1 Introduction

The importance of protection against corrosion in acidic solutions has been increased by the fact that iron materials, which are more susceptible to be attacked in aggressive media, are the commonly exposed metals in industrial environments. Hydrochloric acid, for example, is often used as a pickling acid for iron and its alloys to remove undesirable corrosion products. The chemical acid cleaning will cause metal corrosion upon the already cleaned surface after the elimination of the corrosion products. Corrosion inhibitors efficiently reduce the undesirable destructive effect and prevent metal dissolution [1].

Acid inhibitors are essentially used in metal finishing industries, acidizing of oil wells, cleaning of boilers, and heat exchangers. The efficiency of an inhibitor is largely dependent on its adsorption on the metal surface, which consists of replacement of humidity by the organic inhibitor [2]. Most well-known inhibitors are organic compounds containing hetero atoms such as nitrogen, sulfur, and/or oxygen atoms [3, 4]. In addition, many N-heterocyclic compounds have been demonstrated as effective inhibitors against corrosion of metals and alloys in acid solutions [5,6,7]. The use of organic compounds as inhibitors is one of the most widely used methods for protecting materials from corrosion [8, 9]. Recently, many workers have reoriented their attention to the development of new corrosion inhibitors based on organic compounds such as imidazopyridine [10], imidazole [11, 12], Triazepine Carboxylate [13], and tetrazole [14, 15]. Most organic compounds inhibit corrosion via adsorption on the metal surface. The adsorption of these molecules depends mainly on certain physicochemical properties of the inhibitor molecule such as functional groups, steric factors, aromaticity, electron density at the donor atoms and π orbital character of donating electrons [16, 17], the electronic structure of the molecules [18, 19], and so on.

In this study, we will focus on the efficiency of non-toxic imidazole derivatives as iron corrosion inhibitors in hydrochloric acid and, indeed, the corrosion inhibiting behavior of (2(-4(chloro phenyl-1H-benzo[d]imidazol)-1-yl)) phenylmethanone on ordinary iron in 5 M HCl solution. The aim of this work is devoted to study the inhibition characteristics of this compound for acid corrosion of ordinary steel using both potentiodynamic polarization and electrochemical impedance spectroscopy (EIS). The impedance spectra obtained from this study are analyzed to show the equivalent circuit that fits the corrosion data, also the adsorption behavior of these series is examined. In addition, Correlation between the quantum chemical calculations and molecular structure was discussed using density functional theory (DFT).

2 Experimental Procedure

2.1 Materials

Corrosion tests were performed on ordinary steel which had the following chemical composition by wt % (the rest is ordinary steel balance): C 0.11, Si 0.24, Mn 0.47, Cr 0.12, Mo 0.02, Ni 0.10, Al 0.03, Cu 0.14, Co < 0.0012, V < 0.003, W0.06. The steel specimens used have a rectangular form of 4.0 cm × 1.0 cm × 0.05 cm. The specimen’s surface was prepared by polishing with emery paper at different grit sizes (from 60 to 1200), rinsing with distilled water, degreasing in ethanol, and drying at hot air. The aggressive solution of 5.0 M HCl was prepared by dilution of analytical grade 35% HCl with distilled water. Our inhibitory molecule is shown in Fig. 1.

Fig. 1
figure 1

Chemical structure of (2-(-4(chloro phenyl-1H-benzo[d]imidazol)-1-yl)phenyl)methanone (CBIPM)

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2.2 Electrochemical Cell and Methods

2.2.1 Potentiodynamic Polarization Measurement

The working electrode was pressure-fitted into (2(-4(chloro phenyl-1H-benzo[d]imidazol)-1-yl)phenyl)methanone (CBIPM) exposing only 1 cm2 of area to the solution. Platinum and saturated calomel were used as counter and reference electrode (SCE), respectively.

These three electrodes are connected with the potentiostat/galvanostat (P G Z100) related to a computer with analysis software model (Volta master 4). The latter will display the results, namely the Tafel curves and electrochemical impedance diagrams. The ordinary steel was emerged in different concentrations of the test solution during 25 min stabilizing the electrochemical system until a steady-state of the open circuit potential (Eocp).

The potentiodynamic polarization curves were recorded by changing the electrode potential automatically from negative values to greater ones versus Ecorr (from − 900 to − 100 mV/SCE) using a potentiostat/galvanostat type PGZ 100, at a scan rate of 1 mV/s.

