Author Correction: Adsorption, thermodynamic, and quantum chemical investigations of an ionic liquid that inhibits corrosion of carbon steel in chloride solutions

The purpose of this work lies in the use of ionic liquids as corrosion inhibitors due to the difficulty in some oil fields with the solubility of corrosion inhibitors and these materials can be miscible with water and thus provide a solution to such problems in the industry. The second purpose is concerned with the lower toxicity of these compounds compared with the most common corrosion inhibitors. The study covered the corrosion inhibition performance of the ionic liquid 1-butyl-3-methylimidazolium trifluoromethyl sulfonate ([BMIm]TfO) for carbon steel in 3.5% NaCl solutions. The study comprised electrochemical, adsorption, and quantum chemical investigations. The results manifested that [BMIm]TfO can be considered a promising corrosion inhibitor and the inhibition efficacy intensifies as the concentration rises. The observed inhibitive effect can be correlated to the adsorption of the ionic liquid species and the creation of protecting films on the surface. The mode of adsorption follows the Langmuir adsorption isotherm. The polarization results showed that the ionic liquid [BMIm]TfO functions as a mixed inhibitor. Reliance of the corrosion influence on the temperature in the existence and absence of [BMIm]TfO was demonstrated in the temperature range of 303–333 K using polarization data. Activation parameters were determined and discussed. The observed inhibition performance of [BMIm]TfO was correlated with the electronic properties of the ionic liquid using a quantum chemical study.

www.nature.com/scientificreports/ bearing on the levels of adsorption and inhibition efficiency that may be achieved with those liquids. In a recent study, we demonstrated that the ionic liquid 1-butyl-1-methylpyrrolidinium trifluoromethyl sulfonate ([BMP] TfO) may serve as a bi-functional inhibitor for both the corrosion of carbon steel in chloride solutions and the growth of bacteria.
[BMP]TfO inhibits both types of corrosion 13 . It was also shown that the ionic liquids 1-(2-hydroxyethyl)-3-methylimidazolinium chloride and 1-ethyl-3-methyleimidazolinium chloride are effective corrosion inhibitors and biocides. These findings were published in the journal Ionic Liquids 14 . It was shown that the integration of the hydroxy group in the imidazolium cation enhances the corrosion inhibition impact 15 . In this paper, the corrosion inhibition performance of the ionic liquid [BMIm]TfOfor carbon steel in 3.5% NaCl solutions was demonstrated. The study comprised electrochemical, adsorption, and quantum chemical investigations.

Materials and methods
Materials. High purity [BMIm]TfO, was obtained from Io.Li.Tec.Co., Germany, and it was used as received.
Carbon steel specimens having dimensions of (5.6 cm L, 2.7 cm W, and 0.5 cm T) were used for the standard procedures of the corrosion measurements. Before use, the steel coupons were abraded with proper emery papers to give a homogeneous surface. An aggressive solution of 3.5% NaCl was prepared as a simulated corrosive environment. Different concentrations of the employed ionic liquid, 25, 50, 100, 200, and 500 ppm, were used, and various temperatures of 303, 313, 323, and 333 K, were applied.
Methods. For the electrochemical measurements, a common cell, fitted with a reference electrode-saturated calomel reference electrode (SCE) a counter electrode (CE), platinum, and the working electrode (WE), carbon, steel, was utilized. All electrochemical tests were performed employing a Volta lab 40 Potentiostat PGZ 301. Polarization experiments were carried out by sweeping the electrode potential at a rate of 2 mVs −1 and recordings the current. All polarization data were fitted using the fitting tools implemented in Volta Master 4 software by Tafel extrapolation method. The frequency range of 100 kHz-0.05 Hz with an amplitude peak of 10 mV using an AC signal was applied for the electrochemical impedance measurements. The impedance curves were fitted using the ZSimpWin3.60 software. For weight loss measurements, rectangular-shaped steel specimens with dimensions of 3 cm × 5 cm × 0.05 cm were used. The immersion time was 6 h in 3.5% NaCl at different temperatures in the absence and presence of different concentrations of [BMIm]TfO. A scanning electron microscope, JEOL model JSM-53000, was employed for investigating the morphology of the electrodes. The quantum chemical investigations were executed using MP2 functional with a 3-21 G (d,p) basis set. The energies of high occupied molecular orbital (E HOMO ) and low unoccupied molecular orbital (E LUMO ) were estimated. Furthermore, the energy gap between LUMO and HOMO (ΔE) was determined 16 .

