Experimental and Theoretical Study on the Inhibition Performances of

Article pubs.acs.org/IECR

Experimental and Theoretical Study on the Inhibition Performances of Quinoxaline and Its Derivatives for the Corrosion of Mild Steel in Hydrochloric Acid JiaJun Fu,* HaiShan Zang, Ying Wang, SuNing Li, Tao Chen, and XiaoDong Liu School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, JiangSu Province, China ABSTRACT: The inhibition of mild steel corrosion in 1.0 M HCl solution by quinoxaline and its derivatives were evaluated at 25 °C using weight loss measurement and Tafel polarization technique. These measurements reveal that the inhibition efficiency increased with increase in the concentrations of inhibitors, and the inhibition efficiencies decrease in the order 4-(quinoxalin-2yl)phenol (PHQX) > 2-quinoxalinethiol (THQX) > 2-chloroquinoxaline (CHQX) > quinoxaline (QX). Tafel polarization curves show that all the investigated inhibitors act as mixed-type inhibitors. Quantum chemical calculation was applied to correlate electronic structure parameters of quinoxaline and its derivatives with their inhibition performances. Molecular dynamics simulations were also used to optimize the equilibrium configurations of the inhibitor molecules on the iron surface. The efficiency order of the studied inhibitors obtained by experimental results was verified by theoretical calculations.

1. INTRODUCTION Corrosion of metals is a fundamental academic and industrial problem that has recently received more and more attention because metallic structures are easily destroyed through anodic dissolution.1−3 The prevention of corrosion plays an important role in economics and safety. Among numerous corrosion prevention measurements, the use of inhibitors is one of the most efficient alternatives to protect metals against corrosion, especially in acidic media due to its advantages of economy, high efficiency, and wide applicability.4−6 The existing data show that most of the well-known corrosion inhibitors are organic compounds containing heteroatoms, such as sulfur, phosphorus, nitrogen, or oxygen, and multiple bonds, which act through a process of surface adsorption.7−9 The adsorption occurs due to the interaction of the lone pair or π-orbitals of inhibitor molecules with d-orbitals of the metal surface atoms. The adsorption characteristics of inhibitors which determine the corrosion efficiency depends on not only some physicochemical and electronic properties of inhibitor molecules, including functional groups, the molecular size, the electronic density of donor atoms, etc., but also the characteristics of the environment, such as the nature and surface charge of the metal and the type of the corrosion medium.10−12 With increasingly stringent environmental policies, it is very urgent to search for effective, safe, and environmentally friendly corrosion inhibitors. Traditionally, the large-scale and trial-anderror experimental methods such as the rotation specimen method and dynamic simulation for cooling water are mainly used to assess the performances of corrosion inhibitors.13 However, they are often expensive and time-consuming, and they cannot elucidate the inhibition mechanism. With the improvement of hardware and software in computational science, theoretical chemistry such as quantum chemical calculation and molecular dynamics simulation method has been used recently to explain the mechanism of corrosion inhibition.14−18 Since Vosta first studied the inhibition © 2012 American Chemical Society

mechanism using quantum chemistry calculation in 1971, researchers have focused on exploring the relationship between the corrosion inhibition efficiency and a number of quantum parameters, which will be helpful for obtaining a molecular design of newly effective corrosion inhibitors. However, the disadvantage of this method is that it is not suitable for large systems containing hundreds or even thousands of atoms because of the huge workload. Compared with quantum chemical calculation, the molecular dynamics simulation method would be a better choice for large systems and illustrate the adsorption properties of inhibitor molecules onto the metal surface at a molecular level. In this method, some valuable information about interfacial configuration and interaction energy between inhibitor molecules and the metal surface were calculated, and during the process of calculations the interaction of electrons and global or local reactivity indices of inhibitor molecules are not taken into consideration.19 It seems that the molecular dynamics simulation has the potential to be a supplemental method for quantum chemical calculation in the corrosion computational field. Obviously, it would be facile to obtain full-scale and detailed information by combination of the above-mentioned computational methods, which also provide a new research route in the investigation of inhibition mechanisms. Quinoxaline is a heterocyclic aromatic organic compound which consists of the fusion of benzene and pyrazine. Quinoxaline is commercially available, and the usual synthesis involves cyclization of o-phenylenediamine with glyoxal. Quinoxaline and its derivatives play a vital role in various fields such as dyes, pharmaceuticals, pesticides, and feedstuff.20,21 Although the experimental works of Obot et al. and Hammouti et al. have proved that quinoxaline derivatives are Received: Revised: Accepted: Published: 6377

December 4, 2011 April 8, 2012 April 10, 2012 April 10, 2012 dx.doi.org/10.1021/ie202832e | Ind. Eng. Chem. Res. 2012, 51, 6377−6386

