Corrosion control in the tubing steel of oil wells during matrix acidizing operations

Abstract

Dodecyl dimethyl benzyl ammonium bromide (DDBAB) was used as a corrosion inhibitor for carbon steel pipelines in 8% sulfamic acid solution during matrix acidizing operations. The inhibition efficiency (η%) has been studied using chemical (weight loss) and electrochemical (electrochemical impedance spectroscopy (EIS), potentiodynamic polarization) techniques. The surface active properties of this surfactant were calculated from surface tension measurements. Results obtained from both chemical and electrochemical techniques reveal that this compound is a very good corrosion inhibitor even at low concentrations and the maximum inhibition efficiency (93.7%) was obtained with 150 ppm of DDBAB. Polarization curves showed that the corrosion current density was decreased by increasing the inhibitor concentration until the critical micelle concentration (CMC) is reached. The Tafel polarization data indicate that the selected compound acts as a mixed type inhibitor. The slopes of the cathodic and anodic Tafel lines (β_c and β_a) are approximately constant and independent of the inhibitor concentration. Analysis of the impedance spectra indicates that it is the charge transfer process that mainly controls the corrosion process of carbon steel in 8% sulfamic acid solution both in the absence and presence of the inhibitor. The data obtained using the EIS technique were analyzed to model the corrosion inhibition process through equivalent circuits (ECs). The effect of the molecular structure on the inhibition efficiency was investigated using quantum chemical calculations. The adsorption of this compound on the surface of the carbon steel follows the Langmuir adsorption isotherm. From the adsorption isotherm, the values of the adsorption equilibrium constant (K_ads) and the free energy of adsorption were calculated and discussed. The relatively high value of K_ads reveals a strong interaction between the inhibitor molecules and the carbon steel surface. The strong adsorption ability of this compound can be attributed to the presence of the adsorption center of nitrogen as well as π donor moieties. Finally, EDX and SEM surface analysis tools were used to examine the nature of the protective film formed on a carbon steel alloy.

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1. Introduction

It is well known that the presence of sediments and mud solids retards the permeability of crude oil or natural gas through wells thus affecting the production rate. So the main object of this work is to increase the well productivity through stimulating the flow of hydrocarbons as indicated in Fig. 1.¹ There are different acids used to perform an acid job. A common type of acid employed on wells to stimulate production is sulfamic acid solution (H₄N₂SO₂), which is useful in removing carbonate reservoirs or limestone and dolomite from the rock.^2–4 The use of 8% sulfamic acid solution is preferable in comparison to mineral acids due to its intrinsic safety and desirable water descaling properties, low volatility, and low toxicity. In order to protect the integrity of the completed well, an effective type of corrosion inhibitor must be injected into the well to prohibit the acid from breaking down the steel casing in the well.⁵ Carbon steel, the most widely used engineering material, corrodes in many circumstances, especially in some industrial processes, such as acid cleaning, acid de-scaling and oil well acidizing.^6–8 Excellent corrosion inhibitors are considered to be such organic compounds which not only offer electrons to the unoccupied d orbitals of the carbon steel surface to form a coordinate covalent bond, but can also accept the free electrons from the surface of the carbon steel by using their antibond orbital to form feedback bonds in turn.⁹ Quantum chemistry calculations have been widely used to study the reaction mechanisms and to interpret the experimental results as well as to solve chemical ambiguities. Recently, some corrosion publications have contained large quantum chemical calculations.^10,11 Such calculations are performed here to shed more light on the adsorption mode of the inhibitor. Actually, few papers in the literature deal with the subject of the corrosion and corrosion inhibition of carbon steel in an 8% solution of sulfamic acid, which is the real concentration in the matrix acidization of old oil wells.^12–14 For this purpose, this work aims to study the performance of a new type of cationic surfactant namely, dodecyl dimethyl benzyl ammonium bromide (DDBAB), as a corrosion inhibitor for X-70 type carbon steel in 8% sulfamic acid solution during matrix acidizing operations. Also the work is extended to present a theoretical study on the electronic and molecular structure of dodecyl dimethyl benzyl ammonium bromide obtained through quantum chemistry calculations carried out using the Materials Studio 7.0 program. In addition, we will attempt to find the relationship between the molecular structure of this inhibitor and its inhibition efficiency as calculated using chemical and electrochemical techniques.

Fig. 1 Cross-section of the matrix acidizing process of old oil wells.

2. Experimental

2.1. Chemicals

Commercially available dodecyl dimethyl benzyl ammonium bromide (DDBAB) was purchased from the El Gomhoria Trade Pharmaceuticals and Chemicals Company, Cairo, Egypt. This compound was used without any further purification. The chemical structure of the compound is as follows.

2.2. Preparation of the aggressive solution

The aggressive solution (8% sulfamic acid) was prepared by dilution of sulfamic acid with distilled water. The concentration range of the dodecyl dimethyl benzyl ammonium bromide (DDBAB) cationic surfactant used for corrosion measurements was from 50 to 150 ppm. All solutions were prepared using distilled water.

2.3. Procedure used for corrosion measurements

2.3.1. Gravimetric measurements. Gravimetric measurements were performed with API X70-type carbon steel specimens having a composition of (wt%): 0.12 C, 0.55 Si, 1.60 Mn, 0.036 P, 0.034 S and the remainder Fe. The coupons used for the gravimetric measurements have the dimensions 2.5 cm × 2.0 cm × 0.2 cm. The carbon steel specimens were abraded with a series of emery papers (grade 320, 500, 800, 1000, 1200 and 2500) and then washed with bi-distilled water and acetone.¹⁵ After weighing accurately, the specimens were immersed in a 250 mL solution of 8% sulfamic acid with and without the tested inhibitor (DDBAB) at different concentrations (30, 60, 90, 120 and 150 ppm) for 28 h at 25 °C. All the aggressive acid solutions were closed. After 28 h, the specimens were taken out, washed, dried and weighed accurately. The test was performed for three specimens and the weight was the average of the three specimens.

2.3.2. Electrochemical measurements. Electrochemical experiments were carried out using a Voltalab 80 Potentiostat PGZ 402 in a conventional electrolytic cell with a three-electrode arrangement: the saturated calomel electrode (SCE) was used as a reference electrode, a platinum electrode was used as an auxiliary electrode and the working electrode (WE) had the form of a rod of carbon steel embedded in an epoxy resin of polytetrafluoroethylene (PTFE).¹⁶ Prior to each experiment, the surface of the working electrode was mechanically polished with successive grades of emery papers down to 2500 grade emery paper, rinsed with bi-distilled water and then acetone, and dried quickly.¹⁷ The electrode potential was allowed to stabilize 60 min before starting the measurements. The electrode area exposed to the corrosive solution was 0.7 cm². All experiments were carried out at 25 °C.

Potentiodynamic polarization curves were obtained by changing the electrode potential automatically (from −750 to −350 mV vs. SCE) at an open circuit potential with a scan rate of 2 mV s⁻¹.

