Electrochemical and Quantum Chemical Investigation of Some Azine

Article pubs.acs.org/IECR

Electrochemical and Quantum Chemical Investigation of Some Azine and Thiazine Dyes as Potential Corrosion Inhibitors for Mild Steel in Hydrochloric Acid Solution Eno E. Ebenso,* Mwadham M. Kabanda, Lutendo C. Murulana, Ashish K. Singh, and Sudhish K. Shukla Department of Chemistry, School of Mathematical & Physical Sciences, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa ABSTRACT: The inhibition performances of some selected azine and thiazine dyes, namely, Neutral Red (NR), Azure A Eosinate (AAE), Toluidine Blue (TB), phenosafranin (PS), and Rhodanile Blue (RB), on mild steel corrosion in hydrochloric acid solution was studied the using electrochemical impedance spectroscopy (EIS) and Tafel polarization techniques. Quantum chemical calculations based on the density functional theory (DFT) and semiempirical (PM3) methods were used to investigate the reactivities and selectivities of the studied cationic dyes. The effects of inhibitor concentration on the inhibition efficiency have been studied. Inhibition efficiency increased with increase in concentration of all the studied cationic dyes within the concentration range 100−500 ppm. Potentiodynamic studies revealed that all the inhibitors are of mixed type. The results obtained from the EIS studies showed good agreement with the results from potentiodynamic polarization techniques. The quantitative structure−activity relationship (QSAR) approach was also used to correlate the quantum chemical parameters with the experimentally determined inhibition efficiencies. The results show that thiazine dyes are better corrosion inhibitors than azine dyes; however, when azines contain more electron donor centers than thiazines, they are preferred as corrosion inhibitors to thiazine. Hydrogen bonding could be one of the possible physisorption mechanisms for the adsorption of the selected dyes onto the metal surface because of the many hydrogen bond donor centers in the studied compounds. QSAR results show good correlations between a number of quantum chemical parameters and the determined inhibition efficiency. that have less planar geometry.14−16 While geometric parameters give information about the surface coverage of the metal by the inhibitor, electronic parameters indicate which molecule would have the highest tendency to react (therefore, adsorb) with the metal surface. Such interactions between the inhibitor and the metal surface therefore depend strongly on the electron density distribution in the inhibitors. Regions in the molecule that have high electron densities would preferably donate electrons to partially filled or vacant d orbitals of the metal resulting in a donor−acceptor bond.17 This is the basis for the chemisorption process; molecules that have functional groups with high electron densities have a greater tendency to adsorb onto the metal surface, and they include molecules with heteroatom functional groups (e.g., −CO, −NN and −NR2, SH groups), conjugated double bonds, and aromaticity17. Many authors have reported that the general trend in the inhibition efficiencies of molecules containing heteroatoms is such that O < N < S < P.18−22 This trend is probably related to the tendency of an atom to donate electrons and is therefore related to the electronegativity of the atom. Oxygen has the highest electronegativity value (3.44) and therefore has the least tendency to donate electrons, while phosphorus has the lowest electronegativity value (2.19) and therefore has the highest tendency to donate electrons.

1. INTRODUCTION The corrosion of mild steel causes huge financial damages to industry, which has led to an increase in the search for substances that can delay or slow down the corrosion rate.1,2 Among the various possibilities utilized to prevent corrosion is the use of substances that adsorb on the metal−solution interface, thus blocking the metal from coming into contact with the corrosive solution. Such substances that adsorb onto the surface of the metal both physically and chemically are called corrosion inhibitors.3 They come from various sources, including organic molecules, ionic liquids, amino acid derivatives, etc.4−12 The efficiency of a corrosion inhibitor depends strongly on its adsorbability on the metal surface. However, such a process involves many influencing factors beside the inhibitor, such as the nature of the metal, the environment, and the electrochemical potential at the metal−solution interface.13 Therefore, a careful study of the adsorption process of an inhibitor on the metal surface should take into consideration all the necessary factors. Even in the selection of an appropriate compound (in a set of compounds with similar parent moieties but different functional groups) as a candidate for the role of corrosion inhibitor, the investigator needs to take into consideration several factors that are interdependent. These factors might be classified into two main groups: geometric and electronic properties of the compound. The geometry of the molecule has a strong influence on the adsorbability of the inhibitor on the metal surface as it is related to the optimal way in which the inhibitor might cover the metal surface. Compounds that have planar geometry often have higher inhibition efficiencies than corresponding compounds © 2012 American Chemical Society

Received: Revised: Accepted: Published: 12940

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factors contributing to the difference in their corrosion inhibition potentiality. The role of AAE as a corrosion inhibitor for mild steel in hydrochloric acid (HCl) solution has been investigated both experimentally and theoretically with the results showing that AAE is a good corrosion inhibitor for mild steel in HCl solution.59 Through extensive density functional theory (DFT) calculations with different basis sets, the work identified the possible active sites on azure A that might interact with the metal surface, both in vacuo and in aqueous solution. However, no information is provided on the protonated form of the inhibitor and no comparison with other related structures has been reported. Therefore, the present study on AAE also provides crucial information not only on the interaction of AAE with the solvent but also on the different protonated forms of AAE and compares the results with those for TB, which has not been studied computationally. To strengthen the validity of the work, quantitative structure−activity relationship (QSAR) was performed to correlate some quantum chemical parameters with the reported percentage inhibition efficiency (% IE) of the inhibitors. The structures of these dyes are shown in Figure 1.

The search for effective corrosion inhibitors is ongoing and an increasing number of classes of compounds are being explored for their corrosion inhibition potentialities in different environments. Although dyes have been extracted from natural sources for centuries, it was not until 1856 that a synthetic dye was produced commercially.23−25 Different kinds of dyes are known, viz., heterocyclic dyes (e.g., safranine T, methylene blue), xanthene dyes (e.g., eosin, thymol blue, phenolphthalein, phenol red), anthraquinone dyes (e.g., alixarin red S), and azo dyes (e.g., methyl red, Congo red, methyl orange). Of all the dyes, azo dyes are a class of compounds that are strongly colored. They can be intensely yellow, red, orange, blue, or even green, depending on the exact structure of the molecule. Because of their color, azo compounds are of tremendous importance as dyes. In fact, about half the dyes in industrial use today are azo dyes, which are mostly prepared from diazonium salts.26 Structural features in organic compounds that lead to color are >CCCO, and −NO2. Most importantly, azo (−NN−) and nitro (−NO) groups invariably confer color while the other groups do so under certain circumstances. Dyes have been used to give multicolor effects to anodized aluminum.27−32 Cyanine dyes have been reported as efficient corrosion inhibitors on metal corrodent systems.33 Green S and erythrosine dyes have been studied as potential inhibitors for mild steel corrosion in HCl.34 A survey of the literature also reveals that the corrosion on aluminum in amine solutions by some dyes has been reported.35−42 Preliminary experiments in our laboratories in an earlier study have shown, however, that some azo dyes (metanil yellow, naphthol blue black, and solochrome dark blue) actually inhibit the corrosion of mild steel in HCl medium.43 Many researchers recently reported that organic dyes are quite effective in retarding the corrosion of mild steel and aluminum in acidic or basic environments.44−57 This study is therefore part of an extensive ongoing project in our laboratory to develop new classes of inhibitors from some dyes with good inhibition efficiency and to further elucidate the mechanism of the inhibition process. Therefore, in confirmation of our interest on the corrosion inhibition characteristics of organic dyes, the present paper reports on the inhibiting action of some phenoazine [Neutral Red (NR) and phenosafranin (PS)] and phenothiazine [Azure A Eosinate (AAE) and Toluidine Blue O (TB)] cationic dyes. Also included is the study of the inhibitive effect of Rhodanile Blue B on the corrosion of mild steel in hydrochloric acid using electrochemical impedance spectroscopy (EIS) and Tafel polarization techniques. The results of experimental investigations and quantum chemical calculations are reported, and attempts are made to establish possible correlations between the experimentally obtained inhibition efficiencies and the theoretically estimated inhibition efficiencies. The mechanism of interaction of Neutral Red on corrosion inhibition has been studied previously using thermodynamic and kinetic models, and the results confirmed the significant role of Neutral Red as a corrosion inhibitor.58 However, a survey of the literature shows that there are no quantum chemical calculation results on Neutral Red that would explain the structural features and electronic properties that make Neutral Red such a good inhibitor. Moreover, there are no reported literature works (both experimental and theoretical) on phenosafranin (PS) as a potential corrosion inhibitor. This work therefore is crucial for understanding the mechanism of corrosion inhibition and the main

Figure 1. Structures of the studied cationic dyes.

