uncorrected proof

Journal of Molecular Structure xxx (2018) xxx-xxx

Contents lists available at ScienceDirect

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Journal of Molecular Structure

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journal homepage: www.elsevier.com

Experimental, DFT and molecular dynamics simulation on the inhibition performance of the DGDCBA epoxy polymer against the corrosion of the E24 carbon steel in 1.0 M HCl solution

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Rachid Hsissoua, ∗, Said Abboutb, Avni Berishac, Mohamed Berradia, Mohammed Assouagd, Najat Hajjajib, Ahmed Elharfia a

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Laboratory of Agricultural Resources, Polymers and Process Engineering (LAPPE), Team of Polymeric and Organic Chemistry (TPOC), Department of Chemistry, Faculty of Sciences, Ibn Tofail University, BP 133, 14000, Kenitra, Morocco b Laboratory of Materials, Electrochemistry and Environment, Team of Corrosion, Protection and Environment, Department of Chemistry, Faculty of Sciences, Ibn Tofail University, BP 133, 14000, Kenitra, Morocco c Department of Chemistry, Faculty of Natural and Mathematics Science, University of Prishtina, 10000 Prishtina, Kosovo, Serbia d Team of Materials, Metallurgy and Process Engineering, ENSAM, University Moulay Ismail, B.P. 15290, Al Mansour, Maknes, Morocco

ARTICLE INFO

ABSTRACT

Article history: Received 28 September 2018 Received in revised form 23 November 2018 Accepted 7 December 2018 Available online xxx

The inhibition performances of the epoxy polymer S, S′-diglycidyl O, O′- dicarbonodithioate of bisphenol A (DGDCBA) on the corrosion of the E24 carbon steel in 1.0 M HCl in the absence and in the presence of different concentrations (10−3 to 10−6 M of DGDCBA). Then, the results obtained by using gravimetric measurements and electrochemical methods show that the tested DGDCBA epoxy polymer is a very effective inhibitor to the inhibition of corrosion. Furthermore, the inhibition efficiency of the epoxy polymer increases with increasing concentration and reaches a maximum value of 91%, 98% and 96% for the concentration of 10−3 M of the DGDCBA for gravimetric and electrochemical measurements (stationary and transient methods), respectively. Moreover, this polymer has characteristics which facilitate their adsorption on the surface of the metal substrate, in particular the existence of aromatic rings and heteroatoms (O and S). In addition, we proceeded to compute quantum chemical descriptors using the density functional theory (DFT) method with 6–31 G (d,p) basis sets. Finally, the molecular dynamics simulation confirms the results obtained by the DFT and the experimental data.

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Keywords: Inhibition Polymer DGDCBA Electrochemical DFT Molecular dynamic

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1. Introduction

Currently the problem in the industrial process is corrosion of metals leading to increased manufacturing and production costs. Metal materials are exposed to conditions that facilitate the process of corrosion. In industrial fittings, steel is widely used as building materials because its low costs [1–4]. Hydrochloric acid is the most used in the industry, for scouring, cleaning and elimination of localized deposits. The aggressiveness of this acid solution leads to the use of corrosion inhibitor to reduce the rate of corrosion of metals [5]. In recent years, a very important effort has been made to synthesize new epoxy polymers used as highly effective corrosion inhibitors [6]. These polymers are applied for the protection of the metal surface against the corrosion in acid solutions. Furthermore, epoxy polymers containing aromatic rings, heteroatoms (O and S) with single electron pairs and conjugated bonds are generally considered to be corrosion inhibitors [7,8]. Moreover, the adsorption of the polymer inhibitors depends essentially the physico-chemical properties of the epoxy polymer linked to its functional group [9,10]. When the num

© 2018.

ber of double bonds increases in the macromolecular structure and the formation of the protective film is more rigid [11]. In additionally, the goal of our work is to investigate the corrosion inhibition of the E24 carbon steel in 1.0 M HCl by the DGDCBA as new epoxy polymer using gravimetric and electrochemical methods. Then, the density functional theory (DFT) approach was used to study the correlation between the mechanism of corrosion inhibition and the structure of the DGDCBA epoxy polymer. Finally, we proceeded to molecular dynamics simulation, using Materials Studio [12,13]. 2. Material and methods 2.1. Inhibitor tested The inhibitor used in this work is named the S, S′-diglycidyl O, O′dicarbonodithioate of bisphenol A (DGDCBA) epoxy polymer, which has been synthesized in our laboratory (LAPPE) [14]. Its semi-developed structure is shown in Fig. 1. 2.2. Metal used

∗

Corresponding author.

Email address: [email protected], [email protected] (R. Hsissou) https://doi.org/10.1016/j.molstruc.2018.12.030 0022-2860/ © 2018.

The metal used in this study is an E24 carbon steel whose chemical composition is given in Table 1.