EIS measurements were carried out in the frequency range between 100 kHz and 50 mHz with an amplitude of 10 mV peak-to-peak using AC signals at an open circuit potential. EIS diagrams are given in both Nyquist and Bode plots.¹⁸ Each experiment was repeated three times to ensure reproducibility. Measurements were performed with a Voltalab 80 Potentiostat PGZ 402 controlled by a Tacussel corrosion analysis software model (Voltamaster 4).

2.4. Surface morphology studies

Scanning electron microscopy (SEM) studies and energy dispersive X-ray analysis (EDX) were performed to observe the morphologies and discuss the quantitative analysis of the elements on the surfaces of the corroded specimens using JEOL JSM-5410 before and after exposure to 8% sulfamic acid for 28 h in the absence and presence of 150 ppm of the DDBAB inhibitor at 25 ± 1 °C. The energy of the acceleration beam employed was 30 kV.¹⁹

2.5. Theoretical calculations

Quantum chemical calculations can provide insight into the inhibitor system and elucidate the adsorption process at a molecular level.^20–23 The quantum chemical calculations were performed using the DMOL³ module²⁴ of the Materials Studio 7.0 software (Accelrys Inc.),²⁵ which is designed for the realization of large scale density functional theory (DFT) calculations. DFT semi-core pseudopods calculations (dspp) were performed with the double numerical basis sets plus the polarization functional (DNP). The DNP basis sets are of comparable quality to the 6-31G GAUSSIAN basis sets.²⁶ Delley et al. showed that the DNP basis sets are more accurate than the GAUSSIAN basis sets of the same size.²⁷ The RPBE functional,²⁸ so far the best exchange–correlation functional,²⁹ based on the generalized gradient approximation (GGA), is employed to take account of the exchange and correlation effects of electrons. The geometric optimization is performed without any symmetry restriction. The following quantum chemical indices were considered: the energy of the highest occupied molecular orbital (E_HOMO), the energy of the lowest unoccupied molecular orbital (E_LUMO), the energy gap (ΔE = E_LUMO − E_HOMO), the dipole moment (μ), the electronegativity (χ), the chemical potential (π = −χ), the hardness (η), the softness (σ = 1/η) and the number of electrons transferred (ΔN). The frontier molecular orbitals (HOMO and LUMO) could be used to predict the adsorption centers of the inhibitor molecule. For the simplest transfer of electrons, adsorption should occur at the part of the molecule where the softness, σ, which is a local property, has the highest value.

2.6. Surface tension measurements

Freshly prepared aqueous dodecyl dimethyl benzyl ammonium bromide (DDBAB) cationic surfactant solutions with a concentration range from 0.01–0.0000003 M L⁻¹ were poured into clean 25 mL Teflon holders and allowed to equilibrate for 2 h. The platinum ring was adjusted at the air–water interface of the surfactant solution, then the reading was recorded when the ring detached itself from the solution surface. Apparent surface tension values³⁰ were measured a minimum of three times and the recorded values were taken as the average of these values at 25 °C. The platinum ring was then removed after each reading, and washed with diluted HCl followed by distilled water.

3. Results and discussion

3.1. Gravimetric measurements

Fig. 2 shows the weight loss–time curves of carbon steel immersed in 8% sulfamic acid solution in the absence (blank) and presence of various concentrations of the inhibitor (DDBAB). It is evident from the figure that the curves obtained in the presence of the inhibitor fall significantly below that obtained for the blank. Also, it is clear that the weight loss of the metal decreases with an increase in the inhibitor concentration and increases with increasing exposure time.

Fig. 2 Effect of exposure time on the weight loss of carbon steel immersed in 8% sulfamic acid solution in the absence and presence of different concentrations of the inhibitor (DDBAB).

Also, the corrosion rate was calculated from the weight loss and is presented as a function of the inhibitor concentration of the used cationic surfactant in Fig. 3. It is clear that the corrosion rate of the carbon steel was decreased dramatically by increasing the inhibitor concentration and consequently the inhibition efficiencies of the inhibitor increased due to the adsorption of inhibitor on the carbon steel surface.

Fig. 3 Effect of the inhibitor concentration on the corrosion rate of carbon steel in 8% sulfamic acid solution at 25 °C.

The value of corrosion inhibition efficiency η_w (%) was determined from weight loss using the following equation:^31,32

η_w% = (1 − W_(inh)/W_(free)) × 100 (1)

where W_(free) and W_(inh) are the weight losses in the absence and presence of inhibitor, respectively. Table 1 reports the values of corrosion rate and percentage inhibition efficiency for X-70 type carbon steel immersed in 8% sulfamic acid solution in the absence and presence of various concentrations of the inhibitor (DDBAB). Inspection of the data in Table 1 reveals that increasing the surfactant concentration decreases the weight loss and the corrosion rate of carbon steel so that they are at their lowest at a concentration of 150 ppm. This effect is attributed to the formation of a protective layer from the inhibitor molecules on the carbon steel surface.

Table 1 Data obtained from weight loss measurements for X-70 type carbon steel immersed in 8% sulfamic acid solution in the absence and presence of various concentrations of dodecyl dimethyl benzyl ammonium bromide

Inhibitor dose, ppm	Corrosion rate, mpy	Degree of surface coverage (θ)	Percentage inhibition efficiency, ηw (%)
0	6.0	—	—
30	2.12	0.648	64.8
60	1.64	0.726	72.6
90	1.02	0.832	83.2
120	0.5	0.914	91.4
150	0.46	0.920	92.0

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It is generally agreed that the primary action in the inhibition process by surfactants is the adsorption of the surfactant molecules via their functional groups onto the metal surface.³³ Therefore, it was of particular interest to investigate the phenomenon of the adsorption of such compounds and determine the degree of surface coverage (θ) of the adsorbed surfactant molecules.

The degree of surface coverage is calculated from the weight loss (θ_wtloss) using the following relation:³⁴

θ_wtloss = 1 − W_(inh)/W_(free) (2)

The values of the degree of surface coverage (θ), the percentage inhibition efficiency (η_w%) and the corrosion rate were calculated for the inhibitor (DDBAB) and are summarized in Table 1. Also, from the previous data one can conclude that, by increasing the inhibitor concentration, the surface coverage (θ) of the metal surface by inhibitor molecules was increased and reached θ = 0.92 at 150 ppm for DDBAB. This increase in the degree of surface coverage leads to a decrease in the contact between the metal surface and the aggressive medium and consequently decreases the dissolution of the metal and increases the inhibition efficiency. The values of the degree of surface coverage (θ) obtained from weight loss measurements for the tested inhibitor (DDBAB) have been applied to different adsorption isotherms in order to investigate the type of adsorption. For this purpose, C_i/θ is plotted against C_i for the surfactant (DDBAB) as indicated in Fig. 4. The experimental results give a straight line with a slope nearly equal to unity, suggesting that the inhibitor molecules adsorbed on the carbon steel immersed in 8% sulfamic acid obey the Langmuir adsorption isotherm, which is represented by the following equation:³⁵

C_i/θ = 1/K_ads + C_i (3)

where C_i is the inhibitor concentration and K_ads represents the adsorption equilibrium constant of the inhibitor on a carbon steel surface. The slope of the isotherm deviates from unity. This deviation is generally attributed to the interaction between the adsorbed inhibitor molecules on the carbon steel surface via mutual repulsion or attraction.^36–38 K_ads values were calculated from the intercepts of the straight lines on the C_i/θ axis.³⁹ The free energy of adsorption of the inhibitor on the surface of the carbon steel was calculated as follows:^40,41where R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), T is the absolute temperature (K), and the value 55.5 is the molar concentration of water in solution.