Industrial & Engineering Chemistry Research

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this theorem within DFT, its validity is generally accepted. I and A are related in turn to EHOMO and ELUMO as follows:

efficient inhibitors for mild steel and copper in acidic solution,22−24 the combined use of quantum chemical calculation and molecular dynamic simulation in probing the inhibition mechanisms is scanty. The aim of the present work was to investigate the effects of quinoxaline and its derivatives as alternative acid corrosion inhibitors for mild steel in 1.0 M HCl solution using chemical and electrochemical techniques. The relationships between the inhibition performances of the investigated inhibitors in 1.0 M HCl and some quantum chemical parameters such as the highest occupied molecular orbital energy (EHOMO), the lowest unoccupied molecular orbital energy (ELUMO), the energy gap between ELUMO and EHOMO (ΔELUMO−HOMO), dipole moments (μ), total negative charges on atoms (TNC), molecular volume (MV), electronegativity (χ), global chemical hardness (η), softness (σ), and the fraction of electrons transferred from the inhibitor to the iron surface (ΔN) have also been investigated by quantum chemical calculations. Additionally, molecular dynamics simulations were performed to simulate the adsorption of quinoxaline and its derivatives on an iron surface and advance the understanding of interactions between these inhibitor molecules and the iron surface. After all the calculations, experimental inhibition efficiencies and theoretical results shall be correlated to validate the accuracy of the proposed theoretical methodology for evaluation of inhibition of new inhibitors. Figure 1 represents quinoxaline and its

I = −E HOMO

(1)

A = −E LUMO

(2)

The absolute electronegativity, χ, and absolute hardness, η, of the inhibitor molecule are given by χ=

I+A 2

(3)

η=

I−A 2

(4)

The global softness, σ, can also be defined as follows:

σ=

1 η

(5)

The fraction of electrons transferred from the inhibitor molecule to the metallic atom (ΔN) was calculated according to Pearson from the obtained values of χ and η. For the calculation the following formula was used: χFe − χinh ΔN = 2(ηFe + ηinh) (6) Using a theoretical value, χFe = 7 eV, and a global hardness of ηFe = 0, by assuming that for a metallic bulk I = A, because they are softer than the neutral metallic atoms.27 2.2. Molecular Dynamics Simulations. The molecular dynamics (MD) simulations were conducted using the discover molecular dynamics model in Materials Studio software (Version 5.0) from Accelrys Inc. (San Diego, CA, USA). The Fe(110) surface was chosen for the simulation study due to its stable property. The MD simulation of the interaction between the quinoxaline and its derivatives molecules and the Fe(110) surface was carried out in a simulation box (29 Å × 29 Å × 67 Å) with periodic boundary conditions in order to model a representative part of an interface devoid of any arbitrary boundary effects. The Fe(110) surface was first built by cleaving the Fe crystal and optimizing it to minimum energy using the Smart Minimizer method, and then surface area of Fe(110) was enlarged by the supercell function and its periodicity was changed simultaneously. The number of layers in the structure was chosen to be six, which ensures that the inhibitor molecule will only be involved in nonbond interactions with Fe atoms in the layers of the surface. Finally, a vacumm slab with 20 Å thickness was built on the Fe(110) surface. The behavior of the inhibitor molecule on the Fe(110) surface was simulated using a COMPASS (condensed phase optimized molecular potentials for atomistic simulation studies) force field. COMPASS is a powerful force field supporting atomistic simulation of condensed phase materials and enables accurate and simultaneous prediction of structural, conformational, vibrational, and thermophysical properties for a broad range of molecules in isolation and in condensed phase, and under a wide range of conditions of temperature and pressure.28 The MD simulation was performed under 298 K, NVT ensemble, with a time step of 0.1 fs and simulation time of 50 ps. The simulation temperature was set at 298 K and controlled by an Andersen thermostat. During the process of simulations, all the atoms in the Fe(110) surface were fixed. The interaction energy between the inhibitor molecule and the Fe(110) surface was calculated as follows:

Figure 1. Molecular structures of the investigated inhibitors.

derivatives as corrosion inhibitors: quinoxaline (QX), 2chloroquinoxaline (CHQX), 2-quinoxalinethiol (THQX), and 4-(quinoxalin-2-yl)phenol (PHQX).

