Experimental and Quantum Chemical Studies of Some Bis

Article pubs.acs.org/IECR

Experimental and Quantum Chemical Studies of Some Bis(trifluoromethyl-sulfonyl) Imide Imidazolium-Based Ionic Liquids as Corrosion Inhibitors for Mild Steel in Hydrochloric Acid Solution Lutendo C. Murulana, Ashish K. Singh, Sudhish K. Shukla, Mwadham M. Kabanda, and Eno E. Ebenso* Department of Chemistry, School of Mathematical and Physical Sciences, North West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa ABSTRACT: The corrosion inhibition of mild steel in 1.0 M HCl solution by some selected imidazolium-based ionic liquids, namely 1-propyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([PMIM][NTf2), 1-butyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([BMIM][NTf2), 1-hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([HMIM][NTf2]), and 1-propyl-2,3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([PDMIM][NTf2]) was investigated using weight loss, electrochemical measurements, and quantum chemical calculations. All ionic liquids showed appreciable inhibition efficiency. Among the ionic liquids studied, [PDMIM][NTf2] exhibited the best inhibition efficiency. The results from the weight loss, electrochemical measurements and quantum chemical calculations show that the order of inhibition efficiency by the ionic liquids follow the order [PDMIM][NTf2] > [HMIM][NTf2] > [BMIM][NTf2] > [PMIM][NTf2]. At 303 K, polarization measurements indicated that all the studied compounds are mixed-type inhibitors. The adsorption of the studied ionic liquids obeyed the Langmuir adsorption isotherm. There is good correlation between a composite index of quantum chemical parameters and experimentally determined inhibition efficiency of the inhibitors. The quantitative structure activity relationship (QSAR) approach has provided a good indication that an optimum of at least two quantum chemical parameters is required for a good correlation with the experimentally determined inhibition efficiency of the ionic liquids.

1. INTRODUCTION Mild steel is widely utilized as construction material in many industrial applications due to its exceptional mechanical properties and low cost. However, the environment in which mild steel is utilized and/or the substances that are stored by pipes or tanks that are made out of mild steel are often of corrosive nature, which may lead to the dissolution of the metal. Due to this, there is an increasing search for materials that might help in the reduction or prevention of mild steel corrosion, among which is the use of corrosion inhibitors. Corrosion inhibitors are widely employed in the protection of metal surfaces from possible damage due to corrosion. For an inhibitor to be an effective protector against metal corrosion, it should readily adsorb on the metal surface through either physisorption or chemisorption processes.1 Either of these adsorption processes depends primarily on the physicochemical properties of the inhibitor group such as functional groups, electronic density at the donor atom, molecular structure, etc.2−4 For instance, organic molecules, which have had a wide applicability and that have been extensively studied and used as corrosion inhibitors, often contain nitrogen, oxygen, and sulfur atoms, as well as multiple bonds in their molecules.5 However, most organic inhibitors are not environmentally friendly, and there is an increasing tendency toward the use of environmentally benign corrosion inhibitors such as derivatives of amino acids and ionic liquids.5,6 Ionic liquids (ILs) are molten salts composed of organic cations and various anions. The organic cation usually has a π system and/or a heteroatom, such as nitrogen (e.g., imidazolium-based ILs), sulfur (e.g., sulfonium-based ILs), or phosphorus (e.g., phosphonium-based ILs), as the central © 2012 American Chemical Society

atoms for interaction with the metal surface. ILs possess a large number of physicochemical properties,6−9 mainly, good electrical conductivity, solvent transport, and a relatively wide electrochemical window,9 making them highly efficient for both physisorption and chemisorption processes. Ionic liquids are therefore finding various applications in academic and industrial areas. One of these applications is the use of ionic liquids as inhibitors of metal surface corrosion. Since metal surface corrosion is a major problem facing many industrial applications, it is of vital importance to understand the structure and electronic properties of ionic liquids that make them suitable for the inhibitor role. Such knowledge would assist in the selection of the best IL inhibitor for a particular application, and also, it helps in the design of better IL inhibitors for future applications. Computational methods have been used extensively in the study of the molecular structures of different ionic liquids for various reasons, among which is to understand the preferred type of interactions within the molecules and between ionic liquids and other molecules.10 A survey of literature works on the structure of imidazoliumbased ionic liquids reveals that the preferred arrangement of the cation and the anion in the ion-pair is such that the anion is preferably hydrogen bonded to the C2−H atom of the N1− C2−N3 group. Despite volumes of literature works on the molecular structure of imidazolium based ionic liquids, there is still a scarcity of theoretical information that might help Received: Revised: Accepted: Published: 13282

April 13, 2012 August 16, 2012 August 23, 2012 August 23, 2012 dx.doi.org/10.1021/ie300977d | Ind. Eng. Chem. Res. 2012, 51, 13282−13299

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic representation of the studied ionic liquids and the atom numbering utilized in the discussion. The atoms of the cation and the anion units are numbered separately. [PMIM][NTf2] denote 1-propyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([PMIM][N(SO2CF3)2]2); [BMIM][NTf2] denote 1-butyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([BMIM][N(SO2CF3)2]); [HMIM][NTf2] denote 1-hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([HMIM][N(SO2CF3)2]); [PDMIM][NTf2] denote 1-propyl-2,3methylimidazolium bis(trifluoromethyl-sulfonyl) imide.

2.4. Weight Loss Measurements. Weight loss experiments were done according to the method described previously.15,16 Weight loss measurements were performed at 303 K for 3 h by immersing the mild steel coupons into acid solution (100 mL) without and with various amounts of inhibitors. After the elapsed time, the specimens were taken out, washed, dried, and weighed accurately. The inhibition efficiency (EWT%) and surface coverage (θ) were determined by using following equations:

understand the corrosion inhibition role of ILs. Such lack of theoretical information is mainly due to the large size of the molecules of most ILs, making the use of sophisticated ab initio calculations too computationally expensive to afford. Semiempirical calculations are, however, affordable and have been used previously to describe the inhibitor role of ionic liquids in corrosion processes.11−14 The objective of this work is, therefore, to investigate the corrosion inhibition properties of four imidazolium-based ionic liquids, namely 1-propyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([PMIM][NTf2], 1-butyl-3methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([BMIM][NTf 2 ], 1-hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([HMIM][NTf2]), and 1propyl-2,3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide ([PDMIM][NTf 2]), (where the abreviation NTf2 denotes the N(SO2CF3]2 anion group) using weight loss, electrochemical measurements, and quantum chemical calculations on mild steel in hydrochloric acid medium. The schematic representation of the structures and the atom numbering relevant for the discussion is presented in Figure 1. All four ionic liquids have the same anion unit but different cation units. The investigation intends to determine the effect of different substituents on the cationic units on the corrosion inhibition role of the selected ionic liquids. The factors to investigate include the effect of methylation at C2 atom on corrosion inhibition and the effect of increase in the R chain (the alkyl chain at N1) on the corrosion inhibition.