Fig. 4 Langmuir adsorption isotherm (C_i/θ vs. C_i) of the inhibitor (DDBAB) on a carbon steel surface in 8% sulfamic acid solution.

The values of K_ads and for the DDBAB inhibitor are listed in Table 2. It is clear that the high value of K_ads indicated the strong adsorption ability of the inhibitor on the surface of carbon steel in 8% sulfamic acid. The negative sign of means that the adsorption of the inhibitor on a carbon steel surface is a spontaneous process, and furthermore the negative value of also shows the strong interaction of the inhibitor molecule with the carbon steel surface.^42,43 Generally, if the value of is around −20 kJ mol⁻¹ or lower this is consistent with the electrostatic interaction between the inhibitor and the charged metal surface (i.e. physisorption), while a value more negative than −40 kJ mol⁻¹ involves charge sharing or transfer from the inhibitor molecules to the metal surface to form a coordinate type of bond (i.e. chemisorption)⁴⁴. For the investigated inhibitor (DDBAB), one can see that the calculated value of equals −34.19 kJ mol⁻¹, indicating that the adsorption of dodecyl dimethyl benzyl ammonium bromide (DDBAB) onto the carbon steel in 8% sulfamic acid can be regarded as a mixed physical and chemical adsorption (i.e. physicochemical type).^45–47

Table 2 Estimation of the equilibrium adsorption constant (K_ads) and the free energy of adsorption () of the inhibitor (DDBAB) molecules on the surface of carbon steel immersed in 8% sulfamic acid solution

Property	Value
Kads (M^−1)	17 739.93
	−34.19

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3.2. Tafel polarization measurements

Fig. 5 shows typical polarization curves for the inhibition characteristics of the inhibitor (DDBAB). These curves show the anodic and cathodic polarization plots recorded on a carbon steel electrode in 8% sulfamic acid at various concentrations in the presence and absence of inhibitor (DDBAB). As would be expected both anodic and cathodic reactions of carbon steel electrode corrosion were inhibited with the increase of inhibitor (DDBAB) concentration. This result suggests that the addition of inhibitor (DDBAB) reduces anodic dissolution and also retards the hydrogen evolution reaction. Table 3 shows the electrochemical corrosion kinetic parameters, i.e., corrosion potential (E_corr), cathodic and anodic Tafel slopes (β_c and β_a), polarization resistance (R_P) and corrosion current density i_corr obtained by extrapolation of the Tafel lines. The calculated inhibition efficiency, η_p (%) is also reported from the following equation:⁴⁸where and i_corr correspond to the uninhibited and inhibited corrosion current densities, respectively. The best inhibition efficiency was about 91.1% at a concentration of 150 ppm. It can be seen that by increasing the concentration of the inhibitor, the corrosion rate decreased and the inhibition efficiency η_p (%) increased. This behavior confirms that there is a greater increase in the energy barrier of the carbon steel dissolution process. It is clear that the used cationic surfactant (DDBAB) affects both the anodic and cathodic reaction so that it acts as a mixed type inhibitor but the cathodic effect is more pronounced with a slight shift of E_corr in the cathodic direction. Moreover, this inhibitor causes no change in the cathodic and anodic Tafel slopes, indicating that the inhibitor is first adsorbed onto the carbon steel surface and therefore impedes by merely blocking the reaction sites of the iron surface without affecting the anodic and cathodic reaction mechanisms.^49,50

Fig. 5 Anodic and cathodic polarization curves of the carbon steel electrode in 8% sulfamic acid solution with and without various concentrations of inhibitor (DDBAB).

Table 3 Electrochemical kinetic parameters obtained from potentiodynamic polarization measurements of X-70 type carbon steel immersed in 8% sulfamic acid solution in the absence and presence of various concentrations of dodecyl dimethyl benzyl ammonium bromide

Inhibitor dose, (ppm)	Ecorr, mV (vs. SCE)	Icorr, mA cm^−2	βc, mV dec^−1	βa, mV dec^−1	Rp, kΩ cm^2	θ	ηp%
8% sulfamic acid solution (blank)	−518	0.493	144.2	102.5	0.139	—	—
30 ppm	−536	0.194	142.5	98.4	0.376	0.636	63.6
60 ppm	−543	0.140	124.3	94.5	0.480	0.714	71.4
90 ppm	−552	0.103	126.8	92.1	0.731	0.812	81.2
120 ppm	−564	0.056	128.6	96.3	1.22	0.886	88.6
150 ppm	−568	0.044	122.4	92.6	1.56	0.911	91.1

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3.3. Impedance measurements

The effect of inhibitor (DDBAB) concentrations on the impedance behavior of carbon steel in 8% sulfamic acid solutions is presented in Fig. 6. These curves show a typical set of Nyquist plots for carbon steel in 8% sulfamic acid solution with and without various concentrations of dodecyl dimethyl benzyl ammonium bromide. It is clear from these plots that the impedance response of carbon steel changes significantly after the addition of inhibitor in corrosive media. This indicates that the impedance of an inhibited substrate increases with increasing concentration of inhibitor in 8% sulfamic acid. It is worth noting that the change in concentration of DDBAB inhibitor did not dramatically alter the profile of the impedance behavior, suggesting a similar mechanism for the corrosion inhibition of carbon steel by the inhibitor (DDBAB), Fig. 6. The charge transfer resistance values (R_ct) were calculated from the difference between the impedance values at lower and higher frequencies as suggested by Tsuru et al.⁵¹ The impedance parameters derived from Fig. 6 are given in Table 4. The double layer capacitance C_dl and inhibition efficiency η_I (%) were calculated from the following equations:^52,53where and R_ct are the charge transfer resistances in 8% sulfamic acid solution without and with different concentrations of inhibitor, respectively, and f(−Z′′_img) is the frequency at the maximum imaginary component of the impedance. From Table 4, it is clear that the charge transfer resistance R_ct values were increased and the capacitance C_dl values decreased with an increase in the concentration of the inhibitor. This decrease in the capacitance C_dl, which can result from a decrease in the local dielectric constant and/or an increase in the thickness of the electrical double layer, suggests that the inhibitor molecules act by adsorption at the carbon steel/sulfamic acid solution interface.⁵⁴ The addition of inhibitor (DDBAB) provides lower C_dl values, probably as a consequence of the replacement of water molecules by the adsorption of the inhibitor (DDBAB) at the electrode surface. Also the inhibitor molecules may reduce the capacitance by increasing the double layer thickness according to the Helmholtz model:⁵⁵where ε is the dielectric constant of the medium, ε₀ is the vacuum permittivity, A is the surface area of the electrode and δ is the thickness of the protective layer. The value of C_dl is always smaller in the presence of the inhibitor than in its absence, as a result of the effective adsorption of the inhibitor (DDBAB).

