Corrosion inhibition of N80 steel in 15% HCl by pyrazolone derivatives: electrochemical, surface and quantum chemical studies

Abstract

The corrosion protection of N80 steel in 15% HCl by two pyrazolone derivatives namely 2-(3-amino-5-oxo-4,5-dihydro-1H-pyrazol-1-yl)(p-tolyl)methyl)malononitrile (PZ-1) and 2-((3-amino-5-oxo-4,5-dihydro-1H-pyrazol-1-yl)(phenyl)methyl)malononitrile (PZ-2) has been investigated by using gravimetric, electrochemical and quantum chemical studies. The observed results reveal that PZ-1 is a better inhibitor than PZ-2. Tafel polarization showed that PZs are mixed type inhibitors but dominantly affect the cathodic reaction. Both inhibitors were found to obey the Langmuir adsorption isotherm. Scanning electron microscopy (SEM) and scanning electrochemical microscopy (SECM) images support the protection of the N80 steel in the presence of the PZs. Quantum chemical study reveals that both inhibitors have a tendency to get protonated and this result supports the experimental observations.

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1. Introduction

In the oil industry the acidization of oil wells is carried out through N80 steel tubes, in order to increase the crude oil production, by enlarging the microscopic flow channel of the rocks. The most commonly used acid in the oil industry for acidization is 15% hydrochloric acid (HCl) due to its cost effectiveness and also it does not leave any insoluble reaction product. However, in the presence of HCl, severe corrosion of N80 steel tubes occurs, which results in wastage of money and resources.

The most practical and cost effective method for reducing the corrosion process is use of inhibitor.¹ Mostly organic inhibitors are used for N80 steel in acidic medium, which contains either nitrogen, oxygen and/or sulfur atoms.^2,3

However, in view of strong environmental regulations, research is focused in the field of corrosion to develop environmentally benign inhibitors.^1,4 In this regard, we have synthesized pyrazolone derivates, which possess anti-inflammatory, analgesic, antipyretic, hypoglycemic agent, fungicide, antimicrobial, anti proliferative, cancer chemo preventive, antibacterial, antimyopic, antihistaminic, hypertensive, antirheumatic and antiasthmatic activities.⁵ The literature survey reveals that in recent years pyrazolone derivatives have been used as corrosion inhibitors, but in low acid concentration.^5–10

In recent years quantum chemical calculations is extensively used for correlating the molecular structure of inhibitors and their inhibition properties.^11–13

The aim of the present work is to synthesize two pyrazolone derivative namely 72-(3-amino-5-oxo-4,5-dihydro-1H-pyrazol-1-yl)(p-tolyl)methyl)malononitrile (PZ-1) and 2-((3-amino-5-oxo-4,5-dihydro-1H-pyrazol-1-yl)(phenyl)methyl)malononitrile (PZ-2), and to study their corrosion inhibition behavior for N80 steel in 15% HCl solution by using gravimetric measurements, polarization measurements, electrochemical impedance spectroscopy, scanning electron microscopy (SEM), scanning electrochemical microscopy (SECM) and quantum chemical calculations.

2. Experimental details

2.1. Synthesis of inhibitors (PZs)

The syntheses of inhibitors were carried in laboratory according to the given procedure.¹⁴

Here one pot synthesis procedure is used. In a round bottom flask a mixture of ethyl cyanoacetate (10 mmol), hydrazine hydrate (1 mL, 80%), malononitrile (10 mmol) and carbonyl compound (benzaldehyde and p-methoxybenzaldehyde, 10 mmol) were refluxed in presence of 5 drops of triethylamine. The crude product formed was cooled and filtrated. Recrystallization was done from ethanol. The synthetic scheme, molecular structure and analytical data of the inhibitors are given in Fig. 1 and Table 1 respectively.

Fig. 1 Synthetic route of inhibitors.