E WT% =

θ=

w0 − wi × 100 w0

w0 − wi w0

(1)

(2)

where w0 and wi are the weight loss value in the absence and presence of inhibitor. 2.5. Electrochemical Measurements. A three-electrode cell consisting of a carbon steel working electrode (WE), a platinum counter electrode (CE), and a saturated calomel electrode (SCE) as a reference electrode was used for electrochemical measurements. All experiments were performed in atmospheric condition without stirring. Prior to the electrochemical measurement, a stabilization period of 30 min was allowed, which was proved to be sufficient to attain a stable value of Ecorr. The potentiodynamic polarization curves were recorded in the potential range from −250 to +250 mV (SCE) with scan rate of 1 mV s−1. All potentials were measured against SCE. The EIS measurements were carried out in a frequency range from 100 kHz to 0.00001 kHz under potentiodynamic conditions, with an amplitude of 10 mV peak-to-peak, using the AC signal at Ecorr. 2.6. Quantum Chemical Calculations. The quantum chemical calculations were done in vacuo and in a water solution, by considering both the protonated and the nonprotonated species of the inhibitors. Various quantum chemical parameters, such the dipole moment, energy of the highest occupied molecular orbital (EHOMO), energy of the lowest unoccupied molecular orbital (ELUMO), partial atomic charges, etc., were calculated and utilized to elucidate the reactive centers of the molecule and the selective centers of the molecule. Moreover, quantitative structure activity relationship (QSAR) approach was applied to investigate the possibility of correlating more than one quantum chemical parameters with the obtained experimental inhibition efficiency.

2. EXPERIMENTAL PROCEDURE 2.1. Materials. Tests performed on mild steel having composition (wt %) C = 0.17, Mn = 0.46, Si = 0.26, S = 0.017, P = 0.019, and balance Fe were used for weight loss as well as electrochemical studies. An aggressive solution of hydrochloric acid (AR grade) of 1 M concentration was used for all studies. 2.2. Inhibitors. The studied ionic liquids [PMIM][NTf2], [BMIM][NTf2], [HMIM][NTf2], and [PDMIM][NTf2] were obtained commercially from Sigma Chemical and used without further purification. The molecular structures of the studied ionic liquids are shown in Figure 1. 2.3. Solutions. Aggressive solutions, 1.0 M HCl, were prepared by dilution of AR grade 37% HCl in distilled water. The stock solutions of ionic liquids were diluted to a certain concentration of inhibitor. The inhibitor concentrations in the weight loss studies were in the range 100−500 ppm, and electrochemical study was performed at 100, 300, and 500 ppm concentrations. 13283

dx.doi.org/10.1021/ie300977d | Ind. Eng. Chem. Res. 2012, 51, 13282−13299


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All geometry optimizations and quantum chemical calculations were performed using density functional theory (DFT) using the 6-31G(d) basis set. The Becke’s Three Parameter Hybrid Functional using the Lee−Yang−Parr correlation functional theory (B3LYP,17 was selected for the calculations. The DFT method is widely utilized in the analysis of the characteristics of the inhibitor/metal surface mechanisms and in the description of the structure and nature of the inhibitor in the corrosion process.18 Moreover, DFT/B3LYP is highly recommended for the understanding of chemical reactivity and selectivity in terms of frontier molecular orbitals (the HOMO and the LUMO) and related properties such as polarizability, hardness (η), and electronegativity,19 electron affinity (EA), and ionization potential (IP). In terms of the Koopman’s theorem,20,21 the various quantities are defined as follows: Electronegativity (χ) is the measure of the power of an electron or group of atoms to attract electrons toward itself,22 and it can be estimated by using the equation 1 χ ≅ − (E HOMO + E LUMO) (3) 2 Global hardness (η) measures the resistance of an atom to a charge transfer23 and is estimated using the equation 1 η ≅ − (E HOMO − E LUMO) (4) 2 Global electrophilicity index (ω) is estimated by using the electronegativity and chemical hardness parameters through the equation ω = χ 2 /2η

Figure 2. Plot of inhibition efficiency against concentration using all four ionic liquids used as inhibitors at 30 °C.

be attributed to larger coverage of metal with inhibitor molecules. The order of inhibition efficiency at a given inhibitor concentration has been found as [PDMIM]NTf2 > [HMIM]NTf2 > [BMIM]NTf2 > [PMIM]NTf2. The order of inhibition efficiency is explained on the basis of number and length of alkyl groups attached to imidazolium ring. The greater the length and number of alkyl groups attached to imidazolium ring, the greater the inhibition efficiency. The lowering of inhibition efficiency with increasing temperature may be due to partial desorption of inhibitor molecules. 3.2. Electrochemical Impedance Spectroscopy (EIS). The corrosion behavior of mild steel in 1 M HCl in absence and presence of the ionic liquids were investigated by EIS after immersion for 30 min at 303 ± 1K. Nyquist plots of mild steel in uninhibited and inhibited acid solutions containing various concentrations of studied ionic liquids are presented in Figure 3a−d. EIS spectra obtained consist of one depressed capacitive loop. The increasing diameter of capacitive loop obtained in 1 M HCl in the presence of studied ionic liquids indicated the inhibition of corrosion of mild steel. The capacitive loop may be attributed to the charge transfer reaction. Corrosion kinetic parameters derived from EIS measurements and inhibition efficiencies are given in Table 1. Double layer capacitance (Cdl) and charge transfer resistance (Rct) were obtained from EIS measurements as described elsewhere.27 It is apparent from Table 1 that the impedance of the inhibited system amplified with increasing the inhibitor concentration and the Cdl values decreased with increasing inhibitor concentration. This decrease in Cdl results from a decrease in local dielectric constant and/or an increase in the thickness of the double layer, suggesting that inhibitor molecules inhibit the iron corrosion by adsorption at the metal/acid interface.28 The depression in Nyquist semicircles is a feature for solid electrodes and often referred to as frequency dispersion and attributed to the roughness and other inhomogeneities of the solid electrode.29 In this behavior of solid electrodes, the parallel network charge transfer resistance-double layer capacitance is established where an inhibitor is present. For the description of a frequency-independent phase shift between an applied ac potential and its current response, a constant phase element (CPE) is used, which is defined in impedance representation, as in eq 9:

(5)

A high value of electrophilicity describes a good electrophile, while a small value of elecrophilicity describes a good nucleophile. Global softness (σ) describes the capacity of an atom or group of atoms to receive electrons;23 it is estimated by using the equation σ = 1/η ≅ −2/(E HOMO − E LUMO)

(6)

Electron affinity (A) is related to ELUMO through the equation

A ≅ −E LUMO

(7)

Ionization potential (I) is related to the energy of the EHOMO through the equation I ≅ −E HOMO

(8)

The solvent effects were taken into consideration by using the PCM model incorporated in the Gaussian03 program.24 All geometry optimizations in vacuo were done by using the Spartan 10 V1.01 program.25 Schematic structures were drawn using the ChemOffice package in the UltraChem 2010 version, while optimized structures were drawn using the Spartan 10 V1.01 program. The quantitative structure activity relationships plots and the corresponding equations were derived using the xlstart program.26

3. RESULTS AND DISCUSSION 3.1. Weight Loss Measurement. The variation of inhibition efficiency with inhibitor concentration is shown in Figure 2 at 30 °C. Similar plots were obtained at 40−60 °C (but not shown in this article). It is observed that all the inhibitors showed maximum efficiency at 500 ppm concentration. Better inhibition efficiency at higher concentration may 13284



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Figure 3. Nyquist plot of mild steel corrosion in 1 M HCl in the absence and presence of different concentrations of (a) [PMIM][NTf2], (b) [BMIM][NTf2], (c) [HMIM][NTf2], and (d) [PDMIM][NTf2]. (e) Equivalent circuit of the impedance spectra obtained for [PMIM][NTf2], [BMIM][NTf2], [HMIM][NTf2], and [PDMIM][NTf2].