Fig. 6 Nyquist plots for the corrosion of the carbon steel electrode in 8% sulfamic acid solution with and without various concentrations of inhibitor (DDBAB).

Table 4 Electrochemical parameters of impedance for X-70 type carbon steel immersed in 8% sulfamic acid solution in the absence and presence of various concentrations of dodecyl dimethyl benzyl ammonium bromide

Conc. (ppm)	Rs, (Ω cm^2)	Cf, (μF cm^2)	n1	Rf (Ω cm^2)	Cdl, (μF cm^2)	n2	Rct, (Ω cm^2)	ηI (%)
Blank	4.7	—	0.94	—	22.3	—	85.6	—
30 ppm	5.32	9.8	0.92	19.5	19.5	0.89	230.1	62.8
60 ppm	6.75	7.3	0.88	22.3	16.8	0.87	588.2	85.4
90 ppm	5.55	5.4	0.86	27.8	16.6	0.86	826.3	89.6
120 ppm	5.97	4.6	0.85	33.1	13.4	0.83	1114.8	92.3
150 ppm	6.58	3.9	0.84	34.7	11.1	0.79	1372.4	93.7

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It is clear that η_I was increased with an increase in the inhibitor concentration. This fact suggests that the inhibitor molecules may first be adsorbed on the carbon steel surface and cover some sites of the electrode surface. Then probably, they form monomolecular layers on the carbon steel surface. These layers protect the carbon steel surface from the attack of hydrogen ions and prevent iron dissolution. EIS spectra were analyzed using the equivalent circuit as illustrated in Fig. 7. This figure reveals a single charge transfer reaction. The diameter of the capacitive loop obtained in 8% sulfamic acid solution was increased in the presence of the inhibitor indicating an inhibition of the corrosion process.

Fig. 7 Equivalent circuit used to fit the impedance data for carbon steel in 8% sulfamic acid solution.

Fig. 8 presents the Bode–phase plot for dodecyl dimethyl benzyl ammonium bromide and carbon steel in 8% sulfamic acid solution at 25 °C. The frequency range of the Bode–phase plot was used to describe the different phenomena occurring at the interfaces, and the phase angle at high frequencies was used to provide a general idea for inhibition performance. It is well known that ideal capacitive behavior would be the result if the phase angle value reached −90°.⁵⁶ Fig. 8 shows an increase of the phase angle shift with the increase of inhibitor concentration and thus a gradual approach of the phase angle towards ideal capacitive behavior. The lower values of phase angle for inhibited solutions compared to that for the uninhibited solution reflect the inhibitive action of the dodecyl dimethyl benzyl ammonium bromide.

Fig. 8 Bode and phase angle plots for the carbon steel electrode in 8% sulfamic acid solution with and without various concentrations of inhibitor (DDBAB).

Variation of the inhibition efficiency with (DDBAB) inhibitor concentration as calculated from three different techniques is presented in Fig. 9.

Fig. 9 Variation of the inhibition efficiency with inhibitor concentration as calculated from three different techniques.

3.4. Surface morphology analysis

3.4.1. SEM studies of the carbon steel surface. To confirm the formation of a protective surface film of the inhibitor on the carbon steel surface, SEM was used to characterize the carbon steel surface. The scanning electron microscopy photographs were recorded (Fig. 10(a–c)) to establish the interaction of organic molecules with the carbon steel surface. A photograph of the polished carbon steel surface before immersion in 8% sulfamic acid solution is shown in Fig. 10(a). The photograph shows that the X70 carbon steel surface was smooth and without pits.^57,58 A photograph of the carbon steel surface after immersion in 8% sulfamic acid solution is shown in Fig. 10(b). The photograph reveals that the X70 carbon steel surface appeared to be full of pits and cavities in the absence of the inhibitor. Fig. 10(c) shows a photograph of the carbon steel surface in 8% sulfamic acid solution with 150 ppm of inhibitor (DDBAB), showing a protective layer and the carbon steel surface immersed in inhibitor (DDBAB) was smoother than that of the blank Fig. 10(b). This is because of the formation of an adsorbed film of (DDBAB) inhibitor reducing the corrosion of the X70 carbon steel in 8% sulfamic acid solution. It can be concluded from Fig. 10(a–c) that the corrosion rate was strongly suppressed in the presence of inhibitor molecules for the API X70-type carbon steel surface in 8% sulfamic acid solution.

Fig. 10 SEM and EDX for the carbon steel surface: (A) polished sample, (B) sample immersed in 8% sulfamic acid solution without inhibitor, (C) sample immersed in 8% sulfamic acid solution with 150 ppm of DDBAB inhibitor.

3.4.2. EDX examinations of the carbon steel surface. EDX survey spectra were used to determine which elements were present on the carbon steel surface before and after exposure to the inhibitor solution. Energy dispersive X-ray analysis (EDX) was carried out in order to analyze the surface composition of the protective film formed. The EDX spectrum of the polished carbon steel sample in Fig. 10(a) shows good surface properties, while the EDX spectrum in the case of the carbon steel sample immersed in 8% sulfamic acid for 28 h in the absence of inhibitor molecules was poor because the sample was severely weakened by external corrosion as shown in Fig. 10(b). The oxygen signal apparent in Fig. 10(b) is due to the exposure of the carbon steel surface to the sulfamic acid in the absence of inhibitor (DDBAB). By adding 150 ppm of DDBAB inhibitor, the EDX spectrum in Fig. 10(c) shows that the Fe peak is considerably suppressed relative to the sample prepared in 8% sulfamic acid solution. The suppression of the Fe peak occurs because of the overlying inhibitor film. These results are in agreement with those previously obtained from chemical and electrochemical measurements, which suggest that a surface film inhibited the metal dissolution, and hence retarded the hydrogen evolution reaction. This surface film also increases the charge transfer resistance of the metal dissolution of the carbon steel, Fig. 10(c), slowing down the corrosion rate. The protective film formed by the inhibitor molecules was strongly adherent to the surface, which leads to a high degree of inhibition efficiency.⁵⁹ Therefore, EDX and SEM examinations of the electrode surface support the results obtained from chemical and electrochemical methods that DDBAB can be regarded as an effective inhibitor for carbon steel in 8% sulfamic acid solutions.