2.3. Corrosive test The corrosive medium is a 1.0 M hydrochloric acid solution, prepared from the commercial solution of hydrochloric acid (37%) using distilled water. The concentrations used for the inhibitor range from 10−3 to 10−6 M. Furthermore, these concentrations were determined after studying the solubility of the DGDCBA inhibitor in the corrosive solution. 2.4. Gravimetric test

(4)

Such as and icorr present the corrosion current densities (A.cm−2) in the absence and in the presence of different concentrations of the DGDCBA inhibitor tested, respectively. Transient electrochemical measurements were evaluated by the same apparatus with signal amplitude (10 mV). The frequency domain explored varies from 100 KHz to 10 mHz. Finally, the inhibitory efficiency is determined using equation (5).

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Measurement of weight loss allowed us to calculate the corrosion rate (Cr) without and with different concentrations of the DGDCBA inhibitor epoxy polymer after 6 h of immersion in 1.0 M HCl at 298 K. The corrosion rate is calculated using equation (1). Moreover, the surface of the E24 carbon steel chosen is a rectangular surface of 1 cm2. The latter was prepared before each test, by polishing with sandpaper of grade: 600, 1200 and 1500, they are rinsed with distilled water and then acetone, and dried in air.

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Fig. 1. Semi-developed formula of DGDCBA epoxy polymer.

electrode as against electrode, a saturated calomel reference electrode and E24 carbon steel working electrode. The surface of the E24 carbon steel chosen is 1 cm2. These three electrodes are immersed in a 100 ml container in which are arranged well-spaced orifices of diameters and spacings allowing the introduction of these electrodes and also makes it possible to receive stirring systems, temperature control, aeration and deaeration. Stationary electrochemical measurements were performed in potentiodynamic mode using a potentiostat/galvanostat SP-200 Biologic Science Instruments. The working electrode is previously immersed in the free corrosion potential for 30 min. The scanning speed is 0.5 mV/ s. The determination of the electrochemical parameters (icorr, Ecorr, βa and βc) from the polarization curves is done using a nonlinear regression by the Ec-Lab software. Thus, the inhibitory efficiency is calculated according to equation (4).

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(1)

(5)

and Rct show the charge transfer resistances without and with different concentrations of the DGDCBA inhibitor epoxy polymer, respectively.

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With m1 is the mass of the substrate before the corrosion, m2 the mass of the substrate after the corrosion, S the total surface of the substrate, t the corrosion time and Cr the corrosion rate. The corrosion inhibition efficiency is determined from measurements of the corrosion rate in the absence and in the presence of different concentrations of the DGDCBA inhibitor according to equation (2) [15,16].

2.6. Quantum chemistry descriptors

(2)

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With and Cr show the corrosion rates of the E24 carbon steel without and with different concentrations, respectively. The degree of surface coverage (Φ) was evaluated using equation (3). (3)

2.5. Electrochemical cell

The electrochemical measurements were obtained by means of an assembly of the electrochemical cell with three electrodes: a platinum

We analyzed the relation between the quantum chemistry descriptors of the S, S′-diglycidyl O, O′- dicarbonodithioate of bisphenol A (DGDCBA) epoxy polymer studied and the experimental results. These descriptors were calculated by the density functional theory (DFT) method with 6–31 G (d,p) basis sets was carried out in the aqueous phase [17,18]. All these calculations were made by the Gaussian (09W) software. Molecular orbitals EHOMO and ELUMO present the energy of the highest occupied molecular orbital and the energy of the lowest unoccupied molecular orbital, respectively [19]. The gap energy is the difference between the energy of the lowest unoccupied molecular orbital (ELUMO) and the energy of the highest occupied molecular orbital (EHOMO) (equation (6)). Then, the hardness (η) and softness (σ) are global chemical descriptors measuring the molecular stability and reactivity are calculated using equations (7) and (8) [20].

Table 1 Chemical compositions present in the E24 carbon steel. Elements

Carbon

Manganese

Phosphorus

Sulfur

Iron

Other

Percentage

0,190

0075

0,045

0045

0,625

0020


Inhibitor

Concentration (M)

Cr (mg cm2 h1)

EI (%)

Φ

Blank DGDCBA

1.0 10−6 10−5 10−4 10−3

1.53 0.245 0.214 0.168 0.137

– 84 86 89 91

– 0.84 0.86 0.89 0.91

(8)

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The number of electrons transferred (ΔN) from the epoxy polymer to the surface of metal was determined according to Pearson theory by using to equation (9) [21]. (9)

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where χFe and χint present the absolute electronegativity of the iron and the DGDCBA epoxy polymer, respectively. ηFe and ηint present the absolute hardness of the iron and the DGDCBA, respectively. 2.7. Molecular dynamics simulations

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Table 2 Corrosion rate, inhibition efficiency and surface coverage without and with different concentrations of the DGDCBA at 298 K.