Table 1. Electrochemical Parameters Obtained for the Potentiodynamic Polarization Curves name of inhibitor [PMIM][NTf2]

[BMIM][NTf2]

[HMIM][NTf2]

[PDMIM][NTf2]

ZCPE = Y0−1(iω)−n

concn. of inhibitor (ppm)

−Ecorr (mV vs. SCE)

icorr (μA cm−2)

ba (mV dec−1)

bc (mV dec−1)

EPDP%

100 300 500 100 300 500 100 300 500 100 300 500

448 475 465 490 466 484 490 466 484 490 467 464 480

1400.0 558.6 527.8 471.8 534.8 508.2 435.4 474.6 417.2 340.2 368.2 277.2 186.2

83 78 71 81 78 88 72 74 76 68 80 71 74

120 143 150 155 138 154 179 142 165 170 167 180 159

60.1 62.3 66.3 61.8 63.7 68.9 66.1 70.2 75.7 73.7 80.2 86.7

Figure 3e shows the electrical equivalent circuit employed to analyze the impedance spectra. Excellent fit with this model was obtained for all experimental data. The electrochemical parameters, including Rs, Rct, Y0, and n, obtained from fitting the recorded EIS data using the electrochemical circuit of Figure 3e are listed in Table 1. Cdl values derived from CPE parameters according to eq 10 are listed in Table 1. The order of inhibition efficiency calculated from Rct values is [PDMIM]NTf2 > [HMIM]NTf2 >

(9)

where Y0 is the CPE constant, ω is the angular frequency (in rad s−1), i2 = −1 is the imaginary number, and n is a CPE exponent, which can be used as a gauge of the heterogeneity or roughness of the surface.30 Depending on the value of n, CPE can represent resistance (n = 0, Y0 = R), capacitance (n = 1, Y0 = C), inductance (n = −1, Y0 = L), or Warburg impedance (n = 0.5, Y0 = W). 13285



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Figure 4. Potentiodynamic polarization curves of mild steel in 1 M HCl in the absence and presence of different concentrations of (a)[PMIM][NTf2], (b) [BMIM][NTf2], (c) [HMIM][NTf2], and (d) [PDMIM][NTf2].

Table 2. Parameters of Electrochemical Impedance Spectroscopy name of inhibitor [PMIM][NTf2]

[BMIM][NTf2]

[HMIM][NTf2]

[PDMIM][NTf2]

concn. of inhibitor (ppm)

Rs (Ω cm2)

Rct (Ω cm2)

Y0 (μF cm−2)

n

Cdl (μF cm−2)

EEIS%

100 300 500 100 300 500 100 300 500 100 300 500

1.13 1.10 1.18 1.21 1.11 1.17 1.04 1.15 1.45 1.32 1.10 1.09 1.03

50.2 132.1 152.0 167.2 139.2 157.7 180.4 158.8 180.9 228.4 208.2 306.5 496.2

172.0 127.0 95.2 82.1 128.0 105.1 88.6 112.4 85.5 74.3 110.4 94.9 85.2

0.809 0.816 0.848 0.849 0.812 0.817 0.818 0.823 0.825 0.827 0.810 0.811 0.814

56.02 50.56 44.57 40.97 50.59 43.35 36.04 49.30 35.94 34.26 47.28 42.66 41.35

61.9 66.9 69.9 63.9 68.1 72.2 68.3 72.2 78.0 75.9 83.6 89.9

studied steel. The thickness of the protective layer (d) is related to Cdl, according to the following equation:

[BMIM]NTf2> [PMIM][NTf2]. It can be observed from Table 1 and also from Figure 3a−d that as the chain length of alkyl group and number of alkyl groups attached to imidazolium ring increased, inhibitor molecules tend to adsorb more effectively, justifying, therefore, the order of inhibition efficiency. Cdl = (Y0R ct1− n)1/ n

Cdl =

εε0 d

(11)

where ε is the dielectric constant of the protective layer and ε0 is the permittivity of free space. 3.3. Potentiodynamic Polarization Parameters. The values of corrosion potential (Ecorr), corrosion current density (icorr), and anodic and cathodic Tafel slopes (ba and bc) were evaluated from anodic and cathodic regions of Tafel plots. The linear Tafel segments of anodic and cathodic curves were

(10)

Moreover, the values of double-layer capacitance, Cdl, decreased with increasing ionic liquid concentration. The decrease in Cdl is probably due to a decrease in local dielectric constant and/or an increase in the thickness of a protective layer at electrode surface, therefore enhancing the corrosion resistance of the 13286



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Figure 5. Arrhenius plots for mild steel corrosion in 1 M HCl in the absence and presence of different concentrations of (a)[PMIM][NTf2], (b) [BMIM][NTf2], (c) [HMIM][NTf2], and (d) [PDMIM][NTf2].

of anodic breakdown potential, Eb. This is the potential at which sudden rise in current density takes place. As a result, the surface film is shifted from stable to unstable state. As the concentration of inhibitor increased, Eb shifted to the noble direction. The noble shift of Eb with increasing inhibitor concentration reflects the increased adsorption of inhibitor on the metal surface. The noble shift of Eb and the decrease of the corresponding current densities with increasing inhibitor concentration results in the formation of anodic protective films on the electrode surface. Similar results were obtained by other author. 33 Increase in inhibition efficiencies with increasing concentration of all the four ILs studied reveals that inhibition action is due to adsorption of ILs on mild steel surface, which in turn depends on the chemical structure of the inhibitors. 3.4. Activation Parameters. The activation parameters of the corrosion process and investigation of the mechanism of inhibition were carried out using the weight loss measurements in the temperature range 303−333 K in the absence and presence of different concentrations of studied ionic liquid solutions. The dependence of corrosion rate on temperature can be expressed by Arrhenius equation and transition-state equation:34,35

extrapolated to corrosion potential to obtain corrosion current densities (icorr). The inhibition efficiency was evaluated from the measured icorr values using the relationship E PDP% =

0 i icorr − icorr 0 icorr

× 100 (12)

where i0corr and iicorr are values of corrosion current density in absence and in presence of inhibitor, respectively. Figure 4 represents the potentiodynamic polarization curves of mild steel in 1 M HCl in the absence and presence of various concentrations of the studied ionic liquids. It can be seen from Figure 4 that, in the presence of inhibitor, the curves are shifted to lower current regions, showing the inhibition tendency of the ILs. No definite trend is observed in the Ecorr values in the presence of all the ILs. In the present study, shift in Ecorr values is in the range 30−40 mV, suggesting that they are mixed type of inhibitors.31,32 The values of various electrochemical parameters derived by Tafel polarization of all the inhibitors are given in Table 2. Investigation of Table 2 revealed that the values of ba change slightly in the presence of all the ILs, whereas more pronounced change occurs in the values of bc, indicating that both anodic and cathodic reactions are effected but the effect on the cathodic reactions is more prominent. Thus, all the studied ILs are mixed type, but predominantly cathodic, inhibitors. Moreover, the recorded polarization curves in the presence of inhibitors are characterized by the presence

log C R = 13287

−Ea + log λ 2.303RT

(13)


Industrial & Engineering Chemistry Research CR =

⎛ ΔS* ⎞ ⎛ −ΔH * ⎞ RT exp⎜ ⎟ ⎟ exp⎜ Nh ⎝ R ⎠ ⎝ RT ⎠

Article

Different adsorption isotherms were tested in order to find the best fitted adsorption isotherm for adsorption of the ionic liquid on the surface of mild steel in 1 M HCl solution. The linear regression coefficient of Langmuir adsorption isotherm obtained in this study was found to be close to unity; hence, it was found to be the best fit. With regard to the Langmuir adsorption isotherm, the surface coverage (θ) of the inhibitor on the mild steel surface is related to the concentration (Cinh) of the inhibitor in the bulk of the solution according to the following equation:

(14)

where Ea is apparent activation energy, λ is the pre-exponential factor, ΔH* is the apparent enthalpy of activation, ΔS* is the apparent entropy of activation, h is Planck’s constant, and N is Avogadro's number. The apparent activation energy at different concentrations of these ionic liquids was calculated using the linear plot of log CR and 1/T (Figure 5), and the results are shown in Table 3.

