The route for the synthesis of the two imidazo pyrimidine compounds is shown in Figure 1. Briefly, 0.5 mmol 2-aminobenzimidazole, 0.5 mmol benzaldehyde (or 4-Octylbenzaldehyde), 0.5 mmol phenylacetylene, and 10 mg copper oxide nanoparticles were stirred at 100°C under solvent-free condition until the consumption of 2-aminobenzimidazole. After completion of the reaction, ethanol was added to the reaction mixture, and then the catalyst was separated by centrifugation. The organic layer was concentrated under rotary evaporation to afford the crude product, which was purified by column chromatography. For 2,4-diphenylbenzo [4,5]imidazo [1,2-a]pyrimidine (DPIP), ¹H NMR (CDCl3, 400 MHz) δ 8.24 (br, 2H), 7.91 (d, 1H), 7.66–7.37 (m, 9H), 7.19 (s, 1H), 6.96 (t, 1H, J = 8.24 Hz), 6.62 (d, 1H, J = 8.4 Hz); For 2-(4-octylphenyl)-4-phenylbenzo [4,5]imidazo [1,2-a]pyrimidine (OPIP), ¹H NMR (CDCl3, 400 MHz) δ 8.23 (d, J = 8.24 Hz, 2H), 7.95–7.97 (m, 1H), 7.63–7.72 (m, 5H), 7.44 (t, J = 7.33 Hz, t), 7.34 (d, J = 8.24 Hz, 2H), 7.24 (s, 1H), 7.01 (t, J = 8.01 Hz, 1H), 6.66–6.68 (m, 1H), 2.69 (t, J = 7.79 Hz, 2H), 1.26–1.69 (m, 12H), 0.91 (t, J = 7.33 Hz, 3H);

The mild steel samples used in this study have a chemical composition (% by weight) Fe = 99.13, S = 0.07, P = 0.10, Si = 0.39, Al = 0.02, Mn = 0.07, and C = 0.22. All mild steel samples in this work were polished using 200–2000 grand SiC paper and 0.5 μm Al₂O₃ powder, washed with distilled water, degreased with acetone, and dried in the cool air. HCl solution (1 mol L⁻¹) is obtained by dilution of 37% hydrochloride acid using distilled water. Inhibitor stock solution (1 mmol/L) was prepared by dissolving DPIP and OPIP in a 30% by volume of ethyl alcohol in 1 mol L⁻¹ HCl solution, and the required concentration of inhibitors were prepared by dilution using 1 mol L⁻¹ HCl solution. The amount of ethyl alcohol in all aqueous solution in the presence and the absence of the investigated nutmeg oil were kept constant to remove the effect of the ethyl alcohol on the inhibition efficiency.

A weight loss experiment is a simple method to determine the corrosion rate (CR) of mild steel. The mild steel samples with rectangle shape (50 mm × 25 mm × 2 mm) were immersed in 1 mol L⁻¹ HCl in the absence and presence of each of the studied corrosion inhibitors with different concentrations (from 0.001 to 0.1 mmol L⁻¹) for a period of 3 h at 298, 308, and 318 K. The inhibition performance (η _W %) and surface coverage (θ) were calculated using Eqs. 1 and 2 (Singh et al., 2016): η W ( % ) = C R 0 − C R C R 0 × 100 (1) θ = C R 0 − C R C R 0 (2) where CR ₀ and CR are the CRs without and with different concentrations of DPIP and OPIP, respectively; θ is the degree of surface coverage of DPIP and OPIP.

The electrochemical measurements were carried out with an Ivium workstation; this device is connected to a cell with three electrodes: a working electrode (mild steel sample) with exposure area 1 cm², a reference electrode (saturated calomel electrode), and a counter electrode (platinum sheet). Before the electrochemical test, soak the working electrode in the test solution for 30 min to stabilize the corrosion potential. For potentiodynamic polarization study, the potential sweep ranges from −600 to −100 mV (vs. SCE) with a scan rate of 0.5 mV s⁻¹. Electrochemical parameters such as corrosion potential (E _corr), corrosion current densities (i _corr), and Tafel slopes (β _c, β _a) can be derived by extrapolation of the linear Tafel segments of the polarization curves. Electrochemical impedance spectroscopy (EIS) tests were made in the frequency range of 10⁵–0.01 Hz with an excitation signal of 10 mV.