3.5. Quantum chemical calculations

The electronic parameters give information concerning the interaction between inhibitors and the carbon steel surface. Quantum chemical calculations are the most used method to understand the electronic distribution of the inhibitor molecules.^60–62 Frontier orbital theory is useful in predicting the adsorption centers of the inhibitor molecules responsible for the interaction with the carbon steel. The optimized molecular structure, electron density and HOMO–LUMO of the DDBAB inhibitor are shown in Fig. 11(a)–(d).

Fig. 11 (a) The optimized molecular structure of the dodecyl dimethyl benzyl ammonium bromide (DDBAB) inhibitor. (b) Electron density of the dodecyl dimethyl benzyl ammonium bromide (DDBAB) inhibitor. (c) HOMO of the dodecyl dimethyl benzyl ammonium bromide (DDBAB) inhibitor. (d) LUMO of the dodecyl dimethyl benzyl ammonium bromide (DDBAB) inhibitor.

The quantum chemical parameters obtained from the calculations which are responsible for the corrosion inhibition efficiency of the inhibitor and are thought to directly influence the electronic interaction between Fe atoms in the carbon steel surface and the inhibitor, such as the energy of the highest occupied molecular orbital (E_HOMO), the energy of the lowest unoccupied molecular orbital (E_LUMO), the energy gap (ΔE = E_LUMO − E_HOMO) which represents the function of reactivity, the hardness (η = ΔE/2), the softness (σ), the chemical potential (π), the electronegativity (χ), the dipole moment (μ) and the number of transferred electrons from inhibitor atoms to the carbon steel surface (ΔN) all are collected in Table 5.

Table 5 The calculated quantum chemical parameters obtained from DMOL³ calculations

Inhibitor name	EHOMO (eV)	ELUMO (eV)	ΔE (eV)	D (Debye)	I (eV)	A (eV)	χ (eV)	π (eV)	η (eV)	σ (eV^−1)	ω	ΔN
DDBAB	−3.461	−2.255	1.206	1.0466	3.461	2.255	2.858	−2.858	0.603	1.6584	6.773	3.4345

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According to Koopman’s theorem,⁶³ the energy of the HOMO (E_HOMO) of the inhibitor molecules is directly related to the ionization potential (IP) and characterizes the susceptibility of the molecule to attack by electrophiles.

IP = −E_HOMO (9)

The energy of the LUMO (E_LUMO), which represents the ability to receive electrons, is directly related to the electron affinity (EA) and characterizes the susceptibility of the molecule to attack by nucleophiles.^64,65

EA = −E_LUMO (10)

Other quantum chemical parameters that give valuable information about the reactive behavior of the inhibitor such as the electronegativity (χ), the chemical potential (π), the hardness (η) and the softness (σ) were calculated using the following relations:⁶⁶

The inverse of the global hardness is designated as the softness, σ as follows:

The number of transferred electrons (ΔN) was also calculated depending on the quantum chemical method according to the following equation:^62,63

where χ_Fe and χ_inh denote the absolute electronegativity of iron and the inhibitor molecule, respectively; and η_Fe and η_inh denote the absolute hardness of iron and the inhibitor molecule, respectively. The quantum chemistry calculations in Table 5 reveal that the lower the value of the E_LUMO of the inhibitor, the easier the acceptance of the electrons from atoms in the carbon steel surface, which decreases the energy gap and improves the corrosion efficiency of the inhibitor. A higher value of the E_HOMO of the inhibitor corresponds to the ability of this molecule to offer free electrons to the unoccupied d-orbital of the Fe atoms, which decreases the energy gap (ΔE) and increases the corrosion efficiency of the inhibitor for iron in 8% sulfamic acid solutions. In other words, the inhibition efficiency increases if the inhibitor can donate electrons to the metal surface. In addition, the dipole moment (μ), the first derivative of the energy with respect to an applied electric field, is an index that can also be used for the prediction of the direction of a corrosion inhibition process.^67,68 High values of the dipole moment will favor the accumulation of inhibitor molecules on the carbon steel surface.

The energy gap, ΔE, approach, which is an important stability index, was applied to develop theoretical models to explain the structure and conformation barriers in many molecular systems. The energy band gap decreased and the corrosion efficiency of the inhibitor improved, because the energy needed to remove an electron from the last occupied orbital will decrease and hence the ionization potential will be low.⁶⁹ The value of ΔE in Table 5, suggesting the strong ability of the DDBAB inhibitor to form coordinate bonds with the d-orbitals of the carbon steel surface through donating and accepting electrons, is in good agreement with the experimental results. Absolute hardness, η, and softness, σ, are important properties which measure both the stability and reactivity of a molecule. A hard molecule has a large energy gap and a soft molecule has a low energy gap. Soft molecules are more reactive than hard molecules because they could easily offer electrons to an acceptor. The energy gap indicates that the smaller energy gap results in a high corrosion inhibition implying soft–soft interactions of the inhibitor on the carbon steel surface. For the simplest transfer of electrons, adsorption should occur at the part of the molecule where the softness, σ, which is a local property, has the highest value.⁷⁰

In a corrosion system, the iron surface acts as a Lewis acid (electron acceptor) while the inhibitor acts as a Lewis base (electron donor). A bulk iron surface is a soft acid and thus an inhibitor that behaves as a soft base (proton acceptor) is most effective for the corrosion of carbon steel in 8% sulfamic acid. Accordingly, it was concluded that the inhibitor DDBAB with the highest σ value (1.6584 eV⁻¹) has the highest inhibition efficiency, Table 5, which agrees well with the experimental data.

The electronegativity value will decrease with the enhancement of inhibitive efficiencies, as shown in Table 5, because a good inhibitor donates electrons to the atoms in the carbon steel surface. Using a theoretical χ_Fe value of 7 eV mol⁻¹ and a η_Fe value of 0 eV mol⁻¹,⁷¹ the number of electrons transferred from the inhibitor to the atoms in the carbon steel surface (ΔN) was calculated and listed in Table 5. A positive number of electrons transferred (ΔN) demonstrates that the molecules operate as electron donors, while a negative number of electrons transferred (ΔN) indicates that the molecules behave as electron acceptors⁷². The value of ΔN in Table 5 indicates that the DDBAB inhibitor acts as an electron donor and a higher ΔN implies a very large tendency to interact with atoms of the metal surface. The value of ΔN is less than 3.6, which indicates, based on Lukovits’s study, that the inhibition efficiency increased with the increasing electron-donating ability of the inhibitor at the carbon steel surface. In this study, the DDBAB inhibitor was the electron donor, and the iron surface was the electron acceptor. The DDBAB inhibitor was bound to the surface of the carbon steel through adsorption and thus formed an inhibition adsorption layer which decreases the corrosion.