2. COMPUTATIONAL DETAILS 2.1. Quantum Chemical Method. Quantum chemical calculations were conducted with Gaussian 03, E.01, software. All electron calculations of inhibitor molecules were accomplished by the density functional theory (DFT)/B3LYP method (Becke’s three-parameter hybrid Hartree−Fock (HF)/DFT exchange functional (LYP) was implemented) with the basis set 6-311G++(d,p). DFT has always been adopted to precisely calculate the information about molecular geometric and electron distributions and widely used for analysis of inhibitor efficiencies and inhibitor−surface interactions due to its accuracy and less time requirement from the computational point of view.25 The geometries of all studied inhibitors were optimized all geometric variables without any symmetry constraints. Frequency calculation was executed simultaneously, and no imaginary frequency was found, confirming the minimum-energy structures. The ionization potential (I) and the electron affinity (A) can be calculated according to Koopman’s theorem.26 This theorem establishes a relation between the energies of the HOMO and the LUMO and the ionization potential and the electron affinity, respectively. Although there exists no formal proof of 6378

dx.doi.org/10.1021/ie202832e | Ind. Eng. Chem. Res. 2012, 51, 6377−6386

Industrial & Engineering Chemistry Research E Fe−inhibitor = Etotal − (Esurface + E inhibitor)

Article

a laboratory potentiostat Parstat 2273 advanced electrochemical system and controlled by PowerSuite software. The working electrode was first immersed into the test solution for 30 min to access a steady state open circuit potential (Eocp). Tafel polarization curves were obtained by changing the electrode potential automatically from −250 to +250 mV versus open circuit potential with a scan rate of 0.166 mV s−1. All potential values were recorded with respect to the SCE, and all the electrochemical experiments were performed under the atmospheric ambient. The temperature was thermostatically controlled at 25 ± 1 °C.

(7)

In eq 7, Einhibitor, Esurface, and Etotal represent the energies of an inhibitor molecule, the metal surface without adsorption, and the total system containing an inhibitor molecule and metal surface, respectively. The binding energy between the inhibitor molecule and the Fe(110) surface is the negative value of the interaction energy, namely E binding = −E Fe−inhibitor

(8)

3. EXPERIMENTAL METHODS 3.1. Materials. Mild steel specimens having the chemical composition 0.04% C, 0.35% Mn, 0.027% P, 0.005% S, 0.018% Mo, and remainder Fe were used. The specimens used for weight loss measurements were cut into 4.0 cm × 2.0 cm × 0.05 cm. For the Tafel polarization study, the working electrode was mounted in Teflon with an area of 0.5 cm2 exposed to the electrolyte. Prior to all measurements the mild steel specimens were ground with different emery papers (grades 600, 800, 1200, and 1500), rinsed with double-distilled water, degreased in ethanol, and then dried at room temperature. Quinoxaline and its derivatives used in the work were purchased from Aldrich Chemical Co. The acid solutions (1.0 M HCl) were prepared by dilution of analytical grade 37% HCl with doubledistilled water. The concentration range of all the inhibitors employed was 10−5−10−3 M in acid solutions. 3.2. Weight Loss Measurements. Weight loss measurements were performed at 25 ± 1 °C for 4 h by immersing the mild steel coupons into acid solutions (250 mL) without and with various amounts of inhibitors. After 24 h of immersion, the electrode was withdrawn, rinsed with double-distilled water, washed with acetone, dried, and weighed accurately. All the experiments were performed in triplicate, and average values were reported. The reproducibility of the experiment was higher than 95%. The surface coverage (θ) and inhibition efficiency (IEW, %) were determined by using the following equations: w − w1 θ= 0 w0 (9) IE W (%) =

w0 − w1 ·100 w0

4. RESULTS AND DISCUSSION 4.1. Weight Loss Measurements. The effect of addition of quinoxaline and its derivatives at various concentrations on mild steel corrosion in 1.0 M HCl solutions is investigated by weight loss measurements at 25 ± 1 °C after 4 h immersion. The corrosion parameters such as inhibition efficiency (IEW, %), surface coverage (θ), and corrosion rate (CR) at different concentrations of inhibitors are presented in Table 1. As can be Table 1. Corrosion Parameters for Mild Steel in 1.0 M HCl in the Presence of Different Concentrations of Quinoxaline and Its Derivatives from Weight Loss Measurements at 25 ± 1 °C inhibitor blank QX

CHQX

THQX

(10)

PHQX

where w1 and w0 are the weight loss values in the presence and absence of inhibitors, respectively. θ is the degree of surface coverage of the inhibitor. The corrosion rate (CR) in mg cm−2 h−1 was calculated from the following equation: CR =

ΔW St

C (mol L−1) 1.0 1× 5× 1× 5× 1× 1× 5× 1× 5× 1× 1× 5× 1× 5× 1× 1× 5× 1× 5× 1×

10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3

CR (mg cm−2 h−1)

θ

IEW (%)

10.54 7.64 6.57 5.55 4.21 3.17 6.74 5.43 4.21 3.27 2.89 6.01 5.23 4.11 2.78 2.18 5.55 3.97 3.21 2.34 1.59

− 0.275 0.376 0.473 0.601 0.699 0.361 0.485 0.601 0.690 0.726 0.430 0.504 0.610 0.736 0.793 0.473 0.623 0.695 0.778 0.850

