) from the inhibitory concentration and the key parameters in Tables 5–7.

7

where A and B_n are constants obtained from regression analysis, X_n are the independent variables, and C_n are the inhibitor concentrations. Eqn (7) gives the dependence of the calculated inhibition efficiency on inhibitor concentration. To simplify eqn (7), only the first four terms were used.

8

9

10

11

Eqn (8)–(11) were used to correlate the key parameters with the experimentally determined inhibition efficiency (IE_exp%) of the BBPA and DBPA inhibitors under study. The inhibition efficiencies obtained from electrochemical measurements and the important results obtained from MC and MD simulations were analyzed using multiple regression with eqn (8)–(11) to examine the relationship between the concentration and the theoretical descriptors given in Tables S8–S14. Eqn (9) best fit the experimental data. Table 8 shows that the R² values ranged from 0.9731 to 0.9997, and the RMSE values were low (0.0481–0.2635). The data in Table 8 show that the experimental and calculated inhibition efficiencies are consistent across all three electrochemical methods. Eqn (8) showed lower R² values and a higher RMSE compared to eqn (9). Although eqn (10) improved the fit parameters for some data (Tables S8–S14), the improvement was not consistent enough to justify adopting the higher-order equation⁵⁰ as the common model. Eqn (11) gave a perfect numerical fit. However, this behaviour is expected when fitted to five experimental concentrations. This results from excessive fitting, not improved correlation. The IE_cal% values were not reported separately for the gas, aqueous, protonated, or MC/MD descriptor forms (Table S14), because the theoretical descriptors are constant across the entire concentration series considered for the BBPA and DBDA inhibitors and their states. Therefore, their IE_cal%, R², and RMSE are the same; the results present the calculated efficiencies once to avoid repetition, and this agrees with results that were documented earlier by Shojaie et al.⁴⁹

Table 8. Experimental and calculated inhibition efficiencies for PDP, EFM, and EIS of BBPA and DBPA according to eqn (9).

Inhibitor	C (mM)	IEexp%	IEcal% PDP	IEexp%	IEcal% EFM	IEexp%	IEcal% EIS
BBPA	1	88.67	88.67479	82.88	82.874800	84.81	84.812943
	3	91.72	91.58524	89.77	89.871082	93.1	93.031163
	5	92.72	93.121230	91.92	91.835747	94.44	94.577975
	7	94.18	93.87684	92.98	92.735440	95.24	95.231014
	10	94.45	94.481887	93.20	93.432928	95.78	95.716903
R 2	—	—	0.9875390	—	0.9982107	—	0.9996577
RMSE	—	—	0.2332752	—	0.1621160	—	0.0746276
DBPA	1	91.36	91.352169	84.5	84.510933	90.34	90.341097
	3	92.63	92.812247	91.86	91.612747	93.38	93.350011
	5	94.14	93.779610	92.28	92.727064	94.75	94.835089
	7	94.25	94.263107	93.10	93.173399	95.62	95.561683
	10	94.48	94.652864	93.78	93.495854	96.14	96.142118
R 2	—	—	0.9731170	—	0.9938770	—	0.9994638
RMSE	—	—	0.1965757	—	0.2635321	—	0.0480541