The test solution was thermostatically controlled at ordinary temperature in air atmosphere. The corrosion inhibition efficiency is evaluated from the corrosion current densities values using the relationship:

$${\eta _{{\text{pp}}}}\% =\left[ {{\raise0.7ex\hbox{${(i_{{{\text{corr}}}}^{0} - {i_{{\text{corr}}}})}$} \!\mathord{\left/ {\vphantom {{(i_{{{\text{corr}}}}^{0} - {i_{{\text{corr}}}})} {i_{{{\text{corr}}}}^{0}}}}\right.\kern-0pt}\!\lower0.7ex\hbox{${i_{{{\text{corr}}}}^{0}}$}}} \right] \times 100$$
(1)
$$\theta =\left[ {{\raise0.7ex\hbox{${(i_{{{\text{corr}}}}^{0} - {i_{{\text{corr}}}})}$} \!\mathord{\left/ {\vphantom {{(i_{{{\text{corr}}}}^{0} - {i_{{\text{corr}}}})} {i_{{{\text{corr}}}}^{0}}}}\right.\kern-0pt}\!\lower0.7ex\hbox{${i_{{{\text{corr}}}}^{0}}$}}} \right],$$
(2)

where i0corr and icorr are the corrosion current densities values without and with inhibitor, respectively. And θ is surface coverage.

2.2.2 Electrochemical Impedance Spectroscopy Measurements (EIS)

The electrochemical impedance spectroscopy measurements are carried out using a transfer function analyzer PGZ100 electrochemical system (Voltalab PGZ100, Radiometer Analytical), over the frequency range from 100 to 0.1 Hz with 10 points per decade. The applied amplitude of AC signal is 10 mV/ms. All experiments are performed at the open circuit potential. The obtained impedance data are analyzed in term of equivalent electrical circuit using Bouckamp’s program [20].

The inhibiting efficiency derived from EIS (ηimp) is also added in Table 2 and calculated using the following equation:

$${\eta _{{\text{imp}}}}\% =\frac{{{R_{{\text{ct}}}} - R_{{{\text{ct}}}}^{0}}}{{{R_{{\text{ct}}}}}} \times 100,$$
(3)

where R0ct and Rct are the polarization resistance values in the absence and the presence of inhibitor, respectively.

2.3 UV–Visible Spectroscopy

Spectrophotometric method was carried out on the prepared ordinary steel samples after immersion in 5 M HCl with and without addition of 10−3 M of CBIPM at 298 K for 8 days. All the spectra measurements were carried out using a Beckman DU640 UV/Vis spectrophotometer.

2.4 Quantum Chemical Calculations

Theoretical calculations of the investigated molecules were performed in order to determine a relationship between some quantum chemical parameters obtained from the structure of our compound and the inhibition efficiencies of corrosion obtained experimentally [21, 22]. In this purpose, we have adopted the DFT (B3LYP) method using the 6-31G basis (d, p), and the calculation is done using a Gaussian software 09W [23,24,25]. The geometric optimization of the CBIPM inhibitor was carried out in the gaseous phase.

The various molecular quantum parameters such as electronegativity (χ), electronic affinity (A), ionization potential (I), and gap energy (ΔEgap) are expressed by the following relations [26,27,28,29]:

$$\Delta {E_{{\text{gap}}}}={E_{{\text{LUMO}}}} - {E_{{\text{HOMO}}}}$$
(4)
$$A= - \,{E_{{\text{LUMO}}}}$$
(5)
$$I= - \,{E_{{\text{HOMO}}}}$$
(6)
$$\chi =\frac{{I+A}}{2},$$
(7)

where EHOMO is the energy of the highest occupied molecular orbital and ELUMO is the energy of the lowest vacant molecular orbital.

The overall hardness η and the chemical softness σ are given by the following equations [30]:

$$\eta =\frac{{\Delta {E_{{\text{gap}}}}}}{2}$$
(8)
$$\sigma =\frac{1}{\eta }.$$
(9)

The global electrophile index ω was introduced by Parr [31] and is given by

$$\omega =\frac{{{\mu ^2}}}{{2\eta }},$$
(10)

where µ is the electronic chemical potential, such as \(\mu = - \,{\chi ^2}\).