2. EXPERIMENTAL PROCEDURES Prior to all measurements, the mild steel specimens were abraded successively with emery papers from 600 to 1200 mesh in.−1 grade. The specimen were washed with double distilled water, degreased with acetone, and dried in a hot air blower. After drying, the specimens were placed in desiccators and then used for the various experiments. The aggressive solution of 1 M HCl was prepared by the dilution of analytical grade hydrochloric acid (37%) with double distilled water, and all the experiments were carried out in the unstirred solutions and in triplicate. The electrochemical measurements were carried out on mild steel strips (working electrode) with the dimensions 1.0 cm × 1.0 cm exposed with a 7.5 cm long stem (coated by a commercially available lacquer) and using a saturated calomel electrode (SCE) as reference and 1 cm2 platinum foils as the counter electrode. 12941

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Figure 2. Schematic representation and optimized structures of the studied dye molecules [Neutral Red (NR), phenosafranin (PS), Azure A Eosinate (AAE), and Toluidine Blue O (TB)]. The optimized structures are taken from B3LYP/6-31+G(d,p) results.

2.1. Electrochemical Impedance Spectroscopy (EIS). The EIS tests were performed at 303 ± 1 K in a three-electrode assembly. All the potentials were measured versus SCE. The electrochemical impedance spectroscopy measurements were performed using a Gamry instrument potentiostat/galvanostat with a Gamry framework system based on ESA 400 in a frequency range 10−2−105 Hz under potentiodynamic conditions with amplitude of 10 mV peak to peak, using an ac signal at Ecorr. Gamry applications include the software DC105 for corrosion and EIS300 for EIS measurements and the Echem analyst version 5.50 software package for data fitting. The experiments were carried out after 30 min of immersion in the test solution without deaeration and stirring. The inhibition efficiency of the inhibitor was calculated from the charge transfer resistance values using the following equation: μR = t

(1/R t 0) − (1/R t i) 1/R t i

The inhibition efficiency was evaluated from the measured Icorr values using the following relationship: ηp =

Icorr 0 − Icorr i Icorr 0

·100 (2)

where Icorr0 and Icorri are the corrosion current densities in the absence and presence of inhibitor, respectively. 2.3. Computational Procedures. The schematic representations of NR, PS, AAE, and TB together with the atom numbering for each molecule are shown in Figure 2. Since all four compounds share a central anthracene moiety, they are a series of related compounds and therefore a comparison of their inhibition efficiencies and their molecular quantum parameters provides information on the role of different functional groups in enhancing the inhibition efficiency of the studied molecules. All geometry optimizations and quantum chemical calculations were performed using density functional theory (DFT) because it is a trade-off between computational cost and meaningful results. The Becke’s three parameter hybrid functional using the Lee−Yang−Parr correlation functional theory (B3LYP60) was selected for the calculations. Calculations were done using the 6-31G(d,p) and the 6-31+G(d,p) basis sets to compare the effects of different basis sets on the geometry of the systems. Quantum chemical calculation methods have proved to be very powerful tools in studying the reaction mechanism of corrosion inhibition. DFT is largely utilized in the analysis of the characteristics of the inhibitor/metal surface mechanisms and in the description of the structural nature of the inhibitor on the corrosion process.61 DFT/B3LYP is also recommended for the understanding of chemical reactivity and selectivity in terms of the highest occupied molecular orbital

·100 (1)

where Rt0 and Rti are the charge transfer resistances in the absence and in presence of inhibitor, respectively. 2.2. Potentiodynamic Polarization. The electrochemical behavior of a mild steel sample in inhibited and uninhibited solutions was studied by recording anodic and cathodic potentiodynamic polarization curves. Measurements were performed in the 1 M HCl solution containing different concentrations of the tested inhibitor by changing the electrode potential automatically from −250 to +250 mV versus corrosion potential at a scan rate of 1 mV s−1. The linear Tafel segments of anodic and cathodic curves were extrapolated to the corrosion potential to obtain corrosion current densities (Icorr). 12942

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3. RESULTS AND DISCUSSION 3.1. Potentiodynamic Polarization Measurements. Potentiodynamic polarization measurements were carried out to study the kinetics of the cathodic and anodic reactions. Figure 3 shows the results of the effect of dyes on the cathodic

(HOMO)−lowest unoccupied molecular orbital (LUMO) energy differences and related properties such as polarizability, hardness, and electronegativity.62 Electronegativity (χ) is the measure of the power of an electron or group of atoms to attract electrons toward itself,63 and according to Koopman’s theorem64,65 it is estimated following the equation χ ≅ −(1/2)(E HOMO + E LUMO)

(3)

Chemical hardness (η) measures the resistance of an atom to a charge transfer;66 it is estimated by using the equation η ≅ −(1/2)(E HOMO − E LUMO)

(4)

The global electrophilicity index (ω) is estimated by using the electronegativity and chemical hardness parameters through the equation

ω=

χ2 2η

(5)

A high value of electrophilicity describes a good electrophile. The global chemical softness (σ) describes the capacity of an atom or group of atoms to receive electrons;66 it is estimated by using the equation σ = 1/η ≅ −2/(E HOMO − E LUMO)

(6)

The electron affinity (A) is the energy released when an electron is added to a neutral molecule; it is related to ELUMO through the equation

A ≅ −E LUMO

(7)

The ionization potential (I) is the amount of energy required to remove an electron from a molecule; it is related to the energy EHOMO through the equation I ≅ −E HOMO

(8) Figure 3. Tafel polarization curves for the dyes for mild steel corrosion in 1 M hydrochloric acid solution.

The maximum number of electrons transferred (ΔNmax) in a chemical reaction is given by the equation66 χ ΔNmax = 2η (9)

and anodic polarization curves of mild steel in 1 M HCl, respectively. It is evident from Figure 3 that both reactions were suppressed with the addition of different dyes used in the study, suggesting that they reduced the anodic dissolution reactions and retarded the hydrogen evolution reactions on the cathodic sites. Electrochemical corrosion kinetic parameters, namely, corrosion potential (Ecorr), corrosion current density (Icorr), and anodic and cathodic Tafel slopes (ba and bc) obtained from the extrapolation of the polarization curves are listed in Table 1. It is evident from Table 1 that the value of bc changed with increase in inhibitor concentration and indicates the influence of the inhibitor on the kinetics of the hydrogen evolution. The shift in the anodic Tafel slope, ba, is due to the chloride ion/or inhibitor molecules adsorbed on the metal surface. The corrosion current density (Icorr) decreased by the increase in the adsorption of the inhibitor with increasing inhibitor concentration. According to Ferreira et al.72 and Li et al.,73 if the displacement in corrosion potential is more than ±85 mV with respect to the corrosion potential of the blank solution, the inhibitor can be considered as a cathodic or anodic type. In the present study, the maximum displacement was ±40 mV with respect to the corrosion potential of the uninhibited sample, which indicates that the studied inhibitors are mixed-type inhibitors. 74

and, using the I and A terms, it can be written as ΔNmax =

I+A 2(I − A)

(10)

Because of high computational demand, the study in solution was done as single point calculations on the geometry optimized in vacuo using the 6-31G(d,p) basis set. The results were then compared with the results obtained in vacuo using the same basis set. The solvent effects were taken into consideration by using the SM8 model incorporated in the Spartan program. In the SM8 model, the free energy of interaction between a solute and a solvent is obtained by solving for the solute reaction field (i.e., the reaction field induced in the solvent by the charge distribution of the solute) by solving the generalized Born approximation equation.67−69 All optimization calculations were done using the Spartan 10 version 1.01 program.70 Schematic structures were drawn using the ChemOffice package in the UltraChem 2010 version, while optimized structures were drawn using the Spartan 10 version 1.01 program. The QSAR results were plotted using the XLSTAT program.71 12943

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n, for different dyes obtained from the fitting of the recorded data using the equivalent circuit, are listed in Table 2. Cdl values listed in Table 2 were derived from the CPE parameters calculated by using the following equation.85

Table 1. Tafel Polarization Data of Cationic Dyes for Mild Steel in 1 M HCl Solution dye name Neutral Red (NR)

inhibitor concn −Ecorr (mV Icorr (μA cm−2) (ppm) vs SCE) blank 100

300 500 Azure A Eosinate 100 (AAE) 300 500 Toluidine Blue 100 (TB) 300 500 phenosafranin 100 (PS) 300 500 Rhodanile Blue 100 (RB) 300 500

ba (mV dec−1)

bc (mV dec−1)

IE (%)

448 465

1400 64

83 645

120 152

− 53.9

478 481 465

175 164 631

492 253 59

146 161 123

64.8 81.9 54.9

470 483 464

460 221 541

62 64 61

167 166 161

67.1 84.2 61.4

465 488 463

380 202 492

63 61 59

143 171 145

72.9 85.6 64.8

455 459 477

321 143 603

57 56 56

156 165 135

77.1 89.8 56.9

477 487

450 209

62 60

143 138

67.9 85.1

Cdl = (Y0R t1 − n)1/ n

It is clear from Table 2 that Rt values increased with an increase in the inhibitor concentration. The increase in Rt values is attributed to the formation of a protective film of the inhibitor on the metal/solution interface. The values of the double layer capacitance (Cdl) decreased with increase in the different dye concentrations. The double layer capacitance (Cdl) is related to the thickness of the protective layer (d) by the following equation.86

