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Materials Research

Print version ISSN 1516-1439On-line version ISSN 1980-5373

Mat. Res. vol.23 no.2 São Carlos  2020  Epub June 01, 2020

https://doi.org/10.1590/1980-5373-mr-2018-0610 

Article

Electrochemical and Quantum Chemical Studies on Corrosion Inhibition Performance of 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on Mild Steel Corrosion in 1M HCl Solution

Iman Danaeea  * 
http://orcid.org/0000-0002-1108-8955

S. RameshKumarb 

M. RashvandAveic 

M. Vijayand 

aPetroleum University of Technology, Abadan Faculty of Petroleum Engineering, Abadan, Iran

bSri Vasavi College, Department of Chemistry, Erode, Tamilnadu-638 316, India.

cK. N. Toosi University of Technology, Department of chemistry, Tehran, Iran

dCentral Electrochemical Research Institute, Centre for Conducting Polymers, Electrochemical Materials Science Division, Karikudi, 630006, India


Abstract

The inhibitory effect of Oxethazaine drug, 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on corrosion of mild steel in 1M HCl solution was studied by weight loss measurements, electrochemical impedance spectroscopy and potentiodynamic polarization methods. The results of gravimetric and electrochemical methods demonstrated that the inhibition efficiency increased with an increase in inhibitor concentration in 1M HCl solution. The results from electrochemical impedance spectroscopy proved that the inhibition action of this drug was due to adsorption on the metal surface. Potentiodynamic polarization studies revealed that the molecule was a mixed type inhibitor. The adsorption of the molecule on the metal surface was found to obey Langmuir Adsorption isotherm. Potential of zero charge at the metal-solution interface was measured to provide the inhibition mechanism. The temperature dependence of the corrosion rate was also studied in the temperature range from 30 to 50 °C. Quantum chemical calculations were applied to correlate electronic structure parameters of the drug with its inhibition performance. The obtained theoretical results have been adapted with the experimental data.

Keywords:  Corrosion inhibitors; Potential of zero charge; Impedance; Quantum chemical calculations

1. Introduction

The surface of iron and steel, existing in many forms ranging from exposed metal to oxidized to different degrees, finds many industrial applications1-3. Recent investigations have emphasized the importance for the protection of the metal surfaces in various applications. The spontaneous destruction of metals, starting from their surfaces, due to the corrosive attack of environment brings the undesirable changes at the surfaces and reduces their lifetime, strength and changes the desirable properties of surfaces. In some cases the corrosion products formed are toxic. An accurate description of surface not only helps to identify the prevailing form of corrosion but also the prescription of appropriate anti-corrosion measures. Acid solutions, in general HCl solutions are widely used in industries for many purposes, such as acid pickling, industrial acid cleaning, acid descaling and oil well acidizing4-7. Due to the general aggressive nature of acid solutions, the corrosive attack will be severe4 and bring undesirable changes at the surface of metals. Chemical inhibitors are often used to control the corrosive attack and acid consumptions of environment8,9. Most of the well-known acid corrosion inhibitors are the organic compound containing N,S,O and P atoms10,11. These organic compounds reduce the metal dissolution by the absorption on the metal surfaces12. The adsorption and inhibition efficiency of these compounds greatly depend on the electron density around the hetero atoms, the number of adsorption active centers in the molecule and their surface charge density, molecular size, mode of adsorption and formation of metallic complexes10-21. However, the choice of inhibitors are based on the two considerations, first economic consideration and second the presence of the electronegative atoms such as N,O in the relatively long compounds. Thermodynamic model is an important tool used for analyzing the corrosion inhibition mechanism of inhibitors and their adsorption on the metal surface14,15. Using the type of adsorption isotherm that the molecule follows for the adsorption on mild steel surface, the values of thermodynamic parameters such as adsorption equilibrium constant (Kads) and free energy change of adsorption(ΔGads) can be calculated and used for predicting the adsorption and inhibition mechanism.

Many authors generally agree that drugs are the good corrosion inhibitors that can complete favorably with green corrosion inhibitor. Moreover, most drugs can be synthesized from natural products. The reasons for using drugs as corrosion inhibitors are ;(1) drug molecule contains oxygen, nitrogen and sulphur as active centers, (2) drugs are reported environmentally friendly and important in biological reactions22,23. In modern scenario, development of novel biodegradable and less toxic corrosion inhibitors is gaining importance. Biologically active molecules like sulfadimidine, sulfamethoxazole, cefatrexyl, apart from other antibacterial and antifungal drugs have been reported as good corrosion inhibitors24-26. The use of drugs as corrosion inhibitors for metals in different aggressive environments is widely reported. These include the use of sulpha drugs27,28, antimalerial drugs29 and analgesic drugs30 as efficient corrosion inhibitors for metals in various media. Moreover, many expired drugs have been reported to be very effective corrosion inhibitors for the protection of mild steel in acidic media31-36. This area of research is much important because in addition to being environmentally friendly and ecologically acceptable, expired pharmaceutical drugs are inexpensive, readily available and prevent pollution. On the other hand, deactivation of this expired drug is generally carried out with the risk of air pollution with toxic compounds containing N, S, P or halogen atoms. The expiry date is merely an assurance from the manufacturer that the drug is expected to retain at least 90% of its original efficacy up to that time and its active substance degrades only negligibly. This type of research can solve two major environmental and economical problems: limitation of environmental pollution with pharmaceutically compounds and reduction of the disposal costs of expired drugs. Thus, this area would give effective nonhazardous alternatives to toxic corrosion inhibitors.

Recently, the research activities are centered on the development of cheaper and greener corrosion inhibitors. In this context, the application of expired drugs as corrosion inhibitors can satisfy both environmental and economic provisos of green chemistry. Dohare et al. on 2017 have used expired Tramadol drug as inhibitor for mild steel corrosion in hydrochloric acid35. They employed DFT and experimental studies on the inhibition potentials of expired drug and the inhibition efficiency about 96% was achieved. Anaee et al. on 2019 studied expired Etoricoxib as a corrosion inhibitor for steel in acidic solution36. Expired Etoricoxib indicated high inhibition efficiency in different temperatures.

