Introduction

The search and application for new and efficient corrosion inhibitors is necessary to secure metallic materials against corrosion. The selection of appropriate inhibitors mainly depends on the formulation as well as rational use in various environments. The electronic characteristic of the adsorbate molecules, the solution chemical composition, the nature of the metallic surface, the temperature of the reaction, the immersion time and the electrochemical potential at the metal–solution interface determine the adsorption degree and hence the inhibition efficiency [1].

Most of the efficient inhibitors used in industry are organic compounds having multiple bonds in their molecules, which mainly contain nitrogen and sulfur atoms through which they are adsorbed on the metal surface. Among these, several triazoles [2, 3], pyrazoles [4], imidazoles [5–8], pyridazines [9–11], etc. have been among the best known and the most studied inhibitors. Notwithstanding several structural similarities with some of the above-mentioned compounds, the tetrazole [12–14] and indoline [15, 16] derivatives have been scarcely studied as mild steel corrosion inhibitors.

The aim of the present work is to study the inhibition efficiencies of N-(cyanomethyl) benzamide (BENZA) and N-[(1H-tetrazol-5-yl)methyl]benzamide (BENZA-TET) on mild steel corrosion in 1 M HCl using potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS). The effect of immersion time and temperature on the inhibition efficiency was investigated. In addition to traditional techniques such as electrochemical, a quantum chemical method has been employed in this study. Invaluable quantum chemical parameters such as higher occupied molecular orbital (HOMO), lower unoccupied molecular orbital (LUMO), dipole momentum (μ) and total energy (TE) were obtained by this method, and help to understand the adsorption properties by considering the structure of N-(cyanomethyl)benzamide (BENZA), which is the best inhibitor.

Experimental details

Material preparation and inhibitors

Corrosion tests were performed on a mild steel which had the following chemical composition (wt%): 0.21 % C; 0.09 % P; 0.38 % Si; 0.01 % Al; 0.05 % Mn; 0.05 % S; and the remainder iron. The specimen’s surface was prepared by grinding with emery paper at different grit sizes (from 180 to 1,200), rinsing with distilled water, degreasing in ethanol, and drying before use. The aggressive solution of 1 M HCl was prepared by dilution of analytical grade 37 % HCl with distilled water.

The structural formulas of the examined inhibitors in this study are shown in Fig. 1.

Fig. 1
figure 1

Names and chemical structures of the organic compounds investigated

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Electrochemical measurements

For electrochemical measurements, the electrolysis cell was a borrosilcate glass (Pyrex®) cylinder closed by a cap with five apertures. Three of them were used for the electrode insertions. The working electrode was pressure-fitted into a polytetrafluoroethylene holder (PTFE) exposing only 1 cm2 of surface to the solution. Platinum and saturated calomel were used as counter and reference electrode (sce), respectively. All potentials were measured against this electrode.

The polarization curves were recorded by changing the electrode potential automatically from negative values to positive values versus E corr using a Potentiostat/Galvanostat type PGZ 100, at a scan rate of 1 mV/s after 1 h of immersion time until reaching steady state. The test solution was thermostatically controlled at 298 K in air atmosphere without bubbling.

The evaluation of corrosion kinetics parameters was obtained using a non-linear regression calculation according to the Stern–Geary equation:

$$ i = i_{\text{corr}} \cdot \left\{ {{ \exp }\left[ {b_{\text{a}} \cdot \left( {E - E_{\text{corr}} } \right)} \right] - { \exp }\left[ {b_{\text{c}} \cdot \left( {E - E_{\text{corr}} } \right)} \right]} \right\} $$
(1)

where i corr stands for the corrosion current density, and b a and b c are, respectively, the Tafel constant of anodic and cathodic reactions.

The inhibition efficiency was then evaluated from i corr values determined using the following relationship:

$$ E_{I} \,\% = \frac{{i_{\text{corr}}^{ 0} - i_{\text{corr}} }}{{i_{\text{corr}}^{ 0} }} \times 1 0 0 $$
(2)

where the superscript 0 indicates the corrosion current densities relative to that determined in the absence of inhibitor.