3.10. Corrosion mechanism

The corrosion inhibition performance of BBPA and DBPA toward carbon steel in 1.0 M HCl can be explained by considering the adsorption behavior of the inhibitor molecules at the metal/solution interface. In acidic media, the carbon steel surface becomes negatively charged due to the adsorption of chloride ions from the hydrochloric acid solution. Simultaneously, the Schiff base molecules can exist in both neutral and protonated forms owing to the presence of pyridine and azomethine nitrogen atoms. Therefore, adsorption may occur through both electrostatic interactions (physisorption) and coordinate bond formation (chemisorption). Initially, protonated inhibitor species (BBPAH and DBPAH) are attracted to the steel surface through electrostatic interactions with adsorbed chloride ions, facilitating their approach to the metal interface. Subsequently, the neutral inhibitor molecules adsorb through electron donation from the lone-pair electrons of the nitrogen atoms and the π-electrons of the aromatic rings and azomethine group to the vacant d-orbitals of iron atoms. In addition, back-donation of electrons from the iron surface to the antibonding orbitals of the inhibitor molecules further stabilizes the adsorbed layer. The adsorption process is supported by the Langmuir adsorption isotherm and the calculated values of ΔG_ads (−31 to −35 kJ mol⁻¹), indicating a mixed physisorption–chemisorption mechanism. Quantum chemical calculations revealed that the nitrogen atoms constitute the principal adsorption centers, while the conjugated aromatic framework enhances electron delocalization and adsorption strength. The HOMO and electrostatic potential distributions showed high electron density around the azomethine and pyridine nitrogen atoms, facilitating strong interaction with the steel surface. Monte Carlo and molecular dynamics simulations demonstrated that both inhibitors adsorb preferentially in a nearly parallel orientation on the Fe (110) surface, maximizing surface coverage and interaction area. The adsorption energies and binding energies confirmed the spontaneous and stable adsorption process. DFTB calculations further revealed the formation of strong interfacial interactions between the inhibitor molecules and iron atoms, confirming the contribution of chemisorption to the inhibition mechanism. The superior performance of DBPA compared with BBPA is attributed to the strong electron-donating nature of the dimethylamino substituent, which increases electron density throughout the conjugated molecular framework and enhances charge transfer to the metal surface. In contrast, the bromine substituent in BBPA exerts an electron-withdrawing inductive effect, resulting in comparatively lower adsorption strength. Consequently, DBPA forms a more compact and stable protective film, providing greater resistance to charge transfer and corrosion processes. As a result of adsorption, a dense protective barrier is formed on the carbon steel surface, isolating the metal from aggressive chloride ions and hydronium species, reducing both anodic iron dissolution and cathodic hydrogen evolution reactions. This protective film significantly increases charge-transfer resistance, decreases double-layer capacitance, and ultimately suppresses the corrosion rate of carbon steel in hydrochloric acid solutions. As summarized in Table 9, the inhibition efficiencies of BBPA and DBPA were compared with those of several recently reported corrosion inhibitors under analogous experimental conditions. The results reveal that DBPA achieves protection levels that are on par with or surpass those of the reference compounds, underscoring the effectiveness of the dimethylamino-substituted Schiff base framework.

Table 9. A comparative study of BBPA and DBPA and other related Schiff base molecules from literature.

Compound	Substrate	Medium	Max inhibition efficiency (%)
BBPA	Steel	1.0 M HCl	94.45% (PDP), 92.35% (EIS), 95.78% (EFM)
DBPA	Steel	1.0 M HCl	94.48% (PDP), 88.22% (EIS), 96.14% (EFM)
NVAIP26	Mild steel	1.0 M HCl	92.33%
PT31	Carbon steel	0.1 M HCl	83.3%
PSB8 (ref. 32)	Mild steel	1.0 M HCl	93%
4-DMBPy37	Mild steel	0.1 M HCl	81%

4. Conclusion

In this study, two pyridine-based Schiff bases, BBPA and DBPA, were successfully synthesized and evaluated as corrosion inhibitors for carbon steel in 1.0 M HCl solution. Electrochemical investigations using PDP, EIS, and EFM demonstrated that both compounds exhibit excellent inhibition performance, with efficiencies exceeding 94% at the highest concentration tested. Adsorption studies revealed that the inhibitors follow the Langmuir adsorption isotherm and adsorb on the steel surface through a mixed physisorption–chemisorption mechanism.

Quantum chemical calculations and molecular simulations provided detailed insights into the adsorption behavior and inhibition mechanism. Theoretical results showed that DBPA possesses higher electron-donating ability, lower energy gap, greater softness, and stronger adsorption affinity toward the Fe (110) surface than BBPA. Monte Carlo, molecular dynamics, and DFTB analyses further confirmed the formation of stable adsorbed films and strong inhibitor–metal interactions. SEM observations supported the electrochemical findings by revealing a significant reduction in surface deterioration in the presence of the inhibitors.

Overall, the excellent agreement between experimental and theoretical results demonstrates that both Schiff bases are highly effective corrosion inhibitors, with DBPA exhibiting superior performance. The findings highlight the critical role of electronic substituent effects in controlling adsorption strength and corrosion protection efficiency, providing valuable guidance for the rational design of new Schiff base-based corrosion inhibitors.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The data supporting this study's findings are available upon reasonable request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d6ra05353j.