This index measures the propensity of chemical species to accept electrons. A good more reactive nucleophile is characterized by a lower value of µ, ω.

The number of transferred electrons (ΔN) was calculated as follows [32]:

$$\Delta N=\frac{{{\chi _{{\text{Fe}}}} - {\chi _{{\text{inh}}}}}}{{2\left( {{\eta _{{\text{Fe}}}}+{\eta _{{\text{inh}}}}} \right)}},$$
(11)

where χFe and χinh, respectively, represent the absolute electronegativity of iron and the inhibitor molecule, ηFe and ηinh denote, respectively, the absolute hardness of iron and the molecule of inhibitor. The theoretical value of χFe = 7.0 eV and ηFe = 0 is used to calculate the number of electrons transferred [33].

3 Results and Discussion

3.1 Concentration Effect

3.1.1 Tafel Polarization Study

Figure 2 shows anodic and cathodic polarization plots recorded on ordinary steel electrode in 5 M HCl in the absence and presence of different concentrations of CBIPM inhibitor. Electrochemical corrosion parameters, such as corrosion potential Ecorr (mV/SCE), cathodic βc Tafel slope (mV/dec), the corrosion current density icorr (µA cm−2), and inhibition efficiency ηPP (%), are given in Table 1.

Fig. 2
figure 2

Potentiodynamic polarization curves of ordinary steel in 5.0 M HCl solution containing different concentrations of CBIPM at 298 K

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Table 1 Electrochemical parameters of ordinary steel in 5.0 M HCl solution in the absence and presence of different concentrations of CBIPM
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It is clear from Fig. 2 that the addition of the CBIPM reduces both the cathodic and the anodic currents and therefore hinders the acid attack of the mild steel electrode in 5.0 M HCl. The cathodic Tafel curves obtained in Fig. 2 indicate that the hydrogen evolution is activation-controlled and the reduction mechanism is not affected by the presence of inhibitor [34]. The inhibitor molecule is first adsorbed on the ordinary steel surface and blocking the available reaction sites.

From Table 1, it is clear that the icorr values decrease considerably with the increase of the concentration of CBIPM. Accordingly, ηPP (%) values increase with increasing the inhibitor concentration reaching a maximum value of 98.6% with 10−3 M of CBIPM.

So, the high inhibition efficiency for CBIPM was attributed to the presence of electron donor groups Chloro phenyl in their structure. The adsorption of CBIPM on the metal surface can occur either directly on the basis of donor–acceptor interactions between the π-electrons of the ring and the vacant d-orbital of ordinary steel surface atoms or an interaction of organic nitrogen compounds with already adsorbed groups as proposed in the literature [35].

As shown in Table 1, the corrosion potential values were comparable, with the variation in Ecorr between the absence and presence of the inhibitor being < 85 mV, thus allowing the inhibitor to be defined as a mixed type inhibitor [36, 37].

3.1.2 Electrochemical Impedance Spectroscopic Studies

The corrosion behavior of mild steel in 5.0 M HCl solution in the absence and presence of different concentrations of CBIPM is also investigated by EIS method at Ecorr and at 298 K after 30 min of immersion. The representative Nyquist plots is shown in Fig. 3 and its extracted parameters are presented in Table 2. It is noted that the Nyquist plot of ordinary steel in the absence and presence of inhibitor contains a slightly depressed semi-circular shape and only one time constant appeared indicating that the ordinary steel corrosion is mainly controlled by a charge transfer process. In this case, the equivalent electric circuit, showed in Fig. 4 with one time constants was proposed to reproduce these results by non-linear regression calculation. However, it is seen that the Rct values increased and Cdl values decreased with inhibitor concentration. These can be due to the decrease in local dielectric constant and/or increase in thickness of the electrical double layer, suggesting that CBIPM acts via adsorption at the metal/solution interface [38, 39].