Results and discussions
Potentiodynamic polarization. The curves of Fig. 1 show potentiodynamic polarization responses of carbon steel in 3.5% NaCl solutions free and containing different amounts of [BMIm]TfO. The parameters obtained from the polarization curves, corrosion currents and potentials (i corr , E corr , respectively), corrosion rate (CR), inhibition efficiency based on corrosion current density (EF icorr %), and efficiency based on the corrosion rate (EF CR %), cathodic Tafel slope (b c ), and anodic Tafel slope (b a ) are presented in Table 1. As shown in Fig. 1, the polarization curve recorded in absence of [BMIm]TfO exhibits an active trend as the current steeply rises with sweeping the potential. In addition to the ionic liquid inhibitor, a slight impact was noticed on the cathodic branch of the curve. However, a pronounced effect was recorded on the anodic branch. Both the cathodic and anodic curves shift to more negative and more positive potentials, respectively, on the addition of the [BMIm] TfO revealing the inhibiting influence. www.nature.com/scientificreports/ As the content of [BMIm]TfO increases, the current density decreases, and subsequently the corrosion rate reduces Table 1. The highest inhibition efficiency was 75% for the inhibitor concentration of 800 ppm. The observed inhibition influence is due to the creation of a protecting layer because of the adsorption of the ionic liquid species on the electrode surface. This layer isolates the surface from the corrosive environment which, in turn, leads to the observed inhibition.   TfO. As manifested in Fig. 3, the plots show imperfect capacitive loops. The higher the loop diameter always reveals stop corrosion resistance 18 . With the addition of [BMIm]TfO, the diameter increases signifying its inhibiting effect on the corrosion of carbon steel in the test electrolyte. This is attributable to the adsorption and formation of a protecting film of the ionic liquid on the electrode surface. This film masks the surface, leading to the lessening of the corrosion attack as evidenced by the reduction of the estimated double layer capacitance C dl , Table 2. Also, the values of (R S ), (R P1 ), and (R P2 ) increase as the content of [BMIm]TfO increases 19 .
The equivalent circuit used to fit the Nyquist plots is shown in Fig. 4. The values of the estimated EIS parameters are compiled in Table 2. The parameters include the solution resistance (R s ), the constant phase element (Q), the polarization resistance between the surface and the formed film during the immersion in the test electrolyte (R p1 ), the capacitance of double layer (C dl ), and the corrosion resistance at the surface film/electrolyte interface (R p2 ).

Adsorption isotherms.
Adsorption isotherm studies were performed to explore the nature of the interaction of the ionic liquid species with the carbon steel surface. Several adsorption isotherms can describe the rela-    where (θ) is the surface coverage degree (obtained previously from EIS and PDP measurements), (C inb ) is the concentration of [BMIm]TfO, and (K ads ) is the adsorption equilibrium constant. Plotting the Langmuir relation between C inb /θ and C inb gives significant straight lines with a correlation coefficient of unity and an average slope value of 1.35, Fig. 5a. Thus, it is evidence that the ionic liquid species are adsorbed in absence of any side interactions 18 . The equilibrium constant for [BMIm]TfO adsorption (K ads ) was calculated using the intercept of the C inb /θ versus C inb line, Table 3. Consequently, K ads value was employed to estimate the adsorption standard free energy (ΔG°a ds ) based on the Eq. (2): where R, T, and 55.5 are gas constant, the temperature of the system, and water molecules concentration in molar. The values of ∆Goads were determined for the ionic liquid inhibitor at different temperatures as shown in  www.nature.com/scientificreports/ TfOon the surface and refer to the steadiness state of the adsorbed layer. This behaviour indicates the intensive interaction between the ionic liquid constituents and the electrode surface 21 . As a common concept, the values of ∆G o ads up to − 20 kJ mol −1 are associated with the electrostatic interaction of the charged compounds with the charged surface in which the adsorption process, in this case, is only physical. With increasing the values of ∆G o ads above − 40 kJ mol −1 the chemical adsorption will be found 22 . From the obtained measurements, the values of ∆G o ads were stabilized at − 31 kJ mol −1 in the temperature range from 303 to 333 K. This indicates that the adsorption of ionic liquid species is typical physical sorption. The results reveal that the adsorption of the species of the ionic liquid, typically the imidazolium cation, occurs physically, electrostatically, via the interaction between the imidazolium cation and the charged centers on the electrode surface. The spontaneous nature of the adsorption of the ionic liquid species on the surface is indicated by the negative values of ∆G o ads 23 . The heat of adsorption ∆H o ads was also estimated from the Van't Hoff Eq. (3): By plotting the relation between ln K ads against 1/T a straight line is obtained as manifested in Fig. 5b Table 3, it is obvious that the ∆S o ads value is the negative sign (− 162 J mol −1 K −1 ). The negative signal of ∆S o ads can be correlated to dissolute medium which is generally proved as a growth in the disorder, as the reactants are turning into efficient complexes. Moreover, the observed manner can be explained by the substitution mechanism of more water molecules throughout the adsorption process of ionic liquid on the surface 24 .