Corroded mild steel surface obtained after 3 h immersion in the HCl solution with and without the optimal concentration of 0.1 mmol L⁻¹ inhibitors was analyzed using TESCAN VEGA three SBH scanning electron microscope. The accelerating voltage is 20 kV. AFM was done using a Bruker MULTIMODE eight instrument. AFM was conducted using a tapping mode and a 2.5 Hz scan rate. XPS spectra were obtained using the PHI5000-VersaProbe system using Mg Kα radiation as the excitation source.

Some important toxicity endpoints involving developmental toxicity potential (DTP) and mutagenicity (M) were chosen to represent the toxicities. Generally, predicted values from 0.00 to 0.50 represent low toxicity probabilities, while predicted values >0.50 indicate high toxicity probabilities. The LD₅₀ value should be greater than 300 mg/kg (Supplementary Table S1) (Alhaffar, et al., 2019). With careful inspection of the obtained probability values in Supplementary Figure S1, we can affirm that the toxic level of DPIP and OPIP is in the safe area. The probability for biodegradability (B) is 0.595 and 0.610, respectively, which implies that this substance is biodegradable and environmentally friendly.

The inhibitory performance of the studied imidazo pyrimidine derivatives was realized by the weight loss method after 3 h immersions in 1 mol L⁻¹ HCl solution in the presence and absence of the corrosion inhibitors at different temperatures. Table 1 gives the values of the CR and the inhibition efficiency (η _W %).

From Table 1, the results showed that DPIP and OPIP have good corrosion inhibition properties for mild steel in the 1 mol L⁻¹ HCl solution. The anti-corrosion performance gets better with increase in inhibitor concentration. At a concentration of 0.1 mmol L⁻¹, the inhibition efficiency of OPIP and DPIP reached the maximum 94.1% and 93.4%, respectively. This may be because the corrosion process of mild steel in a corrosion solution could be retarded by the adsorption of corrosion inhibitor molecules on the mild steel surface. The high anti-corrosion property of DPIP and OPIP is probably explained by the adsorption of the electron-rich imidazo pyrimidine group and improved with the carbon chain on the benzene ring.

Table 1 clearly shows that the corrosion degree increases with the increase of temperature. The corrosion inhibition efficiency of DPIP and OPIP decreases, which can be interpreted to mean that organic corrosion inhibitor molecules are easier to desorb from the metal surface with the rise of temperature.

The polarization curves without and with different concentrations of OPIP and DPIP in the 1 mol L⁻¹ HCl solution at 298 K are presented in Figure 2. The electrochemical parameters are reported in Table 2.

By analyzing the cathodic and anodic polarization curves in Figure 2, the corrosion inhibitor has a significant impact on the anodic and cathodic processes of corrosion reaction after adding DPIP and OPIP. A decrease in the cathodic current densities can be explained by the reduction of the exposed surface area caused by the adsorption of inhibitor molecules which leads to a reduction of hydrogen evolution reaction, while the decrease in anodic current density is caused by reduced dissolution reaction of mild steel. The inhibition performance of DPIP and OPIP is related to the adsorption on the working electrode surface and the formation of the barrier film (Monticelli et al., 2019). It is well known that the reduction of hydrogen ions needs two consecutive steps (Singh and Quraishi, 2010; El-Taib Heakal et al., 2012). In this work, the cathodic curves conform to the form of the Tafel curve, and the hydrogen evolution reaction on the mild steel surface is carried out based on the pure activation mechanism.