Fig. 3
figure 3

Nyquist plots for ordinary steel in 5.0 M HCl solution in the absence and presence of different concentrations of CBIPM

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Table 2 Electrochemical data of EIS for ordinary steel in 5.0 M HCl in the absence and presence of different concentrations of CBIPM
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Fig. 4
figure 4

Electrical equivalent circuits used for modeling the metal/solution interface

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Double layer capacitance values were obtained at maximum frequency (fmax) at which the imaginary component of the Nyquist plot is maximum and calculated using the following equation [40]:

$${C_{{\text{dl}}}}=\frac{1}{{2\pi {f_{\hbox{max} }}{R_{{\text{ct}}}}}}.$$
(12)

3.2 Effect of Temperature

The study of the effect of temperature on the corrosion rate and inhibition efficiency facilitates the calculation of kinetic and thermodynamic parameters for the inhibition and the adsorption processes. These parameters are useful in interpreting the type of adsorption by the inhibitor. To calculate the activation energies and to investigate the mechanism of inhibition of the corrosion process, potentiodynamic polarization measurement (Figs. 5, 6) was taken at various temperatures in the presence and absence of 10−3 M of CBIPM. The related electrochemical parameters are presented in Table 3. This table represents the variation of current densities (icorr) of ordinary steel corrosion in 50.0 M HCl in the absence and presence of optimum concentration of the studied compound at different temperatures (298–328 K).

Fig. 5
figure 5

Potentiodynamic polarization curves for ordinary steel in 5.0 M HCl at different temperatures without inhibitor

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Fig. 6
figure 6

Potentiodynamic polarization curves for ordinary steel in 5 M HCl with 10−3 M of CBIPM at different temperatures

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Table 3 Electrochemical parameters of ordinary steel in 5 M HCl in the absence and presence of 10−3 M of CBIPM Mat different temperatures
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The results show that icorr in acid medium increases with increasing solution temperature, while the IE% decreases remarkably in the range of the studied temperature for acid medium, which is attributed to increase in the kinetic energy and decrease in the adsorption ability of organic compound at elevated temperature [41].

The activation parameters for the corrosion process were calculated from Arrhenius-type plot according to the following equations [42]:

$${i_{{\text{corr}}}}=A{e^{\frac{{ - {E_a}}}{{RT}}}}$$
(13)
$$~\ln \left( {\frac{{{i_{{\text{corr}}}}}}{T}} \right)=\left[ {\ln \left( {\frac{R}{{h{N_a}}}} \right)+\left( {\frac{{\Delta {S_a}}}{R}} \right)} \right] - \frac{{\Delta {H_a}}}{{RT}},$$
(14)

where Ea is the apparent activation corrosion energy, A is the Arrhenius factor, h is the Plank’s constant, N is the Avogadro’s number, ΔHa and ΔSa are the enthalpy and the entropy changes of activation corrosion energies for the transition, respectively. R is the perfect gas constant.

The apparent activation energy was determined from the slopes of ln icorr vs 1000/T graph given in Fig. 7. A plot of ln (icorr/T) against 1000/T (Fig. 8) gave a straight line with slope (ΔHa/R) and intercept (ln(R/Nh) + (ΔSa/R)), from which the values of ΔHa and ΔSa were calculated and are listed in Table 4.

Fig. 7
figure 7

Arrhenius plots of ordinary steel in 5.0 M HCl without and with 10−3 M of CBIPM

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Fig. 8
figure 8

Transition Arrhenius plots of ordinary steel in 5.0 M HCl in the absence and presence of CBIPM

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Table 4 The values of activation parameters Ea, ∆Ha, and ∆Sa for mild steel in 5.0 M HCl without and with different concentrations of CBIPM
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The increase in activation energy (Ea) of inhibited solutions compared to the blank solution suggests that inhibitor is physically adsorbed on the corroding electrode surface, whereas either unchanged or lower energy of activation in the presence of inhibitor suggests chemisorptions [43].

Inspection of these data reveals that the thermodynamic parameters ΔHa and ΔSa of dissolution reaction of ordinary steel in 5.0 M HCl in the presence of CBIPM are higher than in the absence of inhibitor. The positive sign of enthalpies reflect the endothermic nature of steel dissolution process meaning that dissolution of steel is difficult [44, 45]. The increase in Ea in the presence of CBIPM may be interpreted as chemical adsorption. This phenomenon suggested that a decrease in randomness occurred on going from reactants to the activated complex. The great negative values of entropies indicate that the activated complex in the rate determining step is an association rather than dissociation step meaning that a decrease in disordering takes place on going from reactants to the activated complex [46, 47].