Cdl =

εε0 d

(13)

where ε is the dielectric constant of the protective layer and ε0 is the permittivity of the free space. Equation 5 suggests that Cdl is inversely proportional to the thickness of the protective layer (d). Therefore, the decrease in the double layer capacitance by increasing the inhibitor concentration shows an increase in the thickness of protective layer. It is also clear from Table 2 that the dyes inhibited the corrosion of mild steel in 1 M HCl solution at all concentrations used in the study. The inhibition efficiency (μRt) values are listed in Table 2. These values suggest that the inhibition efficiency increases with the increase in the inhibitor concentration. The results obtained from the EIS studies showed good agreement with the results obtained from the Tafel polarization. 3.3. Results in Vacuo Using DFT/6-31+G(d,p) Results. The schematic representations and the optimized geometries of the four cationic dyes are shown in Figure 2. The numbering of the atoms of interest, necessary for discussion, is also shown in Figure 2. Selected bond lengths and bond angles are reported in Table 3. The geometries of NR, AAE, and TB are planar (with the exception of the methyl hydrogen atoms in TB), while PS has the phenyl ring at the N4 position perpendicular to the plane of the anthracene ring, which reduces steric effects between the rings. Therefore, PS has the least planar molecular arrangement, which has an impact on its adsorption on the metal surface in relation to the other compounds. The adsorption of the inhibitor on the metal surface is determined by the interplay of both geometric and electronic parameters. The results show that PS is the most preferred corrosion inhibitor, resulting from the fact that it has the highest number of electron donor centers. However, the trends also suggest that the thiazines are better corrosion inhibitors than azines because they have S atoms that have better electron donor capabilities than the N atoms. Although computational methods consistently predict TB to be the best corrosion inhibitor, it is assumed that the high electron density factor in PS provides a stronger binding role than the planarity factor in TB. A similar explanation may be suggested for the preference of TB to AAE, where the only structural difference in the two compounds is the presence of a methyl group in TB. AAE has a higher planar geometry than TB but it has less electron density than TB, so the electron density factor in TB outweighs the planarity factor in AAE. The electronic parameters give information about the tendency of the inhibitor to interact with the metal surface,

3.2. Electrochemical Impedance Spectroscopy. Electrochemical impedance spectroscopy measurements were carried out in order to study the kinetics of the electrode process and the surface properties of the studied system. This method is widely used to investigate the corrosion inhibition process.75 Nyquist plots of mild steel in 1 M HCl solution in the absence and presence of different concentrations of dyes are shown in Figure 4. A high frequency depressed charge transfer semicircle is observed. The high frequency semicircle is attributed to the time constant of charge transfer and double layer capacitance.75−77 The charge transfer resistance increment raises the tendency of current to pass through the capacitor of the circuit. It is clear from Figure 4 that the impedance spectra are not perfect semicircles and the depressed capacitive loop corresponds to surface heterogeneity which may be the result of surface roughness, dislocation, distribution of active sites, or adsorption of the different dye molecules.78−80 The measured data were analyzed using the equivalent circuit given in Figure 5. This circuit is generally used to describe the iron/acid interface model.81 This circuit gives an accurate fit to all experimental impedance data for the dyes. The equivalent circuit consists of solution resistance (Rs), charge transfer resistance (Rt), and a constant phase angle (CPE). The impedance function of CPE is as follows: ZCPE = Y −1(jω)−n

(12)

(11)

where Y is the magnitude of the CPE, ω is the angular frequency, and the deviation parameter n is a valuable criterion of the nature of the metal surface and reflects microscopic fluctuations of the surface. For n = 0, ZCPE represents a resistance with R = Y−1; for n = 1, ZCPE represents an inductance with L = Y−1; for n = 1, ZCPE represents an ideal capacitor with C = Y.82 In an iron/steel system ideal capacitor behavior is not observed due to the roughness and/or uneven current distributions on the electrode surface resulting in the frequency depression.83,84 The electrochemical parameters Rs, Rt, Y0, and 12944

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Figure 4. EIS graphs for the dyes for mild steel corrosion in 1 M hydrochloric acid solution.

meaningful discussion of the current work are reported in Table 4 and include the energy of the HOMO (EHOMO), the energy of the LUMO (ELUMO), the HOMO−LUMO energy difference (EH−L), the dipole moment (μ), the ionization potential (I), etc. However, it would be pertinent to mention here that the information about the molecular reactivity obtained from these quantum chemical descriptors cannot directly be translated into corrosion inhibition efficiency, because the adsorbability of an effective corrosion inhibitor involves more processes such as film formation and the nature of the metal surface. It is for this reason that in some cases a comparison between calculated quantum chemical parameters and inhibition efficiency does not yield a good correlation. The molecular reactivity is related to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Therefore, understanding the electronic distribution of the HOMO and the LUMO provides valuable information on the reactivity of the studied molecules. The electronic

Figure 5. Electrochemical equivalent circuit used to fit the impedance measurements.

and such an ability of an inhibitor lies largely in its electronic distribution. The electronic distribution of molecules is understood by investigating their frontier molecular orbitals and the electron density parameters, such as the dipole moment and the partial atomic charges. The frontier molecular orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for a given molecule. The quantum chemical parameters necessary for a 12945

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Table 2. EIS Data of Cationic Dyes for Mild Steel in 1 M HCl Solution dye name Neutral Red (NR)

Azure A Eosinate (AAE)

Toluidine Blue (TB)

phenosafranin (PS)

Rhodanile Blue (RB)

a

inhibitor concn

Rs (Ω cm2)

Rt (Ω cm2)

Y0 (10−6 Ω−1cm−2)

n

Cdl (μF cm−2)

IEa (%)

blank 100 300 500 100 300 500 100 300 500 100 300 500 100 300 500

0.982 1.42 1.26 1.24 1.34 1.00 1.25 1.30 1.23 1.21 1.15 1.12 1.83 0.95 1.49 1.14

50.24 107.90 149.00 283.70 116.0 159.9 323.5 134.80 179.92 385.81 143.8 230.1 523.5 124.47 171.13 355.56

172.0 130.7 89.59 48.24 138.4 90.9 47.8 139.0 87.8 49.0 108.5 99.4 41.0 115.5 87.1 48.2

0.8090 0.8010 0.7942 0.7888 0.7892 0.7989 0.8015 0.8011 0.8052 0.7989 0.7914 0.7710 0.7850 0.8015 0.8115 0.7946

56.02 45.36 29.28 15.30 45.90 31.33 17.03 51.77 30.30 18.05 36.36 32.36 14.32 40.38 32.78 16.85

− 53.4 66.3 82.3 56.7 68.5 84.5 62.7 72.1 87.0 65.1 78.2 90.4 59.6 70.6 85.9

μRt.

Table 3. Bond Lengths and Bond Angles of the Studied Cationic Dyes (B3LYP/6-31+G(d,p) Results in vacuo) NR C1−C2 C2−C3 C3−N4/S4 N4/S4−C5 C5−C6 C6−C7 C7−C8 C8−C9 C9−C10 C10−N11 N11−C12 C12−C13 C13−C14 C14−C1 C1−N15 C7−N16 C8−C17 N15−C18 N15−C19 C1C2C3 C3N/S4C5 C5C6C7 C6C7C8 C8C9C10 C10N11C12 C12C13C14

AAE

Bond Length (Å) 1.416 1.424 1.389 1.384 1.374 1.750 1.372 1.748 1.390 1.389 1.405 1.412 1.450 1.431 1.371 1.366 1.426 1.432 1.340 1.338 1.335 1.332 1.426 1.433 1.364 1.364 1.449 1.441 1.357 1.352 1.355 1.352 1.507 1.469 1.463 Bond Angle (deg) 120.30 120.27 123.38 103.32 119.82 120.90 120.71 118.02 122.41 122.13 119.42 123.91 121.28 121.71

TB

PS

1.423 1.385 1.749 1.747 1.385 1.412 1.443 1.371 1.431 1.338 1.334 1.432 1.364 1.441 1.353 1.353 1.506 1.469 1.466

1.421 1.384 1.397 1.397 1.384 1.421 1.426 1.374 1.424 1.356 1.356 1.423 1.374 1.426 1.356 1.356

120.91 103.22 120.65 120.45 123.26 123.85 122.13

120.28 120.21 120.28 120.04 121.81 117.09 121.82

Table 4. Quantum Chemical Parameters for the Studied Cationic Dyes [Neutral Red (NR), Azure A Eosinate (AAE), Toluidine Blue O (TB), and Phenosafranin (PS) (B3LYP/ 6-31+G(d,p) Results in Vacuo)] quantum chem param total energy (au) EHOMO (eV) ELUMO (eV) ΔE (eV) μ (D) mol area (Å2) mol volume (Å3) log P polarizability HBD count HBA count ionization potential, I (eV) electron affinity, A (eV) electronegativity (χ) hardness (η) softness (σ) fraction electrons transferred (ΔN) electrophilicity (ω) % IEa

NR

AAE

TB

PS

−800.713 436 −8.814 −6.029 2.785 4.54 285 270 2.31 62.58 1 4 8.814

−1104.199 03 −9.064 −6.493 2.571 2.37 273 285 2.77 61.70 1 4 9.064

−1143.522 43 −8.953 −6.404 2.548 2.23 290 276 3.25 63.16 1 4 8.953

−913.834 906 −9.061 −6.087 2.975 1.94 303 298 2.62 64.77 2 4 9.061

6.030 7.422 1.393 0.718 0.15

6.493 7.779 1.285 0.778 0.30

6.404 7.679 1.274 0.785 0.27

6.087 7.574 1.487 0.672 0.19

19.78 66.87

23.54 68.73

23.14 73.3

19.28 77.23

a

Values of the percent inhibition efficiency are included for comparison purposes.