Density functional theory (DFT) has become a useful theoretical method to interpret the experimental results, enabling one to obtain various structural parameters, even the inhibitor is a larger complex molecule, i.e. DFT links some traditional empirical concepts with quantum mechanical results37,38. Therefore, DFT is a connecting bridge between the experimental results and theoretical structural parameters of inhibitor molecule.

The present work deals with the corrosion inhibition nature of Oxethazaine drug, 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] in the acid medium utilizing; weight loss measurements, the polarization method and electrochemical impedance spectroscopy (EIS). Potential of charge (PZC) was also determined to establish the inhibition mechanism. Quantum chemical calculations have been performed, and several quantum chemical indices are calculated and correlated with the corrosion inhibition nature of the inhibitor in 1 M HCl medium.

2. Experimental

2.1 Materials

Mild steel specimens of dimensions 2.5 cm×1.0 cm ×0.1cm with a composition 0.087% C,0.039%mn, 0.03%P,0.02%S and rest iron were used for weight loss studies. The specimens were mechanically polished using emery sheets of grade 1/0, 2/0, 3/0, 4/0, and 5/0 and thoroughly washed with double distilled water. Finally the specimens were degreased with acetone and dried. A Teflon coated cylindrical mild steel rod, having an exposed area of 0.02826 cm2, with previously mentioned composition was used for electrochemical studies. Solutions of 1 M HCl with and without inhibitor were prepared from A.R. grade reagents using double distilled water. 3% ethanol by volume was added for solubility reasons. The inhibitor purchased from Guide Chem (Analytical Grade), was used as received without further purification. The structure of the inhibitor molecule is shown in Figure 1.

Figure 1 Chemical structure of Oxethazaine drug, (2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethyl phenethyl)-N-methylacetamide]. 

2. 2 Methods

2.2.1 Weight loss measurements

Weight loss measurements were carried out according to the American Society for testing and Materials (ASTM) standard procedure G 31-72. The mild steel specimens in triplicate were immersed for the period of 2 hours in 100 mL of corrosive media with and without the inhibitor at room temperature (300±1 K). The average weight loss of these specimens was used to calculate the inhibition efficiency employing the formula:

IE%=WWW×100 (1)

where W and W´ represent the weight losses in the uninhibited and inhibited solutions respectively. The relative difference between the replica experiments was found to be less than 3% at room temperature, which shows a good reproducibility.

2.2.2 Electrochemical measurements

The impedance measurements were performed using a computer–controlled potentiostat (model Solartron ECI-1286) and the data were analyzed using frequency response analyzer (Solartron FRA-1286). A three electrode set up was used for the electrochemical impedance measurements with a Pt counter electrode and a saturated calomel electrode (SCE) as the reference electrode. A Teflon coated mild steel cylinder, with surface prepared as described in the weight loss experimental method, served as the working electrode. The measurements were carried out in the frequency range 100 kHz to 0.01 Hz at the open circuit potential by super imposing a sinusoidal AC signal of small amplitude (10 mV). The time interval of 25-30 minutes was given for steady state attainment of open circuit potential. The electrochemical impedance parameters such as double layer capacitance (Cdl ) and polarization resistance (Rp) were obtained from the Nyquist plots as described elsewhere.

The potentiodynamic polarization curves were recorded after carrying out the electrochemical impedance measurements, using the same cell setup employed in the impedance measurement, at the potential sweep rate 1.67 mV s-1 from -700 mV to -200 mV vs. SCE. The inhibition efficiencies were calculated using the relationship.

IE%=icorricorricorr×100 (2)

Where Icorr and I´corr are the corrosion current densities in the absence and presence of the inhibitor in 1 M HCl solutions, respectively. The electrochemical impedance spectra were recorded at the 200 Hz applied single AC frequency at different applied DC potentials and the double layer capacitance values obtained were plotted against the applied DC potentials to determine PZC. All the measurements were taken at room temperature (27±1ºC).

2.2.3 Scanning electron microscopy

The surface morphology of mild steel specimen was analyzed after immersing in the blank and inhibited HCl solution by Scanning Electron Microscopy (Model-JEOL-JSM-6390). The surface morphological characterization was carried out at the magnification 2.0 KX operated at an accelerating voltage 15 kV.

2.2.4 Quantum chemical calculations

All quantum chemical calculations were performed with complete geometry optimization using the Gaussian 98 code. The molecular sketches of the inhibitor are drawn using GaussView 3.0. Geometry optimizations were accomplished by two different methods; ab initio methods at the Hartree-Fock (HF) level with the 3-21G and 6-31G(d,p) basis sets and at the density functional theory (DFT) level with the non-local hybrid density functional B3LYP, combining Becke’s three-parameter hybrid exchange functional with the correlation functional of Lee et al at the basis sets 3-21G and 6-31G(d,p)39. After the geometry optimization, vibrational analysis was performed and the resulting geometry was checked with respect to true minima on the potential energy surface, as shown by the absence of imaginary frequencies40.

The quantum chemical investigations were used to explain the results obtained in gravimetric and electrochemical studies on the corrosion inhibition property of 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide], looking for good theoretical parameters to characterize its inhibition performance. Statistical analyses were performed using SPSS program version 15.0 for windows. Non-linear regression analyses were performed by unconstrained sum of squared residuals for loss function and the estimation methods of Levenberg-Marquardt using SPSS program version 15.0 for windows.

3. Results and Discussion

3.1 Weight loss measurements

Weight loss measurements provide the most reliable results concerning the inhibition efficiency of the compounds41. The variation of weight loss of mild steel specimens in 1 M HCl solutions in the absence and presence of the inhibitor is shown in Table 1. It is apparent that the inhibition efficiency increases with an increase in inhibitor concentration in 1M HCl solutions. The decrease in corrosion rate in the presence of inhibitor is due to the strong interaction of the inhibitor molecules with the metal surface which lead to forming protective film by the adsorbed inhibitor on the metal surface, separating it from corrosion medium42,43. The extent of adsorption increases with an increase in the inhibitor concentration and the maximum adsorption was found at 200 ppm. The corrosion suppression ability of the inhibitor might be originated from its tendency to form either strong or weak chemical bonds, with Fe atoms on the metal surface, using the lone pair of electrons present on the O and N atoms and the π electrons in the benzene ring.