− 27.5 37.6 47.3 60.1 69.9 36.1 48.5 60.1 69.0 72.6 43.0 50.4 61.0 73.6 79.3 47.3 62.3 69.5 77.8 85.0

seen in Table 1, all the investigated inhibitors inhibit the corrosion of mild steel at all concentrations in 1.0 M HCl and the inhibition actions are pronounced at higher concentration. Inspection of these data reveals that inhibition efficiency increases and corrosion rate decreases with increasing the concentrations of all the inhibitors. This behavior can be attributed to the increased adsorption and coverage of inhibitors on the mild steel surface with increase in the inhibitor concentration. It is also evident that, all the inhibitors are good inhibitors and, at the same inhibitor concentration, the order for the increase in inhibition efficiency is PHQX > THQX > CHQX > QX. The difference in their inhibitive action can be explained on the basis of the type of functional group present in the pyrazine ring. In order to have a better

(11)

where ΔW is the weight loss of mild steel species, S is the total area of the mild steel specimen, and t is the immersion time. 3.3. Electrochemical Measurements. A three-electrode glass cell with a capacity of 250 mL was used in all electrochemical measurements. The working electrode was prepared from a mild steel specimen. A saturated calomel electrode (SCE) and a high purity platinum foil (99.9%) with a surface area of 2.5 cm2 were used as the reference and counter electrodes, respectively. The tip of the luggin capillary was very close to the surface of the working electrode to minimize IR drop. All electrochemical measurements were carried out using 6379



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Figure 2. Polarization curves for mild steel in 1.0 M HCl in the absence and presence of various concentrations of quinoxaline and its derivatives: (a) QX, (b) CHQX, (c) THQX, and (d) PHQX.

where i0corr and icorr are corrosion current densities in the absence and presence of inhibitors, respectively. Results in Table 2 indicate that the values of corrosion current density in the inhibitor-containing solutions were lower than those for the blank acid solution. For all studied inhibitors, the corrosion current density decreases and the inhibition efficiency increases with increasing concentrations of inhibitors. PHQX shows the maximum efficiency, 98.3% at a concentration of 10−3 M. There is no definite trend in the shift of Ecorr values in the presence of various concentrations of inhibitors, suggesting that these compounds act as mixed-type inhibitors. It also shows that the cathodic Tafel slope (βc) remains almost constant and the anodic Tafel slope slightly increases as the concentration of inhibitor increases. The constant βc values indicate that the retardation of the cathodic reduction reaction is affected without changing the reaction mechanism. The shift in the βa may be due to the chloride ions or inhibitor molecules adsorbing onto the steel surface.30 The efficiency order of inhibitors tested at all concentrations is as follows: PHQX > THQX > CHQX > QX. This order is the same as the one obtained from weight loss measurements and also suggests that the differences in the inhibition efficiencies would be attributed to the differences in the structures among the four inhibitor molecules. Overall, the inhibition efficiencies obtained from Tafel polarization curves are higher than ones obtained from

understanding of the inhibition mechanism of quinoxaline and its derivatives, a detailed study was carried out using Tafel polarization and theoretical calculations. 4.2. Tafel Polarization Curves. Figure 2 represents the cathodic and anodic Tafel plots for mild steel immersed in 1.0 M HCl at 25 ± 1 °C in the absence and presence of different concentrations of QX, CHQX, THQX, and PHQX. From Figure 2, it is clear that the polarization curves in 1.0 M HCl solutions with different concentrations of quinoxaline and its derivatives are similar: both anodic and cathodic reactions of mild steel electrode corrosion were inhibited, which suggested that these organic compounds reduce anodic dissolution and also retard the hydrogen evolution reaction. Cathodic Tafel curves give rise to parallel Tafel lines, indicating that the hydrogen evolution reaction is activation-controlled and the addition of the inhibitors does not affect the reduction mechanism, and their inhibition action is simply blocking the metal surface.29 Electrochemical parameters such as corrosion potential (Ecorr), cathodic and anodic Tafel slopes (βc, βa), corrosion current density (icorr), and inhibition efficiency (IEP, %) are listed in Table 2. The inhibition efficiency, IEP (%), was obtained by extrapolating the Tafel lines to the corrosion potential by using the following equation: ⎛ i ⎞ ⎟ ·100 IE P (%) = ⎜1 − corr 0 icorr ⎠ ⎝

(12) 6380



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Table 2. Electrochemical Parameters and Inhibition Efficiencies of Steel Corrosion in 1.0 M HCl Solutions in the Absence and Presence of Different Concentrations from Quinoxaline and Its Derivatives inhibitor blank QX

CHQX

THQX

PHQX

C (mol L−1) 1.0 1× 5× 1× 5× 1× 1× 5× 1× 5× 1× 1× 5× 1× 5× 1× 1× 5× 1× 5× 1×

10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−3

icorr (μA cm−2)

Ecorr (V/ SCE)

βa (mV dec−1)