Table 1 Molecular structure and analytical data of PZs

Inhibitor	Structure	Analytical data
2-(3-Amino-5-oxo-4,5-dihydro-1H-pyrazol-1-yl)(p-tolyl)methyl)malononitrile (PZ-1)		White powder (mp 321 °C), ^1H-NMR: δ 2.57 (s, 3H, CH3), 5.55 (s, 2H, CH2), 8.42 (s, 2H, NH2); ^13C-NMR: δ = 20.1 (CH3), 76.5 (CH2 pyrazoles), 90.2 (C(CN)2, 116.6, 117.4 (two CN), 155.4 (C-3 pyrazole), 157.1 (C-5 pyrazole)
2-(3-Amino-5-oxo-4,5-dihydro-1H-pyrazol-1yl)(phenyl)methyl)malononitrile (PZ-2)		Yellow powder (m.p. 290 °C), ^1H-NMR: δ = 2.52 (s, 2H, pyrazole CH2), 7.48–7.57 (m, 5H, phenyl), 8.49 (s, 2H, NH2); ^13C-NMR: δ = 41.4 (C-4 pyrazolone), 74.3 (C-CN), 116.3 (CN), 115.5, 127.9, 128.6, 130.2, 134.6, 156.7 (aromatic carbons), 159.2 (C-NH2), 159.6 (C=O);

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2.2. Gravimetric experiments

N80 steel used for corrosion test has following composition (wt%): C 0.31; Si 0.19; Mn 0.92; P 0.010; S 0.008; Cr 0.2, balance iron. The dimensions of the N80 steel used for gravimetric and electrochemical experiments were 5.0 cm × 2.5 cm × 0.2 cm and 2.0 cm × 1.0 cm × 0.025 cm. All corrosion tests were performed in 15% HCl for 6 h immersion. The corrosion rate C_R (mg cm⁻² h⁻¹) was calculated by using the following equation:where W is the average weight loss of N80 steel strip, A is the total area of N80 steel strip and t is immersion time (6 h).

The inhibition efficiency (η%) was estimated by using following equation:

Surface coverage (θ) was calculated using the following relationship:

2.3. Electrochemical measurement

The electrochemical experiments were carried out using a three-electrode cell assembly where N80 steel strip with an exposed area of 1 cm² was used as working electrode, graphite rod as counter electrode and a saturated calomel electrode (SCE) as reference electrode. The working electrode was immersed in the test solution at open circuit potential (OCP) for 30 min before measurement in order to attain a steady state condition. For all electrochemical measurements, Gamry Potentiostat/Galvano stat (Model G-300) connected with a personal computer with EIS software Gamry Instruments Inc., USA was used. The analysis of experiments was carried out using Echem Analyst 5.0 software package.

The potentiodynamic polarization measurements were performed by changing the electrode potential automatically from −250 to +250 mV versus SCE at OCP at a scan rate of 1 mV s⁻¹.

Impedance measurements were carried out by an AC signal with the amplitude of 10 mV peak to peak at the open circuit potential, in the frequency range of 100 kHz to 0.01 Hz. All electrochemical measurements i.e. potentiodynamic polarization and impedance were carried out at 308 K.

2.4. Surface analysis: SEM and SECM

The morphological changes over the N80 steel surfaces in absence and presence of inhibitors were analyzed by SECM and SECM. Here the specimens were first immersed in 15% HCl in absence and presence of optimum concentration (150 mg L⁻¹) of PZs for 6 h at 308 K, respectively, then taken out from the test solutions, cleaned with bi-distilled water and dried it. The SEM images were conducted using a Ziess Evo 50 XVP instrument model, at an accelerating voltage of 5 kV and magnification 5k×. SECM studies were carried out using an electrochemical work station of CHI900C model consisting of the three electrode assembly with N80 steel, platinum electrode, and Ag/AgCl/KCl (saturated) electrode as working, counter and reference electrodes, respectively.