Table 1 Inhibition efficiency from weight loss measurement for mild steel in 1M HCl solutions in the presence and absence of inhibitor. 

Inhibitor Concentration / ppm Corrosion rate / mpy Inhibition efficiency (IE %)
Blank 168 -
20 19.08 88.64
40 17.19 89.77
60 15.29 90.90
100 11.46 93.18
200 7.64 95.45

3.2 Electrochemical impedance spectroscopy

The impedance spectra obtained for the dissolution of mild steel in 1M HCl solutions in the absence and presence of inhibitor at various concentrations are shown in Figure 2. The Nyquist plots obtained are semicircles. The simple -R(CR)- model describes best the situation at the metal solution interface. However, the complex plane plots obtained are depressed semicircles, indicating non-ideal capacitive behavior of metal-solution interface. This capacitance dispersion at the solid surfaces can be attributed to the surface roughness, the degree of polycrystallinity, the chemical inhomogeneities and anion adsorption. A precise modeling for the experimental results was obtained by replacing a capacitor by a constant phase element (CPE) in the equivalent (Figure 3), whose impedance function is given as19:

ZCPE=1Y0jωn (3)

where Y0 represents the admittance of the corrosive system at 1rad s-1 and n, a constant (-1≤ n ≤1). When n = 0, CPE represents a pure resistor, if n = +1 the CPE represents a pure capacitor and an inductor if n = –1.

Figure 2 The Nyquist plots for MS electrode obtained in 1 M HCl solutions in the absence and presence of (2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methyl acetamide] at various concentrations. 

Figure 3 Equivalent circuit for the mild steel surface/corrosive media interface with CPE. 

The electrochemical impedance parameters obtained by fitting the experimental curves into an equivalent circuit shown in Figure 3, are given in Table 2. In this equivalent circuit, polarization resistance Rp indicates the contributions of charge transfer resistance, film resistance, accumulation resistance and double layer resistance. The results demonstrate that the polarization resistance values increase and the double layer capacitance (Cdl) values decrease with an increase in inhibitor concentration. The increase in the Rp values with inhibitor concentration indicates an increase in the surface coverage by the inhibitor molecules, resulting in an increase in inhibitor efficiency44,45. The decrease in Cdl values is caused by decreasing in the surface area of the metal, which is in contact with corroding medium. The adsorption of inhibitor molecules on the metal surface takes place by replacing water molecules at the metal-solution interface that lead to decreasing in local dielectric constant and/or an increase in the electrical double layer. Hence, the change in Cdl values cause by the gradual displacement of water molecules by the adsorption of the inhibitor molecules at the metal-solution interface decreases the extent of metal corrosion46. From Table 2, it can be seen that the value of the constant ‘n’ , which is a measure of the surface heterogeneity, increases with the inhibitor concentration towards unity, indicating that the mild steel surface becomes more and more homogeneous as the concentration of the inhibitor increases due to its uniform surface coverage at higher concentration.

Table 2 Impedance parameter values for the corrosion of mild steel in 1N HCl and 1N H2SO4 solutions in the presence and absence of inhibitor. 

Concentration / ppm Rp / Ωcm2 Y0 (× 10-6) / Ω-1cm-2 n Cdl / µFcm-2 IE %
Blank 14.8 304 0.902 116.5 -
20 135.8 92.4 0.911 38.2 89.1
40 151.1 78.5 0.913 31.2 90.2
60 172.1 64.3 0.929 25.4 91.4
100 255.2 31.4 0.978 19.7 94.2
200 422.9 27.7 0.963 10.4 96.5

3.3 Potentiodynamic polarization studies

The potentiodynamic polarization curves recorded for the corrosion of mild steel in 1M HCl solutions in the presence and absence of inhibitor at various concentrations are shown in Figure 4. From this figure it is clear that the addition of inhibitor to the corrosive medium shows a reduction of both anodic and cathodic currents. This indicates that the inhibitor is of mixed type. Moreover, the cathodic branches in the presence of inhibitor give rise to almost parallel lines, indicating that the increase in inhibitor concentration doesn’t modify the hydrogen evolution mechanism and the reduction of H+ ions at the mild steel surface is charge transfer controlled47,48. The corresponding electrochemical parameters obtained from polarization studies (Tafel plots) are shown in Table 3. As it is apparent from Table 3, the corrosion current density values decrease with an increase in inhibitor concentration. The values of Tafel constants (βc and βa) also change with inhibitor concentration indicating that the addition of inhibitor affects both cathodic and anodic reactions. However, a higher βc value than βa in the presence of inhibitor indicates that the cathodic reaction is retarded to a higher extent than anodic reaction. This behavior can be also seen from the Tafel plots, where the cathodic curves are shifted toward lower current densities to a higher extent than the anodic curves with an increase in inhibitor concentration. The Ecorr values are also shifted to more negative side with an increase in inhibitor concentration. All these could be attributed to the decrease in the rate of hydrogen evolution reaction caused by the adsorption of inhibitor molecules on the mild steel surface49.

Figure 4 Tafel plots for mild steel in 1.0M HCl solution in the absence and presence of the inhibitor at various concentrations. 

Table 3 Tafel polarization curves for mild steel in 1N HCl and 1N H2SO4 solutions in the presence and absence of inhibitor. 