The surface coverage values (θ) have been obtained from polarization curves for various concentrations of inhibitors using Eq. (3) [17]:

$$ \theta = 1 - \frac{{i_{\text{corr}} }}{{i_{\text{corr}}^{ \circ } }} $$
(3)

The electrochemical impedance spectroscopy measurements were carried out using a transfer function analyzer (VoltaLab PGZ 100; Radiometer Analytical), with a small amplitude ac signal (10 mV rms), over a frequency domain from 100 kHz to 10 mHz with ten points per decade. The impedance diagrams were given in the Nyquist representation. In order to ensure reproducibility, all experiments were repeated three times. The evaluated inaccuracy did not exceed 10 %. The results were then analyzed in terms of equivalent electrical circuit using Bouckamp’s program [18]. The inhibition efficiency was evaluated using the relationship:

$$ \eta = \frac{{R_{\text{ct}} - R_{\text{ct}}^{ 0} }}{{R_{\text{ct}} }} \times 1 0 0 $$
(4)

where R 0ct and R ct are the charge transfer resistance values without and with inhibitor, respectively.

Quantum chemical calculations

All theoretical calculations were performed using DFT (density functional theory) with the Beck’s three parameter exchange functional along with the Lee–Yang–Parr nonlocal correlation functional (B3LYP) [19–21] with 6-31G* basis set as implemented in the Gaussian 03 program package [22]. This approach has been shown to yield favorable geometries for a wide variety of systems. The following quantum chemical parameters were calculated from the obtained optimized molecular structure: the energy of the highest occupied molecular orbital (E HOMO), the energy of the lowest unoccupied molecular orbital (E LUMO), the energy band gap (ΔE gap = E HOMO−E LUMO), the dipole moment (μ), and the TE.

Results and discussion

Potentiodynamic polarization curves

Polarization measurements have been carried out in order to gain knowledge concerning the kinetics of the anodic and cathodic reactions. Figure 2 shows the polarization curves for mild steel in 1 M HCl at 298 K in the absence and the presence of different concentration of benzamide derivatives. Various corrosion parameters such as corrosion current densities (i corr), corrosion potentials (E corr), cathodic Tafel slopes (βc), surfaces coverage degree (θ), and inhibition efficiency E I % are listed in Table 1.

Fig. 2
figure 2

Potentiodynamic polarization curves obtained for mild steel at 298 K in 1 M HCl at various concentrations of the studied inhibitors: a BENZA, b BENZA-TET

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Table 1 Electrochemical parameters values evaluated from the cathodic current–voltage characteristics for the system mild steel/1 M HCl/inhibitors at 298 K
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From the recorded results, we can conclude that, in all cases, addition of the studied compounds induced a marked decrease in the cathodic and a slight decrease in the anodic current densities. Accordingly, these inhibitors affect greatly the hydrogen reaction discharge and slightly affect the mild steel dissolution processes. The hydrogen evolution reaction is under activation control since the cathodic portions rise to Tafel lines. The fact that cathodic process slows down can be due to the covering of the surface with a monolayer of the tested molecules due to the adsorbed inhibitors on the mild steel surface then reducing the electrolyte infiltration to the interface.

It can be seen from Table 1 that E corr values show significant shifts cathodically at various concentrations of BENZA-TET, suggesting that BENZA-TET is mainly a cathodic-type inhibitor in 1 M HCl. In contrast, E corr has fewer identical values in the case of BENZA, and this result qualifies BENZA as an inhibitor of mixed type. However, the decrease in cathodic Tafel slope (βc) values suggests that the reaction mechanism of the hydrogen reduction is not the same in the absence and in the presence of the inhibitor. This may probably be due to a diffusion or barrier effect [23]. It can also be seen that the addition of the inhibitors decreased the i corr values of mild steel in 1 M HCl and reached a minimum at 10−3 M of both inhibitors. These results revealed the strong inhibiting effect of the inhibitors studied. This behavior can be attributed to the presence of electron-donating groups (oxygen, nitrogen, aromatic ring) in the organic compound studied. The presence of free electron pairs in nitrogen atoms and π-electrons on aromatic rings favors the adsorption of BENZA and BENZA-TET on the steel surface. Similar results have been recorded with other tetrazole derivatives [24].

In addition, the inhibition efficiency E I % of these compounds follows the sequence: BENZA > BENZA-TET.