The energy of the HOMO (EHOMO) is related to the ability of the molecule to donate electrons, while the energy of the LUMO (ELUMO) is related to the ability of the molecule to accept electrons. The higher the value of EHOMO, the greater is the ability of the molecule to donate electrons, and the lower the value of ELUMO, the stronger is the tendency of the molecule to accept electrons. The energy difference (ΔE) also informs about the reactivity of the studied molecules. Molecules with a small ΔE value have a greater reactivity than molecules that have a large ΔE value.87 The results for the studied dyes (reported in Table 4) show that the tendency to donate electrons to the partially filled d orbital of the metal follows the

density distributions of HOMO and LUMO for the studied dyes are shown in Figure 2 and show that the HOMO is distributed throughout the molecule except on the N4/S4 and N11 atoms. Its amplitude coefficient has maxima on N15, N16, C2, C10, and C12, suggesting that the preferred sites for the electrophilic attack by the metal cation are located on these atoms. The electron density of the LUMO is also distributed throughout the molecule except on the C2 and C6 atoms. Its amplitude coefficient has maxima on the N11, N4/S4, C1, and C3 atoms. 12946

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Table 5. Mulliken Atomic Charges for the Selected Atoms of the Studied Cationic Dyes [Neutral Red (NR), Azure A Eosinate (AAE), Toluidine Blue O (TB), and Phenosafranin (PS) (B3LYP/6-31+G(d,p) Results in Vacuo)] Mulliken atomic charges on nonprotonated species

Mulliken atomic charges on protonated species

atom

NR

AAE

TB

PS

NR

AAE

TB

PS

C1 C2 C3 N4/S4a C5 C6 C7 C8 C9 C10 N11 C12 C13 C14 N15 N16 C17 C18 C19

0.008 −0.255 0.429 −0.406 0.446 −0.294 0.037 0.429 −0.374 0.124 −0.227 0.184 −0.149 −0.184 −0.106 −0.602 −0.681 −0.298 −0.300

0.151 −0.181 −0.144 0.047 −0.009 −0.304 0.260 0.011 −0.256 0.258 −0.138 0.204 −0.076 −0.189 −0.085 −0.578

0.277 −0.182 −0.118 0.044 −0.003 −0.404 0.295 0.445 −0.331 0.159 −0.149 0.223 −0.190 −0.193 −0.088 −0.591 −0.599 −0.280 −0.285

0.216 −0.288 0.327 −0.117 0.327 −0.288 0.216 −0.268 −0.194 0.271 −0.240 0.271 −0.194 −0.268 −0.606 −0.606

−0.013 −0.220 0.388 −0.387 0.411 −0.270 0.068 0.350 −0.339 0.234 −0.306 0.300 −0.149 −0.151 −0.087 −0.552 −0.637 −0.287 −0.296

0.110 −0.148 −0.170 0.121 −0.033 −0.258 0.236 0.029 −0.231 0.314 −0.195 0.300 −0.085 −0.127 0.056 0.524

0.241 −0.155 −0.157 0.119 −0.022 −0.354 0.290 0.389 −0.314 0.248 −0.202 0.323 −0.183 −0.151 −0.062 −0.536 −0.573 −0.278 −0.283

0.199 −0.311 0.401 −0.090 0.401 −0.311 0.199 −0.066 −0.366 0.305 −0.333 0.304 −0.346 −0.066 −0.548 −0.548

−0.284 −0.290

−0.281 −0.288

a

In Neutral Red and phenosafranin structures, position 4 is occupied by a N atom, while in Azure A Eosinate and Toluidine Blue O, position 4 is occupied by a S atom.

order NR > TB > PS > AAE and the tendency to accept electrons follows the order AAE > TB > PS > NR. A comparison of the ΔE values shows that the reactivity of the molecules follows the order TB > AAE > NR > PS. TB has greater reactivity than AAE because of the presence of the electron donating CH3 group at C8 in TB. The electron donating inductive effect of the CH3 activates the anthracene ring in TB, making it more reactive. The results also suggest that phenathiazinium cationic dyes would have a greater tendency to react with the metal surface than phenazinium cationic dyes. The structures of TB and NR differ only on the heteroatom at position 4; TB has a S atom at position 4 on the ring while NR has a N atom at position 4 on the ring. Therefore, the increased reactivity of the phenathiazinium dyes suggests that the presence of a S atom (as opposed to a N atom in phenazinium cationic dyes) increases the tendency toward corrosion inhibition, a phenomenon caused by the electronegativity difference between S and N. The order of reactivity TB > AAE > NR correlates well with both experimental and theoretical results. However, experimental results predict PS to have the highest inhibition efficiency (i.e., greater reactivity) while theoretical results predict PS to have the lowest reactivity. The discrepancy in the two approaches may be explained by the interplay between two competing factors in PS: steric and electron density factors. As observed earlier, PS has the least planar geometry (more steric effects) stemming from the perpendicularity of the benzene ring at C4 and the anthracene parent ring. It is therefore reasonable to infer that PS would have the least tendency to adsorb on the metal surface. However, of all the structures, PS has the highest electron density distribution arising from the presence of the benzene ring at C4, which provides more π conjugate double bonds and aromatic systems. These π double bonds could donate electrons to the partially filled or vacant d orbitals of the metal. It is difficult to quantify, from a theoretical point of view, which of these factors (steric

factor that has a negative influence toward inhibition and electron density distribution factor that has a positive influence toward inhibition) has a greater influence than the other, and therefore experimental results provide useful insights into the most dominant factor. In this way, the effectiveness of PS as a corrosion inhibitor may be attributed to the presence of a phenyl ring at C4 in conjugation with the anthracene ring. Global hardness (η) and softness (σ) are molecular properties that also facilitate the analysis of molecular reactivity and selectivity. These quantities are often associated with the Lewis theory of acids and bases and Pearson’s hard and soft acids and bases;88 a hard molecule has a large ΔE and therefore is less reactive; a soft molecule has a small ΔE and is therefore more reactive. Adsorption occurs most probably at the region of the molecule where σ has the highest value.89 The values of σ reported in Table 4 show that the adsorbability follows the order TB > AAE > NR > PS. The trend in the first three dyes agrees well between quantum chemical and experimental results and the peculiarity of the PS could be explained following an analogous discussion given for the ΔE value. The adsorbability of an inhibitor on the metal surface is also related to the charges on the chelating atom. The higher the negative partial atomic charge of the adsorbed center, the more easily the atom donates its electron to the partially filled or vacant d orbital of the metal.90 The Mulliken atomic charges on the atoms of the studied molecules are reported in Table 5. The results show interesting trends for the individual dyes and across structures. For the individual dyes, the highest negative atomic charge is on N atoms of the unsubstituted amino group: N16 in NR; N15 and N16 in PS; N16 in AAE; N16 in TB. These atoms would be the preferred sites for donating electrons to the mild steel surface to form a coordinate bond. There is also a substantial amount of excess negative charge on N4 in NR and PS, on N11 in all the dyes, and on N15 in AAE and TB. However, the S atoms (S4) in AAE and TB show electron deficiencies of 0.047e and 0.044e, respectively, suggesting that 12947

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Table 6. Bond Order for Atoms of the Studied Cationic Dyes in Nonprotonated and the Protonated Forms (B3LYP/ 6-31+G(d,p) Results in Vacuo) bond order in nonprotonated species

bond order in protonated species

bond distance

NR

AAE

TB

PS

NR

AAE

TB

PS

C1−C2 C2−C3 C3−N4/S4 N4(S4)−C5 C5−C6 C6−C7 C7−C8 C8−C9 C9−C10 C10−N11 N11−C12 C12−C13 C13−C14 C14−C1 C1−N15 C7−N16 C8−C17 N15−C18 N15−C19

1.600 1.382 0.954 0.842 1.368 1.618 1.235 1.382 1.231 0.909 1.035 1.248 1.711 1.186 1.104 0.845 0.581 0.801 0.814