Concentration / ppm Ecorr / mV Icorr / μA cm-2 βc / mV βa / mV Corrosion rate / mpy IE %
Blank -429 1.88×103 127 68 858.27 -
20 -448 2.09×102 228 103 95.41 89
40 -451 1.88×102 219 109 85.83 90
60 -452 1.69×102 286 140 77.15 91
100 -452 1.32×102 292 179 60.26 93
200 -454 7.50×101 331 151 34.24 96

According to Tables 1 and 3, the variation of calculated corrosion rates with respect to inhibitor concentrations from weight loss and Tafel polarization have the same manner but with almost different values. This is due to high applied cathodic and anodic overpotentials in the Tafel diagrams. More accurate data can be obtained by weight loss method. Moreover, weight loss is according to standard for corrosion rate calculation but needs long time. For weight loss method, test condition is more similar to natural situation and therefore more precision data can be calculated. The predominance of potentiodynamic polarization technique which used in most of research is the corrosion rate calculation in very low experiment time. In addition, the obtained inhibition efficiencies by Tafel are in agreement with weight loss and impedance measurements.

3.4 Adsorption isotherm

Adsorption isotherm provides information about the nature of interaction between inhibitor molecules and metal surface50. As mentioned earlier, the adsorption process can be considered as the replacement of water molecules at the corroding surface by inhibitor molecules51. Various adsorption isotherms were tested for the data obtained in weight loss measurements (also impedance and Tafel) and the data fit well with the Langmuir Adsorption isotherm, given by the expression;

Cinhθ=Cinh+1Kads (4)

Where Cinh is concentration of the inhibitor, θ is fraction of total surface covered by inhibitor molecules and Kads is adsorption equilibrium constant. The plot is linear with a correlation coefficients higher than 0.99. The value of Kads, determined from the plot of Cinh/θ vs. Cinh at constant temperature is used to calculate the value of standard free energy of adsorption (ΔGads) using the expression52:

Kads=1/55.5expΔG/RT (5)

The calculated value of ΔGads for adsorption of inhibitor molecules on the mild steel surface in 1 M HCl solution is -32 kJ mol-1. The negative value of ΔGads shows that the interaction between the inhibitor molecule and metal surface is strong and the adsorption of the inhibitor molecules on to the mild steel surface takes place spontaneously53,54. In general, the values of -ΔGads less than 20 kJ mol-1 imply the columbic electrostatic interaction between the charged molecules and the metal surface55,56 and greater than 40 kJ mol-1 imply the formation of chemical bond between the inhibitor molecules and the atoms on the metal surface through charge sharing or charge transfer57. Any value in between these two values corresponds to adsorption of inhibitor molecules on the metal surface by both physisorption and chemisorption. In the present study the calculated -ΔGads value is close to 40 kJ mol-1 and far from 20 kJ mol-1, indicating that the adsorption of inhibitor molecules on the metal surface involves both physisorption and chemisorption.

3.5 Effect of temperature

The change of corrosion rate with the temperature was studied in M HCl solutions with and without inhibitor by weight loss measurements at the temperatures 30, 40 and 50 ˚C by weight loss measurements. The variation of corrosion rate with temperature is shown in Figure 5 using the Arrhenius type plot according to the equation58:

Figure 5 Typical Arrhenius plots for corrosion of mild steel in 1 M HCl solutions in the absence (■) and presence (♦) of inhibitor (200 mg/L) at various temperatures. 

lncorrosionrate=lnAEa/RT (6)

The calculated values of activation energy from the slopes of Arrhenius type plots are 72.34 kJ mol-1 and 64.23 kJ mol-1 for the uninhibited and inhibited (200 ppm) solutions respectively. The lower activation energy in the presence of inhibitor suggests that the inhibitor molecules are adsorbed on the metal surface by chemisorptions59.

3.6 Potential of zero charge (PZC) and inhibition mechanism

The adsorption of inhibitor molecules on the metal surface generally depends on the surface charge of the metal, the charge on the inhibitor molecule or the dipole moment of the inhibitor molecule and the other ions that are specifically adsorbed on the metal surface53. The surface charge on the metal surface in the corroding medium is determined from the position of open circuit potential with respect to PZC54. At the open circuit potential the surface charge on the mild steel surface is given by the expression:

Er=EOCPEPZC (7)

where Er is Antropov’s “rational” corrosion potential60. The values of EOCP and Er determined from Figure 6 for mild steel in 1M HCl solutions in the presence and absence of inhibitor are given in Table 4. As it is clear from this table that the surface charge on the mild steel surface in the inhibited and uninhibited solutions to be positive. Being Lewis base, in the acidic medium some of the inhibitor molecules can protonate using the lone pair of electrons on the heteroatoms (O and N) and the protonated molecules will have positive charge. Based on the surface charge and the positive charge on the protonated inhibitor molecules the following mechanism was proposed for the corrosion of mild steel in 1 M HCl solutions in the presence and absence of inhibitor54,60,61. In the uninhibited HCl solution, at the open circuit potential the metal surface is positively charged, the dissolution of metal involves successively the reversible adsorption of the Cl- ions to the mild steel surface, release of electrons from the adsorbed anions to the metal surface and desorption of the adsorbed anion along with Fe+2 ions, after picking up the electrons from the Fe atoms60,61. In the inhibited 1M HCl solution, the protonated inhibitor molecules at O and N atoms are in equilibrium with the corresponding molecular (unprotonated) form. Due to electrostatic repulsion, it is difficult for a positively charged molecule to approach the positively charged metal surface. The positively charged molecules can get adsorbed on the mild steel surface via Cl- ions, which form connecting bridge between the protonated inhibitor molecules and the metal surface62,63. In addition to this type of physical adsorption, the adsorption of unprotonated form of inhibitor molecules can also take place through donor acceptor interactions between π electrons of, benzene rings and the lone pair of electrons on N and O atoms and the vacant‘d’ orbitals of surface iron atoms.

Figure 6 The plot of differential capacitance vs. applied electrode potential in 1 M HCl solution (o) and 1 M HCl containing 200 mg/L of the inhibitor solution (□). 

Table 4 Excess charge on MS electrode in 1N HCl and 1N H2SO4 solutions in the presence and absence of inhibitor. 