Electrochemical impedance spectroscopy (EIS) study

EIS provides more information on both the resistive and capacitive behaviors of the interface and makes it possible to evaluate the performance of the inhibitors. Figure 3 shows the Nyquist plots for mild steel in 1 M HCl containing newly synthesized organic inhibitors at different concentrations after 1 h of immersion time at corrosion potential, E corr. It is noticeable that these diagrams exhibit one semicircle, the center of which lies under the abscissa, and this difference has been attributed to frequency dispersion [25] imputed to different physical phenomena, such as roughness and non-homogeneities of the solid surface. The EIS results were interpreted in terms of an equivalent circuit as described elsewhere [26]. These diagrams have a similar shape, which is maintained throughout all tested concentrations, indicating that almost no change in the corrosion mechanism occurred due to the addition of the inhibitors. This behavior can be attributed to charge transfer of the corrosion process. It is also noticeable that the diameter of the semicircle increases with increasing inhibitor concentration.

Fig. 3
figure 3

Nyquist plots for mild steel at 298 K in 1 M HCl in various concentrations of the studied inhibitors: a BENZA, b BENZA-TET

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EIS spectra were analyzed using the equivalent circuit in Fig. 4, which was used previously to model the iron/acid interface [27]. The impedance parameters derived from these figures are given in Table 2.

Fig. 4
figure 4

Equivalent circuit model for system mild steel/1 M HCl/inhibitors. R s solution resistance, R ct charge transfer resistance, C dl double-layer capacitance

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Table 2 EIS data for mild steel in 1 M HCl containing different concentrations of studied inhibitors
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Table 2 shows that R ct values increased and C dl decreased with concentration. The decrease in C dl values indicated that the inhibitors function by adsorption at the metal/solution interface originally by gradual displacement of water molecules and/or chloride ions on the mild steel surface [28], leading to a protective solid film, inhibiting species or both on the mild steel surface, then decreasing the extent of dissolution reaction [29, 30]. This decrease of C dl concentration can be explained by the decrease in local dielectric constant and/or an increase in the protective layer thickness on the electrode surface. In addition, the inhibition efficiencies, obtained from electrochemical impedance measurements, increase with concentration and show the same trend as those obtained from polarization measurements.

Thermodynamic parameters of the adsorption process

The adsorption isotherm type can provide additional information about the tested compounds properties. The coverage surface values (θ) can be easily determined by the ratio IEimp %/100. In the present study, the inhibiting efficiency is evaluated from impedance measurements (Table 2). The experimental results have been fitted to a series of adsorption isotherm (Fig. 5). The Langmuir adsorption isotherm can be expressed as [31]:

$$ \frac{{C_{inh} }}{\theta } = \frac{1}{{K_{ads} }} + C_{inh} $$
(5)

where K ads is the equilibrium constant of the adsorption process and C inh is the inhibitor concentration.

Fig. 5
figure 5

Langmuir adsorption isotherm plot for mild steel in 1 M HCl at different concentrations of the studied inhibitors

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The linear coefficient regression, r, was used to choose the best fit experimental data (Table 3). K ads is related to the standard free energy of adsorption \( \Updelta G_{ads}^{ \circ } \) according to Eq. (6) [32]:

$$ K_{ads} = \frac{1}{55.5}\exp \left( {\frac{{ - \Updelta G_{ads}^{o} }}{RT}} \right) $$
(6)

where R is the universal gas constant and T is the absolute temperature. The value 55.5 in the above equation is the water concentration in solution in mol/L.

Table 3 Free energy of adsorption for BENZA and BENZA-TET on mild steel in 1 M HCl at 298 K
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Figure 5 shows the dependence of C inh/θ against C inh. To calculate the adsorption parameters, the straight line was drawn using the least squares method. A very good fit is observed with the regression coefficient up to 0.999 and the line obtained has slopes very close to unity, which suggests that the experimental data are well described by the Langmuir isotherm and exhibit single-layer adsorption characteristics. This kind of isotherm involves the assumption of no interaction between the adsorbed species on the electrode surface [33]. Thermodynamic parameters are important to study the inhibitive mechanism. The values of K ads, R 2 and \( \Updelta G_{\text{ads}}^{ \circ } \) are calculated and are given in Table 3. The high K ads values reflect the high adsorption ability of these inhibitors on the mild steel surface.