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(6)

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Fig. 2. Corrosion rate and surface coverage according to different concentrations at 298 K.

concentration, indicating that the DGDCBA epoxy polymer is adsorbed on the surface of the E24 carbon steel. Moreover, this inhibitor DGDCBA adsorbs more on the surface of the E24 carbon steel and covers the active sites which cause the formation of a protective layer which reduces the reactivity of the metal. Finally, the adsorption of this epoxy polymer studied can be attributed to the heteroatoms of oxygen and sulfur which provide their electronic pairs to the metal by forming bonds with the latter [25].

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Molecular dynamic simulation of the DGDCBA epoxy polymer tested was performed in a simulation box with periodic boundary conditions using materials studio version 6.0 [22]. The first step was to import the iron crystal, its cleaved surface along the plane (110) with a thickness of 15.5 Å. Their mesh parameters a = b = 40.537 Å and c = 4.753 Å. Furthermore, the surface of the Fe (110) was relaxed by minimizing its energy using an intelligent minimization method. The second step was to create a supercell (10 × 10) to increase the surface area of Fe (110) and change its periodicity. Moreover, the optimized structure of the DGDCBA epoxy polymer was used in this simulation. The third step, is a supercell having a size of a = b = 40.537 Å, c = 4.753 Å, contains 50 molecules of water (H2O) and polymer tested was created. Finally, the layer builder was used to create the entire model with a size of a = b = 40.537 Å and c = 4.753 Å. The molecular dynamic simulation was performed in a simulation box (40.537 × 40.537 × 4.753 Å3) using the discovery module with a time step of 1 fs and a simulation time of 500 ps done at 298 K, set NVT and force field COMPASS [23,24]. 3. Results and discussion

3.1. Gravimetric measurement

3.1.1. Effect of concentration The corrosion rate, the inhibition efficiency and the surface coverage in the absence and in the presence of different concentrations of the DGDCBA epoxy polymer after 6 h of immersion of the E24 carbon steel in 1.0 M HCl at 298 K are mentioned in Table 2. Fig. 2 present the variation of the corrosion rate and the surface coverage in the absence and in the presence of different concentrations of the DGDCBA epoxy polymer of the E24 carbon steel in 1.0 M HCl at 298 K. From this figure, we observed that the inhibition power of the DGDCBA epoxy polymer increases when the concentration of the inhibitor increases in the corrosive solution. Furthermore, this power affected a maximum value of the order of 0.91 for the 10−3 M concentration. Thus, the corrosion rate decreases with

3.1.2. Effect of temperature The stability of a corrosion inhibitor in an aggressive environment and at temperatures data usage is very important for its application. Furthermore, increasing the temperature would promote desorption of the inhibitor DGDCBA and rapid dissolution of the epoxy polymer studied, thereby weakening the corrosion resistance of the E24 carbon steel. Moreover, we examined the influence of temperature on the evolution of the corrosion rate and on the inhibition efficiency in a temperature range of 25 °C–55 °C (Table 3). Finally, Fig. 3 shows the corrosion rate and the inhibition efficiency for the 10−3 M of the DGDCBA inhibitor in the presence of different temperatures. From this figure, we remarked that the corrosion rate increases with the in

Table 3 Corrosion rate and inhibition efficiency without and with 10−3 M of the DGDCBA inhibitor epoxy polymer at different temperatures. Inhibitor

Temperature (K)

Cr (mg cm−2 h−1)

EI (%)

θ

Blank

298 308 318 328 298 308 318 328

1.53 2.94 5.86 9.76 0.137 0.441 1.523 3.220

– – – – 91 85 74 67

– – – – 0.91 0.85 0.74 0.67

DGDCBA


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Fig. 3. Corrosion rate and inhibition efficiency for the 10−3 M at different temperatures.

crease of temperature, contrariwise the inhibition efficiency decreases with the increase of the latter [25].

Fig. 4. Ln (Cr) according to fraction 1000/T without and with 10−3 M.

entropy

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3.1.3. Thermodynamic parameters The Arrhenius-type dependence observed between the corrosion rate and the temperature, allowed us to calculate the value of the activation energy at different temperatures, in the absence and in the presence of the inhibitor epoxy polymer, according to equation (10) [26]. The standard activation enthalpy and the standard activation are determined according to equations (11) and (12) [27].

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(10)

(11)

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(12)

where Cr is the corrosion rate, Ea is the activation energy, R is the constant of the perfect gas, T is the temperature, h is the Planck constant and N is the Avogadro number. Fig. 4 present the variation in the logarithm of the corrosion rate of the E24 carbon steel in 1.0 M HCl in the absence and in the presence of the inhibitor epoxy polymer as a function of fraction 1000/T for the 10−3 M concentration. Fig. 5 present the variation of Ln (Cr/T) as a function of the fraction 1000/T. From this figure we obtained straight lines with a slope equal to (/1000R) and extrapolating these lines gives the values of the (Ln (R/Nh) +

/R).