Medium Eocp (mV) PZC (mV) Excess Charge
1M HCl -429 -500 +
1M HCl + 200 ppm of inhibitor -454 -620 +

3.7 Scanning electron microscopy

Figure 7a and b show the SEM micrographs of the mild steel specimen immersed in the 1 M HCl solutions in the absence and presence of inhibitor respectively. The SEM monograph of mild steel specimen shows localized attack whereas the SEM monograph of mild steel specimen immersed in the inhibited solution indicates improvement in the surface morphology which could be due to the blocking of active centers on the mild steel surface by the inhibitor molecules.

Figure 7 SEM monographs of mild steel specimen immersed in 1 M HCl solutions in the absence (a) and presence (b) of inhibitor. 

3.8 Molecular orbital theoretical studies

Some of the molecular properties, describing the global reactivity such as; the total energy (ET), the energy of the Highest Occupied Molecular Orbital (EHOMO), the energy of the Lowest Unoccupied Molecular Orbital (ELUMO), the dipole moment, the Ionization Potential (I), the Electron Affinity (A), the electronegativity (χ), the global hardness (η), the global softness (S), the fraction of electron transferred (ΔN) and electrophilicity index (ω) are calculated using quantum chemical calculations. Other parameters describing the local selectivity of the studied molecule such as the local charge populations and the condensed Fukui functions are also considered. Some of these molecular parameters can be estimated following various approaches64. For instance, in the molecular orbital theory, the Koopmans’ theorem64 stipulates that the HOMO energy is related to I whereas the LUMO energy is linked to A, as follows:

I=-EHOMO (8)
A=-ELUMO (9)

According to Pearson, operational and approximate definitions of the electronic chemical potential (μ) and the absolute hardness (η) of a chemical system are given by the following equations:

-μ=(I+A)2=χ (10)
η=(I-A)2 (11)

While the global softness, which is the inverse of the global hardness, is given as:

S=12η (12)

The fraction of transferred electrons (ΔN), evaluating the electronic flow in a reaction of two systems with different electronegativities, in particular case; a metallic surface and an inhibitor molecule, is calculated according to Pearson theory as follows65:

ΔN=χM-χI2(ηM+ηI) (13)

where the subscripts M and I represent the metal and inhibitor, respectively. ηM and ηI denote the absolute hardness of Fe atom and the inhibitor molecule, respectively. A theoretical value for the electronegativity of bulk iron is χM=7eV and a global hardness is ηM=0eV , by assuming that for a metallic bulk I = A, because they are softer than the neutral metallic atoms. Recently, Li and Parr66 and Gomez et al.67 and Chattaraj et al.68 and Liu69 have introduced an electrophilicity index (ω) defined as;

ω=μ22η (14)

Recent progress in computational methods has provided a very useful tool for understanding the properties and for describing the behavior of atoms in molecules. Recently, computational methods have become very popular due to their accuracy and less computational burden. The mechanism of the inhibition action can be elucidated with the help of quantum chemical calculation, which is widely reported in the literature70-72. In this study, quantum chemical calculations are carried out at two different methods; ab initio methods at the Hartree-Fock (HF) level and the density functional theory (DFT) level with the 3-21G and 6-31G(d,p) basis sets by geometry optimization of the studied molecule to establish the relationship between the molecular structure of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] and its inhibition effects. It is obvious that the inhibition performance of an inhibitor on a metal surface is determined by the interplay of both spatial molecular and electronic parameters71. Figure 8 represents the optimized structure of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide]. The selected bond lengths and bond angles for 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] are tabulated in Table 5. It can be seen that, the studied molecule is not completely planar, which may result in relatively weak interaction between molecule and metal surface. However, elucidation of orientation of organic molecules on the electrode surface needs to consider different factors. The interaction between atoms and groups of the inhibitor molecules and the electrode surface depend on the geometry of the inhibitor as well as the nature of their frontier molecular orbitals.

Figure 8 Different perspective of DFT optimized structure of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] obtained at the B3LYP/6-31G(d,p). 

Table 5 Selected Bond Lengths (in angstroms) and Bond Angles (in degrees) of the oxetacaine with B3LYP/6-31G(d,p). 

Oxetacaine
Bong lengths
C1-C2 1.51891
C1-C8 1.57368
C8-C9 1.54404
C8-C10 1.54313
C8-N1 1.52506
N1-C12 1.37926
N1-C11 1.47386
C12-O1 1.25651
C12-C13 1.54886
C13-N2 1.45299
N2-C14 1.46445
C14-C15 1.53759
C15-O2 1.46285
N2-C16 1.44272
C16-C17 1.55497
C17-O3 1.25633
C17-N3 1.38034
N3-C18 1.47461
N3-C19 1.53139
C19-C20 1.54441
C19-C21 1.54391
C19-C22 1.57095
C22-C23 1.51985
Avg. of (C-C)Ar 1.40184
Bond angles
C9-C8-C10 110.95813
C20-C19-C21 111.28902
C1-C8-N1 107.38026
C22-C19-N3 108.53638
N1-C12-C13 118.77695
N3-C17-C16 118.79765
C13-N2-C16 119.63392
C1-C8-N1-C12 161.48218
C8-N1-C12-C13 -168.54489
N1-C12-C13-N2 139.89526
C12-C13-N2-C16 -108.15446
C13-N2-C16-C17 76.44796
N2-C16-C17-N3 164.04930
C16-C17-N3-C19 -176.78487
C17-N3-C19-C22 172.19852
N2-C14-C15-O2 -179.98150

The HOMO and LUMO populations of the studied molecule are shown in Figure 9. It can be seen in Figure 9 that, the frontier molecular orbital distribution obtained from four different calculation methods have given very close results. The compound investigated in the present study contains of two symmetrical parts consisting of two benzene rings and two imide groups. The LUMO location of inhibitor is relatively distributed over the benzene ring and a small part of the carbon chain that occur one side of the molecule whereas the HOMO is entirely localized on the heteroatoms. According to HOMO distribution, it can be said that 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] molecule carries its rich negative center in a small region. The molecules are oriented toward to cathodic sites of the steel surface through the parts of the molecules with low HOMO density and afterwards adsorption occurs by sharing of electrons. In addition, the inhibitor molecule can accept electrons from a Fe atom with its antibonding orbitals to form back-donating. These donation and back-donation processes strengthen the adsorption of inhibitor onto the mild steel surface73.