1.367 1.402 1.036 0.955 1.412 1.589 1.248 1.544 1.256 1.043 1.180 1.225 1.683 1.299 1.141 0.828

1.398 1.351 1.047 0.864 1.392 1.555 1.148 1.407 1.288 1.039 1.113 1.252 1.714 1.239 1.137 0.783 0.620 0.798 0.809

1.525 1.426 0.857 0.858 1.425 1.525 1.376 1.594 1.234 1.096 1.095 1.233 1.594 1.375 0.832 0.833

1.564 1.443 0.891 0.813 1.400 1.600 1.211 1.501 1.217 0.927 0.913 1.265 1.720 1.195 1.178 0.917 0.656 0.798 0.806

1.335 1.452 1.021 0.943 1.444 1.547 1.251 1.638 1.263 1.021 1.044 1.240 1.716 1.284 1.205 0.911

1.371 1.405 1.033 0.853 1.427 1.506 1.133 1.510 1.258 1.033 1.008 1.254 1.750 1.224 1.203 0.890 0.696 0.790 0.803

1.536 1.450 0.818 0.818 1.450 1.536 1.279 1.638 1.283 1.019 1.019 1.283 1.638 1.279 0.849 0.849

0.800 0.813

0.791 0.805

and therefore greater adsorbability of the inhibitor on the metal surface. The results for the calculated cationic dyes show that the log P value increases in the order NR < PS < AAE < TB (Table 4), which suggests that phenathiazinium cationic dyes would have a greater tendency to adsorb on the metal surface than phenazinium cationic dyes in acidic solution. The molecular volume (MV) gives information on the contact surface between the inhibitor and the metal. The inhibition efficiency is usually proportional to the fraction of the surface covered by the adsorbed inhibitor.93 Table 4 also reports the molecular volume values for the studied cationic dyes. The results show that the molecular volume increases in the order PS > AAE > TB > NR. In this regard, both experimental and theoretical results show that PS is the most preferred inhibitor and NR is the least preferred inhibitor. The difference between experimental and quantum chemical results is in the preference for AAE and TB. In these two structures the geometric planarity and charge distribution factors also have strong influences. AAE is more planar than TB; however, it has a smaller charge density distribution than TB. Therefore, although AAE may be more likely to cover a greater surface on the metal (because of its planarity and large molecular volume), it has less charge density to provide to the metal compared to TB. The local selectivity of an inhibitor (i.e., the site on the molecule at which a particular reaction is likely to occur) is often analyzed by using condensed Fukui functions. These functions (indices) provide information about which atoms in a molecule have a higher tendency to either donate or accept an electron or pair of electrons. The nucleophilic and electrophilic Fukui functions can be calculated using the finite difference approximation, which when reduced to Mulliken atomic charges is written as94

the absorption of these inhibitors on the metal surface is strongly through the N atoms. Besides charges on the atoms, the strength of individual bonds in the molecule provides an idea of the regions that are susceptible to attack by electrophilic species. Such information is provided by analyzing the bond order in the molecule. Bond order is related to the distribution of charges between two atoms that are bonded to each other. For instance, in the Mulliken bond order analysis, a large positive value of bond order characterizes strong bonding between the atoms of interest, whereas negative values imply that electrons are displaced away from the interatomic region and point to an antibonding interaction. Table 6 reports the Mulliken bond order for the different cationic dyes. Among the C−N bonds, N15−C18 and N15−C19 bonds (i.e., the alkylammonium bonds) are the weakest; they are weaker in the thiazine dyes than in the azine dyes. Other bonds that are weak include the C7−N16 and N4−C5 bonds in azine and the S4−C5 bond in thiazine. These bonds may facilitate the interaction between the metal surface and the inhibitor. The fact that the weakest C−N and C−S bonds are found in the thiazine dyes might explain the preference of thiazine dyes to azine dyes in the adsorption on the metal surface. The dipole moment is another indicator of the electronic distribution in molecules, and it is a good indicator of the hydrophilic/hydrophobic character of a given system. A high dipole moment indicates polar character for the molecule, while a low dipole moment indicates nonpolar character for the molecule. Trends in the calculated dipole moments and observed inhibition efficiency are not always univocal.91,92 The results in the present study show that the dipole moment increases following the order PS < TB < AAE < NR, suggesting that the inhibition efficiency increases with the decrease in the dipole moment of the inhibitors. Another chemical parameter/quantity that is related to the hydrophilic/hydrophobic nature of the molecule is log P (where P is the octanol/water partition coefficient). A large value of log P implies less solubility of the inhibitor in solution 12948

f + = qN + 1 − qN

(14)

f − = qN − qN − 1

(15)

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Industrial & Engineering Chemistry Research Table 7. Fukuia Condensed Functions, f

+

Article

and f −, on the Atoms of the Studied Cationic Dyesb f−

f+ atom

a

NR

AAE

TB

PS

NR

AAE

TB

PS

C1

0.012

0.007

0.004

0.029

0.049

0.034

0.032

0.031

C2

−0.052

−0.043

−0.042

−0.043

−0.073

−0.056

−0.057

−0.053

C3

−0.003

−0.017

−0.017

−0.033

0.004

−0.015

−0.016

−0.009

S4

−0.049

−0.117

−0.114

−0.014

−0.030

−0.045

−0.044

−0.010

C5

−0.017

−0.024

−0.031

−0.033

−0.001

−0.018

−0.021

−0.009

C6

−0.050

−0.035

−0.029

−0.043

−0.046

−0.038

−0.032

−0.054

C7

0.012

0.017

0.009

0.028

0.020

0.026

0.016

0.032

C8

0.007

−0.056

0.008

−0.060

−0.013

−0.060

−0.012

−0.055

C9

−0.042

−0.048

−0.039

−0.051

−0.009

−0.019

−0.009

−0.022

C10

0.020

0.032

0.038

0.017

−0.027

−0.022

−0.016

−0.030

N11

−0.113

−0.116

−0.114

−0.114

−0.052

−0.052

−0.049

−0.051

C12

0.010

0.013

0.008

0.017

−0.011

−0.017

−0.016

−0.030

C13

−0.038

−0.040

−0.038

−0.051

−0.021

−0.018

−0.019

−0.022

C14

−0.055

−0.052

−0.053

−0.060

−0.049

−0.057

−0.054

−0.055

N15

−0.018

−0.018

−0.017

−0.064

−0.072

−0.066

−0.065

−0.105

N16

−0.065

−0.067

−0.067

−0.063

−0.081

−0.091

−0.087

−0.106

C17

−0.065

C18

−0.015

C19

−0.009

−0.061 −0.008

−0.047

−0.009

−0.005

−0.007

−0.001

The two Fukui functions were estimated by utilizing the finite difference approximation equations:

−0.047 0.000 0.001

0.001

80

f + = qN + 1 − qN

(14)

f − = qN − qN − 1

(15)

where qN is the Mulliken charge on the atom with N electrons and qN−1 and qN+1 are the Mulliken charges on the atom of the molecule with N − 1 and N + 1 electrons, respectively. bThe reported data do not include the Fukui functions on the H atoms. B3LYP/6-31+G(d,p) results in vacuo.

where qN+1, qN, and qN−1 are the charges of the atoms on the systems with N + 1, N, and N − 1 electrons, respectively. The preferred site for nucleophilic attack is the atom or region in the molecule where the value of f + is the highest, while the preferred site for electrophilic attack is the atom or region in the molecule where the value of f − is the highest. The calculated values of the Fukui functions for the non-hydrogen atoms in the four cationic dyes are reported in Table 7. The value of f + is highest on N11 in NR and in PS, and on S4 and N11 in AAE and in TB. These regions on each structure represent the preferred sites for nucleophilic attack. The value of f − is highest on N15, N16, and C2 in NR and in AAE, and on N15 and N16 in PS and in TB. These atoms represent regions on the molecules for which there is a high preference for electrophilic attack. The information obtained from the Fukui condensed functions entirely agrees with the analysis of the HOMO/LUMO and the Mulliken atomic charges, that certain CC π bonds in the aromatic rings, the amino group, and alkylammonium group have the highest tendency to donate electrons. The S atom and the N11 atom have the highest tendency to accept electrons from the metal. 3.4. Results of the Calculations on Protonated Species. The presence of heteroatoms in the molecules of NR, PS, AAE, and TB suggests a high tendency toward protonation in acidic solution. Therefore, it is important to investigate the protonated forms of the studied structures in order to determine the preferred form of the dyes in acidic solution. The extent of

protonation is provided by the proton affinity (PA) of the inhibitors which might be estimated by using the equation PA = Eprot + E H2O − Enonprot − E H3O+