βc (mV dec−1)

IEP (%)

807 466 343 267 182 128 393 259 142 99.3 60.6 311 207 130 69.4 36.3 222 124 67.0 35.5 13.7

−0.486 −0.493 −0.496 −0.494 −0.496 −0.488 −0.483 −0.487 −0.493 −0.500 −0.498 −0.488 −0.487 −0.489 −0.495 −0.491 −0.500 −0.493 −0.497 −0.496 −0.491

83.5 95.7 99.5 98.9 101 97.5 92.4 99.7 106 110 106 89.7 99.5 106 103 107 105 111 110 108 99.7

148.6 149.2 150.1 149.7 151.1 149.6 153.4 151.9 149.3 152.9 148.7 146.8 149.2 147.5 145.9 149.8 145.2 149.7 151.2 148.5 148.3

− 42.3 57.5 66.9 77.5 84.2 51.3 67.9 82.4 87.7 92.5 61.5 74.4 83.9 91.4 95.5 72.5 84.6 91.7 95.6 98.3

weight loss measurements, which is attributed to the different experimental conditions.31 4.3. Quantum Chemical Calculations. In order to investigate the effect of the different substituents in quinoxaline and its derivatives on the inhibition mechanism and efficiency, quantum chemical calculations were performed. The theoretical calculations were usually carried out in the gas phase, but it is well-known that the phenomenon of electrochemical corrosion appears in the liquid phase. As a result, it is important to include the effect of a solvent in the computational calculations. The solvent effect is studied by a model known as the polarized continuum model (PCM), in which the solvent is a continuum of uniform dielectric constant and the solute is placed in the cavity within it (ε = 78.5). The optimized molecular structures, HOMO orbitals, and LUMO orbitals of quinoxaline and its derivatives obtained from the calculations in the gas phase and in the solvent are given in Figures 3 and 4, respectively, where all the atoms are labeled by numbers. All the quantum chemical parameters in the gas phase and in the solvent phase are given in Tables 3 and 4, respectively. According to the frontier molecular orbital theory, the density distribution of HOMO and LUMO is very critical for distinguishing the adsorption centers of the inhibitor molecules, which are responsible for the interaction with metal surface.32 From Figures 3 and 4, it can be easily observed that both HOMO and LUMO energy orbitals are extensively distributed on the area of the quinoxaline ring and the different substituent groups, such as chloro in CHQX, mercapto in THQX, and phydroxyphenyl in PHQX, indicating that these sites would be preferentially adsorbed onto metal surface as active sites. However, it is important to point out that the density distributions of the HOMO and LUMO for the investigated inhibitors in the gas phase as well as in the solvent phase do not exhibit any significant difference.

Figure 3. Optimized molecular structures, HOMOs, and LUMOs of the inhibitors in gas phase.

Generally speaking, the adsorption of the inhibitor on the metal surface can be considered on the basis of donor−acceptor interaction between inhibitor molecules and the metal surface. EHOMO is often associated with the electron-donating ability of a molecule. Increasing values of EHOMO indicates that there is a high tendency for the inhibitor molecules to donate electrons to the appropriate acceptor molecules, having empty molecular orbitals. On the other hand, ELUMO indicates the ability of a molecule to accept electrons. The lower the ELUMO value, the easier the acceptance of electrons from the metal surface, which means better inhibition efficiency.33 As for the values of ΔE, low values of ΔE will provide good inhibition efficiencies, because the excitation energy gap is more polarizable and is generally associated with a high chemical reactivity. As indicated in Tables 3 and 4, the values of EHOMO show the relation PHQX > THQX > QX > CHQX, while the order of the values of ELUMO is CHQX < THQX ≈ QX < PHQX in both gas and solvent phases. There are no direct relationships between EHOMO, ELUMO, and the inhibition efficiencies. From the orders of EHOMO and ELUMO, it can be inferred that introducing the mercapto and p-phenol groups at the C9 atom position increases the energy level of HOMO and, in contrast, substitution of hydrogen atom at the same position by a chloro atom decreases the energy level of LUMO. This facilitates their adsorption abilities and therefore increases their inhibition efficiencies. However, the most important point is the values of ΔE follows the order PHQX > THQX > CHQX > QX. This expectation is in good agreement with the experimental observations, suggesting that the efficiency of the corrosion 6381