θ=

Table 3. Activation Parameters name of inhibitor [PMIM][NTf2]

[BMIM][NTf2]

[HMIM][NTf2]

[PDMIM][NTf2]

concn. of inhibitor

Ea (kJ mol−1)

ΔH* (kJ mol−1)

ΔS* (J K−1 mol−1)

100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500

155.1 147.1 144.8 141.2 143.6 141.2 148.0 147.4 147.3 146.2 145.0 146.4 145.6 144.7 144.2 142.3 143.6 142.5 141.3 140.2 138.2

152.57 144.57 142.34 138.66 141.12 138.71 145.45 144.82 142.26 143.71 142.48 143.84 145.10 142.10 141.60 139.70 141.00 139.90 138.74 137.60 135.80

−384.78 −379.78 −365.98 −345.67 −342.23 −338.25 −369.87 −359.90 −351.90 −344.60 −336.80 −346.00 −336.88 −330.20 −324.40 −320.20 −330.40 −327.80 −322.10 −312.90 −308.20

K adsC inh 1 + K adsC inh

(15)

where Kads is the equilibrium constant for the adsorption/ desorption process. This equation can be rearranged to C inh 1 = + C inh θ K ads

(16)

It is a known fact that Kads represents the strength between adsorbate and adsorbent. Large values of Kads imply more efficient adsorption and hence better inhibition efficiency.38 From the intercepts of the straight lines on the Cinh/θ-axis (Figure 7a), Kads can be calculated, which is related to free energy of adsorption, ΔGads ° , as given by eq 17. ° ΔGads = −RT ln(55.5K ads)

(17)

The negative values of ΔGads ° ensure the spontaneity of the adsorption process and stability of the adsorbed film on the mild steel surface.39 It is usually accepted that the value of around −20 kJ mol−1 or lower indicates the electrostatic interaction between charged metal surface and charged organic molecules in the bulk of the solution, while those around −40 kJ mol−1 or higher involve charge sharing or charge transfer between the metal surface and organic molecules.40 The thermodynamic parameters ΔHads ° and ΔSads ° were calculated from the following equation:

The increase in activation energy after the addition of the inhibitor to the 1 M HCl solution indicated that physical adsorption (electrostatic) occurs in the first stage. At higher concentrations, the activation energy gradually decreased. At higher inhibitor concentration, lowering of activation energy is an indication of chemisorption. The value of enthalpy and entropy of activation was calculated using the transition state plot of log CR/T versus 1/T (Figure 6). The value of ΔH* is lower in the presence of inhibitor, indicating that less energy barrier for the reaction in the presence of inhibitor is attained and hence exhibiting high inhibition efficiency at elevated temperatures.36 The values of ΔS* in the absence and presence of inhibitor are large and negative. This indicates that the activated complex in the rate determining step represents an association step rather than a dissociation step, meaning that a decrease in disordering occurs on going from reactants to the activated complex.37 3.5. Adsorption Isotherm. The adsorption on the corroding surfaces never reaches the real equilibrium and tends to reach an adsorption steady state. When the corrosion rate is sufficiently decreased in the presence of inhibitor, the adsorption steady state has a tendency to attain quasiequilibrium state. Now, it is reasonable to consider quasiequilibrium adsorption in thermodynamics using the appropriate adsorption isotherm. The degree of surface coverage (θ) for the inhibitor was obtained from average weight loss data.

° ° ° ΔGads = ΔHads − T ΔSads

(18)

A plot of ΔG°ads vs T gave straight line for the different ionic liquids studied (Figure 7b), with the slope equal to −ΔS°ads and the value of ΔHads ° obtained from the intercept. The calculated values of free energy of adsorption, Kads, enthalpy and entropy of adsorption are listed in Table 4. 3.6. Quantum Chemical Results. 3.6.1. Results of the Calculations in Vacuo for the Ion Pair. The optimized geometries of the four imidazolium-based ionic liquids are shown in Figure 8, together with the HOMO and the LUMO. The HOMO is exclusively localized on the anion, which suggests that, on interaction with the metal surface, the inhibitor binds to the metal by donating electrons from the anion unit. In all the studied ionic liquids, the LUMO has a strongly π* (antibonding) character and is localized on the C2 atom of the cation. However, electron acceptance in this orbital is not favorable because of the aromatic requirement of the imidazolium ring.41 Other molecular quantum chemical parameters related to the reactivity of molecules are reported in Table 5 and include the energy of the highest occupied molecular orbital (EHOMO), energy of the lowest unoccupied molecular orbital (ELUMO), the energy gap (ELUMO−HOMO, ΔE), dipole moment (μ), molecular polarizability (α), and molecular volume (MV), etc. EHOMO is 13288



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Figure 6. Transition state plots for mild steel corrosion in 1 M HCl in the absence and presence of different concentrations of (a)[PMIM][NTf2], (b) [BMIM][NTf2], (c) [HMIM][NTf2], and (d) [PDMIM][NTf2].

Figure 7. (a) Langmuir adsorption isotherm plots for the four ionic liquids used and (b) ΔGads ° vs T plots for the four different ionic liquids.

reported in Table 5 show that the trend across structures in the ELUMO is such that [PDMIM][NTf2] > [HMIM][NTf2] > [BMIM][NTf2] > [PMIM][NTf2], which is also in good agreement with the trend in the experimental inhibiton efficiency. ΔE informs about the reactivity of a molecule toward other chemical species. Molecules with large value of ΔE are highly stable (i.e., they have low reactivity to chemical species) while molecules with small values of ΔE have a high reactivity. The data reported in Table 5 show [PDMIM][NTf2] has the smallest ΔE value and therefore corresponds to the most reactive compound. This means that [PDMIM][NTf2] would easily bind onto the metal surface leading to high inhibition efficiency. This result agrees with the experimental observation that [PDMIM][NTf2] is the most efficient corrosion inhibitor.

often associated with the electron donating ability of a molecule,42 and a higher EHOMO value indicates higher tendency of the molecule to donate electron(s) to an electron deficient species. The results reported in Table 5 show that EHOMO for the different inhibitors follows the order [PDMIM][NTf2] > [HMIM][NTf2] > [BMIM][NTf2] > [PMIM][NTf2]. Therefore, [PDMIM][NTf2] has the highest tendency to donate electrons to the surface of the metal and therefore would have the highest tendency to adsorb onto the metal surface. In this way, this is in agreement with the experimental % inhibition efficiency (IE) results obtained from weight loss: [PDMIM][NTf2] > [HMIM][NTf2] > [BMIM][NTf2] > [PMIM][NTf2] The ELUMO indicates the ability of the molecule to accept electrons, and the lower the value of ELUMO is, the easier it is that the molecule would accept electrons.45 The results 13289



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Table 4. Thermodynamic Adsorption Parameters name of inhibitor [PMIM][NTf2]

[BMIM][NTf2]

[HMIM][NTf2]

[PDMIM][NTf2]

temp. (K)

Kads (103 × mol−1)

° −ΔGads (kJ mol−1)

° ΔHads (kJ mol−1)

303 313 323 333 303 313 323 333 303 313 323 333 303 313 323 333

1.70 1.83 2.14 2.33 1.97 2.16 2.55 2.82 3.19 3.76 4.56 5.40 5.71 6.92 8.69 11.67

−28.86 −30.01 −31.38 −32.58 −29.23 −30.44 −31.85 −33.11 −30.44 −31.87 −33.41 −34.91 −31.91 −33.46 −35.14 −37.07

26.10 27.16 28.44 29.54 26.10 27.21 28.51 29.67 25.94 27.22 28.61 29.96 25.80 27.15 28.63 30.36

° ΔSads (J K−1 mol−1)

−9.13

−10.34

−14.88

−20.17

Figure 8. Optimized geometries and the corresponding HOMO and LUMO for the studied ionic liquids (B3LYP/6-31G(d,p) results in vacuo).