2.5. Quantum chemical calculations

Gaussian 03-program package was used for all Quantum chemical calculations.¹⁵ Optimization of molecular structures of inhibitors carried out by using DFT (density functional theory) on local correlation functional (B3LYP) using 6-31G (d,p) basis set.^16,17 The following quantum chemical indices were taken into consideration: energy of the highest occupied molecular orbital (E_HOMO), energy of the lowest unoccupied molecular orbital (E_LUMO), energy gap: ΔE = E_LUMO − E_HOMO, dipole moment (μ), electronegativity (χ), hardness (η), softness (σ), the fraction of electrons transferred (ΔN). All calculations were carried both on neutral and protonated molecules.

The ionization potential (IP) and electron affinity (EA) were calculated according to Koopman's theorem¹⁸ and is related to E_HOMO and E_LUMO as follows:

IP = −E_HOMO

EA = −E_LUMO

Electronegativity (χ), measures electron attraction ability by a group of atoms toward itself and according to Koopman's theorem; it can be calculated as follows:

Global hardness (η) measures the charge transferring resistance and inverse of it is global softness (σ). These two are given as follows:¹⁹

The fraction of electrons transferred (ΔN) from the inhibitor to N80 steel surface can be calculated by using the χ and η values, by using the following equation:²⁰

where χ_Fe and χ_inh denote the absolute electronegativity of iron and the inhibitor molecule respectively; η_Fe and η_inh denote the absolute hardness of iron and the inhibitor molecule respectively. The values of χ_Fe and η_Fe are taken as 7 and 0 eV mol⁻¹ respectively.²⁰

Monte Carlo simulations were performed using Forcite module in the Material Studio Software 7.0 from BIOVIA-Accelrys, USA.^21,22 The simulation was carried out with Fe (110) crystal with a slab of 5 Å in depth with periodic boundary conditions in order to simulate a representative part of an interface devoid of any arbitrary boundary effects. The Fe (110) plane was next enlarged to a (10 × 10) supercell to provide a large surface for the interaction of the inhibitors. After that, a vacuum slab with 30 Å thickness was built above the Fe (110) plane. The Fe (110) surface was fixed before simulations. For the whole simulation procedure, the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field was used to optimize the structures of all components of the system of interest. The MD simulations were performed in NVT canonical ensemble at 298 K with a time step of 1.0 fs and a total simulation time of 500 ps using Anderson thermostat.

3. Results and discussion

3.1. Gravimetric experiments

3.1.1. Effect of inhibitor concentration. Inhibitor concentration effect was studied in the range of 25 to 150 mg L⁻¹ doses and is represented in Fig. 2(a). Fig. 2(a), reveals that the inhibition efficiency increases with the increase in the PZs concentration. This result indicates the adsorption of PZs on the N80 steel.

Fig. 2 (a) Variation of inhibition efficiency (η%) with inhibitor concentration at 308 K. (b) Variation of inhibition efficiency (η%) with solution temperature (308–338 K) at higher concentration of inhibitors. (c) Arrhenius plots of the corrosion rate (C_R) of N80 steel in 15% HCl in absence and presence of higher concentration of inhibitors.

3.1.2. Effect of temperature. Gravimetric measurements were carried out at various temperatures (308–338 K) in the absence and presence of optimum concentration (150 mg L⁻¹) of PZs. The results obtained are listed in Table 2 and shown in Fig. 2(b). The inhibition efficiency decrease with the increase in temperature [Fig. 2(b) and Table 2], this could be due to desorption of PZs molecules from N80 steel surface.