There is no defined trend for the shift of E _corr value. However, if the E _corr value deviates more than ±85 mV from the blank E _corr value, the inhibitor can be classified as a cathodic or anodic inhibitor; otherwise, it can be regarded as a mixed inhibitor affecting cathodic reaction (hydrogen evolution) and anodic reaction (metal dissolution) (Anusuya et al., 2017; Haque et al., 2017; Ouici et al., 2017; Salhi et al., 2017). In this study, the addition of different concentrations of corrosion inhibitors will lead to a slight change in the E _corr value, which is no more than 85 mV compared with the blank E _corr value. Therefore, the undefined trend shift of E _corr for DPIP and OPIP showed a mixed inhibition behavior.

The inhibition efficiencies calculated by the corrosion current density without and with inhibitors at different concentrations are shown in Eq. 11: η i ( % ) = i c o r r 0 − i c o r r i c o r r 0 × 100 (11) where i ⁰ _corr and i _corr are the corrosion current density without and with DPIP and OPIP, respectively. The results give kinetic information of cathodic and anodic reactions. Also, the results match the weight loss method.

EIS was used to obtain information about the mechanism of charge transfer, diffusion, and adsorption between the electrode surface and the studied corrosion inhibitors. Nyquist diagrams of the mild steel immersed in 1 mol L⁻¹ HCl without and with different concentrations of DPIP and OPIP are presented in Figure 3.

It is noted from the Nyquist graphs that the impedance spectra consist of single depressed semicircle capacitive loops, which are caused by the frequency dispersion and the heterogeneity of the electrode surface (Khadiri et al., 2018; El Faydy et al., 2018). The shape of impedance spectra obtained in different electrolyte solutions (containing different concentrations of corrosion inhibitor and blank) are the same, which suggests that the corrosion mechanism of mild steel has not changed, and the radius of capacitive loops increases significantly after increasing the corrosion inhibitor concentration. The behavior of the impedance can be illustrated by adapting an electrochemical equivalent circuit (Figure 3) including a solution resistance (R _s), constant phase element (CPE), and the charge transfer resistance (R _ct) (Pan et al., 2020). The electrochemical parameters are listed in Table 3.

CPE values are calculated using Eq. 12 (Zhang et al., 2012): Z C P E = Q − 1 ( i w ) − n (12) where Q, w, i, and n stand for CPE constant, the angular frequency, imaginary root, and the deviation indicator related to the homogeneity of the work electrode surface, respectively. In addition, double-layer capacitance (C _dl) values are defined using Eq. 13 (Brug et al., 1984): c d l = Q 1 / n ( R s R c t R s + R c t ) ( 1 − n ) / n (13)

The inhibition efficiency was evaluated using the following expression: η R ( % ) = R c t − R c t 0 R c t × 100 (14) where R ⁰ _ct and R _ct mean the charge transfer resistance of blank electrolyte and electrolyte with inhibitors, respectively.

It is observed that the highest R _ct [329.2 (Ω·cm²) for DPIP and 387.8 (Ω·cm²) for OPIP] has been obtained at 0.1 mmol L⁻¹. With the increase of inhibitor concentration in the corrosive medium, the adsorption of inhibitor molecules on the surface of mild steel increases, which means that the exposed surface area of mild steel decreases, the charge transfer resistance increases, and the inhibition efficiency improves. On the other hand, the increase of R _ct value coincides with the decrease of C _dl value of the inhibitors, which can be explained as replacing Cl⁻ ions and H₂O molecules from the mild steel surface with inhibitor molecules. This process reduced the surface reaction of mild steel in the corrosive medium, increasing the resistance to charge and mass transfer (McCafferty and Hackerman, 1972).