From Table 3, the negative values of standard free energy of adsorption indicate spontaneous adsorption of organic molecules on the metallic surface and also the strong interaction between inhibitor molecules and the mild steel surface [34, 35]. Generally, the standard free energy values of −20 kJ mol−1 or less negative are associated with an electrostatic interaction between charged molecules and charged metal surface (physical adsorption); those of −40 kJ mol−1 or more negative involve charge sharing or transfer from the inhibitor molecules to the metal surface to form a co-ordinate covalent bond (chemical adsorption) [36, 37]. Based on the literature [38], the calculated \( \Updelta G_{ads}^{o} \) values in this work indicate that the adsorption mechanism of BENZ on mild steel is both electrostatic-adsorption (ionic) and chemisorption (molecular) [39]. But the adsorption mechanism of BENZA-TET is generally made by chemisorption rather than by physisorption.

Thermodynamic parameters of the activation corrosion process

In order to gain more information about the adsorption type and the performance of the investigated inhibitors at higher temperatures, potentiodynamic polarization measurements (Fig. 6a, b) were carried out at different temperatures (range 298–328 K) for mild steel in 1 M HCl without and with optimal concentrations of inhibitors after 1 h of immersion time at corrosion potential. Electrochemical corrosion kinetics parameters, at different concentration of inhibitors, derived from the Stern–Geary equation, as well as inhibitor efficiencies and coverage surface values, are listed in Table 4.

Fig. 6
figure 6

Effect of temperature on the behaviour of mild steel/1 M HCl interface in a uninhibited solution, b at 10−3 M of BENZA, and c 10−3 M of BENZA-TET

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Table 4 Electrochemical characteristics for mild steel in 1 M HCl with and without 10−3M of BENZA and BENZA-TET at different temperatures
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It is shown that i corr values increase with temperature. This increase is much more pronounced in uninhibited than in inhibited media. Moreover, no clear trends are observed in E corr values at higher temperatures in free medium and with BENZA as well as BENZA-TET. These results reflect the enhancement of both the cathodic hydrogen evolution reaction as well as anodic mild steel dissolution with the rise of temperature. However, the values of E I % and θ remain almost constant in the case of BENZA, whereas a considerable increase is noticed in the presence of BENZA-TET. As reported elsewhere [40], the fact that the E I % increases with temperature is explained by some authors as likely specific interaction between the iron surface and the inhibitor. Ivanov [41] explains this increase with temperature by the change in the nature of the adsorption mode; the inhibitor is being physically adsorbed at lower temperatures, while chemisorption is favored by increasing the temperature.

Activation parameters like activation energy (E a), enthalpy (ΔH a), and entropy (ΔS a) for the dissolution of mild steel in 1 M HCl in the absence and presence of 10−3 M BENZA and BENZA-TET were calculated from the Arrhenius equation (Eq. 7) and the transition state equation (Eq. 8) [42]:

$$ i_{corr} = A\exp \left( { - \frac{{E_{a} }}{RT}} \right) $$
(7)
$$ i_{corr} = \frac{RT}{Nh}\exp \left( {\frac{{\Updelta S_{\text{a}} }}{R}} \right)\exp \left( { - \frac{{\Updelta H_{\text{a}} }}{RT}} \right) $$
(8)

where i corr is the corrosion rate, E a is the apparent activation energy, A is the pre-exponential factor, h is Planck’s constant, N is the Avogadro number, R is the universal gas constant, ΔH a is the enthalpy of activation, and ΔS a is the entropy of activation.

Figure 7 showed the Arrhenius plot of Ln i corr versus 1/T which gave straight lines with slopes equal to (−E a/R). Again, the Arrhenius plots of Ln (i corr/T) versus 1/T gave straight lines (Fig. 8) with slope (−ΔH a/R) and intercept \( ( {\text{Ln}}R/Nh + \Updelta S_{\text{a}} /R ) \) from which ΔH a and ΔS a values were calculated. The activation parameters are given in Table 5.

