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

Accepted Manuscript 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

Rachid Hsissou, Said Abbout, Avni Berisha, Mohamed Berradi, Mohammed Assouag, Najat Hajjaji, Ahmed Elharfi PII:

S0022-2860(18)31451-0

DOI:

10.1016/j.molstruc.2018.12.030

Reference:

MOLSTR 25967

To appear in:

Journal of Molecular Structure

Received Date:

28 September 2018

Accepted Date:

07 December 2018

Please cite this article as: Rachid Hsissou, Said Abbout, Avni Berisha, Mohamed Berradi, Mohammed Assouag, Najat Hajjaji, Ahmed Elharfi, 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, Journal of Molecular Structure (2018), doi: 10.1016/j. molstruc.2018.12.030

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ACCEPTED MANUSCRIPT 1

Experimental, DFT and molecular dynamics simulation on the inhibition

2

performance of the DGDCBA epoxy polymer against the corrosion of the E24

3

carbon steel in 1.0 M HCl solution

4 5

Rachid Hsissou1*, Said Abbout2, Avni Berisha3, Mohamed Berradi1, Mohammed Assouag4, Najat Hajjaji2, Ahmed Elharfi1

6 7 8 9 10 11 12 13 14 15

1 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. 2 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. 3 Department of Chemistry, Faculty of Natural and Mathematics Science, University of Prishtina, 10000 Prishtina, Kosovo. 4 Team of Materials, Metallurgy and Process Engineering, ENSAM, University Moulay Ismail, B.P. 15290, Al Mansour, Maknes, Morocco.

16 17 18 19 20

Corresponding author (Rachid HSISSOU) E-mail: [email protected] /[email protected]

21

Abstract

22

The inhibition performances of the epoxy polymer S, S’-diglycidyl O, O'- dicarbonodithioate

23

of bisphenol A (DGDCBA) on the corrosion of the E24 carbon steel in 1.0 M HCl in the

24

absence and in the presence of different concentrations (10-3 to 10-6 M of DGDCBA). Then,

25

the results obtained by using gravimetric measurements and electrochemical methods show

26

that the tested DGDCBA epoxy polymer is a very effective inhibitor to the inhibition of

27

corrosion. Furthermore, the inhibition efficiency of the epoxy polymer increases with

28

increasing concentration and reaches a maximum value of 91%, 98% and 96% for the

29

concentration of 10-3 M of the DGDCBA for gravimetric and electrochemical measurements

30

(stationary and transient methods), respectively. Moreover, this polymer has characteristics

31

which facilitate their adsorption on the surface of the metal substrate, in particular the

32

existence of aromatic rings and heteroatoms (O and S). In addition, we proceeded to compute

33

quantum chemical descriptors using the density functional theory (DFT) method with 6-31 G

34

(d,p) basis sets. Finally, the molecular dynamics simulation confirms the results obtained by

35

the DFT and the experimental data.

36

Keywords: Inhibition, polymer, DGDCBA, electrochemical, DFT, molecular dynamic.

To appear in: Received Date: Revised Date: Accepted Date:

Journal of Molecular Structure XX 2018 XX 2018 XX 2018

1

ACCEPTED MANUSCRIPT 1

1. Introduction

2

Currently the problem in the industrial process is corrosion of metals leading to increased

3

manufacturing and production costs. Metal materials are exposed to conditions that facilitate

4

the process of corrosion. In industrial fittings, steel is widely used as building materials

5

because its low costs [1-4]. Hydrochloric acid is the most used in the industry, for scouring,

6

cleaning and elimination of localized deposits. The aggressiveness of this acid solution leads

7

to the use of corrosion inhibitor to reduce the rate of corrosion of metals [5]. In recent years, a

8

very important effort has been made to synthesize new epoxy polymers used as highly

9

effective corrosion inhibitors [6]. These polymers are applied for the protection of the metal

10

surface against the corrosion in acid solutions. Furthermore, epoxy polymers containing

11

aromatic rings, heteroatoms (O and S) with single electron pairs and conjugated bonds are

12

generally considered to be corrosion inhibitors [7-8]. Moreover, the adsorption of the polymer

13

inhibitors depends essentially the physico-chemical properties of the epoxy polymer linked to

14

its functional group [9-10]. When the number of double bonds increases in the

15

macromolecular structure and the formation of the protective film is more rigid [11]. In

16

additionally, the goal of our work is to investigate the corrosion inhibition of the E24 carbon

17

steel in 1.0 M HCl by the DGDCBA as new epoxy polymer using gravimetric and

18

electrochemical methods. Then, the density functional theory (DFT) approach was used to

19

study the correlation between the mechanism of corrosion inhibition and the structure of the

20

DGDCBA epoxy polymer. Finally, we proceeded to molecular dynamics simulation, using

21

Materials Studio [12-13].