The adsorption isotherm gives the chance to better understand the interaction between the inhibitor molecules and the metal surface. Langmuir, Temkin, Freundlich, Flory Huggins, and El Awady adsorption isotherms (Eqs 15–20) are employed to obtain more information about adsorption behavior and the relationship between surface coverage and inhibitor concentration. The values of surface coverage are obtained from the weight loss data. C θ = 1 K a d s + C           L a n g m u i r (15) ln ( θ 1 − θ ) = ln ⁡ K + y ⁡ ln ⁡ C     ( K a d s = K 1 / y )           E l − A w a d y (16) n ( θ C ) = ln ⁡ K a d s + x ⁡ ln ( 1 − θ )           F l o r y − H u g g i n s (17) ln ⁡ θ = ln ⁡ K a d s + Z ⁡ ln ⁡ C           F r e u n d l i c h (18) ln [ ( θ 1 − θ ) × ( 1 C ) ] = − ln ⁡ K a d s + 2 d θ           F r u m k i n (19) θ = − 1 2 a ln ⁡ K a d s − 1 2 a ln ⁡ C           T e m k i n (20)

Analysis of the different isotherms shows that the fitting provided by the Langmuir isotherm has a regression coefficient R ² of 0.999 for DPIP and OPIP at 298 K (Figure 4). The slope of the adsorption isotherm equation is slightly greater than 1 due to the inhomogeneity of the surface.

The values of the adsorption equilibrium constant K _ads can be accessed from the values of the standard free adsorption energies ΔG _ads by the following equality (Zhao et al., 2020): Δ G a d s = − R T ⁡ ln ( 55.5 × K a d s ) (21) where C _H2O is 55.5 mol L⁻¹ in the solution; R is the constant of gases, and T is the temperature.

As we all know, if the value of ΔG _ads is near −20 kJ mol⁻¹ or more positive, it can be regarded as physical adsorption. However, when the value of ΔG _ads is equal to or less than −40 kJ mol⁻¹, it is thought to be chemisorption through the interaction between lone pair electrons in inhibitor molecules and metal surface (Nahle et al., 2018; Rahmani et al., 2019b; Farhadian et al., 2021). In the present work, the values of ΔG _ads are less than −40 kJ mol⁻¹, which shows that the inhibitor molecules are adsorbed on the mild steel surface by strong chemical bonds. Chemical bindings with Fe unfilled orbitals are through the combination of donating lone electron pairs and/or π-electrons of the DPIP and OPIP molecules and Fe empty orbitals (chemical adsorption).

From the weight loss measurement, the inhibitory performance decreased with rising temperature, so in this part, the effort of temperature on the inhibition performance of DPIP and OPIP was studied. The corrosion kinetic process of mild steel in the corrosive solution without and with inhibitors was described by the Arrhenius equation as follows (Khadraoui et al., 2016): C R = k ⁡ exp ( − E a R T ) (22) where k is the frequency factor and E _a is the activation energy. The value of E _a of metal dissolution in the inhibitor-free or inhibitor-containing solution is based on the slope (−E _a/R) of the plot of lnCR∼1/T (Figure 5).

The thermodynamic parameters such as enthalpy and entropy were described by the transition state equation (Khadraoui et al., 2016): C R = R T N a h exp ( Δ S R ) exp ( − Δ H R T ) (23) where ΔH, ΔS, N _a , and h are enthalpy, entropy, Avogadro number, and Planck's constant, respectively. The relationship of ln [CR/T] ∼ 1/T is showed in Figure 6. The values of ΔH and ΔS were obtained with the slope and intercept of the fitted line. The corrosion kinetic process of mild steel in the absent or present inhibitors solutions was described by the Arrhenius equation. The values of ΔH, ΔS, and E _a are listed in Table 4.