However, the trend in ΔE across all the ionic liquids does not correlate well with the trend in the experimental inhibition efficiencies.

The dipole moment gives information about the polarity of the compounds and also informs about the reactivity of molecules. In the study of corrosion inhibitors, the dipole 13290



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Table 5. Quantum Chemical Parameters for Ionic Liquids (B3LYP/6-31G(d,p) Results in Vacuo)

a

quantum chem. param.

[PMIM]NTf2

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

EHOMO (eV) ELUMO (eV) ΔE (eV) μ (Debye) molecular vol. (A3) polarizability ionization potential, I (eV) electron affinity, A (eV) electronegativity, χ hardness, η softness, σ fraction of electrons transferred, ΔN electrophilicity, ω %IEa

−7.177 −1.282 5.895 14.73 309 65.07 7.177 1.282 4.230 2.947 0.339 0.47 3.035 61.9

−7.176 −1.270 5.906 15.56 328 66.56 7.176 1.270 4.223 2.953 0.339 0.47 3.019 63.9

−7.173 −1.265 5.908 14.55 365 69.55 7.173 1.265 4.219 2.954 0.339 0.47 3.013 68.3

−6.952 −1.107 5.845 14.81 326 66.43 6.952 1.107 4.029 2.922 0.342 0.51 2.778 75.9

The experimental percentage inhibitor efficiency (%IE) is included in the last row for comparison purpose.

Table 6. Mulliken Atomic Charges on the Selected Atom of the Cation for the Studied Ionic Liquids (B3LYP/6-31G(d) Results in Vacuo) atom Cation Unit N1 C2 N3 C4 C5 C6 C7 C8 C9 C10 C11 C12 Anion Unit O1 O2 O3 O4 S1 S2 N F1 F2 F3 F4 F5 F6 C1 C2

[PMIM][NTf2]

[BMIM][NTf2]

[HMIM][NTf2]

[PDMIM][NTf2]

−0.404 0.276 −0.409 0.023 0.021 −0.375 −0.176 −0.255 −0.458

−0.404 0.276 −0.409 0.023 0.021 −0.375 −0.182 −0.254 −0.264

−0.404 0.276 −0.408 0.023 0.021 −0.375 −0.182 −0.261 −0.270 −0.250 −0.250 −0.443

−0.422 0.626 −0.453 0.031 0.027 −0.350 −0.153 −0.291 −0.459

−0.569 −0.502a −0.568 −0.500a 1.170 1.172 −0.829 −0.253 −0.219b −0.233b −0.220 −0.232b −0.260 0.590 0.590

−0.569 −0.502a −0.568 −0.500a 1.170 1.171 −0.829 −0.253 −0.219b −0.233b −0.220b −0.232b −0.260 0.590 0.590

−0.568 −0.503a −0.568 −0.500a 1.170 1.171 −0.829 −0.253 −0.220b −0.233b −0.220b −0.232b −0.259 0.590 0.590

−0.581 −0.493a −0.591 −0.495a 1.122 1.123 −0.691 −0.244 −0.246 −0.223b −0.247 −0.255 −0.220b 0.599 0.586

a

This O atom is not engaged in intermolecular hydrogen bond with the cation. bThis F atom is not engaged in intermolecular hydrogen bond with the cation.

ionic liquids and the trend in their corrosion inhibition efficiecies in this study shows that there is no direct correlation. The molecular volume (MV) gives information about the contact surface between the corrosion inhibitor and the metal surface. The inhibitive efficiency is usually proportional to the fraction of the surface covered by the adsorbed inhibitor.46 However, this is not always the case, considering the fact that corrosion inhibition is often influenced by multiple factors that

moment does not always show univocal trend: several research works have reported that the dipole moment increases with increase in the inhibition efficiencies of the inhibitors;43 other reports have shown that dipole moment decreases with increase in the inhibition efficiencies of the inhibitors.44 There are also reports that show that the dipole moment does not have good correlation with the inhibition efficiencies of the inhibitors.45 A comparison of the trend in the dipole moment of the studied 13291



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Table 7. Condensed Fukui Functions on the Atoms of the Studied Ionic Liquids (B3LYP/6-31G(d) Results in Vacuo) f atom

[PMIM]NTf2

−

f

function

+

function

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

[PMIM]NTf2

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

Cation Unit N1 −0.001 C2 −0.030 N3 −0.007 C4 −0.019 C5 −0.021 C6 0.003 C7 0.009 C8 0.009 C9 0.001

−0.001 −0.030 −0.007 −0.020 −0.021 0.003 0.009 0.006 0.197

−0.001 −0.027 −0.005 −0.014 −0.020 0.003 0.007 0.006 0.003 0.007 0.008 0.005

0.003 0.003 −0.001 −0.025 −0.026 0.010 0.011 0.010 0.001

−0.002 −0.240 −0.006 −0.038 −0.040 0.039 0.042 0.023 0.006

−0.002 −0.239 −0.006 −0.038 −0.040 0.039 0.040 0.021 0.011

−0.002 −0.239 −0.007 −0.038 −0.040 0.039 0.040 0.020 0.008 0.008 0.007 0.004

−0.009 −0.153 −0.023 −0.043 −0.028 0.039 0.042 0.022 0.008

Anion Unit O1 −0.089 O2 −0.120 O3 −0.089 O4 −0.124 S1 −0.032 S2 −0.031 N −0.110 F1 −0.029 F2 −0.021 F3 −0.037 F4 0.013 F5 −0.034 F6 −0.061 C1 −0.039 C2 −0.036

−0.089 −0.119 −0.089 −0.124 −0.032 −0.032 −0.109 −0.029 −0.021 −0.037 0.013 −0.034 −0.061 −0.038 −0.036

−0.079 −0.111 −0.082 −0.116 −0.030 −0.030 −0.100 −0.026 −0.019 −0.035 −0.020 −0.031 −0.024 −0.039 −0.034

−0.085 −0.088 −0.092 −0.097 −0.032 −0.032 −0.114 −0.014 −0.026 −0.024 −0.019 −0.028 −0.028 −0.028 −0.033

0.014 −0.030 0.012 −0.030 −0.007 −0.011 0.044 0.007 −0.028 0.003 −0.010 −0.015 0.011 −0.013 −0.012

0.014 −0.029 0.012 −0.030 −0.007 −0.010 0.044 0.007 −0.028 0.003 −0.010 −0.015 0.011 −0.013 −0.012

0.013 −0.028 0.012 −0.030 −0.007 −0.010 0.044 0.007 −0.027 0.003 −0.010 −0.015 0.010 −0.013 −0.011

0.037 −0.027 0.059 −0.028 −0.009 −0.013 −0.021 −0.008 0.006 −0.015 0.003 0.000 −0.018 −0.009 −0.006