The inhibitor may adsorb on the carbon steel surface atoms in the form of a cation and share electrons between the nitrogen atoms in the inhibitor molecule and the atoms in the carbon steel surface. The other possibility is that the inhibitor molecules are adsorbed through electrostatic interactions between the negatively charged carbon steel surfaces and the positively charged inhibitor molecules.⁷³

It is shown in Fig. 11(a) that the DDBAB inhibitor has a nearly planar structure, which can offer the largest contact area between the atoms in the carbon steel surface and the inhibitor molecules. The inhibiting effect of this inhibitor was attributed to its parallel adsorption at the carbon steel surface by the active centers of adsorption. Due to the planar geometry of the inhibitor, the molecular adsorption probably occurs in such a way that the surface metal atoms and the molecular plane are parallel to each other by donation and back donation between the molecule and the carbon steel surface.

Furthermore, the HOMO level of the DDBAB inhibitor is mostly localized on the phenyl moiety and the nitrogen atom, which indicates that the phenyl moiety and the nitrogen atom are the preferred sites for the electrophilic attack on the carbon steel surface and are probably the primary sites of the bonding at the carbon steel surface, Fig. 11(c). This means that the phenyl moiety and the nitrogen atom with high coefficients of HOMO density are oriented towards the carbon steel surface and the adsorption probably occurs through the π-electrons of the phenyl moiety and the lone pair electrons of the nitrogen atom. Also, the calculations showed that the charge density of the LUMO level is completely delocalized on the phenyl moiety and the nitrogen atom for the DDBAB inhibitor which means that this phenyl moiety and the nitrogen atom could react as electrophiles or Lewis bases (electron donors), Fig. 11(d). It is concluded that this is the region of active centers transforming electrons from N atoms to the iron surface of carbon steel. The electron configuration of iron is [Ar] 4s²3d⁶; the 3d orbitals are not fully filled with electrons. N atoms have lone electron pairs that are important for bonding with the unfilled 3d orbitals of the iron atom and determining the adsorption of the molecules on the metal surface. There is a general consensus by several authors that the more positively charged the heteroatom is, the more it can be adsorbed on the iron surface of carbon steel through donor–acceptor type reactions.^74,75

The molecular electrostatic potential (MEP) is related to the electronic density and is very helpful. The negative region can be regarded as an electrophilic center, whereas the region with a positive electrostatic potential is a potential nucleophilic site. Moreover, the electrostatic potential makes the polarization of the electron density visible. The calculations showed that the phenyl moiety and the nitrogen atom have negative electrostatic potentials which means that these sites are the active centers for the binding to the carbon steel surface, Fig. 12. The structure of the DDBAB inhibitor has a phenyl ring which acts as an electron withdrawing group, and increases the delocalization of the electron cloud on the molecule which enhances its adsorption and improves the corrosion inhibition efficiency. The structure of the inhibitor molecules can affect the adsorption by influencing the electron density at the functional group; the regions of high electron density are generally the sites of electrophilic attack. The electron density is focused on the N atom and the phenyl moiety. This means that these regions have the strongest ability to bond to the metal surface.

Fig. 12 The molecular electrostatic potential of the optimized structure of the DDBAB inhibitor.

3.6. Surface active characteristics

The surface tensions (γ) of the various concentrations of DDBAB cationic surfactant (inhibitor) were measured. The relationship between the surface tension (γ) and the log of the concentration (log C) of the cationic surfactants is shown in Fig. 13. From the obtained curve, it was found that a significant decrease in the surface tension was observed with the increase of the surfactant concentration until the CMC is reached, above which the surface tension is not affected by a further increase in the surfactant concentration. The surface active properties of the DDBAB cationic surfactants were calculated and are summarized in Table 6. The critical micelle concentration (CMC) value of the DDBAB cationic surfactant (1.78 × 10⁻³ mol dm⁻³) was estimated from the intersection point in the γ–log C plot. It is clear that the CMC acts as an effective boundary condition below which, the adsorption of surfactant molecules is typically below the mono-layer level and above which multi-layers of physically adsorbed surfactant molecule can exist,⁷⁶ and lowering the CMC leads to better solubility which is normally from the surfactant concentration in the bulk solution phase.⁷⁷ The data showed that the DDBAB cationic surfactant is considered a strong surface active agent at the air–water interface.

Fig. 13 Surface tension vs. −log C concentration of dodecyl dimethyl benzyl ammonium bromide (DDBAB).

Table 6 Surface activity and thermodynamic properties of dodecyl dimethyl benzyl ammonium bromide (DDBAB) at 25 °C

Compound	CMC (mM L^−1)	πCMC (mN m^−1)	γCMC (mN m^−1)	δγ/∂ log C	Tmax × 10^10 (mol cm^−2)	Amin (Å^2)	pC20 (M L^−1)
DDBAB	1.78	39.3	33	−8.2227	1.66	100.053	−5.1	−15.69	−18.06

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The effectiveness of the DDBAB cationic surfactant (39.3 mN m⁻¹) is good for lowering the surface tension of pure water (72.3 mN m⁻¹) to the detected value (33 mN m⁻¹). The explanation of this result was attributed to the structure of the DDBAB cationic surfactant and the strong binding ability of its counter ion (bromide ion). The surface excess concentration value was 1.66 × 10¹⁰ mol cm⁻². This data means that by increasing the hydrophobic chain length, as in the case of dodecyl dimethyl benzyl ammonium bromide, the hydrophobicity increases. Therefore, the DDBAB cationic surfactant molecules are directed to the interface and the surface energy of the solution decreases. This leads to an increase in the maximum surface excess.⁷⁸

The surface activity of the DDBAB cationic surfactant revealed that the surface pressure (π_CMC = 39.3 mN m⁻¹) of the cationic surfactant increases with a decrease in the minimum surface area (A_min = 100 Ų) of the adsorbed surfactant molecules.⁷⁹ The low value of A_min suggested that the surfactant molecules at the air/water interface are close-packed; therefore, the orientation of the surfactant molecule at the interface was almost perpendicular to the interface leading to the low surface tension at the CMC.

The surface active characteristic results showed a negative value for and for the DDBAB cationic surfactant. This result showed the spontaneity of these two processes in the aqueous phase, i.e., the adsorption and micellization processes occurred in the solution in an exothermic process without the need for energy. Additionally, the value of is more negative than the value of , which indicates that the DDBAB cationic surfactant prefers to be adsorbed at the air/water interface than make micelles in the bulk solution. The adsorption tendency is reflected in the sharp decrease in the surface tension values with a small increase in the concentration.⁸⁰

3.7. Corrosion inhibition mechanism

The cationic surfactant molecules are adsorbed onto the carbon steel surface through a van der Waals attraction force between the head groups and the surface of the carbon steel, in addition to the formation of pπ–dπ bonds between the filled p-orbitals of the surfactant molecules and the vacant d-orbitals of steel surface, Fig. 14(a). One can conclude that the increase in inhibition efficiency achieved at higher inhibitor concentrations indicates that more inhibitor molecules were adsorbed onto the metal surface, thus, providing a wider surface coverage which demonstrates that this compound acts as an adsorption inhibitor, Fig. 14(b). Meanwhile at the overdose concentration (where the maximum inhibition efficiency is obtained), the inter space area between the adsorbed inhibitor molecules on the surface may be less than the area of the inhibitor molecules. So the inhibitor molecules turn out to form double layer adsorption as shown in Fig. 14(c).⁸¹

Fig. 14 Schematic representation for the mode of adsorption of (DDBAB) cationic surfactant molecules on a carbon steel surface immersed in 8% molar sulfamic acid at (a) low concentration, (b) moderate concentration and (c) high concentration of inhibitor.