Table 2 Adsorption parameters for PZs calculated from different adsorption isotherm for N80 steel in 15% HCl solution at 308 K

Adsorption isotherm	Inhibitor	Correlation coefficient	Slope
Temkin	PZ-1	0.954	0.340
	PZ-2	0.990	0.333
Frumkin	PZ-1	0.962	5.913
	PZ-2	0.991	5.457
Flory & Huggins	PZ-1	0.947	0.847
	PZ-2	0.971	1.261
Langmuir	PZ-1	0.998	0.984
	PZ-2	0.998	1.036

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The Arrhenius plots are used for the calculation of activation energy (E_a), which is a plot between corrosion rate [C_R (mg cm⁻² h⁻¹)] vs. T and can be given by the following relation:²³

where E_a is the activation energy, T is the absolute temperature, A is the Arrhenius pre-exponential factor and R is the universal gas constant. The Arrhenius plots are shown in Fig. 2(c). The values of E_a were calculated from the slope of the plots [Fig. 2(c)]. In absence of PZs the value of E_a is 34.58 kJ mol⁻¹ and in presence of PZs it becomes 73.52 kJ mol⁻¹ (PZ-1) and 64.24 kJ mol⁻¹ (PZ-2) respectively at their optimum concentration (150 mg L⁻¹). The E_a values in presence of PZs are higher than in their absence, which reveals that PZs molecules are strongly adsorbed over N80 steel surface and increased the double layer thickness.²⁴

3.1.3. Adsorption isotherm. Adsorption isotherm was used in view to gather information for the interaction of PZs molecules and N80 steel surface. To understand strength and adsorptive nature of PZs on N80 steel, the experimental data's were fitted to various isotherms like Langmuir, Temkin, Frumkin and Flory–Huggins. Their correlation coefficient (R²) and slope values are tabulated in Table 3. The slope and correlation coefficient (R²) values in case of Langmuir isotherm is least deviated from unity as compared to other isotherms (Table 3). Thus, Langmuir adsorption isotherm, which is plot between C/θ against C, is the best fit and is given by the following equation:²⁵

C/θ = 1/K_ads + C (9)

where θ is the surface coverage, C is the inhibitor concentration, K_ads is the equilibrium constant of adsorption process. The Langmuir adsorption isotherms of PZs are shown in Fig. 3.

Table 3 Electrochemical impedance parameters for N80 steel in 15% HCl in absence and presence of optimum concentration (150 mg L⁻¹) of PZs at 308 K

Cinh (mg L^−1)	Rs (Ω)	Rct (Ω cm^2)	n	Y0 (μF cm^−2)	Cdl (μF cm^−2)	τ (s)	η (%)
Blank	0.820	4.58	0.755	603	134.24	0.000614	—
PZ-1	0.823	75.37	0.882	137	74.77	0.005635	93.9
PZ-2	0.447	32.03	0.868	174	91.23	0.002881	85.4

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Fig. 3 Langmuir's isotherm plots for adsorption of inhibitors on N80 steel surface in 15% HCl.

The equilibrium constants (K_ads) and standard free energy of adsorption (ΔG^°_ads) are correlated according to the equation:²⁶

ΔG^°_ads = −RT ln(55.5K_ads) (10)

where R is the gas constant and T is the absolute temperature. The value of 55.5 is the concentration of water in solution in mol L⁻¹.

K_ads values were calculated from the intercepts of the straight lines and are as follows: 2.0 × 10⁴ M⁻¹ (PZ-1) and 1.6 × 10⁴ M⁻¹ (PZ-2). In the present study ΔG_ads adsorption values are −35.67 kJ mol⁻¹ (PZ-1) and −35.22 kJ mol⁻¹ (PZ-2), which is less than −40 kJ mol⁻¹ but more than −20 kJ mol⁻¹, showing that PZs adsorption are both physical and chemical.^27,28

3.2. Electrochemical measurements

3.2.1. Electrochemical impedance spectroscopy. Electrochemical impedance spectroscopy (EIS) was used to investigate the surface layer created by the adsorbed PZs molecules. The impedance behavior of the PZs molecules at optimum concentration (150 mg L⁻¹) in the form Nyquist plots are shown in Fig. 4(a). The inspection of the Nyquist plots reveals that in the presence of PZs the diameter of the semicircle is larger than in their absence. By applying the equivalent circuit [Fig. 4(b)] following impedance parameters were extracted, such as solution resistance (R_s), the charge transfer resistance (R_ct) and the constant phase element (CPE) and are listed in Table 4. Fitness accuracy of this circuit was checked by plotting the simulated Nyquist and Bode phase angle plots and is shown in Fig. 4(c–f).