Figure 9 HOMO and LUMO populations of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] obtained at different levels. 

It is important to consider the situation corresponding to a molecule that is going to receive a certain amount of charge at some center and is going to back-donate a certain amount of charge through the same center or another74. To describe the energy change associated with these two processes, the second order simple charge transfer formula is regarded as a two-parameter expression, in which the donation and back-donation processes are differentiated through the use of the values of the chemical potential for each case, while the hardness is fixed to the value of η=(μ+μ) in both situations. Thus, when the molecule receives a certain amount of charge, ΔN+74,75,

ΔE+=μ+ΔN++12ηΔN+2 (15)

and when the molecule back-donates a certain amount of charge, ΔN, then

ΔE=μΔN+12ηΔN2 (16)

If the total energy change is approximated by the sum of the contributions from Equations 15 to 17, and the amount of charge back-donated is equal to the amount of charge received, ΔN = -ΔN+, then;

ΔET=ΔE++ΔE=μ+μΔN++ηΔN+2 (17)

The most favorable situation corresponds to the case when the total energy change becomes a minimum with respect to ΔN+, which implies that ΔN+=μ+μ/2η and

ΔET=μ+μ24η=η4 (18)

The calculations from Table 6 indicate that η > 0 and ΔET < 0 in all used computational methods. This result implies that the charge transfer to inhibitor molecule followed by back-donation from the molecule is energetically favorable. Similar observation has been reported76. However, it is important to note that ΔET values obtained don’t predict that a back-donation process is going to occur; it only establishes that if both processes occur (charge transfer to the molecule and back-donation from the molecule), the energy change is directly proportional to the hardness of the molecule.

Table 6 Some quantum chemical parameters for oxetacaine obtained at (A) B3LYP/6-31G(d,p), (B) B3LYP/3-21G, (C) HF/6-31G(d,p) and (D) HF/3-21G. 

quantum chemical properties A B C D
total energy (eV) -40305.741 -40096.458 -40041.844 -39836.299
ELUMO (eV) -0.116 -0.077 3.831 3.885
EHOMO (eV) -5.009 -4.797 -8.693 -8.530
∆E (eV) 4.893 4.720 12.523 12.415
dipole moment (D) 5.827 5.729 5.259 5.881
ionization potential (I/eV) 5.009 4.797 8.693 8.530
electron affinity (A/eV) 0.116 0.077 -3.831 -3.885
hardness (η/ev) 2.446 2.360 6.262 6.207
softness (S/eV) 0.204 0.212 0.080 0.081
electronegativity (χ) 2.563 2.437 2.431 2.322
fraction of electrons transferred (∆N) 0.907 0.967 0.365 0.377
electrophilicity (ω) 1.342 1.258 0.472 0.434
∆ET -0.612 -0.590 -1.565 -1.552
molar volume (cm3 mol-1) 316.023 388.615 353.746 397.661

The binding ability of the inhibitor to the metal surface increases with increasing HOMO and decreasing LUMO energy values. Thus, the lower the value of ELUMO, the most probable it is that the molecule would accept electrons. Moreover, the gap between the HOMO and LUMO energy levels (ΔE) of the molecule is an important parameter that determines the reactivity of the inhibitor molecule toward the adsorption on the metallic surface. In addition to ΔE parameter, for effective overlapping, the energy difference between the orbitals generally must be low, and the overall energy difference between the orbitals (HOMO and HOMO-1) is 1.02 eV for the studied compound, indicating their participation in the metal-ligand interaction. In addition, the energy difference between the HOMO-2 and HOMO-1 is very low confirming the involvement of HOMO-1 and HOMO-2 in the ligand-metal interaction (as shown in Figure 10) and also, suggesting that the parameters of orbitals such as HOMO, HOMO-1 and HOMO-2 are important for chemical reactivity over metal surface77-79.

Figure 10 (Left) molecular orbitals LUMO, HOMO, HOMO-1 and HOMO-2 of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] obtained at the B3LYP/6-31G(d,p) level and their energies. (Right) the electron density of corresponding orbitals for the studied compound. 

The fraction of electrons transferred from inhibitor to the iron molecule by different computational methods, is calculated and listed in Table 6. According to other reports80,81, the values of ΔN show inhibition effect resulted from electrons donation. Agreeing with Lukovits’s study81 if ΔN < 3.6, the inhibition efficiency increases with increasing electron-donating ability at the metal surface. Thus, in the present study, inhibitor molecule is donor of electrons and the mild steel surface is the acceptor of electrons. The electrophilicity index, ω, which measures the electrophilic power of a molecule, is calculated for this molecule. The positive value of ω suggests the high capacity of the molecule to accept electrons82. This process increases the adsorption capacity of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on the steel surface. In a corroding system, it is important to note that the inhibitor acts as a Lewis base while the metal acts as a Lewis acid.

The Fukui functions indicate the regions on the inhibitor molecule on which nucleophilic and electrophilic reactions are likely to occur. The Fukui function is defined as83:

f(r)=2Eν(r)N=ν(r)N=ρ(r)Nν (19)

where ν(r) is the external potential, ρ(r) is total charge density, and N is the total number of electrons. Due to discontinuity in the ρ(r) versus N curve, we can define three different types of Fukui function, viz

fk+=qk(N+1)qk(N) (for nucleophilic attack) (20)
fk=qk(N)qk(N1) (for electrophilic attack) (21)
fk0=qk(N+1)qk(N1)/2 (for radical attack) (22)

Where qk(N) , qk(N+1) and qk(N1) are the electron population of the kth atom for N, N+1, and N-1 electron systems, respectively.