From Table 4, the value of the activation energy obtained in the presence of the 10−3 M of the DGDCBA epoxy polymer is greater than that of the 1.0 M HCl (without DGDCBA). This behavior is related to the phenomenon of physisorption of inhibitor on the surface of the metal substrate [28,29]. The positive sign of these standards

Fig. 5. Ln (Cr/T) according to fraction 1000/T without and with 10−3 M. Table 4 Thermodynamic parameters without and with 10−3 of the epoxy polymer.

Inhibitor Blank 10−3 M for DGDCBA

(J mol−1

(kJ

Ea (kJ mol−1)

mol )

K )

50.82 87.13

48.22 84.55

−79.56 22.78

−1

−1

activations enthalpies reflects the endothermic nature of the dissolution process of E24 carbon steel [30,31]. The large negative value of standard activation entropy in the presence of HCl (without inhibitor) indicates that the activation state is more organized than the resting-state. In other words, the corrosion reaction occurs on the surface of the E24 carbon steel. However, the result in the presence of 10−3 M of the DGDCBA shows a positive value of standard activation entropy, indicating an entropic activation state. This result shows that the


3.3. Electrochemical impedance spectroscopy

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Fig. 6 (a, b) shows the cathodic and anodic polarization curves of the E24 carbon steel traced after 1 h of immersion in 1.0 M HCl, in the absence and in the presence of different concentrations of the DGDCBA epoxy polymer studied as inhibitor. This shows that the addition of the inhibitor results in a displacement of the free potential to higher values and a decrease in the current density in the cathodic and anodic domains [33,34]. However, the inhibition efficiency of the corrosion current is a maximum at 10−3 M of the inhibitor tested. The values of the electrochemical parameters are grouped in Table 5. From the analysis of the parameters regrouped in Table 5, we observed that increasing of the inhibitor concentration decreases the corrosion current density to lower values. Thus, the inhibition efficiency increases with the addition of the DGDCBA epoxy polymer inhibitor concentration. The different concentrations of the polymer studied reduce the values of the slope of Tafel, compared with that obtained for the acid alone. Furthermore, this phenomenon suggests that the addition of the DGDCBA inhibitor to the electrolyte has an effect on the mechanism of hydrogen reduction [35,36]. Moreover, the inhibition efficiency affected 98% at 10−3 M for DGDCBA, because the benzene rings are rich in electrons which vent to the increase of the electron density of these. This facilitates its adsorption on the E24 carbon steel and consequently the improvement of inhibition efficiency [37,38]. Finally, these results were confirmed by the plot of the electrochemical impedance diagrams.

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3.2. Polarization curves

bition efficiency increases caused by adsorption of the epoxy polymer on the surface of the E24 carbon steel [39,40]. Then, the planar geometry of the DGDCBA promotes adsorption on the surface as a protective layer. Additionally, the double-layer capacities are best described by a charge-transfer function with constant phase elements (CPE) to obtain a more adjustment accurate of the experimental data set. Finally, the electrochemical parameters are given in Table 6. The analysis of the Table 6 shows that the charge transfer resistance value Rct increases with increasing concentration of the epoxy polymer and reaches a maximum value of 944.4 Ω cm2 at 10−3 M of the DGDCBA inhibitor. Furthermore, this increase in charge transfer resistance leads to metal protection and decreases the numbers of active sites that are created by adsorption against chloride ions on the E24 carbon steel surface that is positively charged [41]. Moreover, the values of the double layer capacity Cdl calculated in the presence of the DGDCBA epoxy polymer inhibitor are lower in comparison with the witness value. This can be attributed to the adsorption of the DGDCBA used on the surface of the E24 carbon steel leading to the formation of a protective layer [42]. For example, the value of the double layer capacity is 114 μF cm−2 in the witness and 85.42 μF cm−2 in the presence of the epoxy polymer inhibitor at 10−3 M of the concentration. In addition, this behavior means that the charge rate at the metal-solution interface is greatly reduced and that this inhibitor is well adsorbed on the surface of the electrode. Finally, the inhibition efficiency of the DGDCBA increases with the increase of the inhibitor studied and reaches at 96% for the 10−3 M concentration. The Bode diagrams of 1.0 M HCl of the E24 carbon steel in the absence and in the presence of the epoxy polymer at different concentrations are illustrated in Fig. 8. From this figure, we observed increasing phase angles with increasing of the DGDCBA inhibitor. This increase in phase angles confirms higher protection by increasing the epoxy polymer concentration. From the Bode diagram we have found that there are three frequency domains: low frequencies, high frequencies and intermediate frequencies. Furthermore, for low frequencies increase in absolute values of impedance confirm the greatest protection with increase the concentration of the DGDCBA on the E24 carbon steel. Moreover, at high frequency, the values of log |Z| and the phase angle are close to zero. This indicates that the behavior of the electrode that corresponds to the resistance of the solution (Rs). Then, for intermediate frequencies a linear relation between log |Z| as a function of log (frequency) with a slope close to −1 and the phase angle is close to 72° has been observed. This indicates that the capacitive behavior at intermediate frequencies [43,44].