3.3 Adsorption Isotherm

The corrosion inhibition of metals as organic compounds was explained by their adsorption which possibly involves two types of interaction with metallic surface (physisorption, chemisorption). So, the adsorption process depends upon the charge and the nature of the metal surface, the chemical structure of inhibitor, and the electrolyte type [48]. Hence, the physisorption involves weak undirected interactions due to electrostatic attraction between inhibitor and the charge of metallic surface. However, the chemisorption process involves charge sharing or charge transfer from the inhibitor molecules to vacant d-orbitals of the metal surface in order to form a coordinate type bond [49].

However, several adsorption isotherms are usually used to describe the adsorption process, including Temkin, Frumkin, Parsons, and Flory–Huggins [50,51,52,53]. The best fit is obtained with the Langmuir isotherm. The Langmuir adsorption isotherm is given by [54]

$$\frac{{{C_{{\text{inh}}}}}}{\theta }~=\frac{1}{{{K_{{\text{ads}}}}}}+{C_{{\text{inh}}}},$$
(15)

where Cinh is the equilibrium inhibitor concentration and Kads is the adsorptive equilibrium constant.

The plots of Cinh/θ against Cinh at different temperatures are presented in Fig. 9. They give the straight lines indicating the adsorption of CBIPM on ordinary steel surface obeys to the Langmuir adsorption isotherm.

Fig. 9
figure 9

Plot of Langmuir adsorption isotherm of CBIPM on the ordinary steel surface at 298 K

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Thermodynamic parameters including the heat of adsorption, free energy of adsorption, and entropy of adsorption are important in the explanation of the corrosion inhibition mechanism. The free energy of adsorption (ΔGads) can be obtained from the equation [55]:

$${K_{{\text{ads}}}}=\left( {\frac{1}{{55.5}}} \right)\exp \left( { - \frac{{\Delta G_{{{\text{ads}}}}^{0}}}{{RT}}} \right),$$
(16)

where R is gas constant, T is absolute temperature of experiment, and the constant value of 55.5 is the concentration of water in solution in mol l−1.

As it can be seen from Table 5, the addition of inhibitors causes negative values of ΔGads, indicating that adsorption of studied CBIPM is a spontaneous process [56]. It is generally accepted that when the values of ΔGads are greater than − 20 kJ mol−1, the type of adsorption is regarded as physisorption, the inhibition acts due to the electrostatic interactions between the charged molecules and the charged metal, while when values around − 40 kJ mol−1 or lower, the type of adsorption is seen as chemisorption, which is due to the charge sharing or a transfer from the inhibitor molecules to the metal surface to form a covalent bond [57, 58]. The values of ΔGads in our measurements are − 46.52 KJ/mol (Table 5), which suggests that the adsorption of CBIPM inhibitor involves a chemisorption interaction.

Table 5 Thermodynamic parameters for the adsorption of CBIPM on ordinary steel in 5.0 M HCl
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3.4 UV–Visible Spectroscopy

A substantial support for the formation of metal complex is often obtained by UV–visible spectroscopic investigation. Since there is often a certain quantity of metal cation in the solution that is first dissolved from the metal surface, such procedures were conducted in the present work to confirm the possibility of the formation of [CBIPM-Fe2+] complexes as described in the literature [59]. Furthermore, the change in position of the absorbance maximum and change in the value of absorbance indicate the formation of a complex between two species in solution [60]. In order to confirm the possibility of the formation of CBIPM-Fe complex, UV–visible absorption spectra obtained from 5.0 M HCl solution containing 10−3 M CBIPM before and after 6 days of ordinary steel immersion are shown in Fig. 10. The electronic absorption spectra of CBIPM before the steel immersion display a band of a high wavelength in the range of 200–340 nm due to the π–π* transition of aromatic ring of compound and a short band at around 500 and 520 nm which is attributed to a n–π* electronic transition involving the lone pair of electrons on the chlorophenyl benzo[d]imidazol nitrogen atom. After 6 days of steel immersion, it is evident that there is a remarkable translation of the curve to the right (from 340 to 400 nm) and it is clearly seen that the band in the region of 500–520 nm has been completely disappeared, indicating that the (Chloro phenyl) groups are strongly held up in the complex with Fe. In the mean time, there is an increase in the absorbance of this band. These experimental findings give strong evidence for the possibility of the formation of a complex between Fe2+ cation and CBIPM in HCl [61, 62].