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determine the molecular stability and reactivity. A hard molecule has a large value of ΔE, while a soft molecule has a small value of ΔE. Therefore, a soft molecule is more reactive than a hard molecule because a decreased value in ΔE easily leads to the electron transfer process between molecular inhibitors and the metal surface. It can be observed from Tables 3 and 4 that the order of the values of η for the investigated inhibitors is PHQX < THQX < CHQX < QX. According to eq 5, the order of the values of σ is in the opposite trend. PHQX with the highest σ value and the lowest η value has the highest inhibition efficiency. These calculated results are all in good agreement with the experimental inhibition efficiency. The number of electrons transferred from quinoxaline and its derivatives to the iron surface was also calculated and summarized in Tables 3 and 4. According to Lukovits’s study,36 if ΔN < 3.6, the inhibition efficiency increases with increasing electron-donating ability. All the investigated inhibitors are donors of electrons, and the order by of the ability of these inhibitors to donate electrons to the metal surface is PHQX > THQX > QX > CHQX, which is in accordance with the order of the EHOMO. The same order of ΔN and EHOMO verifies that the electron-donating ability of the substituent groups at the C9 atom position follows the order pphenol > mercapto > chloro. Combining these calculation results and experimental data, it can be easily seen that the substituent group of chloro atom has a negative effect on enhancing the electron-donating ability, but it can still accept free electrons from the metal surface and form feedback metal− inhibitor bonds. Therefore, the higher inhibition effects of CHQX in comparison with QX may be attributed to the excellent electron-accepting ability of the chloro group. Furthermore, in order to confirm the adsorption sites of the four inhibiting molecules when adsorbed on the iron surface, the local reactivities of these molecules were investigated by the analysis of their Fukui indices.37 The Fukui function f k is defined as the first derivative of the electronic density (ρ(r)⃗ ) with respect to the number of electrons N in a constant external potential v(r)⃗ .

Figure 4. Optimized molecular structures, HOMOs, and LUMOs of the inhibitors in solvent phase.

inhibitor is dependent on comprehensive abilities of electrons donated to unoccupied orbitals of the metal and free electrons accepted from the metal surface atoms. The dipole moment (μ) is another reference index that can also be applied to discuss and rationalize the molecule structure. The influence of the dipole moment on corrosion inhibition is debated endlessly.34,35 In this study, whether in the gas phase or in the solvent phase, there is no obvious correlation between μ and the inhibition efficiency. However, it may be reluctantly considered that the lowest value of μ was shown for QX with the lowest inhibition efficiency. The molecular volume of the inhibitors follows the trend PHQX > THQX > CHQX > QX, which is also in accordance with the inhibition efficiency. PHQX has the highest molecular volume among quinoxaline and its derivatives, which is attributed to the presence of the additional phenol ring. This provides the largest coverage area between the molecular inhibitor and surface, which explains the highest inhibition efficiency. The global reactivity parameters, such as electronegativity, χ, global chemical hardness, η, global softness, σ, and the fraction of transferred electrons, ΔN, are important properties to

⎛ ∂ρ( r ⃗) ⎞ ⎟ fk = ⎜ ⎝ ∂N ⎠v( r )⃗

(13)

By finite difference approximation, the condensed Fukui functions can be written as f k+ = qk (N + 1) − qk (N )

(for nucleophilic attack) (14)

f k−

= qk (N ) − qk (N − 1)

(for electrophilic attack) (15)

Herein, qk(N + 1), qk(N), and qk(N − 1) represent the atomic charges of the anionic, neutral, and cationic species, respectively. The condensed Fukui functions were obtained through the finite difference approximation using Mulliken population analysis in the gas phase.

Table 3. Quantum Chemical Parameters for Inhibitors Calculated with DFT Method in Gas Phase molecule

EHOMO (eV)

ELUMO (eV)

ΔE (eV)

μ (D)

MV (cm3/mol)

TNC (e)

η (eV)

σ (eV−1)

χ (eV)

ΔN

QX CHQX THQX PHQX

−7.048 −7.241 −6.660 −6.231

−2.350 −2.582 −2.357 −2.259

4.698 4.659 4.303 3.972

0.59 2.38 1.40 1.26

104.9 116.0 121.8 154.9

−1.18 −1.99 −1.58 −3.50

2.349 2.330 2.152 1.986

0.426 0.429 0.465 0.504

4.699 4.912 4.509 4.245

0.490 0.448 0.579 0.694

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Table 4. Quantum Chemical Parameters for Inhibitors Calculated with DFT Method in Solvent Phase molecule

EHOMO (eV)

ELUMO (eV)

ΔE (eV)

μ (D)

MV (cm3/mol)

TNC (e)

η (eV)

σ (eV−1)

χ (eV)

ΔN

QX CHQX THQX PHQX

−7.022 −7.127 −6.648 −6.177

−2.391 −2.552 −2.392 −2.367

4.631 4.575 4.256 3.810

0.80 3.27 1.93 2.28

106.4 127.0 135.3 178.9

−1.70 −2.20 −2.35 −3.92

2.316 2.288 2.128 1.905

0.432 0.437 0.470 0.525

4.707 4.840 4.520 4.272

0.495 0.472 0.582 0.716

Figure 5. Fukui functions for quinoxaline and its derivatives calculated by DFT.