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DGDCBA is preventing the corrosion of the E24 carbon steel surface as a protective layer [32].

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The corrosion behavior of the E24 carbon steel in 1.0 M HCl in the absence and in the presence of the DGDCBA is also examined by the EIS technique after 1 h immersion at 298 K. The Nyquist diagrams obtained are given in Fig. 7. The impedance spectra have a single capacitive loop whose size increases with the DGDCBA inhibitor concentration, this loop means that a phenomenon occurs. Furthermore, this phenomenon indicates that the corrosion is controlled by a process of charge transfer, which acts on the variation of the double layer capacity. Moreover, the addition of the DGDCBA inhibitor to the corrosive solution leads to the increase of the size of the capacitive loops as the epoxy polymer concentration increases in comparison with the witness impedance diagram. As a consequence, the inhi

Fig. 6. Cathodic (a) and anodic (b) polarization curves of the E24 carbon steel in 1.0 M HCl in the absence and in the presence of different concentrations of the DGDCBA inhibitor.


protective film over time up to 6 h. Therefore, the protective properties of the film formed on the surface of the E24 carbon steel are enhanced for the immersion time. In addition, the developed passive film is likely to dissolve in a high immersion time [45].

Table 5 Electrochemical parameters for different concentrations of the DGDCBA inhibitor.

1.0 10−6 10−5 10−4 10−3

457.7 461 557 582 561

icorr μA cm−2

550 114 93 21.8 9.26

Tafel slopes (mV dec−1) - βc

βa

114 48 55 63 49

102 46 53 57 80

EI (%)

3.5. Adsorption isotherm – 79 83 96 98

The corrosion inhibitor of the E24 carbon steel by the DGDCBA epoxy polymer is explained by their adsorption on the surface of this metal. There are two main types of adsorption: adsorption physisorption and chemisorption. It depends on the charge of the metal, the chemical structure of the epoxy polymer studied and the type of the electrolyte. Furthermore, the physical adsorption requires the presence of an electrically charged metal surface and charged species in the solution. Moreover, the chemical adsorption involves an electron transfer between the inhibition epoxy polymer and the unsaturated orbitals of the metal surface making it possible to form coordinate bonds and covalent bonds. Then, the adsorption phenomenon of the DGDCBA epoxy polymer on the metal surface follows the Langmuir adsorption isotherm. Finally, the recovery rate of the metal surface is given by equation (13) [46,47].

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Blank DGDCBA

- Ecorr mV

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Inhibitor

Concentration M

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(13)

With K denotes the equilibrium constant of the adsorption process and C is the concentration of the epoxy polymer inhibitor. The rearrangement of the equation (13) gives the relation 14. The value of the adsorption coefficient (Kads) is related to the standard free energy of adsorption by equation (15).

Fig. 7. Nyquist impedance diagram for the E24 carbon steel in 1.0 M HCl in the absence and in the presence of different DGDCBA concentrations at 298 K.

(14)

(15)

where R is the constant of perfect gases (J mol−1 K−1) and T is the temperature (K), the value 55.5 is the concentration of water in solution (mol L−1). The variation of C/θ as a function of the concentration the DGDCBA epoxy polymer inhibitor at 298 K is presented in Fig. 11. The adsorption isotherm value is regrouped in Table 7. The value of the variation of free energy is negative, which indicates the stability of the adsorbed layer on the metal surface. Furthermore, the calculated value of the DGDCBA epoxy polymer inhibitor in an acid medium is greater than - 40 kJ mol−1. This involves electron transfer between the epoxy polymer inhibitor and the

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3.4. Immersion time

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The curves presented in the Bode and Nyquist diagrams show the existence of an equivalent electrical circuit that contains a constant phase element on the metal/solution interface in all the frequencies examined (Fig. 9). The equivalent electrical circuit used is composed of the solution resistance (Rs), the charge transfer resistor (Rct) and the constant phase element (CPE).