(16)

where Eprot and Enonprot are the total energies of the protonated and the nonprotonated inhibitors, respectively, EH2O is the total energy of a water molecule, and EH3O+ is the total energy of the hydronium ion. All the possible protonation sites in each structure were considered. Table 8 shows the relative energies of the optimized protonated forms for each structure. The results show that, in all the structures, the preferred site for protonation is N11; in the thiazine dyes, the least site for protonation is the S4 atom; N16 is the least preferred protonation site of all N atom sites. This means that the amino group has the least preference for protonation compared to the N11 and the alkylammonium group (N15 in NR, AAE, and TB). Since the preferred site for protonation is N11, all discussions in the next paragraphs are concerned solely with the species protonated at N11. Table 9 shows the total energies of the nonprotonated and protonated species and the proton affinity of each of the studied molecules. The values of the proton affinity show that the protonation is downhill exothermic by about 0.26 for NR, 0.37 for PS, 0.41 for AAE, and 0.29 for TB. A comparison of the calculated molecular descriptors between the protonated and the nonprotonated forms of the studied cationic dyes provides information on the changes in molecular property trends on 12949

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Table 8. Total Energies (au) and Relative Energies (kcal/ mol) of the Different Protonated Forms of the Studied Dyes (B3LYP/6-31+G(d,p) Results) protonated species NR-prot-N11 NR-prot-N15 NR-prot-N16 AAE-prot-N11 AAE-prot-N15 AAE-prot-N16 AAE-prot-S4 TB-prot-N11 TB-prot-N15 TB-prot-N16 TB-prot-S4 PS-prot-N11 PS-prot-N15

total energy (au)

relative energy (au)

Neutral Red −800.977 624 0.000 −800.971 973 0.006 −800.955 471 0.022 Azure A Eosinate −1104.457 87 0.000 −1104.450 19 0.008 −1104.436 93 0.021 −1104.387 57 0.070 Toluidine Blue O −1143.785 47 0.000 −1143.777 14 0.008 −1143.762 62 0.023 −1143.714 28 0.071 Phenosafranin −914.095 099 0.000 −914.074 945 0.020

Table 10. Quantum Chemical Parameters for the Protonated Species of the Studied Cationic Dyes [Neutral Red (NR), Azure A Eosinate (AAE), Toluidine Blue O (TB), and Phenosafranin (PS) (B3LYP/6-31+G(d,p) Results in Vacuo)]a

relative energy (kcal/mol)

quantum chem param

NR-P

AAE-P

TB-P

PS-P

0.000 3.765 13.805

total energy (in vacuo) (au) total energy (aq) (au)

0.000 5.020 13.178 43.926

solvation energy (kJ/mol) EHOMO (eV) ELUMO (eV) ΔE (eV) μ (D) mol area (Å2) mol volume (Å3) log P polarizability HBD count HBA count ionization potential, I (eV) electron affinity, A (eV) electronegativity (χ) hardness (η) softness (σ) fraction electrons transferred (ΔN) electrophilicity (ω) % IEb

−800.977 624 −801.211 789 −614.80

−1104.457 87 −1104.694 63 −624.62

−1143.785 47 −1144.016 36 −606.20

−914.095 099 −914.333 352 −625.54

−12.403 −10.411 1.993 1.40 289 272 1.94 62.99 1 4 12.403

−12.710 −10.805 1.905 2.55 276 261 2.40 62.09 1 4 12.710

−12.525 −10.662 1.863 1.55 293 279 2.88 63.54 1 4 12.525

−12.759 −10.525 2.235 5.35 311 300 2.25 65.15 2 4 12.759

10.411 11.407 0.996 1.004 2.21

10.805 11.757 0.953 1.050 2.50

10.662 11.594 0.932 1.073 2.47

10.525 11.642 1.1174 0.895 2.08

65.30 66.87

72.56 68.73

72.14 73.3

60.65 77.23

0.000 5.227 14.339 44.672 0.000 12.550

protonation. The results, reported in Table 10, show that, with the exception of the dipole moment, the trends in the molecular properties (such as EHOMO, ELUMO, ΔE, MV, etc.) across structures are similar for the nonprotonated and the protonated inhibitors. For instance, among the protonated inhibitors, NR has the highest EHOMO value while AAE has the lowest ELUMO value; TB has the smallest ΔE value. A comparison of the molecular properties between the protonated and the nonprotonated species of the individual structures shows that the protonated form has the lower EHOMO, which suggests that protonation decreases the tendency of an inhibitor to donate electrons. This phenomenon may be explained as follows: the protonation of a molecule results in an increased nuclear charge so that the nuclear charge pulls more strongly on the outer electrons. As a result, the ionization energy (i.e., the energy required to remove an electron) is higher in the protonated species than in the nonprotonated species. Since the energy of the HOMO is related to the ionization energy (IE) through the equation EHOMO = −IE, an increase in the ionization energy implies a lower EHOMO value. The protonated species also has the lower value of the ELUMO, suggesting that protonation increases the tendency of an inhibitor to accept electrons. The protonated species also has the smaller ΔE value, indicating that for each structure the protonated species is the more reactive form. The protonated form also has the lower hardness and the higher softness values. However, since the protonated species are less likely to donate electrons, they would rarely be involved in a chemisorption process, which means that the interaction between the protonated species and the metal is through physisoption in which the protonated inhibitors are

The letter “P” at the ends of the names of the dyes denote that the species are protonated. bValues of the percent inhibition efficiency are included for comparison purposes.

a

electrostatically attracted to the metal surface by the already adsorbed Cl anions as suggested in ref 95, but this does not rule out chemisorption, which means that the interaction between the inhibitors and the metal surface is mixed type. The Mulliken partial atomic charges on atoms of the protonated species are also reported in Table 5 and show interesting patterns. The N atom of the amino group (N15 and N16 in PS, N16 in NR, AAE, and TB) has more negative charge in the nonprotonated form than in the protonated form; N11 has more negative charge in the protonated form than in the nonprotonated form. In NR and PS, N4 has less charge in the protonated species than in the corresponding nonprotonated species, while in AAE and TB, S4 is less negative charge deficient in the nonprotonated species than in the corresponding protonated species. Therefore, overall, the nonprotonated species has more negative charge than the protonated species and would therefore have the greatest tendency to donate electrons to the partially filled or vacant d orbitals of Fe. The interaction with

Table 9. Energies (au) of the Cationic Dyes, Energies (au) of the Protonated Species at N11, and Proton Affinities (PA, eV) [(B3LYP/6-31+G(d,p) Results in Vacuo)] cationic dye

Enonprot (au)

EprotN1 (au)

EH2O (au)

EH3O+ (au)

PA (eV)

NR AAE TB PS

−800.713 436 −1104.199 03 −1143.522 43 −913.834 906

−800.977 624 −1104.457 87 −1143.785 47 −914.095 099

−76.434 046 3 −76.434 046 3 −76.434 046 3 −76.434 046 3

−76.707 771 2 −76.707 771 2 −76.707 771 2 −76.707 771 2

0.26 0.41 0.29 0.37

12950

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the metal surface would most probably take place at N11 because N11 is linked to the double bond (i.e., it has an sp2 hybridization) that could break to allow the formation of a metal−inhibitor coordination bond in an addition or substitution reaction. This possibility is not present for N15 and N16, though they have the highest negative charge and are saturated N atoms. 3.5. Results of the Calculations in Aqueous Solution. So far the discussion has been based on the interaction between the inhibitor and the metal surface in vacuo, but electrochemical corrosion phenomena take place in solution, where the solvent might influence the adsorbability of the inhibitor on the metal surface. It is therefore important to obtain quantum chemical properties of the inhibitor in solution for better understanding of the role of the inhibitor on interacting with the metal surface. All the lowest energy conformers of the calculated dyes have near-planar geometry (except PS) in vacuo, and since these molecules do not have significant rotatable single bonds, there are no major geometry changes that would be expected in aqueous solution. Therefore, quantum chemical parameters in aqueous solution were obtained by running single point calculations on the optimized geometry in vacuo. Such calculations provide information on the molecular properties of the inhibitor in solution at the same geometry as in vacuo. The most interesting quantity to consider is the free energy of solvation (ΔGsolv). Solvation energy as defined by most continuum solvation models is given as ΔGsolv = (Esoln + Gnes) − Egas

Table 11. Quantum Chemical Parameters of the Studied Dyesa quantum chem param

NR

AAE

TB

PS

total energy (aq) (au)

−800.788 867 4 −44.68

−1104.269 198 8 41.45

−1143.590 383 8 −39.82

−913.908 643 −40.45

−5.864 −3.135 2.729 6.82 5.864

−6.099 −3.607 2.492 3.328 6.099

−6.052 −3.580 2.472 3.425 6.052

−6.134 −3.251 2.883 2.758 6.134

3.135

3.607

3.580

3.251

4.499 1.364 0.733 −0.916

4.853 1.246 0.803 −0.862

4.816 1.236 0.809 −0.884

4.693 1.442 0.694 −0.800

7.420 66.87

9.450 68.73

9.383 73.3

7.638 77.23

solvation energy, ΔGsolv (kcal/mol) EHOMO (eV) ELUMO (eV) ΔE (eV) μ (D) ionization potential, I (eV) electron affinity, A (eV) electronegativity (χ) hardness (η) softness (σ) fraction electrons transferred (ΔN) electrophilicity (ω) % IEb a

Results in aqueous solution were obtained through SM8 single point calculations on the input geometry optimized in vacuo. bValues of percent inhibition efficiency are included for comparison purposes.