Fig. 10
figure 10

UV–visible spectra of the solution containing 5.0 M HCl (10−3 Mol/l) CBIPM before (black) and after 6 days of ordinary steel immersion (red). (Color figure online)

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3.5 Quantum Chemical Studies Using Density Functional Theory (DFT)

3.5.1 Calculation of the Main Quantum Parameters

The experimental study was completed by a theoretical study at the B3LYP/6-31G (d, p) level in order to correlate the results obtained from the experimental study with the structure and electronic properties of the inhibitor CBIPM. For this purpose, we will present the results of the theoretical study of the molecule CBIPM, which allowed us to identify a number of structural and electronic parameters of inhibitor used in this work such as the energy of the highest occupied molecular orbital (EHOMO), the energy of the lowest unoccupied molecular orbital (ELUMO), the energy gap between the HOMO and the LUMO (ΔEgap), the ionization potential (I), electron affinity (A), dipole moment (µ), electronegativity (χ), global hardness (η), charge transfer rate (ΔN), and partial natural populations of Mulliken.

HOMO energy is often associated with the molecule’s ability to give away its electrons to suitable vacant orbital. Thus, the HOMO high energy values of the inhibitor indicate its tendency to give electrons to an acceptor having an empty or vacant orbital molecular. The increase in EHOMO values facilitates adsorption by influencing the transfer process through the adsorbed layer. On the other hand, LUMO gives information on the acceptance of electrons in the molecule. The decrease in the ELUMO value is an indicator of the molecule’s ability to accept electrons from the surface of iron. And as it is well known in the literature, a good corrosion inhibitor is often the one that not only yields its electrons but also capable of accepting the electrons of the metal surface; the lower the ELUMO is, the higher the inhibitory efficiency is [63]. The adsorption performance between the inhibitors and the metal surface increases when ΔEgap decreases because the energy to remove an electron from the lowest occupied orbital will be low [64]. Molecular optimization, electron density distributions of the boundary molecular orbitals, HOMO and LUMO of the CBIPM inhibitor are presented in Fig. 11. From Fig. 11, it can be seen that the electron density of the HOMO site is located on the chemical surface of the inhibitor (2-(4-chlorophenyl)-1H-benzo[d]imidazol-1-yl) CBIPM. On the other hand, the electron density of the unoccupied molecular orbital (LUMO) is distributed on the chemical surf of phenyl methanone of the inhibitor CBIPM. The calculated quantum parameters are summarized in the following Table 6.

Fig. 11
figure 11

Optimized molecular structure (a), HOMO (b) and LUMO (c) of the inhibitory molecule CBIPM using DFT/B3LYP/6-31 G (d, p)

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Table 6 Calculated chemical quantum parameters of CBIPM
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The data grouped in Table 6 show that the CBIPM inhibitor has a high HOMO (− 5.981 eV) energy and a low LUMO energy (− 2.076 eV), as well as a low energetic difference value ΔEgap (3.905 eV) between EHOMO and ELUMO, which reinforces its inhibitory action on the surface of the metal.

The dipole moment (µ) is the parameter most used to describe the polarity of a molecule [64]. It is defined as the charge product in the atom and the distance between two polar covalent bonds. However, the total dipole moment reflects only the global polarity of the molecule. It is clearly proved in the literature that molecules with high dipole moments are more reactive. In our study, the value of the dipole moment of CBIPM is 5.195 Debyes.

On the other hand, chemical hardness (η) and softness (σ) are important chemical properties for measuring molecular stability and reactivity; the results of these two parameters are also listed in Table 6. The inhibitory efficiency of adsorption of the inhibitor studied increases with chemical reactivity; normally the molecule with the smallest hardness value should have the greatest inhibition efficiency [66]. The CBIPM inhibitor has good chemical reactivity with the surface of the metal due to the increase in the softness value (σ = 0.512 eV−1) and the decrease in hardness (η = 1.952 eV).

The fraction of electrons transferred from the inhibitor molecule to the metal surface (ΔN) was also calculated in this work. According to the Lukovits study [67], if the value of ΔN < 3.6, the inhibitory efficacy is judged to be good. In our case, the charge transfer rate is equal to ΔN = 0.761 eV, and it is lower than the limit value set by Lukovits. It can be concluded that the inhibitor CBIPM has an inhibitory effect against corrosion of the metal.