substituent group. The most susceptible sites for electrophilic attack of QX and CHQX are on the C3 and C6 atoms in the benzene ring and the N7 atom of pyrazine, those of THQX are mainly on the sulfur atom from teh substituting group and the C2 and C3 atoms of the benzene ring, and those of PHQX are mainly on all the carbon atoms and the O17 atom in the pphenol ring and the C2 atom of the benzene ring. Figure 5 supports the information obtained from the distributions of HOMO and LUMO. The HOMO and LUMO distributions on each investigated inhibitor are identical with the atoms that exhibit the greatest values of f −k and f +k , respectively, indicating that these reactive sites would be the adsorption centers during the process of corrosion inhibition. In addition, the highest inhibition efficiency of PHQX should be attributed to the increasing number of centers of adsorption on the inhibitor

The local reactivity is analyzed by means of the condensed Fukui function, which was applied to distinguish the chemical behavior of each atom of the investigated inhibitors with different substituting groups and is depicted in Figure 5. The atoms that possess the deeper color represent the greater value of f +k or f −k . The molecular sites with large values of f +k are the sites where the molecular will accept electrons when attacked by a nucleophilic reagent. On the other hand, the molecular sites with large values of f −k are the preferred sites through which the molecule will donate electrons when attacked by an electrophilic reagent. The most susceptible sites for nucleophilic attack of QX are on the C8 and C9 atoms of the pyrazine ring, those of THQX and PHQX are on the C8, C9, and N7 atoms of the pyrazine ring and the C1 and C2 atoms of the benzene ring, and those of CHQX are not only on the C8, C9, C1, C2, and N7 atoms but also on the Cl11 atom from the 6383



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Figure 6. Equilibrium configurations for adsorption of quinoxaline and its derivatives on Fe(110) surface.

whole simulation process, which indicates that PHQX will adsorb more strongly on the iron surface and possess better inhibition performance than the other inhibitors. This result is consistent with the order of the inhibition efficiency. In order to simulate the realistic situation, it is important to take the effect of solvent into account. Amorphous cell module and build layer function have been used to construct a solvent/ quinoxaline derivative layer, which consists of 600 H2O molecules and a single dissolved inhibitor molecule on the Fe(110) surface. The corresponding simulation result is presented in Figure 7, and the calculated interaction energy and binding energy are listed in Table 6. It can be seen from Figure 7 that the optimization configuration of quinoxaline and its derivatives in aqueous solution is similar to that in the nonaqueous system. Furthermore, the order of EFe−inhibitor obtained from calculations in the aqueous solution is the same as the one in the nonaqueous system. However, the values of EFe−inhibitor in aqueous solution are far higher than those in the nonaqueous system. The parallel adsorption configurations under different environments ensures that the iron surface can be maximally covered by the investigated inhibitor molecules and form a barrier layer between the iron surface and the aggressive media, thus enhancing the inhibition efficiency.

molecules and the highest electron density confirmed by the highest value of the TNC. 4.4. Molecular Dynamics Simulations. The molecular dynamic simulations were performed to study the adsorption behavior of the QX, CHQX, THQX, and PHQX on the Fe(110) surface. The equilibrium configurations for the four corrosion inhibitors are shown in Figure 6. By careful examination of Figure 6, it can be noticed that, during the process of simulation, quinoxaline and its derivatives molecules moved gradually near the Fe(110) surface. After the system reached equilibrium, all the investigated inhibitors adsorbed nearly parallel to the Fe(110) surface, especially PHQX, and there is no obvious dihedral angle between the quinoxaline ring and the phenol ring. According to the equilibrium configurations of the four inhibitors adsorbed on the Fe(110) surface, the conclusion can be drawn that these organic inhibitors can be adsorbed on the iron surface through the quinoxaline ring and different substituent groups. The values of the interaction and binding energies of the four inhibitors on Fe(110) surface are listed in Table 5. The calculations of the single point energy Table 5. Interaction and Binding Energies between Quinoxaline and Its Derivatives and Fe(110) Surface inhibitor

Einteraction (kJ mol−1)

Ebinding (kJ mol−1)

QX CHQX THQX PHQX

−321.1 −344.4 −370.7 −523.1

321.1 344.4 370.7 523.1

5. CONCLUSIONS 1. Quinoxaline and its derivatives act as excellent inhibitors for the corrosion of mild steel in 1.0 M HCl. All experimental methods employed in the study demonstrate the same order of inhibition efficiency: PHQX > THQX > CHQX > QX. 2. Results of Tafel polarization studies show that the investigated inhibitors behave as mixed-type inhibitors. 3. Most of the quantum chemical parameters in gas and solvent phases of the inhibitors calculated by the B3LYP/ 6-311G++(d,p) level show good correlation with inhibition efficiency, and well explain the differences in inhibition efficiencies of the inhibitors.