Fig. 7
figure 7

Arrhenius plots for mild steel in 1 M HCl with and without 10−3 M of the studied inhibitors

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Fig. 8
figure 8

The plots of Ln (i corr/T) versus 1/T for mild steel in 1 M HCl with and without 10−3 M of the studied inhibitors

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Table 5 Activation parameters values of E a, ΔH a and ΔS a for mild steel in 1 M HCl with and without 10−3 M of each inhibitor
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Table 5 shows that the values of A as well as E a in the presence of BENZA follow the same trend and are lower than those in uninhibited solution while that in the presence of BENZA-TET is higher than those in uninhibited solution. It is well recognized that the inhibition effect depends to the temperature and the comparison of the apparent activation energy values, E a, of the corrosion process in the absence and presence of inhibitors can provide further evidence [42, 44] concerning the inhibition action mechanism. The decrease of inhibition efficiencies with temperature, which refers to a higher value of E a, when compared to free solution, is interpreted as an indication for an electrostatic character of the inhibitor’s adsorption. However, the lower value of E a in inhibited solution compared to uninhibited solution can be explained by a strong chemisorption bond between the inhibitor and the metal. Some authors reported that electrostatic adsorption proceeds irrespective of the fact that the E a value in the presence of inhibitor is lower than that in free solution [26].

Hence, the addition of inhibitors affects the E a values; this modification may be attributed to the change in the corrosion process mechanism in the presence of inhibitor [27]. The lower activation energy values of the corrosion process in the presence of inhibitors are attributed to their chemisorption, while the opposite is generally attributed to the physical adsorption [43]. Then, it can be suggested that BENZA adsorbs by forming strong chemisorption bonds while the BENZA-TET adsorbs by physicosorption on metallic surfaces.

The positive sign of the enthalpies ΔH a reflects the endothermic nature of the steel dissolution process, whereas large negative values of entropies ΔS a from BENZA imply that the activated complex in the rate-determining step represents an association rather than a dissociation step, meaning that a decrease in disordering takes place on going from reactants to the activated complex [45–47]. Thus, the positive ΔS a value from BENZA-TET indicates that the inhibition process becomes less favorable as the temperature is increased. For the remainder of this work, we chose the best inhibitor (BENZA) for the study of the immersion time effect and a theoretical study.

Effect of immersion time

Figure 9 shows the impedance spectra at different immersion times in 1 M HCl containing 10−3 M of BENZA. It is noteiceable that these diagrams exhibit one capacitive loop. It is also of note that the increasing of immersion time affects the diameter loops.

Fig. 9
figure 9

Effect of immersion time on the behavior of the mild steel/1 M HCl interface in the presence of 10−3 M of inhibitor

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The inhibition efficiency, IEimp %, of the investigated inhibitor was derived from the R ct values at different immersion times. It is clear from Fig. 10 that IEimp % remained constant at the same time for the BENZA inhibitor. These results demonstrate that the formation of surface film, and therefore the BENZA adsorption, on the electrode surface is stable with respect to immersion time.

Fig. 10
figure 10

EIS parameters obtained under open circuit conditions at different immersion times: system mild steel/1 M HCl with 10−3 M of BENZA inhibitor added at 298 K

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Computational study

The Gaussian program offers a wide variety of density functional theory (DFT) models for discussion of DFT methods and applications. Energies, analytic gradients, and true analytic frequencies are available for all DFT models. This method also serves as an efficient computational tool which can yield rapid quantitative estimates for a number of properties. Highest occupied molecular orbital energy (E HOMO), lowest unoccupied molecular orbital energy (E LUMO), and dipole moment (μ) are very popular quantum chemical parameters. These orbitals, also called the frontier orbitals, determine the way the molecule interacts with other species. According to the frontier molecular orbital theory, the formation of a transition state is due to an interaction between the frontier orbital’s HOMO and LUMO of reactants. E HOMO is often associated with the electron-donating ability of the molecule. High E HOMO values indicate that the molecule has a tendency to donate electrons to appropriate acceptor molecules with low energy empty molecular orbitals. Increasing values of E HOMO facilitate adsorption (and therefore inhibition) by influencing the transport process through the adsorbed layer. E LUMO indicates the ability of the molecules to accept electrons. The lower the value of E LUMO, the more probable the molecule would accept electrons. A low value of the energy band gap (ΔE = E LUMO  − E HOMO) gives good inhibition efficiencies, because the energy required to remove an electron from the last occupied orbital will be low. Consequently, less negative HOMO energy and smaller energy gap (E HOMO − E LUMO) are reflected in a stronger chemisorptions bond and perhaps greater protection efficiency. For dipole moment (μ), lower values of (μ) will favor accumulation of the inhibitor. Meanwhile, several authors state that the inhibition efficiency increases with increasing dipole moment values. On the other hand, a survey of the literature reveals that irregularities appeared in the case of the correlation of dipole moment with efficiency. In this way, some quantum chemical parameters, which are thought important to directly influence electronic interaction between the carbon steel surface and the inhibitor, are listed in Table 6. All these quantum chemical parameters, E HOMO, E HOMO, ∆E, μ, and TE, were obtained after geometric optimization of the studied benzamid (BENZA) with respect to all the nuclear coordinates using the Kohn–Sham approach at DFT level. The fully optimized molecular structure of BENZA is given in Fig. 11.