Concentrations M

Rs Ω cm2

Q μF

ndl

Cdl μF cm−2

Rct Ω cm2

EI (%)

1.0 10−6 10−5 10−4 10−3

1.22 1.426 2.681 2.817 5.298

308 128.5 108 28.37 24.77

0.823 0.837 0.810 0.860 0.895

114 85.42 57.11 15.35 15.31

40 599.1 642.2 804.6 944.4

– 93 94 95 96

Electrochemical impedance spectroscopy is a useful technique for testing the long-time immersion inhibition process. These experiments are conducted to observe the evolution of the phenomena that occur at the interface of the metal substrate at different immersion times from ½ h to 48 h. Fig. 10 shows the evolution of the impedance diagrams at different immersion times in 1.0 M HCl in 10−3 M of the DGDCBA inhibitor. From the results of this figure, the charge transfer resistance increases with increasing immersion time after 6 h and decreases after 24 h of immersion time. Furthermore, this behavior indicates that this is attributed to an increase in the strength of the

Table 6 Parameters of EIS and inhibition efficiency of the E24 carbon steel in 1.0 M HCl without and with different DGDCBA concentrations. Inhibitor Blank DGDCBA

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Fig. 8. Bode diagram for the metal/DGDCBA/HCl.

Fig. 11. Langmuir adsorption isotherm of the DGDCBA epoxy polymer inhibitor on the surface of the E24 carbon steel at 298 K.

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Table 7 Adsorption parameters of the DGDCBA epoxy polymer inhibitor. Inhibitor

Kads

R2

DGDCBA

2261062

1

(KJ mol-1)

- 46.201

3.6. Quantum chemistry descriptors calculation

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Fig. 9. Equivalent electrical circuit of the metal/DGDCBA/HCl.

To confirm the sites of adhesion of the DGDCBA epoxy polymer to the substrate, we proceeded to the quantum chemistry calculation using the Gaussain software 09W [49,50]. Then, the different quantum descriptors were performed by the density functional theory (DFT) method on the 6-31G (d,p) basis sets. The optimized geometric structure and density distribution electrons of EHOMO and ELUMO are illustrated in Fig. 12. The electron density (HOMO) is located on the aromatic ring surface, on the methylene group bonded to the quaternary carbon and on the epoxy group of the difunctional DGDCBA epoxy polymer, respectively (Fig. 12). Furthermore, the electron density (LUMO) is located on the epoxy group and on the C S group linked to the epoxy, respectively. Then, the Table 8 groups the different quantum chemistry descriptors calculation of the DGDCBA epoxy polymer. The energy of the highest occupied molecular orbital (EHOMO) shows the ability of the DGDCBA epoxy polymer to donate electrons. Moreover, the higher energy value of the HOMO orbital facilitates the tendency of the epoxy polymer to give up electrons to electron-accepting species having unoccupied molecular orbitals whose energy level is low. Then, the energy of lower unoccupied molecular orbital (ELUMO) is related to the ability of the epoxy polymer to accept electrons, a low value of energy LUMO means that the DGDCBA epoxy polymer accepts electrons [51]. In addition, the adsorption of the DGDCBA epoxy polymer inhibitor on the surface of the substrate increases when the gap energy is lower [52]. The highest hardness value (1.396 eV) and the lowest softness value (0.716 eV-1) of the DGDCBA epoxy polymer have a very good chemical reactivity with the surface of the E24 carbon steel. The value of the number of electrons transferred (0.891) is less than 3.6 indicates the tendency of the epoxy polymer to give elec

Fig. 10. Impedance spectroscopy obtained after different immersion times in 1.0 M HCl in 10−3 M of the DGDCBA.

metal surface to form a bond. Then, according to the data of the literature, it is a physisorption [48]. Finally, the linear correlation coefficient R2 is equal to 1, which shows that the adsorption on the surface of the steel obeys the Langmuir isotherm.


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Fig. 12. Optimized structure, HOMO and LUMO orbitals of the DGDCBA epoxy polymer. Table 8 Different quantum chemistry descriptors of the DGDCBA epoxy polymer. Quantum descriptors

EHOMO eV

ELUMO eV

ΔE gap eV

η eV

σ eV−1

ΔN eV

Values

−3.026

−0.234

2.792

1.396

0.716

0.891

3.7.1. Mulliken atomic load distribution and dipole moment Fig. 13 shows the dipole moment and the distribution of the Mulliken atomic charges on the atoms of the DGDCBA, respectively. Then, we have observed that the oxygen atoms and some carbon atoms of the epoxy polymer studied have negative charges. Finally, we conclude that these atoms are responsible for a nucleophilic attack towards the surface of the E24 carbon steel.

trons to the surface of the substrate [53]. Then, this result shows that the quality of the protective film is well formed. The latter is in agreement with Lukovit's study [54]. 3.7. Electrostatic potential

The determination of the electrostatic potential is very interesting for the studies of epoxy polymer interactions. Furthermore, the negative regions of electrostatic potential are favorable for electrophilic attack. While, positive regions are more sensitive to nucleophilic attacks [55].

Fig. 13. Mulliken atomic charge distribution of the DGDCBA epoxy polymer with the dipole moment vector.