4. Conclusions

The main conclusions of the present study can be stated in the following points:

• The cationic surfactant, namely dodecyl dimethyl benzyl ammonium bromide (DDBAB), acts as an effective inhibitor for the corrosion of carbon steel in 8% sulfamic acid solution.

• The corrosion inhibition efficiency is due to the adsorption of the inhibitor molecules on the carbon steel surface according to Langmuir’s adsorption isotherm and the blocking of its active sites.

• Weight loss data showed that the addition of DDBAB decreases the dissolution and corrosion rates of carbon steel even after 28 h of the coupons immersion; this effect increases upon increasing the DDBAB concentration.

• Potentiodynamic polarization curves indicated that the selected compound suppresses both anodic and cathodic processes and thus acts as a mixed-type inhibitor.

• The results of EIS indicate that the value of C_dl tends to decrease and both R_ct and η% tend to increase upon increasing the inhibitor concentration. This result can be attributed to the increase of the thickness of the electrical double layer.

• Results obtained from DC polarization, AC impedance and weight loss techniques are in reasonably good agreement and show increased inhibition efficiency with increasing inhibitor concentration.

• The surface active properties of the cationic surfactants were calculated from surface tension measurements.

• Quantum chemical calculations show that the inhibition effect of DDBAB is mainly attributed to the mixed adsorption mechanism assisted by H-bond formation with the carbon steel surface.

• Quantum chemical calculations revealed that the inhibition efficiency of the inhibitor increased with the increase in E_HOMO and the decrease in E_HOMO − E_LUMO.

• The areas containing N atoms and phenyl moieties are the most probable sites for bonding to the metal iron surface by donating electrons to the metal.

• The adsorption of dodecyl dimethyl benzyl ammonium bromide (DDBAB) on a carbon steel surface can occur directly via donor–acceptor interactions between the π-electrons of the phenyl moieties and the vacant d-orbitals of the carbon steel or by electrostatic attraction forces between the positively charged nitrogen atoms and the negatively charged carbon steel surface.

• Surface analysis tools such as SEM and EDX indicated that the DDBAB inhibitor molecules formed a good protective film on the carbon steel surface which isolates the surface from the aggressive environment.

• A smaller band gap favors the adsorption of the DDBAB cationic surfactant on the iron surface and enhances the corrosion inhibition.

• The data obtained from the experimental chemical and electrochemical results are confirmed by theoretical data obtained from quantum chemical calculations.