were carried out to obtain Etotal, Esurface and Einhibitor, and then EFe−inhibitor can be obtained according to eq 7. The calculated values of EFe−inhibitor are −321.1, −344.4, −370.7, and 523.1 kJ mol−1 for QX, CHQX, THQX, and PHQX, respectively. All values of EFe−inhibitor are negative, which means that the adsorption can occur spontaneously. The binding energies are found to increase in the order PHQX > THQX > CHQX > QX. PHQX gives the maximum binding energy during the 6384



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Figure 7. Equilibrium configurations for adsorption of quinoxaline and its derivatives on Fe(110) surface in aqueous solutions. (4) Ji, G.; Shukla, S. K.; Dwivedi, P.; Sundaram, S.; Prakash, R. Inhibitive Effect of Argemone Mexicana Plant Extract on Acid Corrosion of Mild Steel. Ind. Eng. Chem. Res. 2011, 50, 11954−11959. (5) Ameer, M. A.; Fekry, A. M. Corrosion inhibition of mild steel by natural product compound. Prog. Org. Coat. 2011, 71, 343−349. (6) Alvarez-Bustamante, R.; Negron-Silva, G.; Abreu-Quijano, M.; Herrera-Hernandez, H.; Romero-Romo, M.; Cuan, A.; PalomarPardave, M. Electrochemical study of 2-mercaptoimidazole as a novel corrosion inhibitor for steels. Electrochim. Acta 2009, 54, 5393−5399. (7) Fu, J. J.; Li, S. N.; Wang, Y.; Liu, X. D.; Lu, L. D. Computational and electrochemical studies on the inhibition of corrosion of mild steel by L-Cysteine and its derivatives. J. Mater. Sci. 2011, 46, 3550−3559. (8) Negm, N. A.; Ghuiba, F. M.; Tawfik, S. M. Novel isoxazolium cationic Schiff base compounds as corrosion inhibitors for carbon steel in hydrochloric acid. Corros. Sci. 2011, 53, 3566−3575. (9) Touir, R.; Dkhireche, N.; Touhami, M. E.; Sfaira, M.; Senhaji, O.; Robin, J. J.; Boutevin, B.; Cherkaoui, M. Study of phosphonate addition and hydrodynamic conditions on ordinary steel corrosion inhibition in simulated cooling water. Mater. Chem. Phys. 2010, 122, 1−9. (10) Tang, Y. M.; Yang, X. Y.; Yang, W. Z.; Chen, Y. Z.; Wan, R. Experimental and molecular dynamics studies on corrosion inhibition of mild steel by 2-amino-5-phenyl-1,3,4-thiadiazole. Corros. Sci. 2010, 52, 242−249. (11) Gece, G. Drugs: A review of promising novel corrosion inhibitors. Corros. Sci. 2011, 53, 3873−3898. (12) Kokalj, A.; Peljhan, S.; Finsgar, M.; Milosev, I. What Determines the Inhibition Effectiveness of ATA, BTAH, and BTAOH Corrosion Inhibitors on Copper? J. Am. Chem. Soc. 2010, 132, 16657−16668. (13) Hsieh, M. K.; Dzombak, D. A.; Vidic, R. D. Effect of Tolyltriazole on the Corrosion Protection of Copper against Ammonia and Disinfectants in Cooling Systems. Ind. Eng. Chem. Res. 2010, 49, 7313−7322. (14) Gece, G. The use of quantum chemical methods in corrosion inhibitor studies. Corros. Sci. 2008, 50, 2981−2992. (15) Mousavi, M.; Mohammadalizadeh, M.; Khosravan, A. Theoretical investigation of corrosion inhibition effect of imidazole and its derivatives on mild steel using cluster model. Corros. Sci. 2011, 53, 3086−3091. (16) Khaled, K. F. Molecular modeling and electrochemical investigations of the corrosion inhibition of nickel using some

Table 6. Interaction and Binding Energies between Quinoxaline and Its Derivatives and Fe(110) Surface in Aqueous Solution

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inhibitor

Einteraction (kJ mol−1)

Ebinding (kJ mol−1)

QX CHQX THQX PHQX

−614.5 −715.5 −752.7 −1104.1

614.5 715.5 752.7 1104.1

4. The molecular dynamics simulation results reveal that quinoxaline and its derivatives adsorb on the iron surface by a parallel adsorption configuration. According to the calculated binding energy, it can be conclude that the inhibition performance for the investigated inhibitors follows the order PHQX > THQX > CHQX > QX, which agrees well with the experimental results.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 025 84315609. Fax: +86 025 84315609. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are pleased to acknowledge the financial support provided by the National Natural Science Foundation of China (51102135), the Natural Science Foundation of Jiangsu Province, China (BK2011711), and NUST Research Funding, No. 2011ZDJH24.

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Experimental and Theoretical Study on the Inhibition Performances of

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