The preferred site for nucleophilic attack is the atom in the molecule where the value of f + is the highest while the preferred site for electrophilic attack is the atom in the molecule where f - has the highest value. However, the average of both measures reactivity towards a radical. The calculated values of the Fukui functions for the non-hydrogen atoms are reported in Table 7. In addition to oxygen atoms, the value of f + is highest on C4, C7, C23 and C26 atoms in 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] indicating that these atoms are likely to be the preferred sites for nucleophilic attack. These results agree with the analysis of the electron density of this molecule in the case of N+1 electron system which indicated that each C and O atoms is able to stabilize additional electrons (top panel of Figure 11). The value of f -is highest on the same atoms approximately, in addition to N1 and N2 atoms. From bottom panel of Figure 11, it can be seen that these sites are the regions where electron removal destabilizes the molecule the least. The observed similarity in the sites for electrophilic and nucleophilic attacks suggests similarity in mechanism of inhibition.

Table 7 The Mulliken population analysis of the condensed Fukui functions and local softness parameters on the selected atoms of oxetacaine

Selected atoms Mullikene charge fk+ fk fko S+(eV) S(eV) So(eV) S+S SS+
C1 -0.328 -0.001 -0.005 -0.003 0.000 -0.001 -0.001 0.290 3.445
C2 0.104 -0.006 -0.001 -0.004 -0.001 0.000 -0.001 5.059 0.198
C3 -0.151 0.019 0.001 0.010 0.004 0.000 0.002 23.742 0.042
C4 -0.128 0.034 0.004 0.019 0.007 0.001 0.004 8.516 0.117
C5 -0.122 0.001 0.007 0.004 0.000 0.001 0.001 0.076 13.238
C6 -0.128 0.017 0.004 0.010 0.003 0.001 0.002 4.551 0.220
C7 -0.152 0.035 0.001 0.018 0.007 0.000 0.004 26.153 0.038
C8 0.192 -0.005 -0.023 -0.014 -0.001 -0.005 -0.003 0.215 4.646
C9 -0.425 -0.002 -0.003 -0.002 0.000 -0.001 0.000 0.810 1.235
C10 -0.402 -0.003 0.000 -0.002 -0.001 0.000 0.000 24.857 0.040
C11 -0.249 -0.009 -0.016 -0.013 -0.002 -0.003 -0.003 0.533 1.877
C12 0.589 0.003 0.010 0.007 0.001 0.002 0.001 0.262 3.811
C13 -0.147 -0.004 -0.050 -0.027 -0.001 -0.010 -0.006 0.076 13.073
C14 -0.081 -0.007 -0.064 -0.036 -0.001 -0.013 -0.007 0.113 8.833
C15 -0.040 0.002 -0.007 -0.002 0.000 -0.001 0.000 -0.326 -3.070
C16 -0.188 -0.007 -0.043 -0.025 -0.001 -0.009 -0.005 0.170 5.896
C17 0.553 0.017 0.012 0.015 0.004 0.002 0.003 1.445 0.692
C18 -0.247 -0.012 -0.014 -0.013 -0.002 -0.003 -0.003 0.845 1.184
C19 0.196 -0.011 -0.017 -0.014 -0.002 -0.003 -0.003 0.642 1.558
C20 -0.415 -0.002 -0.002 -0.002 0.000 0.000 0.000 0.738 1.355
C21 -0.405 -0.004 -0.001 -0.002 -0.001 0.000 0.000 6.457 0.155
C22 -0.336 -0.007 -0.006 -0.006 -0.001 -0.001 -0.001 1.217 0.822
C23 0.104 0.023 -0.002 0.011 0.005 0.000 0.002 -13.928 -0.072
C24 -0.151 0.008 0.000 0.004 0.002 0.000 0.001 29.694 0.034
C25 -0.128 0.014 0.003 0.008 0.003 0.001 0.002 4.832 0.207
C26 -0.122 0.039 0.006 0.023 0.008 0.001 0.005 6.510 0.154
C27 -0.128 0.002 0.003 0.003 0.000 0.001 0.001 0.808 1.237
C28 -0.150 0.021 0.000 0.011 0.004 0.000 0.002 98.626 0.010
N1 -0.546 -0.003 0.012 0.005 -0.001 0.003 0.001 -0.201 -4.969
N2 -0.477 -0.002 0.111 0.055 0.000 0.023 0.011 -0.016 -60.921
N3 -0.553 0.000 0.008 0.004 0.000 0.002 0.001 0.031 32.623
O1 -0.504 0.014 0.054 0.034 0.003 0.011 0.007 0.250 4.002
O2 -0.619 0.010 0.056 0.033 0.002 0.012 0.007 0.169 5.915
O3 -0.486 0.012 0.023 0.017 0.002 0.005 0.004 0.500 1.998

Figure 11 Iso-surface representation of electrostatic potential of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] as a system based on the independent single-point calculation for corresponding N+1, N and N-1 electron systems, top to bottom respectively, at the B3LYP/6-31G(d,p) level. 

The local reactivity of molecules is often analyzed in terms of the local softness index s, which is defined as the product of the Fukui function and the global softness, S. It is expressed using the equations84:

s+=(f+)S (23)
s=(f)S (24)
s0=(f0)S (25)

Also, the relative nucleophilicity (s+/s-) and relative electrophilicity (s-/s+) are the indices that are also related to the local softness and can be applied for the prediction of the sites for nucleophilic and electrophilic attacks. It is observed that both the approaches and the local softness values give results similar to those obtained from the Fukui function calculations.

Figure 12 (top panel) shows the Mulliken atomic charges calculated for inhibitor compound. It has been reported that the more negative the atomic charges of the adsorbed center, the more easily the atom donates its electron to the unoccupied orbital of the metal85. It is clear from Figure 12, that the oxygen and nitrogen atoms as well as some carbon atoms carry negative charge centers which could offer electrons to the mild steel surface to form a coordinate bond. The direction of the dipole can be understood by considering the electrostatic potential (middle and bottom panels of Figure 12), which discerns electron density rich regions centered on the mentioned atoms, indicating the preferred zone for nucleophilic attack.