[PDMIM][NTf2] > [HMIM][NTf2] ≈ [BMIM][NTf2] ≈ [PMIM][NTf2], which also confirms that [PDMIM][NTf2] has the highest tendency to donate electrons and therefore the highest tendency to bind onto the metal surface Among the parameters that give information about the selectivity of the molecule include the partial atomic charges and the condensed Fukui functions. The partial atomic charges on the atoms have proven to be another useful quantum chemical parameter in the study of corrosion inhibitors.52−54 Table 6 shows the partial atomic charges for the studied ionic liquids. The charges are reported for both cationic and anionic moieties. The highest negative charge is on O atoms and the N atom of the anions. These results are in agreement with the analysis of the HOMO that showed that the HOMO is located on the anion part of the ionic liquid. The more negative the atomic charge of the adsorbed center is, the easier it is for the atom to donate its electrons.55 It is therefore reasonable to anticipate that the inhibitors would interact with the metal surface through the heteroatoms of the anion that are not interacting with the cation. The condensed Fukui functions provide information about the atoms in a molecule that have a tendency to either donate (nucleophilic character) or accept (electrophilic character) an electron or pair of electrons. The nucleophilic and electrophilic Fukui functions can be calculated using the finite difference approximation as follows:56

are interdependent. The trend in the molecular volume values, reported in Table 5, is such that [HMIM][NTf2] > [BMIM][NTf2] > [PDMIM][NTf2] > [PMIM][NTf2]. This trend does not correlate well with the trend in the experimental inhibition efficiencies of the inhibitors. Global hardness (η) and softness (σ) are molecular properties that also facilitate the analysis of the molecular reactivity and selectivity. The relationship between these quantum chemical parameters and corrosion inhibition is often discussed based on the Lewis theory of acid and bases and Pearson’s hard and soft acids and bases.47 A hard molecule has a large ΔE value, while a soft molecule has a small ΔE value. In this regard, adsorption could occur at the region of the molecule where σ has the highest value.48 The trend across structures in the σ values, reported in Table 5, is such that [PDMIM][NTf2] > [HMIM][NTf2] ≈ [BMIM][NTf2] ≈ [PMIM][NTf2], which also suggests that [PDMIM][NTf2] is the most reactive compound. The number of transferred electrons (ΔN) gives information about the number of electrons a molecule can transfer to the acceptor molecule, and it is estimated using the equation49−51 ΔN = χFe − χinh /2(ηFe − ηinh)

(19)

where χFe and χinh denote the absolute electronegativity of iron and the inhibitor molecule, respectively, and ηFe and ηinh denote the absolute hardness of iron and the inhibitor molecule, respectively. The values of χFe and ηFe are taken as 7 eV mol−1 and 0 eV mol−1, respectively.50,51 The results, as reported in Table 5, show that the order of electron transfer is such that

f + = q(N + 1) − qN 13292

(20)



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Figure 9. Optimized geometries, the HOMO and the LUMO for the protonated species of the studied ionic liquids (B3LYP/6-31G(d,p) results in vacuo). The letter P at the end of the name denote that these compounds are protonated.

f − = qN − q(N − 1)

nucleophilic attack is due to the high positive charge at C2 arising from the electron deficiency in the NC bond. The preferred site for electrophilic attack is the O and N atoms of the anion, which is in agreement with the fact that the HOMO is on the anion. More importantly, the results show that the O atoms that have the highest Fukui functions are the O atoms that are not interacting with the cation, which further confirms the earlier inference that corrosion inhibitors binds with the metal surface by utilizing the heteroatoms that are not engaged in intermolecular hydrogen bond with the cation.

(21)

where q(N+1), q, and q(N−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 site for electrophilic attack is the atom/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 ionic liquids are reported in Table 7. The preferred sites for nucleophilic attack is the C2 atom and the preference for C2 atom for 13293



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Table 8. Quantum Chemical Parameters for the Protonated Species of the Studied Ionic Liquids (B3LYP/6-31G(d,p) in Vacuo)

a


[PMIM]NTf2

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

EHOMO (eV) ELUMO (eV) ΔE (eV) μ (Debye) molecular volume (A3) polarizability Ionization potential, I (eV) electron affinity, A (eV) electronegativity, χ hardness, η softness, σ fraction of electrons transferred, ΔN electrophilicity, ω %IEa

−11.035 −4.179 6.856 6.88 314 65.22 11.035 4.179 7.607 3.428 0.292 −0.089 8.440 61.9

−11.020 −4.136 6.884 8.25 332 66.70 11.020 4.136 7.578 3.442 0.291 −0.084 8.342 63.9

−10.702 −4.113 6.589 11.96 369 69.76 10.702 4.114 7.407 3.295 0.304 −0.062 8.327 68.3

−10.635 −4.013 6.622 6.92 331 66.65 10.635 4.013 7.324 3.311 0.302 −0.049 8.101 75.9


Table 9. Quantum Chemical Parameters for Ionic Liquids (B3LYP/6-31G(d,p) Results in Water)

a


[PMIM]NTf2

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

ΔGsolv EHOMO (eV) ELUMO (eV) ΔE (eV) μ (Debye) ionization potential, I (eV) electron affinity, A (eV) electronegativity, χ hardness, η softness, σ fraction of electrons transferred, ΔN electrophilicity, ω %IEa

−0.30 −7.416 −0.537 6.879 18.03 7.416 0.537 3.977 3.439 0.291 0.440 2.299 61.9

0.89 −7.414 −0.532 6.882 17.99 7.414 0.532 3.973 3.441 0.291 0.440 2.294 63.9

2.50 −7.410 −0.532 6.878 18.00 7.410 0.532 3.971 3.439 0.291 0.440 2.293 68.3

−2.45 −7.064 −0.420 6.644 17.99 7.064 0.420 3.742 3.322 0.301 0.490 2.108 75.9


3.6.2. Results of the Protonated Inhibitors in Vacuo. On interaction with the acidic medium, the ionic liquids are likely to be protonated, which implies that both the protonated and the nonprotonated species coexist in solution. It is therefore essential to investigate the preferred species of the ionic liquid to interact with the metal surface and to determine the preferred mode of interaction by either of the species. As shown in the previous discussion, the anion part of the ion-pair has the highest electron density, and this electron density is located largely on the N and O atoms. Therefore, a proton (electron deficient species) would preferentially interact with the anion part of the cation−anion pair. Moreover, the proton would preferentially bind to the O atom that is not interacting with the cation because such O atoms are more free and accessible. Based on these considerations, input geometries with the proton attached to the free O atom of the anion were prepared and optimized. The optimized protonated species together with the corresponding HOMO and the LUMO are shown in Figure 9. The results show that the HOMO is entirely spread above and below the imidazolium ring. This is an entirely different trend from the results on nonprotonated species, where it was observed that the HOMO is entirely on the anion. Moreover, this result suggests that the positive charge of the proton has been distributed in the anion unit of the ion pair and proton is stabilized by accepting electrons from the anion part of the ion pair.

The LUMO is also entirely localized into the imidazolium ring with its maximum amplitude on the C2 atom. These results suggest that, in the protonated species, the anion has minimal role in the interaction with the metal surface. A comparison of the calculated molecular descriptors across structures of the protonated species and nonprotonated species provides information on the variation of the trends in the molecular properties due to protonation effect. The results, reported in Table 8, show that, with the exception of the dipole moment, the trends in the EHOMO, ELUMO, and ΔE are similar between the nonprotonated and the protonated inhibitors. The results show that EHOMO is much lower in the protonated species than in the nonprotonated species, which implies that the nonprotonated species are better electron donors than the protonated species; ELUMO is much lower in the protonated species than in the nonprotonated species; the number of electrons transferred is lower in the protonated species than in the nonprotonated spices. The electrophilicity index is higher for the protonated species than for the nonprotonated species. All these factors indicate that the protonated species has the least tendency to donate electrons to the metal surface. Therefore, its interaction with the metal surface would preferentially involve electrostatic interaction rather than chemical bond formation. 3.6.3. Results of the Calculation in Water Solution for the Nonprotonated Species. The electrochemical phenomenon 13294



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Table 10. Mulliken Atomic Charges on the Atoms of the Studied Ionic Liquids (B3LYP/6-31G(d) Results in Water Solution) in vacuo atom

[PMIM]NTf2

in solution

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

[PMIM]NTf2

[BMIM]NTf2

[HMIM]NTf2

[PDMIM]NTf2

Cation Unit N1 −0.404 C2 0.276 N3 −0.409 C4 0.023 C5 0.021 C6 −0.375 C7 −0.176 C8 −0.255 C9 −0.458