3.5.2 Calculation of the Atomic Loads of Mulliken

It has been reported that the more negative the atomic charges of the adsorbed center are, the more easily the atom gives away its electrons to the unoccupied orbital of the metal [68]. The distribution of the Mulliken charges and the orientation of the polar moment are shown schematically in Fig. 12.

Fig. 12
figure 12

Mulliken charge distribution of the CBIPM inhibitor

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The values of the charges distribution are also grouped in Table 6.

From Fig. 12 and Table 7, it can be seen that the nitrogen, oxygen, and some carbon atoms have high charge densities. The regions of the greatest electronic densities are generally the sites where electrophiles can attack [69]. Thus, N, O, and some C atoms are the active centers that have the greatest ability to bind to the surface of the metal. On the other hand, some carbon atoms carry positive charges where nucleophiles can attack. Therefore, caffeine can accept iron electrons through these atoms, and these observations can be confirmed by the study of the Fukui indices.

Table 7 Mulliken charge distribution of CBIPM inhibitor
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3.5.3 Study of the CBIPM Inhibitor’s Local Reactivity by Using the Fukui Indices

The inhibitory molecules adsorb on the metal surfaces by donor–acceptor interactions. This means that it is essential to analyze the atoms in the molecule that participate in this type of interaction. The condensed form of Fukui functions in a molecule with N electrons has been proposed by Yang and Mortier [70]:

$$f_{k}^{+}={P_k}(N+1) - {P_k}(N)\quad {\text{For nucleophilic attack}}$$
(17)
$$f_{k}^{ - }={P_k}(N) - {P_k}(N - 1)\quad {\text{For electrophilic attack}}$$
(18)
$${P_k}\left( N \right):{\kern 1pt} \;{\text{Electronic population of the atom k in the neutral molecule}}.$$
$${P_k}\left( {N{\text{+}}1} \right):\;{\text{Electron population of the atom k in the anionic molecule}}.$$
$${P_k}\left( {N - 1} \right):\;{\text{Electron population of the atom k in the cationic molecule}}.$$

Here \(f_{k}^{+}\) and \(f_{k}^{ - }\) represent the ability of the k atom to react with a nucleophile and electrophile, respectively. The high value of \(f_{k}^{+}\) shows that the k atom has an electrophilic character indicating a high probability for a nucleophilic attack at that site. On the other hand, a high value of \(f_{k}^{ - }\) means that the k-site is more nucleophilic and available for electrophilic attacks [71]. The calculated Fukui indices for the CBIPM inhibitor are shown in Table 8.

Table 8 Fukui indices calculated for the CBIPM inhibitors using DFT/B3LYP/6-31 G (d, p)
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The results of Table 8 show that the CBIPM inhibitor possesses the greatest values of \(f_{k}^{+}\), and these values are located on the atoms N9, C17, O18, C20, C22, and C24. These atoms participate in the acceptance of electrons from the metal surface. On the other hand, the atoms C2, C4, and Cl16 are electron donors as atoms possess higher \(f_{k}^{ - }\) values. The theoretical results were found to be consistent with the experimental results of inhibition of metal corrosion by the CBIPM inhibitor.

4 Conclusion

The examined CBIPM is an effective corrosion inhibitor for ordinary steel in 5.0 M HCl solution. The potentiodynamic polarization curves indicated that these compounds act as mixed type inhibitors and their inhibition efficiencies increased with their concentrations to reach a maximum at 10−3 M. It is found also that the mechanism of the hydrogen reduction and the iron dissolution reactions change by the inhibitor addition. It acts by adsorption mechanism at the metallic surface and its inhibition depended on the nature of the N–H presented in their structures and the CBIPM compound is the best inhibitor. In addition, the inhibition efficiency decreased slightly with temperature. The thermodynamic study indicated that CBIPM can be acted by chemical adsorption at the metallic surface. The EIS measurements indicated that the plots were composed by one capacitive loop. The inhibition efficiencies of the studied compound were confirmed by all techniques’ measurements. On the other hand, it was interesting to study the action mode of these compounds using UV–visible spectroscopy analysis techniques; it provided information about the nature of adsorption of CBIPM on the metallic surface. It could be interesting also to study the effect of these compounds on the corrosion of another metal in another acidic medium such as H2SO4 and H3PO4.