Fig. 4 (a) Nyquist plots for mild steel in 15% HCl in absence and presence of higher concentration of inhibitors at 308 K. (b) Equivalent circuit model used to fit the EIS data. (c and d) Fitted Nyquist and Bode plot for PZ-1. (e and f) Fitted Nyquist and Bode plot for PZ-2 (g): Bode (log f vs. log|Z|) and phase angle (log f vs. α°) plots of impedance spectra for N80 steel in 15% HCl in absence and presence of optimum concentration of inhibitors at 308 K.

Table 4 Electrochemical polarization parameters for N80 steel in 15% M HCl in absence and presence of optimum concentration (150 mg L⁻¹) of PZs at 308 K

Inhibitor	Ecorr (mV/SCE)	Icorr (μA cm^−2)	βa (mV dec^−1)	−βc (mV dec^−1)	η (%)
Blank	−443	3201	85.7	100.8	—
PZ-1	−473	256	89.2	108.9	92.0
PZ-2	−446	474	95.1	104	85.1

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The inhibition efficiency of the PZs is calculated by using charge transfer resistance according to the following equation:²⁹

R_ct and R_ct(i) respectively represent the charge transfer resistance in absence and presence of inhibitors.

The impedance of the CPE can be given as follows³⁰

Z_CPE = Y₀⁻¹(jω)⁻ⁿ (12)

where Y₀ is the amplitude comparable to a capacitance, j is the square root of −1, ω is angular frequency and n is the phase shift.

Double layer capacitance (C_dl) can be calculated as follows³⁰

where, ω is the angular frequency (ω = 2π f_max) at which the imaginary part of impedance (−Z_im) is maximal and n is the phase shift.

The data in Table 4 reveals that in presence of PZs the values of charge transfer resistance is increased but at the same time double-layer capacitance values is decreased.

The double layer formed between the charged N80 steel surface and solution could be considered as an electrical capacitor. The adsorption of PZs molecules over N80 steel surface causes the decrease in its electrical capacity because PZs causes the displacement of pre-adsorbed water molecules. So, this decrease in the electrical capacity in presence of PZs indirectly supports their protective layer formation on N80 steel surface.³¹

The values of the relaxation time constant (τ) of charge-transfer process can be calculated by using the following equation:³²

τ = C_dlR_ct (14)

So, it's important to take τ values under discussion. It could be observed from Table 4 that in presence of PZs the values of τ is more than in their absence. This indicates that time of adsorption process becomes higher, which reveals that adsorption process in presence of PZs is slow.^33,34 In PZ-1 τ value is higher than PZ-2, which implies slower adsorption of PZ-1 than PZ-2.

The Bode and phase angle plots for N80 steel in 15% HCl in absence and presence of optimum concentration of PZs are shown in Fig. 4(g). The Bode phase angle plots have only one maximum i.e. one time constant at the intermediate frequencies and broadening of this maximum in presence of PZs suggests the formation of a protective layer on N80 steel surface. Also increase in the phase angle values in presence of PZs reveals their inhibitive action. The impedance values in presence of PZs are larger than their absence [(Fig. 4(g)], which indicates the reduction of corrosion process.

3.2.2. Tafel polarization. Tafel polarization curves of N80 steel in absence and presence of optimum concentration of PZs are shown in Fig. 5. All the Tafel polarization parameters i.e. corrosion potential (E_corr), cathodic Tafel slope (β_c), anodic Tafel slope (β_a) and corrosion current density (I_corr) obtained from the extrapolation of Tafel lines are given in Table 5. The percentage of inhibition efficiencies (η%) are calculated by using the following equation:³⁵where I_corr and I_corr(i) are the uninhibited and inhibited corrosion current densities, respectively.