−0.404 0.276 −0.409 0.023 0.021 −0.375 −0.182 −0.254 −0.264

−0.404 0.276 −0.408 0.023 0.021 −0.375 −0.182 −0.261 −0.270 −0.250 −0.250 −0.443

−0.422 0.626 −0.453 0.031 0.027 −0.350 −0.153 −0.291 −0.459

−0.402 0.274 −0.407 0.006 0.009 −0.373 −0.173 −0.259 −0.462

−0.402 0.274 −0.407 0.006 0.008 −0.374 −0.180 −0.258 −0.265

−0.402 0.274 −0.407 0.006 0.008 −0.373 −0.180 −0.265 −0.271 −0.254 −0.253 −0.447

−0.423 0.622 −0.454 0.007 0.001 −0.359 −0.150 −0.295 −0.461

Anion Unit O1 −0.569 O2 −0.502 O3 −0.568 O4 −0.500 S1 1.170 S2 1.172 N −0.829 F1 −0.253 F2 −0.219 F3 −0.233 F4 −0.220 F5 −0.232 F6 −0.260 C1 0.590 C2 0.590

−0.569 −0.502 −0.568 −0.500 1.170 1.171 −0.829 −0.253 −0.219 −0.233 −0.280 −0.256 −0.293 0.969 0.942

−0.568 −0.503 −0.568 −0.500 1.170 1.171 −0.829 −0.253 −0.220 −0.233 −0.220 −0.232 −0.259 0.590 0.590

−0.581 −0.493 −0.591 −0.495 1.122 1.123 −0.691 −0.244 −0.246 −0.223 −0.247 −0.255 −0.220 0.599 0.586

−0.560 −0.543 −0.570 −0.541 1.165 1.165 −0.812 −0.241 −0.225 −0.233 −0.225 −0.233 −0.245 0.599 0.600

−0.560 −0.543 −0.570 −0.541 1.165 1.165 −0.811 −0.241 −0.225 −0.233 −0.225 −0.233 −0.245 0.599 0.600

−0.560 −0.543 −0.570 −0.541 1.164 1.165 −0.811 −0.241 −0.225 −0.233 −0.225 −0.233 −0.245 0.598 0.600

−0.555 −0.533 −0.563 −0.534 1.110 1.114 −0.724 −0.237 −0.238 −0.228 −0.240 −0.243 −0.225 0.611 0.599

in water solution, which suggests that the presence of the solvent decreases the reactivity of the corrosion inhibitors; ΔN is also smaller in water solution than in vacuo confirming the fact that in solution, the inhibitors have fewer tendencies to transfer/donate electrons. The dipole moment is higher in water solution than in vacuo, an indication of the polarization effect of the solvent on the solute molecule (i.e., the inhibitor) The charges on the atoms are also influenced by the presence of the solute−solvent interactions. Polar solvents in particular have a tendency to polarize the solute molecule (i.e., the inhibitor) and therefore alter the charge distribution of the inhibitor molecule. The Mulliken atomic charges on selected atoms of the studied ionic liquids are reported in Table 10. A comparison of the Mulliken charges between the results in vacuo and in water solution shows that there is a general increase in the negative charge on the heteroatoms of the anion and a general decrease in the atomic charge (e) in water solution on all other atoms. 3.7. Quantitative Structure Activity Relationship (QSAR). In the results reported so far, an attempt has been made to correlate given quantum chemical parameters to the observed inhibition efficiencies of the inhibitors. The approach in which several quantum chemical parameters form a composite index that is then correlated to the experimentally determined inhibition efficiency is called quantitative structure activity relationship. Several quantitative structure activity relationship equations are utilized to correlate the quantum chemical index with the experimental inhibition efficiencies. The selection of the appropriate model equation depends

takes place in the liquid phase; therefore, it is crucial to take into consideration the solvent effects on the inhibitor when studying the adsorption of the inhibitor on the metal surface. A comparison of the molecular reactivity and selectivity indices between the results in vacuo and the results in solution provides understanding of the influence of the solvent on reactivity and selectivity of the inhibitors. The results show that, in solution, the HOMO is spread above and below the imidazolium ring (i.e., the HOMO is due to the π-electron density above and below the imidazolium ring, arising from the C4−C5 double bond) and is entirely absent in the anion. The unavailability of the anion to interact with metal surface in water solution could probably suggest that the anion interacts strongly with water molecules through intermolecular hydrogen bonds, as reported earlier,57 and the LUMO is entirely localized on C2 atom. Therefore, the interaction of the inhibitor with the metal surface is entirely determined by the cation part of the ionic liquids. Table 9 shows the quantum chemical parameters calculated in water solution. The trends in EHOMO, ΔN, ω, σ, and η are similar for the results in vacuo and in water solution. However, trends in other molecular properties, such as the ELUMO, ΔE, and the dipole moment do not show correlation for the results in vacuo and in water solution. A comparison of EHOMO, ELUMO, and ΔE between the results in water solution (Table 9) and the results in vacuo (Table 5) for individual ionic liquids shows that EHOMO is higher in vacuo than in water solution, suggesting that the presence of the solvent decreases the electron donor role of the corrosion inhibitors. ELUMO and ΔE are lower in vacuo than 13295



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Figure 10. Representative plots of the correlation between experimental inhibition efficiency (%IE) and the predicted inhibition efficiency (pred(% IE)) obtained by utilizing the Lukovits equations of (a) linear and (b) nonlinear multiple regressions. The quantum chemical parameters utilized for the plot are shown on top of each plot.

for the prediction of theoretical inhibition efficiency and the corresponding R2, SSE, and RMSE values. For the linear multiple regression equations, the combination of EHOMO and polarization quantum parameters provides the best quantum index for correlation with experimental inhibition efficiencies:

strongly on the type of adsorption mechanism. Among the equations utilized to develop quantitative structure activity relationship when the adsorption obeys Langmuir isotherms (as is the case with the ionic liquids studied in this work) is the linear and the nonlinear multiple regression equations developed by Lukovits.58,59 The linear multiple regression equation is of the form IEtheor = Ax i C i + B

IEtheo = 53.880E HOMO + 1.386pol + 358.375

(22)

R2 = 1.000

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. The nonlinear multiple regression equation is of the form IEtheor =

(AXi + B)Ci × 100 1 + (AXi + B)Ci

SSE = 0.008

RMSE = 0.089

The equation suggests that a high EHOMO and a high molecular polarization results in greater inhibition efficiency; the second equation (Table 11) suggest that a high EHOMO and a large molecular volume results in high inhibition efficiency; the third equation (Table 11) suggests that a higher molecular volume and a small electronegativity results in greater inhibition efficiency. The goodness of the model show that the R2 value has a range from 0.873 to 1.000, SSE values are in the range from 0.008 to 14.610, and the RMSE is in the range from 0.089 to 3.822. For the derived nonlinear multiple regression equations (Table 11), the combination of EHOMO and polarization also provides the best quantum index to correlate with experimental inhibition efficiencies. Since for most of the equations the values of R2 are reasonably high (0.763−1.000) while the values of SSE (0.000−27.424) and RMSE 90.021−5.237) are reasonably small, it is reasonable to infer that the combination of two quantum chemical parameters provides a better correlation between quantum chemical parameters and experimentally determined inhibition efficiency of the inhibitors.