As showed in Table 4, the value of E _a for the mild steel in the inhibited solution is higher than that obtained for the uninhibited solution. The value of E _a in the inhibited solution (at least 26.38 kJ mol⁻¹ for DPIP and 26.35 kJ mol⁻¹ for OPIP) is higher than that in the blank solution and is 8.2 kJ mol⁻¹. It is well known that a higher value of the E _a than without inhibitors means that the inhibitors offer a thin adsorption film on the mild steel surface that creates a physical barrier for charge and mass transfer (Kannan et al., 2014). In addition, the activation energy was augmented with the increased inhibitors concentration, indicating that the dissolution rate of mild steel decreased in the corrosive medium (Sliem et al., 2019). The positive value of ΔH reflects that the dissolution process of mild steel in the studied solution is endothermic. Moreover, the difference between E _a and ΔH being greater than 0 also showed that gaseous reduction reaction (hydrogen evolution) occurred in the corrosion process (Zhang et al., 2021). Further analysis found that the average value of E _a − ΔH is about 2.56 kJ mol⁻¹, which is basically consistent with the value of RT (2.57 kJ mol⁻¹), indicating that the corrosion process is a unimolecular reaction (Gomma and Wahdan, 1995). Negative values of ΔS indicate the decrease in disorder. The adsorption process goes from the reagents to the activated complex, and complex compound formation was associated with the rate-determining step (Saady et al., 2021).

The performances of the studied molecules to the migration of corrosive species like Cl⁻, H₃O⁺, and H₂O are investigated with the help of diffusion coefficient values. The MSD is a microscopic parameter that is involved, defined as: M S D ( t ) = [ 1 N ∑ i = 1 N | R i ( t ) − R i ( 0 ) | 2 ] (24) D = 1 6 lim t → ∞ d d x ∑ i N [ | R i ( t ) − R i ( 0 ) | 2 ] (25) where |R _i (t) − R _i (0)|² and N represents the MSD number of target molecules, respectively. The positions of corrosive particles at time t and 0 are given by R _i (t) and R _i (0), respectively.

The MSD curves of Cl⁻, H₃O⁺, and H₂O in the protective film of DPIP and OPIP are shown in Supplementary Figure S3. The magnitude of diffusion coefficients for Cl⁻, H₃O⁺, and H₂O are 0.3222, 0.7830, and 2.3920 × 10^–9 m²/s, respectively (Ehteshamzade et al., 2006). However, the calculated diffusion coefficients for Cl⁻, H₃O⁺, and H₂O decrease significantly in the film of DPIP and OPIP (Supplementary Table S3). This observation reveals that the addition of DPIP and OPIP into the corrosive media generates a protective film over the mild steel surface and creates hindrance in the migration of corrosive species. The reduction in the diffusion coefficient values of OPIP is higher as compared to DPIP, which suggests more protective film formation in the case of OPIP over the metal surface than DPIP. This result further reinforces the superior performance of OPIP than DPIP and supports the experimental finding.

Figure 10 gives the top and side views of the stable adsorption configuration of DPIP and OPIP molecules on the Fe (1 1 0) surface in the presence of chloride ions with the temperatures of 298 K. It can be seen from the figure that the molecules of DPIP and OPIP are adsorbed on the Fe (1 1 0) surface in parallel in the presence of H₂O, H₃O, and Cl⁻. This is due to a high number of active electron donor units in the imidazopyrimidine group, which is easier to adsorb with surface atoms on the mild steel substrate (Hsissou et al., 2020).

The interaction energy (E _interaction) and adsorption energy (E _binding) are employed to measure the interaction and adsorption capacity of DPIP and OPIP with the very fine surface of Fe (1 1 0), respectively. E _interaction and E _binding values are calculated according to the following two equations and listed in Table 5 (Asadi et al., 2019): E int e r a c t i o n = E t o t a l − ( E s u r f a c e + s o l u t i o n + E i n h i b i t o r ) (26) E b i n d i n g = − E int e r a c t i o n (27)

The high absolute value of interaction and binding energy indicates the ability to replace the corrosive ions and H₂O molecules to form a protective layer against the corrosive medium (Guo et al., 2017; Rbaa et al., 2019). In this work, the interactions with the Fe (1 1 0)/OPIP interface are greater compared to interactions with the Fe (1 1 0)/DPIP interface, which is due to the carbon chain effect, so that leads to an increase in interactions at the interface. The data in Table 5 show that the E _binding value of OPIP is higher than that of DPIP, indicating the higher adsorption capacity of the compound.