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3.7.2. Molecular electrostatic potential The representation of the molecular electrostatic potential of the DGDCBA epoxy polymer studied was determined to identify the electron density regions (Fig. 14). This strong electron density is presented by a red color, however the low electron density is presented by a blue color. The electronic density decreases in the following order: red > orange > yellow > green > blue [56,57]. Furthermore, the highest electron density is located on the oxygen atoms. Then, the low electron density is located on the sulfur atom and the some carbon atoms. Fig. 15 shows the contour of the molecular electrostatic potential of the epoxy polymer DGDCBA. In addition, we observed that the surface of the contour of the molecular electrostatic of the epoxy polymer studied present on the surface of two benzene groups. This indicates that these benzene groups are adsorbed plane way on the surface of the metal substrate. 3.8. Molecular dynamics simulations

Fig. 16. Optimization energy of DGDCBA in the neutral forms using DMol3.

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The adsorption of the DGDCBA on the iron surface has been optimized using a molecular dynamics simulation to understand the interactions between the epoxy polymer inhibitions studied and the iron surface. Molecular dynamics simulation can reasonably predict the most favorable configuration at the Fe (110)/DGDCBA/50H2O interface. Furthermore, Fig. 16 shows the energy curve of the DGDCBA epoxy polymer inhibitor in its optimized neutral and isolated forms before being placed on the surface of the metal substrate using the DMol3/GGA/DNP basis sets. According to this figure, the DGDCBA polymer inhibitor has an optimal energy (−2784.186 Ha) [58].

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The study of the fluctuating interaction energies between the DGDCBA epoxy polymer, the metallic surface of Fe (110) and the water molecule was calculated by molecular dynamics simulation, optimizing the whole Fe (110)/DGDCBA/50H2O system. Furthermore, the adsorption energy distribution for the Fe (110)/DGDCBA/50H2O pair in hydrochloric acid as a solution by the adsorption locator model is shown in Fig. 17. The latter shows that the adsorption energy of the epoxy polymer studied has reached a value of −268 kcal/mol. This indicates that the adsorption power on the metal surface is appropriate. Fig. 18 shows the interaction energies fluctuant curves calculated by optimizing the whole Fe (110)/DGDCBA/50H2O system. Moreover, the calculation of the energies namely: the total energy, the average total energy, the van der Waals energy, the electrostatic energy and the intramolecular energy between the DGDCBA epoxy polymer and the surface of the metallic substrate converge in the adsorption process [59]. Molecular dynamics simulation was performed to better understand the interaction between the DGDCBA epoxy polymer and the surface of Fe (110). Then, the simulations were carried out in the system containing 50 molecules of water and one molecule of the DGDCBA. Furthermore, the radial distribution function (RDF) (or pair

Fig. 14. Molecular electrostatic potential of the DGDCBA epoxy polymer.

Fig. 15. Contour of the molecular electrostatic potential of the DGDCBA epoxy polymer.

Fig. 17. Adsorption energy distribution for Fe (110)/DGDCBA/50H2O system using adsorption locator model.


correlation function) g (r) can be obtained after this analysis. The RDF is used as a useful method to estimate the length of the link. The peak occurs from 1 Å up to 3.5 Å, it is an indication of the length of small bonds, which is correlated with chemisorption. While physical interactions are associated with peaks greater than 3.5 Å. Moreover, the RDF of the epoxy polymer atoms shows that the bond length of iron is less than 3.5 Å (Fig. 19) [60]. Finally, the results obtained confirm the greater adsorption capacity of the DGDCBA inhibitor tested and, consequently, the protection of the metal against dissolution, because of their greater ability to give and to accept electrons on the surface of the metal through these active sites. Molecular dynamics simulations are performed to study the adsorption behavior of the DGDCBA epoxy polymer on the Fe (110) surface in solution. Furthermore, the side and top views of stable adsorption configuration of the best low-energy of the DGDCBA adsorbed on the surface of Fe (110) with the presence of the water molecule (Fe (110)/DGDCBA/50H2O) obtained using the adsorption locator module are shown in Fig. 20. Finally, we can conclude that the studied epoxy polymer can be adsorbed plane way on the surface of the Fe (110) and offers a larger surface area to stop the dissolution of the metal surface. The parameters presented in Table 9 include the total energy in Kcal mol−1 of the substrate/adsorbate system. Then, the total energy is defined as the sum of the adsorption energy and the internal energy of the sorbate. Furthermore, the adsorption energy (EAds) of the DGDCBA epoxy polymer on the surface of the Fe (110) in the presence of the water molecule was corrected by the basic superposition error (BSSE). Indeed, the by formula 16.

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Fig. 18. Interaction energies fluctuant curves for Fe (110)/DGDCBA/50H2O system.