3.6. Adsorption Mechanism on the Metal Surface: Hydrogen Bonding. The possibility of the formation of passive oxide film (i.e., Fe2O3 and Fe3O4) on the mild steel surface, as a result of corrosion, suggests that hydrogen bond formation has an important role in most of the inhibitory action on mild steel.98−100 It is therefore important to consider the number of hydrogen bond donor (HBD) and hydrogen bond acceptor (HBA) centers as they indicate the possibility of hydrogen bond formation between the molecule and the surface of the metal. The results show that PS has the highest total number of HBA and HBD centers and would therefore have the highest prevalence of the hydrogen bond interactions between the inhibitor and the metal surface. However, because positive charges are conducive to the formation of hydrogen bonds,101 all the cationic dyes studied in this work have very high tendencies to adsorb on the metal surface. The nonprotonated species preferably adsorb onto the metal surface by donating electrons to the partially filled or vacant d orbitals of the metal, thereby coordinating to the metal surface in a chemisorption process. The protonated species adsorb on the metal by binding to the Cl ions in solution. Since the Cl ions are negatively charged, they bind to the metal, and in turn the protonated species are attracted to these Cl ions through electrostatic forces. 3.7. Semiempirical AM1 and PM3 Calculations in Vacuo. Semiempirical calculation methods are widely used in the study of corrosion inhibition because some of the inhibitor molecular systems are often medium-to-large molecules and would therefore be computationally inhibitive for sophisticated ab initio calculations. Moreover, semiempirical methods have been reported to yield good results.102 In this study, semiempirical AM1 and PM3 methods have been used in order to afford the ability to study Rhodanile Blue (RB), a molecule that is computationally expensive (within our computational capability) to calculate with the DFT/B3LYP/6-31+G(d,p) method. All other molecular systems studied with DFT/B3LYP/ 6-31+G(d,p) were also studied at the semiempirical level to compare their molecular properties with those of RB.

(17)

where Esoln is the electronic energy of the inhibitor molecule in solution and Egas is the electronic energy of the inhibitor molecule in vacuo; Gnes represents the total sum of any nonelectrostatic contributions (e.g., cavitation and dispersion− repulsion interactions) to the solvation free energy.96 The solvation energy therefore indicates the extent of the solute−solvent interactions on the different inhibitors (i.e., it is an indication of solubility). The inhibitor with a lower value of the solvent effect has fewer tendencies to be solvated, while the inhibitor with a high value of the solvent effect has a higher tendency to be solvated. A high tendency to be solvated implies that the inhibitor spends more time in the solvent and has fewer tendencies to interact with the metal surface.97 In the current study the solvation free energy (kJ/mol) was found to be −44.68 for NR, −40.45 for PS, −41.45 for AAE, and −39.82 for TB, which implies that the order of adsorbability on the metal surface would preferentially be NR < AAE < PS < TB. The trend in aqueous solution is therefore much closer to the experimental inhibition efficiency than the trend in vacuo. Table 11 shows the calculated quantum chemical properties in aqueous solution for the calculated compounds. The results show that the trends are similar to the results in vacuo; however, a comparison of individual molecular properties across media shows interesting patterns. The EHOMO, ELUMO, and ΔE values are smaller in aqueous solution than in vacuo, which suggests increased reactivity of the inhibitors in aqueous solution; the dipole moment is higher in aqueous solution than in vacuo and this is a result of increased charge polarization in aqueous solution. These results suggest that electrostatic interactions between the inhibitor and the metal surface might have a greater influence in aqueous solution. The values of global hardness (η) and global softness (σ) show that the inhibitors are softer in solution than in vacuo. The changes in the molecular parameters between the results in vacuo and the results in aqueous solution are entirely related to the solute−solvent effects. 12951

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Figure 6. Optimized geometry, HOMO, LUMO, and electrostatic potential maps (EPM) for Rhodanile Blue (RB) calculated using AM1 and PM3 semiempirical methods. Results in vacuo.

rhodamine unit is entirely electron deficient (deep blue color). All the heteroatoms in the molecule are electron rich as shown by the red color on those atoms. Table 12 shows the calculated AM1 and PM3 quantum chemical parameters for all the studied compounds. The results of semiempirical calculations (using both AM1 and PM3 methods) on NR, AAE, TB, and PS show that the trends in their molecular properties are more or less similar to the trends identified by DFT/B3LYP, with AM1 results being much closer to DFT results than PM3 results. When RB is included, results show interesting trends across structures. RB has the highest energy of the HOMO, which implies that it has the greatest tendency to donate electrons; it has the lowest ΔE value and the highest σ value (global softness value) and therefore it has the highest tendency toward

The optimized structure, the HOMO, the LUMO, and the electrostatic potential map (EPM) of RB are shown in Figure 6. It has two major components, an oxazine structural part (i.e., Nile Blue A) and a xanthene structural part (i.e., rhodamine type of structure). Overall, RB has the highest number of heteroatoms and hydrogen bond donor groups than any other dye studied so far in this work. However, the optimized geometry suggests that the overall molecule is highly nonplanar, which might have an influence in its adsorbability on the metal surface The HOMO is entirely localized in the Nile Blue A unit of the molecule, while the LUMO is entirely localized in the rhodamine unit. The electrostatic potential map confirms the analysis of the HOMO and the LUMO, showing that the Nile Blue A unit is slightly electron rich (green color) while the 12952

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Table 12. Quantum Chemical Properties for the Studied Dyes Calculated at AM1 and PM3 Semiempirical Levelsa AM1 results

PM3 results

quantum chem param

NR

AAE

RB

TB

PS

NR

AAE

RB

TB

PS

EHOMO (eV) ELUMO (eV) ΔEb (eV) μ (D) MVc (Å3) log P polarizability HBD count HBA count IP, I (eV) EA, A (eV) electronegativity hardness (η) softness (σ) ΔNc electrophilicity

−11.385 −4.998 6.387 3.67 271 2.31 61.86 1 4 11.385 4.998 8.192 3.194 0.313 0.187 10.506

−11.410 −5.360 6.050 2.78 258 2.77 60.86 1 4 11.410 5.360 8.385 3.025 0.331 0.229 11.622

−9.592 −4.603 4.989 10.53 684 6.57 40.19 0 8 9.592 4.603 7.097 2.495 0.401 0.019 10.096

−11.332 −5.321 6.011 2.62 276 3.25 62.32 1 4 11.332 5.321 8.326 3.006 0.333 0.221 11.534

−11.503 −4.941 6.562 1.13 299 2.62 64.04 2 4 11.503 4.941 8.222 3.281 0.305 0.186 10.301

−11.448 −5.291 6.157 3.47 270 2.31 61.86 1 4 11.448 5.291 8.369 3.078 0.325 0.222 11.377

−11.422 −5.683 5.739 1.50 259 2.77 61.02 1 4 11.422 5.683 8.552 2.869 0.349 0.271 12.746

−9.774 −4.880 4.894 13.33 682 6.57 40.21 0 8 9.774 4.880 7.327 2.447 0.409 0.067 10.970

−11.364 −5.660 5.704 2.00 277 3.25 62.47 1 4 11.364 5.660 8.512 2.852 0.351 0.265 12.703

−11.604 −5.266 6.338 1.77 298 2.62 64.06 2 4 11.604 5.266 8.435 3.169 0.316 0.226 11.227

a The average experimental determined inhibition efficiency for each dye is 66.87 for NR, 68.73 for AAE, 69.70 for RB, 73.30 for TB, and 77.23 for PS. bΔE is calculated as ELUMO minus EHOMO. cMV is molecular volume, IP is ionization potential, EA is electron affinity, and ΔN is the fraction of electrons transferred.