Kinetic activation. Additional to the thermodynamic investigations, the kinetic activation model is also
an important technique to study the inhibition mechanism and explain the features of the protective action of [BMIm]TfO at different temperatures. Arrhenius equation was employed to estimate the activation parameters of the corrosion see Eq. (5) 25 : where, (CR) represents the corrosion rate, (E a ) is the energy of activation, (R) is the gas constant, and (A) is the pre-exponential factor.
The Arrhenius plots of the relation between the ln (CR) and 1/T are depicted in Fig. 6a. As seen, a linear behavior is obtained and the slopes of the straight lines is (− E a /R) hence, the values of the activation energy (E a ) in the presence and absence of various concentrations of [BMIm]TfO were determined. Moreover, there is another formulation for the transition state as described in the following Eq. (6) 26 .
The terms of the equation are, Plank's constant (h), Avogadro's number (N), the activation entropy (∆S * ), and the activation enthalpy (∆H * ). The plots of ln CR/T versus 1/T for the ionic liquid inhibitor are presented in Fig. 6b. The slope of the obtained lines equals (−∆ H * /R) and the intercept is (lnR/Nh + ∆S * /R), hence the values of ∆H * and ∆S * can be estimated. At definite concentration ranges of the ionic liquid inhibitor, the activation parameters for carbon steel in sodium chloride medium are gathered and illustrated in Table 4. The results reveal that with the existence of [BMIm]TfO the activation energy rises, and the activation enthalpy slightly reduces meanwhile the values of the entropy for the corrosion process significantly rise. The energy of activation (Ea), which is the minimal amount of energy required to launch a chemical reaction, reaches a value of 24 kJ mol −1 at a high ionic liquid content and for the blank solution is only 16 kJ mol −1 . The increase of the E a value under the effect of ionic liquid inhibitor might be attributed to the physical sorption regime 27 . Additional explanation reported that the raising of the activation energy value might also be attributable to the gradual reduction in the adsorption process of [BMIm]TfO on the surface under the effect of heat. Based on these phenomena, as the adsorption process reduces more desorption action of ionic liquid species occurs as the protection and dissolution systems are in balance. It is also revealed that the sequential values of E a and ∆H o as presented in Table 4 are varied in the same trend confirming the common thermodynamic phenomena. On particular monitoring, it has been observed that the value of the activation entropies is negative signifying that the activated complex is in the rate-determining stage and demonstrating combination rather than separation 28 . www.nature.com/scientificreports/ Surface analysis. The utilization of surface analytical techniques is quite significant for realizing the characteristics of materials, especially the metallic surfaces after exposure to the various aggressive environments. SEM-EDX examination of the electrode surface following dipping in the test electrolytes was performed. The SEM images of Fig. 7a and b show the surface after the exposure to3.5% NaCl without and with the addition of [BMIm]TfO, respectively. Figure 7a representative the SEM image of the uninhibited steel surface shows a deteriorated, rough surface as a result of the corrosion 29 .
In the absence of [BMIm]TfO the whole surface of the carbon steel is usually concealed with the corrosion products. The porous corrosion product layer is unable to protect the surface from extreme corrosion. The addition of the ionic liquid inhibitor to the test electrolyte reduced the aggressive attack on the steel surface as revealed in Fig. 7b. The surface is relatively free from the corrosion products and compared with the uninhibited sample the surface is smoother signifying the inhibiting action of [BMIm]TfO 30 . Figure 8 represents the EDX spectrum of the uninhibited sample Fig. 8a and inhibited sample Fig. 8b since it shows confirms the SEM results as, in addition to the Fe, O, and C peaks, a peak of N is recorded owing to the adsorption of the imidazolium cation leading to the observed corrosion inhibition. Furthermore, under the  www.nature.com/scientificreports/ continuation of the IL coverage, the spectrum intensities decrease because of the formation of the IL adsorptive layer on the surface 31 .
Quantum chemical studies. As known, the application of quantum chemical calculations is necessary to demonstrate the relation between the molecular/electronic structure of the inhibitor and its corrosion inhibiting efficiency 32 . Furthermore, the theoretical studies allow the optimum pre-selection of the inhibitor with the desired characteristics 33 . The molecular geometry of the employed ionic liquid was optimized using the PM6 semiempirical method. The optimized structures were then re-optimized by ab initio Hartree-Fock method (HF) using 6-31 + G(d,p) basis set at Hartree-Fock level (HF) 34 , and by density functional theory (DFT) method using 6-31 + G(d,p) basis set. The values of the calculated bond length, bond angle, and dihedral angle using the DFT 6-31 + G (d,p) method are compiled in Table 5. All calculations were made by gaussian 09 W software using the B3LYP functional 35 . B3LYPutilizesBache's three-parameter functional (B3) and comprises a combination of HF with DFT exchange terms and the Lee, Yang, and Parr (LYP) correlation functional 36 .
The optimized molecular structure, the electrostatic potential feature, and the identical HOMO and LUMO electron density surfaces of the ionic liquid inhibitor, as demonstrated patterns by IL employing PM3 model chemistry, are symbolized in Fig. 9a-d. From the optimized structure, Fig. 9a it is seen the planar pentagon structure of the imidazolium ring. The electrostatic potential Fig. 9b it shows the electron cloud around the chemical structure. The sequential distribution of electrons of HOMO Fig. 9c shows information about the positions or locations that are significant in the system to accord the electrons to the contrasting orbital of the recipient molecule. On the other hand, the prevalence of electrons of LUMO Fig. 9d shows information about the molecule sites that are restricted to recognize the electron from a-convenient granter one 37 .
From Fig. 9c, it is obvious that the electron density of the HOMO is generally combined with the imidazolium cation in the ionic liquid structure indicating the contribution of the imidazolium ring in the adsorption of ionic liquid on the steel surface. This is consistent with the recently published results which indicated, based on quantum chemical studies, that the imidazolium ring is likely the crucial active site in imidazolium-based ionic liquids 38 . The calculated values of the quantum chemical parameters, E HOMO , E LUMO, and ΔE, which are mainly affected by the electron interactions between the steel surface and the ionic liquid inhibitor were illustrated in Table 6. The E HOMO value describes the ability of the inhibitor to donate electrons to the electrode surface, while the E LUMO measures the capability to receive electrons into the LUMO molecule from a suited donor molecule [39][40][41] . The energy gap (ΔE), which is obtained from the difference between E LUMO and E HOMO , is also a substantial factor that can be employed to detect the molecule's activity. Mainly, the minimal ΔE value is related to large inhibition efficiency and chemical reactivity [42][43][44] . This means the inhibitor on the surface more easily gives/receives www.nature.com/scientificreports/ electrons and subsequently the adsorption of the inhibitor on the surface becomes easier. The negative sign of E HOMO refers to the physical adsorption nature of the ionic liquid inhibitor [45][46][47] .
In the light of the above results, it can be concluded that the employed ionic liquid is electrostatically adsorbed on the steel surface and the imidazolium cation is responsible for the observed inhibiting influence as the imidazolium ring is parallelly absorbed on the steel surface.