Fig. 5 Tafel curves for N80 steel in 15% HCl in absence and presence of optimum concentration of inhibitor at 308 K.

Table 5 Calculated quantum chemical parameters of neutral PZs^a

Inhibitors	μ^b	EHOMO	ELUMO	ΔE	EA	IP	χ	η	σ^c	ΔN	ΔEback-donation
a All energy values are in eV.b μ is in Debye.c σ is in eV^−1.
PZ-1	7.483	−4.448	−1.052	3.396	4.448	1.052	2.750	1.698	0.588	1.251	−0.424
PZ-2	7.635	−4.669	−0.913	3.756	4.669	0.913	2.791	1.878	0.532	1.120	−0.416

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Table 5, shows that the difference between cathodic Tafel slope (β_c) and anodic Tafel slope (β_a) are not much higher, which indicates that, PZs control both cathodic and anodic reactions.

The polarization curves reveal that cathodic currents are reduced but no such definite trend is observed in anodic curves as the PZs are added and also the shifts in E_corr occurs towards more negative direction with respect to blank. This shift in the E_corr values concludes that the inhibitor is mixed type but dominantly affecting cathodic reaction.³⁶ The cathodic Tafel lines are parallel (Fig. 5), showing that hydrogen evolution mechanism with the addition of PZs has not modified, and hydrogen ions reduction mainly takes place through charge transfer mechanism.³⁷ It can be observed from Table 5 that the I_corr values in presence of PZs decreases. It is also evident that the performance of PZ-1 is better than PZ-2, which is due to the presence of electron donor CH₃ group in PZ-1.

3.3. Surface analysis: SEM and SECM

In absence of inhibitor significant damage of N80 steel surface is observed (Fig. 6(a)), indicating its severe corrosion. However in presence of PZs (Fig. 6(b) and (c)), the surface is protected, which is supported by the smooth N80 steel surface morphology. So, in the presence of PZs corrosion is restricted due to the adsorption of PZs molecules. This result is in agreement with the results obtained by electrochemical measurement.

Fig. 6 (a–c) SEM micrographs of N80 steel surfaces (a) blank 15% HCl (b) with PZ-1 (c) with PZ-2.

The SECM tests were performed in AC-amperometry mode to obtain the color mapping and 3-D figures of the N80 steel surface.^38,39 Fig. 7(a–f) shows the y-axis images of the N80 steel surface as visualized by scanning electrochemical microscope. A probe approach curve test was performed on y-axis to confirm that the tip was in the vicinity of the metal surface.^40,41

Fig. 7 (a–c) SECM figures for (a) 15% HCl y axis (b) 15% HCl y axis 3D (c) PZ-1 y axis (d) PZ-1 y axis 3D (e) PZ-2 y axis (f) PZ-2 y axis 3D.

The color mapping figure in absence of PZs is shown in Fig. 7(a). The variation in color (Fig. 7(a)) is due to rapid change in the current when the tip was close to the N80 steel surface. The variation in the color was slightly changed in presence of PZ-1 and PZ-2, as shown in Fig. 7(c) and (e). The color mapping figures hints that the surface is less corroded in presence of PZs while rough in its absence. A lower current is observed when the tip of the probe is brought near the N80 steel surface with PZs (insulating surface). This may be ascribed to the insulating film that blocks the diffusion of oxygen towards the tip as shown in Fig. 7(d) and (f).^42,43 On the other hand, the current increases when the tip of the probe is brought near the N80 steel surface without inhibitor (conducting surface). This may be accounted to the presence of redox mediator that revived at the surface.⁴⁴ The N80 steel surface remains conductive devoid of PZs, and insulating in existence of PZs, that can be confirmed by the enhancement in the current (conducting) and by reduction in the current (insulating).⁴⁵