(23)

where A and B are constants obtained by regression analysis; Xi is a quantum chemical index characteristic for the molecule; and Ci is the inhibitor concentration in μM. Both equations were utilized to correlate the composite index of quantum chemical parameters with the experimental inhibition efficiency of the studied ionic liquids (Figure 10). The results show that both equations gave good correlation between quantum chemical parameters and experimental inhibition efficiency. An optimum of two quantum chemical parameters was sufficient to produce a good correlation with experimentally determined inhibition efficiency. A combination of the quantum chemical parameters that provided the best correlation is reported in Table 11 together with the equations 13296



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Table 11. Pair of Quantum Chemical Parameters Utilized to Derive the Linear and the Nonlinear Multiple Regression Equation That Correlates the Theoretically Estimated and the Experimentally Determined Inhibition Efficienciesa,b quantum param.

derived QSAR equation

Multiple Linear Regression Equation EHOMO, pol IE = 53.880EHOMO + 1.386pol + 358.375 EHOMO, MV IE = 53.947EHOMO + 0.111MV + 414.715 MV, χ IE = 0.104MV − 61.453χ + 289.684 ELUMO, pol IE = 71.893ELUMO + 1.183pol +76.845 ELUMO, μ IE = 67.703ELUMO − 2.271μ + 184.706 μ, ω IE = −2.291μ − 45.668ω + 236.885 EHOMO, ELUMO IE = −5.496EHOMO + 76.777ELUMO + 122.875 Multiple Nonlinear Regression Equations EHOMO, pol IE = (1.155 × 10−2EHOMO + 3.378 × 10−4pol − 0.955)/(1 + (1.155 × 10−2EHOMO + 3.378 × 10−4pol − 0.955)) MV, ΔN IE = (2.657 × 10−5MV + 6.850 × 10−2ΔN − 1.057)/(1 + (2.657 × 10−5MV + 6.850 × 10−2ΔN − 1.057)) MV, χ IE = (2.557 × 10−5MV − 1.319 × 10−2χ − 0.969)/(1 + (2.557 × 10−5MV − 1.319 × 10−2χ − 0.969)) MV, η IE = (3.732 × 10−5MV − 9.028 × 10−2η − 0.762)/(1 + (3.732 × 10−5MV − 9.028 × 10−2η − 0.762)) ELUMO, μ IE = (1.400 × 10−2ELUMO − 5.829 × 10−4μ − 0.989)/(1 + (1.400 × 10−2ELUMO − 5.829 × 10−4μ − 0.989)) μ, χ IE = (−5.714 × 10−4μ − 1.178 × 10−2χ − 0.957)/(1 + (−5.714 × 10−4μ − 1.178 × 10−2χ − 0.957)) μ, ΔN IE = (−5.347 × 10−4μ + 6.065 × 10−2ΔN − 1.036)/(1 + (−5.347 × 10−4μ + 6.065 × 10−2ΔN − 1.036)) EHOMO, ΔN IE = (0.115EHOMO − 0.619ΔN + 0.100)/(1 + (0.115EHOMO − 0.619ΔN + 0.100))

R2

SSE

RMSE

1.000 1.000 0.999 0.998 0.895 0.889 0.873

0.008 0.015 0.089 0.220 12.087 12.795 14.610

0.089 0.122 0.299 0.469 3.477 3.577 3.822

1.000 1.000 1.000 0.991 0.888 0.867 0.851 0.763

0.000 0.002 0.026 1.007 12.847 15.274 17.068 27.424

0.021 0.049 0.160 1.004 3.584 3.908 4.131 5.237

a

The R2 value, the SSE, and the RMSE values are also reported. The quantum chemical parameters were obtained from the in vacuo results calculated using the B3LYP/6-31G(d) method. bR2 is the coefficient of determination, and SSE and RMSE are defined as n

SSE =

∑ (IEpred − IEexp)2 i=1

RMSE =

1 n

n

∑ (IEpred − IEexp)2 j=1

where IEpred is the predicted inhibition efficiency, IEexp is the experimental determined inhibition efficiency, and n is the number of observations (compounds) considered.

4. CONCLUSIONS The following conclusions can be drawn from the results of the study: • The results obtained from the weight loss and electrochemical measurements are in good agreement. • The thermodynamic and kinetic parameters (Gibbs free energy of adsorption, ΔGads, enthalpy of activation, ΔHads, entropy of activation, ΔSads, and apparent activation energy, Ea) obtained from the studies show that the reaction between the mild steel and the ionic liquid corrosion inhibitors was spontaneous since the Gibbs free energy of adsorption values were negative. The mechanism of mixed type inhibitor adsorption was proposed from potentiodynamic polarization studies. The electrochemical impedance spectroscopy results showed that the inhibitor molecules inhibit mild steel corrosion by adsorption at the metal/acid interface. • The ionic liquids obeyed the Langmuir adsorption isotherm. • The effect of the substituent alkyl chains on the imidazolium cations were studied, and the improvement in the effectiveness of the corrosion inhibitors was found to increase as the alkyl chain attached to the imidazolium cation was increased or as it was more substituted. • Calculations done using DTF were performed both in vacuo and in water solution and by taking into consideration the protonated and the nonprotonated species. It was observed that the EHOMO showed [PDMIM][NTf2] had the highest tendency to donate

electrons to the surface of the metal while [PMIM][NTf2] had the least. This observation meant that [PDMIM][NTf2] possessed the highest tendency to donate electrons to the surface of the metal. The ELUMO values showed that [PMIM][NTf2] had more tendency to accept electrons, while [PDMIM][NTf2] had the least tendency to accept electrons. The Fukui function results indicated that the preferred sites for nucleophilic attack was the C2 atom in the cation while the preferred site for electrophilic attack was on the O and N atoms of the anion. This was true for the protonated and the nonprotonated species and in both media, in vacuo and water solution. The increase in the inhibition efficiency with the increase in the length of the R chain maybe related to the increase in the hydrophobic nature of the molecule. [PDMIM][NTf2] has the highest number of hydrophobic alkyl groups around the imidazolium ring, implying that the molecule has the least tendency to remain in water solution. The protonated species have poor electron donor character and have a higher electron accepting characters. Therefore, in comparison to the nonprotonated species, the protoanted speices have least tendency to chemically adsorb onto the metal surface. The most probable mode of adsorption for the protonated speices is through electrostatic interaction with the metal surface. In this mechanism, the protonated speices are attracted to the metal surface by the already adsorbed negatively charged Cl− anions. This explains the possibility of both chemical 13297



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and physical adsorption of the inhibitor onto the metal surface as suggested by experimental techniques. • Trends in the quantum chemical parameters are similar between the results in water solution and the results in vacuo. However, the comparison of the individual quantum chemical parameters suggests strong solute− solvent effects. • The quantitative structure activity relationship (QSAR) approach has provided a good indication that an optimum of two quantum chemical parameters is required for good correlation with experimentally determined inhibition efficiency of the inhibitors. The information provided could be utilized in the search for other ionic liquids (that have similar characteristics like the ionic liquids studied in this work) that could be better corrosion inhibitors. Moreover, this information may be used to determine better corrosion inhibitors. • The results from the weight loss, electrochemical analysis, and quantum chemical studies show that the order of the inhibition efficiency for the mild steel corrosion by the ionic liquids inhibitors follows the order [PDMIM][NTf2] > [HMIM][NTf2] > [BMIM][NTf2] > [PMIM][NTf2].

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.C.M. thanks Sasol-Inzalo Foundation for Science Fellowship for postgraduate studies. M.M.K., A.K.S., and S.K.S. are grateful to the North West University for granting them a Postdoctoral Fellowship enabling them to participate in this work. We are also grateful to the group of T. Arslan of Eskisehir Osmangazi University in Turkey for providing us with access to run calculations using Gaussian03 program from their center. E.E.E. acknowledges the National Research Foundation (NRF) of South Africa for funding.

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Experimental and Quantum Chemical Studies of Some Bis

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