References

1. D. Jayaperumal, S. Muralidharan, P. Subramanian, G. Venkatachari and S. Senthilvel, Anti-Corros. Methods Mater., 1997, 44(4), 265–268.
2. S. Zhang, Z. Tao, W. Li and B. Hou, Appl. Surf. Sci., 2009, 255, 6757–6763.
3. M. Abdallah, Corros. Sci., 2004, 46(8), 1981–1996.
4. M. S. Morad, J. Appl. Electrochem., 2008, 38(11), 1509–1518.
5. M. A. Migahed and I. F. Nassar, Electrochim. Acta, 2008, 53(6), 2877–2882.
6. J. R. Kish, N. J. Stead and D. L. Singbeil, Corrosion, 2009, 65(7), 491–500.
7. T. Shahrabi, H. Tavakholi and M. G. Hosseini, Anti-Corros. Methods Mater., 2007, 54(5), 308–313.
8. M. Mahdavian and S. Ashhari, Electrochim. Acta, 2010, 55(5), 1720–1724.
9. P. Zhao, Q. Liang and Y. Li, Appl. Surf. Sci., 2005, 252(5), 1596–1607.
10. M. A. Migahed, M. M. Shaban, A. A. Fadda, T. Awad Ali and N. A. Negm, RSC Adv., 2015, 5, 104480–104492.
11. K. F. Khaled and M. A. Amin, Corros. Sci., 2009, 51, 2098–2106.
12. M. Motamedi, A. R. Tehrani-Bagha and M. Mahdavian, Corros. Sci., 2013, 70, 46–54.
13. M. Motamedi, A. R. Tehrani-Bagha and M. Mahdavian, Electrochim. Acta, 2011, 58, 488–496.
14. A. A. Hermas and M. S. Morad, Corros. Sci., 2008, 50(9), 2710–2717.
15. K. F. Bonhoffer and K. E. Heascer, Z. Phys. Chem., 1956, 8, 390.
16. Experimental Electrode Kinetics, ed. N. D. Greene, Rensselaer Polytechnic Institute, New York, 1963.
17. X. Liu, S. Houyi Ma, G. Liu and L. Shen, Appl. Surf. Sci., 2006, 235, 814.
18. N. M. Van Os, Non-ionic surfactant organic chemistry, Surfactant Science Series, Marcel Dekker, New York, 1998, vol. 72.
19. M. A. Amin, J. Appl. Electrochem., 2006, 36(2), 215–226.
20. J. Vosta, J. Eliasek and P. Knizek, Corrosion, 1976, 32(5), 183–187.
21. Y. Tang, X. Yang, W. Yang, R. Wan, Y. Chen and X. Yin, Corros. Sci., 2010, 52(5), 1801–1808.
22. Y. Tang, X. Yang, W. Yang, Y. Chen and R. Wan, Corros. Sci., 2010, 52(1), 242–249.
23. S. M. A. Hosseini, M. Salari, E. Jamalizadeh and A. H. Jafari, Corrosion, 2012, 68(7), 600–609.
24. B. Delley, J. Chem. Phys., 2000, 113(18), 7756–7764.
25. Modeling and Simulation Solutions for Chemicals and Materials Research, Materials Studio (Version 7.0), Accelrys software Inc., San Diego, USA, 2011, http://www.accelrys.com.
26. W. J. Hehre, L. Radom, P. V. R. Schlyer and J. A. Pople, Ab Initio Molecular Orbital Theory, John Wiley, New York, 1986.
27. A. Kessi and B. Delley, Int. J. Quantum Chem., 1998, 68(2), 135–144.
28. B. Hammer, L. B. Hansen and J. K. Nørskov, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59(11), 7413–7421.
29. A. Matveev, M. Staufer, M. Mayer and N. Rösch, Int. J. Quantum Chem., 1999, 75(4–5), 863–873.
30. N. A. Negm, A. F. El Farargy, A. M. Al Sabagh and N. R. Abdelrahman, J. Surfactants Deterg., 2011, 14(4), 505–514.
31. Z. Tao, S. Zhang, W. Li and B. Hou, Corros. Sci., 2009, 51(11), 2588–2595.
32. I. Aiad, M. M. El-Sukkary, E. A. Soliman, M. Y. El-Awady and S. M. Shaban, J. Ind. Eng. Chem., 2014, 20(5), 3524–3535.
33. I. L. Rozenfeld, Corrosion Inhibitors, McGraw-Hill, New York, 1981.
34. I. Ahamad and M. A. Quraishi, Corros. Sci., 2009, 51(9), 2006–2013.
35. S. A. Abd El-Maksoud and A. S. Fouda, Mater. Chem. Phys., 2005, 93(1), 84–90.
36. A. S. Fouda, H. A. Mostafa, M. N. Moussa and Y. M. Darwish, Bull. Soc. Chim. Fr., 1987, 2, 261.
37. A. A. Abdul-Azim, L. A. Shalaby and H. Abbas, Corros. Sci., 1974, 14(1), 21–24.
38. I. B. Obot and N. O. Obi-Egbedi, Port. Electrochim. Acta, 2009, 27(4), 517–524.
39. F. Tang, X. Wang, X. Xu and L. Li, Colloids Surf., A, 2010, 369(1–3), 101–105.
40. G. Quartarone, M. Battilana, L. Bonaldo and T. Tortato, Corros. Sci., 2008, 50(12), 3467–3474.
41. P. Morales-Gil, G. Negrón-Silva, M. Romero-Romo, C. Ángeles-Chávez and M. Palomar-Pradavé, Electrochim. Acta, 2004, 49(26), 4733–4741.
42. M. Abdallah, Corros. Sci., 2002, 44(4), 717–728.
43. Y. S. Ding, M. Zha, J. Zhang and S. S. Wang, Colloids Surf., A, 2007, 298(3), 201–205.
44. P. Kuteja, J. Vosta, J. Pancir and N. Hackerman, J. Electrochem. Soc., 1995, 142(6), 1847–1850.
45. M. A. Migahed, R. O. Aly and A. M. Al-Sabagh, Corros. Sci., 2004, 46(10), 2503–2516.
46. C. Okafor and Y. Zheng, Corros. Sci., 2009, 51(4), 850–859.
47. M. Behpour, S. M. Ghoreishi, N. Soltani, M. Salavati-Niasari, M. Hamadanian and A. Gandomi, Corros. Sci., 2008, 50(11), 2172–2181.
48. K. Bhrara, H. Kim and G. Singh, Corros. Sci., 2008, 50(10), 2747–2754.
49. M. N. H. Moussa, A. A. El-Far and A. A. El-Shafei, Mater. Chem. Phys., 2007, 105(1), 105–113.
50. K. C. Emregül and M. Hayvalí, Corros. Sci., 2006, 48(4), 797–812.
51. S. Haruyama, T. Tsuru and B. J. Gijutsu, Japan Society of Corrosion Engineering, 1978, 27, 573–581.
52. M. A. Migahed, A. M. Al-Sabagh, E. G. Zaki, H. A. Mostafa and A. S. Fouda, Int. J. Electrochem. Sci., 2014, 9, 7693–7711.
53. G. E. Badr, Corros. Sci., 2009, 51(11), 2529–2536.
54. Y. Tang, X. Yang, W. Yang, Y. Chen and R. Wan, Corros. Sci., 2010, 52(1), 242–249.
55. E. E. Oguzie, Y. Li and F. H. Wang, Electrochim. Acta, 2007, 53(2), 909–914.
56. M. A. Hegazy, A. Abdel Nazeer and K. Shalabi, J. Mol. Liq., 2015, 209, 419–427.
57. S. Deng and X. Li, Corros. Sci., 2012, 55, 407–415.
58. ASTM E 45-87, Annual Book of ASTM Standard, ASTM, Philadelphia, PA, 1980, vol. 11, p. 125.
59. M. A. Amin, S. S. Abd El-Rehim, E. E. F. El-Sherbini and R. S. Bayoumi, Electrochim. Acta, 2007, 52(11), 3588–3600.
60. F. Bentiss, M. Lagrenee, B. Elmehdi, B. Mernari, M. Traisnel and H. Vezin, Corrosion, 2002, 58(5), 399–407.
61. K. F. Khaled, Corros. Sci., 2010, 52(10), 3225–3234.
62. I. Lukovits, E. Kalman and F. Zucchi, Corrosion, 2001, 57(1), 3–8.
63. V. S. Sastri and J. R. Perumareddi, Corrosion, 1997, 53(8), 617–622.
64. S. Zor, M. Saracoglu, F. Kandemirli and T. Arslan, Corrosion, 2011, 67(12), 125003.
65. L. A. F. Costa, H. S. Breyer and J. C. Rubim, Vib. Spectrosc., 2010, 54(2), 103–106.
66. R. R. Zaky, K. M. Ibrahim, H. M. Abou El-Nadar and S. M. Abo-Zeid, Spectrochim. Acta, Part A, 2015, 150, 40–53.
67. C. Hansch and A. Leo, Substituentz for Correlation Analysis in Chemistry and Biology, Wiley, New York, NY, USA, 1979.
68. A. L. R. Silva, V. M. F. Morais and M. D. M. C. Ribeiro da Silva, J. Mol. Struct., 2014, 1078, 197–206.
69. F. Khaled, Appl. Surf. Sci., 2008, 255(5), 1811–1818.
70. S. Martınez, Mater. Chem. Phys., 2002, 77(1), 97–102.
71. H. Ju, Z. Kai and Y. Li, Corros. Sci., 2008, 50(3), 865–871.
72. E. El Ashry, A. El Nemr and S. Ragab, J. Mol. Model., 2012, 18(3), 1173–1188.
73. A. Lalitha, S. Ramesh and S. Rajeswari, Electrochim. Acta, 2005, 51(1), 47–55.
74. G. Bereket, C. Ogretic and C. Ozsahim, J. Mol. Struct.: THEOCHEM, 2003, 663, 39–46.
75. A. Hegazy and F. M. Atlam, J. Mol. Liq., 2016, 218, 649–662.
76. M. A. Migahed, N. A. Negm, M. M. Shaban, T. A. Ali and A. A. Fadda, J. Surfactants Deterg., 2016, 19(1), 119–128.
77. M. J. Rosen, Surfactants and Interfacial Phenomena, Wiley, New York, 2nd edn, 1992.
78. T. Dam, J. B. F. N. Engberts, J. Karthäuser, S. Karaborni and N. M. van Os, Colloids Surf.,A, 1996, 118(1–2), 41–49.
79. N. A. Negm and A. S. Mohamed, J. Surfactants Deterg., 2008, 11(3), 215–221.
80. M. Behpour, S. M. Ghoreishi, N. Soltani and M. S. Niasari, Corros. Sci., 2009, 51(5), 1073–1082.
81. A. M. Al-Sabagh, M. A. Migahed and M. Abd El-Raouf, Chem. Eng. Commun., 2012, 199, 737–750.

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