3.4. Quantum chemistry method

3.4.1. Non-protonated PZs. All quantum chemical parameters are given in Table 6 for PZs in their neutral forms. The optimized geometries (with Mulliken charges), HOMO and LUMO distributions of PZ-1 and PZ-2 are shown in Fig. 8(a–f). It is reported in the literature that interaction between the reactants takes place via the involvement of frontier molecular orbital's i.e. HOMO and LUMO. HOMO energy is associated with electron donation ability of the inhibitor. So, higher the HOMO energy, more easily the electrons can be donated by the inhibitor to the unoccupied d-orbital's of the metal. However, LUMO energy is associated with the electron acceptation tendency of the molecule. Thus, lower the LUMO energy; more easily inhibitor molecule can accept electrons from the filled metal orbitals. Consequently, the value of the energy gap ΔE = E_LUMO − E_HOMO, represents the reaction tendency of the inhibitor i.e. lower its value, higher would be the inhibition efficiency. The dipole moment (μ) is also an important parameter. However in literature there is no correlation exist between the dipole moment and inhibition efficiency.⁴⁶

Table 6 Atomic charges on heteroatoms and proton affinity values

Inhibitors	Na	Nb	Nc	Od	PA (kcal mol^−1)
					Na	Nc	Od
PZ-1	−0.499	−0.234	−0.752	−0.449	−96187.98	−96220.19	−96168.25
PZ-2	−0.500	−0.235	−0.752	−0.448	−96187.31	−96219.47	−96167.35

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Fig. 8 (a and b) Optimized geometries of non-protonated (a) PZ-1 (b) PZ-2, 8(c–f) Frontier molecular orbital's of non-protonated PZ-1 (c) HOMO (d) LUMO and PZ-2 (e) HOMO (f) LUMO.

The value of E_HOMO is higher in the case of PZ-1 than PZ-2, which is due to the presence of electron donor CH₃ group in the molecular framework of PZ-1. So, PZ-1 has higher electron donating ability. The variation in the energy of E_LUMO is misrelating with the inhibition efficiency order. However, ΔE is lower in case of PZ-1, which further supports its more inclination to adsorb on the N80 steel surface. This is in good agreement with the experimentally observed result i.e. PZ-1 is better inhibitor than PZ-2.

The number of electrons transferred (ΔN) is calculated and given in Table 6. The value of ΔN < 3.6, which indicates that PZs has electron donating tendency to the metal surface. Thus, more the electron donating ability of the inhibitor, higher would be its inhibition efficiency.^47,48 The order of electron donating ability of the PZs are as follows: PZ-1 (1.251) > PZ-2 (1.120). This result also supports that PZ-1 is a better inhibitor than PZ-2.

Recently proposed by Gomez et al.⁴⁹ about donation and backdonation of charges. So, as per this concept, if both the transfer of electrons from inhibitor to the metal and back-donation from the metal to inhibitor occurs simultaneously, then the energy change is directly proportional to the hardness of the molecule and is given by the following expression:

If the ΔE_{back-donation} < 0, then the back-donation from the molecule to metal is energetically favored.⁴⁷ Table 6, reveals that the trend of ΔE_{back-donation} is in accordance with the inhibition efficiency order obtained from experimental data.

The σ value is higher in PZ-1 than PZ-2, which reveals its soft nature and also its greater adsorption.

From the HOMO and LUMO distribution, it is revealed that both PZ-1 and PZ-2 contains negative charges on the pyrazolone ring, on nitrogen of cyanide group and carbon atom of benzene rings of the alkyl chain. HOMO of both the PZs is distributed on the pyrazolone ring, some carbon of the phenyl and two nitrogen of cyanide group. So, these groups are actively involved in adsorption. On the other hand, LUMO is distributed over the pyrazolone ring and two nitrogen of the cyanide group.

3.4.2. Protonated PZs. In aqueous system inhibitor molecules have the tendency to undergo protonation by using their lone pairs of electrons. It has been reported that these protonated species can also take part in adsorption process. So, it becomes necessary to explain the adsorption of these protonated species. In the present case, PZs have four heteroatoms, out of these only three have most negative Mullikien charge (Table 7). Thus, the preferred sites for protonation in both PZs include N_a, N_c and O_d.