Table 6 Calculated quantum chemical parameters of BENZA
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Fig. 11
figure 11

Optimized molecular structure of BENZA by the B3LYP-6-31 G(d) method

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Frontier orbital theory is useful in predicting adsorption centers of the inhibitor molecules responsible for the interaction with surface metal atoms [48, 49]. Terms involving the frontier molecular orbital could provide a dominant contribution, because of the inverse dependence of stabilization energy on orbital energy difference [48]. The high value of E HOMO (−7.1456 eV) indicates a tendency of the molecule to donate electrons to the appropriate acceptor molecules with low energy and empty molecular orbital, whereas the value of E LUMO (−1.05 eV) indicates the ability of the molecule to accept electrons. Consequently, low values of the energy band gap (ΔE gap = −5.8351 eV) can indicate a good stability of the formed complex (BENZA-Fe) on the metal surface, therefore improving the corrosion resistance of mild steel in 1 M HCl medium [50]. On the other hand, the dipole moment (μ) of BENZA is 4.5266 Debye, which is higher than that of H2O (1.88 Debye). The high value of the dipole moment of BENZA probably indicates strong dipole–dipole interactions of BENZA molecules and the metallic surface [51]. Accordingly, the adsorption of BENZA molecule from the aqueous solution can be regarded as a quasi-substitution process between the BENZA molecules in the aqueous phase (BENZAsol) and the water molecules at the electrode surface (H2Oads).

The reactive ability of the inhibitor is considered to be closely related to their frontier molecular orbitals, the HOMO and LUMO. A typical electron density distribution of HOMO and LUMO for BENZA are shown in Fig. 12. Analysis of this figure shows that the distribution of the two energies, HOMO and LUMO, are mainly localized in the atoms of the benzamid ring. Consequently, this is the favorite sites for interaction with the steel surface. The TE of the BENZA is equal to −14,483.87 eV, which indicates that BENZA is favorably adsorbed through the active centers of adsorption.

Fig. 12
figure 12

The frontier molecular orbital density distributions of BENZA

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Conclusion

  1. 1.

    Reasonably good agreement was observed between the data obtained from potentiodynamic polarization and electrochemical impedance spectroscopy techniques.

  2. 2.

    Polarization measurements showed that the inhibitor BENZA-TET is a cathodic type, but BENZA acts as a mixed type inhibitor. EIS measurements also indicate that the inhibitor addition increases the charge transfer resistance and show that the inhibitive performance depends on molecules adsorption on the metallic surface.

  3. 3.

    The adsorption model of all inhibitors obeys the Langmuir isotherm at 298 K. The negative values of \( \Updelta G_{\text{ads}}^{ \circ } \) indicate spontaneous adsorption of the inhibitor on the mild steel surface.

  4. 4.

    The lower values of the apparent activation energy in the presence of BENZA showed a compensation effect. Very good inhibition efficiency was observed with BENZA at 328 K (>95 %). These results reveal the nature character of adsorption which seems to be only chemisorption.

  5. 5.

    The inhibition efficiency remained slightly constant with time. These results reveal the chemisorption character for BENZA. Very good inhibition efficiency was observed with BENZA after 12 h (>87 %).

  6. 6.

    The quantum chemical approach was adequately used to explain the correlation between the mild steel corrosion inhibition and molecular structure of BENZA. It was found that the corrosion inhibition power of this benzamid derivative is closely related to its quantum chemical parameters.