Conclusions
[BMIm]TfO was examined as a possible corrosion inhibitor for carbon steel in chloride solutions. The results revealed the inhibiting action of [BMIm]TfO which increases as the concentration increases. The potentiodynamic polarization results showed that the ionic liquid is a mixed inhibitor as both cathodic and anodic processes were influenced. The inhibiting act of [BMIm]TfO is attributable to the adsorption of the imidazolium cations on the carbon steel surface establishing a barrier layer that protects the surface from the aggressive medium. The adsorption of the [BMIm]TfO was found to obey Langmuir isotherm. The free energy of adsorption revealed that the adsorption of the ionic liquid species occurs physically via the electrostatic interaction of the imidazolium cation with the charged centers on the electrode surface. The results proved that ionic liquids can be used as corrosion inhibitors for carbon steel in brine solutions with a high efficiency that enables them to compete with the commercial inhibitors currently used, despite their high price, they are considered competitive for more than one reason, including their effectiveness and the most important reason is that they are less toxic and therefore www.nature.com/scientificreports/ in line with the global trend to replace toxic materials. So, it could be currently used with potential effects and less toxic materials, which makes these materials ready to compete in the field of oil and gas industry. www.nature.com/scientificreports/

Data availability
The datasets generated and/or analyzed during the current study are available in this published article.