Figure 12 Electrostatic properties of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] at the B3LYP/6-31G(d,p) level: Mulliken charge population and the side view of the dipoles are displayed on the top while the middle and bottom panels show the contour and iso-surface representation of electrostatic potential, respectively. 

3.9 Quantitative structure activity relationship (QSAR).

An attempt has been made to correlate the results obtained from quantum chemical studies and the observed inhibition efficiencies of the inhibitor. The approach in which several quantum chemical parameters form a composite index that is 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 strongly on the type of adsorption mechanism. Among the equations utilized to develop quantitative structure activity relationship, when the adsorption of the inhibitor molecules on the metal surface obeys Langmuir adsorption isotherm, is the linear and the nonlinear multiple regression equations developed by Lukovits86,87. The linear and nonlinear multiple regression equations are given by the Equations 26 and 27 respectively;

IETheor=AxiCi+B (26)
IETheor=Axi+BCi1+Axi+BCi×100 (27)

where IETheor is the inhibition efficiency, A and B are the regression coefficients determined by regression analysis, xi is a characteristic quantum index for the inhibitor molecule (i), and Ci denotes the concentration of the inhibitor. Such linear approach is not found to be satisfactory for correlating the present results. Consequently, the nonlinear model (NLM) proposed by Lukovits et al.81 and also used by Khaled88 for studying the interaction of corrosion inhibitors with metal surfaces in acidic solutions based on the Langmuir adsorption isotherm and a combination of the quantum chemical parameters that provided the best correlation together with the Equations 28 to 31 were used for the prediction of theoretical inhibition efficiency at the B3LYP/3-21G and HF/3-21G levels using the basis sets B3LYP/6-31G(d,p) and HF/6-31G(d,p) respectively.

IETheor=(3.91EHOMO8.22ELUMO+4.31ΔE+2.06ΔN+4.51μ0.10V+1.45)Ci1+(3.91EHOMO8.22ELUMO+4.31ΔE+2.06ΔN+4.51μ0.10V+1.45)Ci×100 (28)
IETheor=(1.05EHOMO+1.00ELUMO+0.95ΔE+0.99ΔN+0.94μ0.02V+0.99)Ci1+(1.05EHOMO+1.00ELUMO+0.95ΔE+0.99ΔN+0.94μ0.02V+0.99)Ci×100 (29)
IETheor=(1.06EHOMO+0.97ELUMO+0.92ΔE+1.00ΔN+0.96μ0.03V+0.99)Ci1+(1.06EHOMO+0.97ELUMO+0.92ΔE+1.00ΔN+0.96μ0.03V+0.99)Ci×100 (30)
IETheor=(1.06EHOMO+0.97ELUMO+0.91ΔE+1.00ΔN+0.96μ0.03V+0.99)Ci1+(1.06EHOMO+0.97ELUMO+0.91ΔE+1.00ΔN+0.96μ0.03V+0.99)Ci×100 (31)

From the results obtained, it can be seen that there is a good and acceptable coefficient correlation (R2=0.8491) between the experimental and calculated/estimated inhibition efficiencies of the stud1ied inhibitor using the B3LYP/6-31G(d,p) method as shown in Figure 13A (other computational methods show the same results). Figure 13B shows a plot of the theoretical and experimental inhibition efficiencies versus the concentrations of the studied inhibitor, which confirms the accuracy of the obtained results from Figure 13A. It is also important to mention that it is difficult to predict the corrosion inhibition ability of a compound through an inclusive approach or to find some universal type of correlations. Other than a number of excluded parameters such as, effect of solvent molecules, surface nature, adsorption sites of the metal atoms or oxides sites or vacancies, competitive adsorption with other chemical species in the fluid phase and solubility should also be taken into consideration. Thus, the electron rich heteroatoms such as O and N can be protonated and this form could be in equilibrium with the molecular(unprotonated) form. The positively charged protonated form of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] can get adsorbed on to the metal surface by physisorption.

Figure 13 (A) Correlation of experimental and theoretical inhibition efficiencies of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] using the B3LYP/6-31G(d,p) method. (B) Plot of IEexp% and IETheor% versus 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] concentrations. 

4. Conclusion

The adsorption and the inhibition effect of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on the corrosion behavior of mild steel in the 1 M HCl was studied by using weight loss and electrochemical methods and the experimentally observed inhibition efficiency was explained theoretically using quantum chemical calculations. The following points emphasized the conclusion of the present work:

    1. 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] showed an excellent inhibition effect on corrosion of mild steel in 1M HCl solution, which was concentration and temperature dependent.

    2. The inhibition performance can be attributed to the adsorption of this molecule on mild steel surface to form a protective film.

    3. The inhibition behavior obtained from electrochemical studies showed the same trend as noticed in the weight loss studies. The inhibition efficiency increased with the increase in inhibitor concentration. The adsorption mechanism involved both physisorption and chemisorption.

    4. The potentiodynamic polarization curves indicated that the inhibitor act as a mixed type of inhibitor with properties more cathodic in nature.

    5. The adsorption of inhibitor on the metal surface followed Langmuir adsorption isotherm and the ΔGads value calculated from adsorption studies had negative sign, indicating that the adsorption is spontaneous.

    6. Determination of PZC indicated the formation of chloride bridge between protonated form of inhibitor molecules and metal surface.

    7. Different computational methods were correlated to the inhibitive effect of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] .

    8. The Fukui function results indicated that the preferred sites for both nucleophilic and electrophilic attack were nitrogen, oxygen, and some carbon atoms. 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, it 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.

    9. The quantitative structure activity relationship (QSAR) approach has provided a good indication that an optimum of some quantum chemical parameters is required for good correlation with experimentally determined inhibition efficiency of the inhibitor.

5. Acknowledgements

The authors gratefully acknowledge the respective management and universities for providing sufficient facilities to carry out this research work and financial support.

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Received: September 07, 2018; Revised: January 13, 2020; Accepted: March 16, 2020

*e-mail: danaee@put.ac.ir

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