where A and B are the regression coefficients determined through regression analysis, xi is a quantum chemical index characteristic of the molecule i, and Ci is the experimental concentration of the inhibitor. QSAR was performed using the quantum chemical parameters obtained using the B3LYP/6-31G (d,p) method and those obtained using the AM1 and PM3 methods in an attempt to correlate more than one quantum chemical parameter to the observed inhibition efficiency. The results of the QSAR analysis on the quantum chemical parameters obtained with the B3LYP/6-31G(d,p) method show that a combination of two quantum chemical parameters to form a composite index provides the best correlation with the experimental data and the best three equations obtained are of the form

reactivity; it has the highest HBA count, which implies that it has the highest tendency to interact through the formation of hydrogen bonds. All these factors indicate that RB would be the most effective inhibitor to interact with the metal surface. However, experimental results show that it has a lower inhibition efficiency than both TB and PS. The lower inhibition efficiency for RB might be attributed to its largely nonplanar geometry suggesting that many of its electron donor centers may not directly interact with the metal surface, resulting in poor inhibition efficiency. However, since several molecular properties might be contributing simultaneously to the interaction of the inhibitor with the metal surface, it might be necessary to take into consideration more than one quantum chemical parameter for a meaningful interpretation of the results. We consider this option in section 3.8, where we attempt to derive equations that correlate more than one quantum chemical parameter with the experimental inhibition efficiency. 3.8. Statistical Analysis of the Data Using Quantitative Structure−Activity Relationship (QSAR) Approach. The correlation of individual quantum chemical parameters with the inhibition efficiency of the inhibitor is usually less informative because of the complexity of the adsorption process. It is therefore essential to combine several quantum chemical parameters to form a composite index that could be correlated to the experimental inhibition efficiency. A correlation between quantum chemical parameters and the observed inhibition efficiency is studied by means of the quantitative structure−activity relationship (QSAR) approach in which relevant mathematical equations are used to relate the quantum chemical parameter to the observed inhibition efficiency (IE) of an inhibitor. The derived equations are used to predict the percent IE from the concentrations of the inhibitors and to provide theoretical explanations for the effects of different variables studied.103 In the present work, two models were tested: the linear model and the nonlinear model proposed by Lukovits et al. for the study of interaction of corrosion with metal surface in acidic solutions.104 However, the linear model alone produced the best correlation results between experimental and theoretical data. This equation has the form IEtheor = AxiC i + B

IE = 15.672 log P − 30.634ΔE − 67.467; R2 = 0.999 and SSE = 0.081

(19)

IE = 4.790(Pol) − 11.976E LUMO − 318.135; R2 = 0.997 and SSE = 0.212

(20)

IE = − 1.931μ + 2.939(Pol) − 121.231; R2 = 0.970 and SSE = 2.431

(21)

2

where R is the coefficient of determination and SSE is the sum of squared errors defined as SSE =

∑ (IE%exptl − IE%theor)2

(22)

Equation 19 suggests that a higher log P and smaller ΔE results in greater inhibition efficiency. Equation 20 suggests that the higher the polarization of an inhibitor and the lower the ELUMO, the greater the inhibition efficiency of the inhibitor, and eq 21 suggests that smaller dipole moment and higher polarization result in greater inhibition efficiency. Figure 7 shows the corresponding representative plots of the correlation between experimental inhibition efficiencies and theoretically estimated inhibition efficiencies, while Table 13 shows all the combinations of quantum chemical parameters from AM1, PM3,

(18) 12953

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Figure 7. Representative plots of correlation between the theoretically estimated % IE and experimentally obtained % IE. The items above each plot indicate the quantum chemical parameters used to form the composite index. The quantum chemical properties are obtained from B3LYP/631+G(d,p) results.

Table 13. Combination of Quantum Chemical Parameters Used in the QSARa Analysis and the Corresponding Derived Equations, R Values, and SSE Values for Calculation with Different Methods R2 value

SSE value

IE = 15.671 log P − 30.634ΔE − 67.467

0.999

0.081

Pol and ELUMO

IE = 4.280(Pol) − 11.255E LUMO − 318.135

0.997

0.212

μ and Pol

IE = − 1.931μ + 2.939(Pol) − 121.231

0.970

2.431

Pol and EHOMO

IE = 3.354(Pol) − 13.460E HOMO − 273.478

0.891

8.904

μ and ELUMO

IE = 16.058E LUMO − 4.787μ + 172.418

combination of quantum descriptors

derived equation

B3LYP/6-31+G(d,p) log P and ΔE

0.877

10.123

MV and Pol

−2

IE = (8.623 × 10 )MV + 3.136(Pol) − 163.295

0.829

13.984

μ and ΔE

IE = − 12.679ΔE − 3.317μ + 33.452

0.756

20.039

EHOMO, ELUMO, and log P

IE = − 38.041E HOMO + 17.509E LUMO + 15.086 log P − 313.457

0.999

0.095

EHOMO, ELUMO, and μ

IE = 21.198E HOMO + 2.706E LUMO − 5.197μ + 340.53

0.969

2.085

0.962

2.576

AM1

μ, MV, and log P

−2

IE = − 3.527μ + (4.380 × 10 )MV + 2.300 log P + 62.129 −2

EHOMO, μ, and MV

IE = 16.032E HOMO − 4.822μ + (1.935 × 10 )MV + 261.363

0.959

2.736

EHOMO, ELUMO, and MV

IE = − 43.962E HOMO − 15.98E LUMO + 0.214(MV) − 571.482

0.830

11.383

EHOMO, ELUMO, and log P

IE = − 36.088E HOMO + 9.747E LUMO + 13.949 log P − 326.844

0.999

0.041

EHOMO, ELUMO, and MV

IE = − 38.190E HOMO − 17.738E LUMO + 0.181(MV) − 513.192

0.884

7.787

EHOMO, μ, and MV

IE = − 12.444E HOMO + − 2.878μ + 0.127(MV) − 99.879

0.852

9.905

EHOMO, ELUMO, and μ

IE = 48.317E HOMO + 40.485E LUMO − 9.602μ + 867.851

0.760

16.088

PM3

a

QSAR analysis using the DFT results involved Neutral Red (NR), Azure A Eosinate (AAE), Toluidine Blue (TB), and phenosafranin (PS) while QSAR analysis of the semiempirical results involved Neutral Red (NR), Azure A Eosinate (AAE), Rhodanile Blue (RB), Toluidine Blue (TB), and phenosafranin (PS). The abbreviations Pol, MV, and μ denote molecular polarization, molecular volume, and dipole moment, respectively. 12954

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utilized to suggest possible routes to modify the studied dye inhibitors to obtain more effective corrosion inhibitors.

and B3LYP/6-31+G(d,p) methods that have produced satisfactory correlations between theoretically estimated inhibition efficiencies and experimentally obtained inhibition efficiencies.

■

AUTHOR INFORMATION

Corresponding Author

4. CONCLUSIONS All the dyes studied showed excellent inhibitive performance and acted as mixed-type inhibitors. The inhibition efficiencies increased with the concentrations of the dyes. The inhibition efficiencies obtained from the EIS and Tafel polarization are comparable. The quantum chemical calculations using DFT, AM1, and PM3 semiempirical methods were performed on selected azine and thiazine dyes to obtain the optimized molecular structures and the electronic properties of the dyes. Quantitative structure−activity relationship (QSAR) analysis was also performed to correlate the experimental obtained inhibition efficiencies and the theoretically determined inhibition efficiencies. The results show that thiazine dyes are preferred to azine dyes, indicating that the presence of both S and N atoms in an inhibitor results in greater inhibition efficiency than the presence of N atoms alone. However, structures in which the azine dyes have more electron donor centers (e.g., the presence of an aromatic system that might not be present in thiazine) than thiazine, the azine dyes might be preferred to thiazine as corrosion inhibitors. The results also show that electronic factors, such as electron density, often have a greater influence in determining a good corrosion inhibitor than geometric factors of cases where more of the inhibitor is in contact with the metal surface. Therefore, even if a molecule has less planar geometry but manages to have most of its electron donor centers in contact with the metal surface, it would have greater inhibition efficiency than a molecule that is planar but has less electron density. However, molecules that are highly nonplanar with the metal surface are poor corrosion inhibitors, even if they have an overall high charge density. The adsorption of the studied dyes on the metal surface is probably through the nitrogen atoms of the amino and the dimethylamino groups, in addition to the availability of π-electrons in the aromatic system. This work also suggests that hydrogen bonding might have a significant influence on the physisorption process because of the positive charge on the metal surface and the number of hydrogen bond donor centers in the inhibitors. This suggestion may also help explain the preference for PS as a good corrosion inhibitor since it has the highest numbers of HBD and HBA centers. The results in aqueous solution show similar trends in the molecular properties across the studied dyes. However, a comparison of the individual molecular properties across structures suggests a strong influence of the solvent on the molecular properties. The quantitative structure−activity relationship analysis has shown that at least two molecular properties are needed to produce a good correlation between the experimentally determined inhibition efficiency and the theoretically estimated inhibition efficiency. The values of R2 and SSE obtained come within a reasonable range for good correlations between experimentally determined inhibition efficiencies and quantum chemically determined inhibition efficiencies. The results point to the suitability of the selected cationic dyes as corrosion inhibitors, indicating that a combination of several factors needs to be taken into account for a good selection of possible effective corrosion inhibitors. The results of quantitative structure−activity relationships may also be

*E-mail: [email protected]. Tel.:+27 183892113. Fax: +27183892052. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS M.M.K., A.K.S., and S.K.S. are grateful to the North-West University for granting them Postdoctoral fellowships enabling them to participate in this work. E.E.E. thanks the National Research Foundation (NRF) of South Africa for funding.

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REFERENCES

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