The adsorption energy is defined as the algebraic sum of the rigid adsorption energy (R.A.E) and the deformation energy (DE) for the adsorbed components. Furthermore, the rigid adsorption energy therefore reports the energy released (Kcal mol−1) when the DGDCBA epoxy polymer of adsorbate not released before the step of optimizing the geometry, that is adsorbed on the surface of the Fe (110) in presence of 50 molecules of water. Contrariwise, the deformation energy reports the released energy (Kcal mol−1) when the adsorbed epoxy polymer inhibitor is released on the surface of the Fe (110). Then, the Table 9 also gives the desorption energy (dEads/dNi) which reports the energy of the substrate-adsorbate configuration where one

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Fig. 19. Radial distribution function of the DGDCBA on the Fe (110) surface in solution.

(16)

Fig. 20. Side and top views of stable adsorption configuration for Fe (110)/DGDCBA/50H2O system obtained using the adsorption locator module.


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Table 9 Outputs and descriptors using an adsorption locator module for the lowest adsorption configurations for Fe (110)/DGDCBA/50H2O system (all values in Kcal mol−1). ETotal 10+3

EAds

R.A.E 10+3

DE

dEAds/dNi H2O

dEAds/dNi DGDCBA

Fe (110) - 1 Fe (110) - 2 Fe (110) - 3 Fe (110) - 4 Fe (110) - 5 Fe (110) - 6 Fe (110) - 7 Fe (110) - 8 Fe (110) - 9 Fe (110) - 10

−6.25 −6.20 −6.20 −6.20 −6.19 −6.19 −6.19 −6.18 −6.18 −6.17

−6471.63 −6428.81 −6424.97 −6421.35 −6414.06 −6412.20 −6411.85 −6404.10 −6402.06 −6392.02

−6.85 −6.79 −6.78 −6.79 −6.78 −6.79 −6.78 −6.77 −6.76 −6.77

379.204 363.863 358.483 366.398 369.402 378.666 368.394 365.113 360.744 379.531

−12.102 −11.906 −13.398 −11.042 −12.188 −10.175 −9.718 −10.317 −12.025 −10.273

−240.735 −266.041 −265.294 −223.815 −180.856 −184.083 −170.190 −262.269 −251.483 −166.014

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In this work, we investigated the performances of the corrosion inhibition of the difunctional S, S′-diglycidyl O, O′- dicarbonodithioate of bisphenol A (DGDCBA) epoxy polymer in the hydrochloric acid of the E24 carbon steel in the presence of different concentrations (10−3 to 10−6 M). Furthermore, the experimental results we obtained in this study concerning the inhibition of the metal substrate in the presence of different concentrations are very interesting. Then, the phenomenon of adsorption of the DGDCBA epoxy polymer on the metal surface is physisorption. In additionally, the potentiodynamic polarization shows that a decrease in the corrosion current density in the cathodic range with an inhibitory efficiency is of the order of 98% at the concentration 10−3 M of the DGDCBA. However, the electrochemical impedance spectroscopy has a better inhibitory efficiency of 96% for the concentration 10−3 M of the studied epoxy polymer. Moreover, the prediction of the quantum chemistry descriptors, namely: the energy of the highest occupied molecular orbital (EHOMO), the energy of the lowest unoccupied molecular orbital (ELUMO), the gap energy (ΔE), the chemical hardness (σ), the chemical sweetness (ƞ), and the number of electrons transferred (ΔN) confirm the adhesion sites of the difunctional DGDCBA epoxy polymer. Finally, the theoretical (density functional theory and molecular dynamics) and experimental results are in good agreement.

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I would like to thank Professor Ahmed Elharfi, responsible for the Team of Polymers and Organic Chemistry, Department of Chemistry, Faculty of Science, Ibn Tofail University, Professor Najat HAJJAJI, responsible for the Team of Corrosion, Protection and Environment, Department of Chemistry, Faculty of Science, Ibn Tofail University and Salma Kantouch who collaborated to the success of this paper. References

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of the adsorbed components has been removed. In addition, the negative adsorption energy values mean that the adsorption of the epoxy polymer studied could occur spontaneously [61]. The high adsorption energy (−6471.63 kcal mol−1) of the DGDCBA epoxy polymer indicates that the adsorption of the inhibitor on the surface of Fe (110) is adsorbed by involving the displacement of H2O molecules on the iron surface and sharing of electrons between the heteroatoms in the polymer inhibitor and the surface of Fe (110). This gives the possibility of bond formation (Π-Π) resulting from the overlap of electrons (3d) of the iron atom and free doublet of sulfur and oxygen atoms. The high values of the adsorption energies of DGDCBA epoxy polymer are due to the flatness and the presence of a pair of electrons on the heteroatoms ( S and O ), favoring a greater adsorption on the surface of the Fe (110). Then, the protection of the metal surface is obtained by a forte adsorption of the macromolecular matrix and avoiding that it is easily corroded. Thus, the Table 9 also shows (dEAds/dNi) which reports the configuration energy of iron component where one of the inhibitor molecules was removed [62,63].

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