Table 7 Calculated quantum chemical parameters of protonated inhibitors^a

Inhibitors	μ^b	EHOMO	ELUMO	ΔE	EA	IP	χ	η	σ^c	ΔN	ΔEback-donation
a All energy values are in eV.b μ is in Debye.c σ is in eV^−1.
PZ-1^+	9.560	−3.673	−0.339	3.334	3.673	0.339	2.006	1.667	0.599	1.497	−0.469
PZ-2^+	10.688	−3.764	−0.373	3.391	3.764	0.373	2.068	1.695	0.589	1.454	−0.423

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The preferred site for protonation can be obtained by comparing the proton affinity (PA) at the different sites i.e. N_a, N_c, O_d. The proton affinity (PA) is calculated by using the following equation:

PA = E_prot + E_H2O − E_non-prot + E_H3O⁺

where, E_prot and E_non-prot are the total energies of protonated and non-protonated inhibitors respectively, E_H2O is the total energy of a water molecule and E_H3O⁺ is the total energy of hydronium ion. So, the preferred site for protonation would be at N_c in both PZs (Table 7). The optimized geometry (with Mulliken charges), HOMO and LUMO distribution of the preferred prototion site (N_c) are shown in Fig. 9(a–f).

Fig. 9 (a and b) Optimized geometries of protonated (a) PZ-1 (b) PZ-2, (c–f) Frontier molecular orbital's of protonated PZ-1 (c) HOMO (d) LUMO and PZ-2 (e) HOMO (f) LUMO.

Table 7 represents the quantum chemical parameters of the preferred protonated species.

After comparing the ΔE values of neutral and protonated PZs (Tables 6 and 7), it could be said that the values of ΔE in both PZs are lower in protonated forms than neutral forms, which reveals that protonated species are more reactive than neutral species i.e. greater tendency to interact with the metal. Thus, protonated forms of PZs are more likely to get adsorbed on the N80 steel surface than neutral forms. This discussion also confirmed the experimentally observed adsorption phenomenon i.e. both physical and chemical.

3.5. Monte Carlo simulations

Fig. 10(a and b) represents Monte Carlo simulations for the adsorption of PZs on Fe (110) surface. It is documented in the literature that stronger the binding energy, more stable will be the interaction.⁵⁰ The order of binding energy is PZ-1 (148.42 kcal mol⁻¹) > PZ-2 (124.46 kcal mol⁻¹). Thus, PZ-1 can strongly adsorb as compared to PZ-2. Also it is clear from Fig. 10(a and b) that PZs adsorbed totally in a flat manner on Fe, which enhances its surface coverage on N80 steel. So, this study also supports the experimentally observed results.

Fig. 10 (a and b) Monte Carlo simulations (a) side view for PZ-1 (b) top views for PZ-1 (c) side view for PZ-2 (d) top views for PZ-2.

4. Conclusions

All the studies i.e. gravimetric, EIS and Tafel polarization revealed that PZs are good corrosion inhibitors for N80 steel in 15% HCl. Tafel polarization study shows that PZs are mixed-type inhibitors but favoring more cathodic reaction suppression. Langmuir adsorption isotherm is obeyed by both PZs. ΔG^°_ads adsorption reveals that the adsorption of PZs is both physical and chemical. SEM micrographs show that N80 steel surface protection in presence of PZs.

Quantum chemical study revealed that both PZs have a tendency to get protonated, and also these protonated forms of PZs have greater interaction and adsorption capacity than neutral forms. Monte Carlo simulations also support the experimentally observed results.

Acknowledgements

K. R. Ansari gratefully acknowledges Ministry of Human Resource Development (MHRD), New Delhi, India for the financial assistance and facilitation of study.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra25441h

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