22

2. Material and methods

23

2.1. Inhibitor tested

24

The inhibitor used in this work is named the S, S’-diglycidyl O, O'- dicarbonodithioate of

25

bisphenol A (DGDCBA) epoxy polymer, which has been synthesized in our laboratory

26

(LAPPE) [14]. Its semi-developed structure is shown in Figure 1. H2 C S

27 28

O

CH3 C S

O

O CH3

C S

S

H2 C

O

Figure 1: Semi-developed formula of DGDCBA epoxy polymer.

29

2

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2.2. Metal used

2

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

3

Table 1.

4

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

Carbon 0,190

Manganese 0,075

Phosphorus 0,045

Sulfur 0,045

Iron 0,625

Other 0,020

5

2.3. Corrosive test

6

The corrosive medium is a 1.0 M hydrochloric acid solution, prepared from the commercial

7

solution of hydrochloric acid (37%) using distilled water. The concentrations used for the

8

inhibitor range from 10-3 to 10-6 M. Furthermore, these concentrations were determined after

9

studying the solubility of the DGDCBA inhibitor in the corrosive solution.

10

2.4. Gravimetric test

11

Measurement of weight loss allowed us to calculate the corrosion rate (Cr) without and with

12

different concentrations of the DGDCBA inhibitor epoxy polymer after 6 hours of immersion

13

in 1.0 M HCl at 298 K. The corrosion rate is calculated using equation 1. Moreover, the

14

surface of the E24 carbon steel chosen is a rectangular surface of 1 cm2. The latter was

15

prepared before each test, by polishing with sandpaper of grade: 600, 1200 and 1500, they are

16

rinsed with distilled water and then acetone, and dried in air.

18

(m1 -m 2 ) (1) S.t With m1 is the mass of the substrate before the corrosion, m2 the mass of the substrate after

19

the corrosion, S the total surface of the substrate, t the corrosion time and Cr the corrosion

20

rate.

21

The corrosion inhibition efficiency is determined from measurements of the corrosion rate in

22

the absence and in the presence of different concentrations of the DGDCBA inhibitor

23

according to equation 2 [15-16].

17

Cr =

IE(%) =(1-

24

Cr )×100 C0r

(2)

25

With C0r and Cr show the corrosion rates of the E24 carbon steel without and with different

26

concentrations, respectively.

27

The degree of surface coverage (Φ) was evaluated using equation 3. C Φ =(1- 0r ) (3) Cr

28

3

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2.5. Electrochemical cell

2

The electrochemical measurements were obtained by means of an assembly of the

3

electrochemical cell with three electrodes: a platinum electrode as against electrode, a

4

saturated calomel reference electrode and E24 carbon steel working electrode. The surface of

5

the E24 carbon steel chosen is 1cm2.

6

These three electrodes are immersed in a 100 ml container in which are arranged well-spaced

7

orifices of diameters and spacings allowing the introduction of these electrodes and also

8

makes it possible to receive stirring systems, temperature control, aeration and deaeration.

9

Stationary electrochemical measurements were performed in potentiodynamic mode using a

10

potentiostat/galvanostat SP-200 Biologic Science Instruments. The working electrode is

11

previously immersed in the free corrosion potential for 30 minutes. The scanning speed is

12

0.5mV/s. The determination of the electrochemical parameters (icorr, Ecorr, βa and βc) from the

13

polarization curves is done using a nonlinear regression by the Ec-Lab software. Thus, the

14

inhibitory efficiency is calculated according to equation 4.

15

 i 0corr - i corr IE% =  0  i corr

  ×100 

(4)

16

0 Such as icorr and i corr present the corrosion current densities (A.cm-2) in the absence and in

17

the presence of different concentrations of the DGDCBA inhibitor tested, respectively.

18

Transient electrochemical measurements were evaluated by the same apparatus with signal

19

amplitude (10 mV). The frequency domain explored varies from 100 KHz to 10 mHz. Finally,

20

the inhibitory efficiency is determined using equation 5.

21

 R -R 0 IE%=  ct ct  R ct

  ×100 

(5)

22

R 0ct and R ct show the charge transfer resistances without and with different concentrations of

23

the DGDCBA inhibitor epoxy polymer, respectively.

24

2.6. Quantum chemistry descriptors

25

We analyzed the relation between the quantum chemistry descriptors of the S, S’-diglycidyl

26

O, O'- dicarbonodithioate of bisphenol A (DGDCBA) epoxy polymer studied and the

27

experimental results. These descriptors were calculated by the density functional theory

28

(DFT) method with 6-31 G (d,p) basis sets was carried out in the aqueous phase [17-18]. All

29

these calculations were made by the Gaussian (09W) software.

4

ACCEPTED MANUSCRIPT 1

Molecular orbitals EHOMO and ELUMO present the energy of the highest occupied molecular

2

orbital and the energy of the lowest unoccupied molecular orbital, respectively [19].

3

The gap energy is the difference between the energy of the lowest unoccupied molecular

4

orbital (ELUMO) and the energy of the highest occupied molecular orbital (EHOMO) (equation

5

6). Then, the hardness (η) and softness (σ) are global chemical descriptors measuring the

6

molecular stability and reactivity are calculated using equations 7 and 8 [20].

7

ΔE = E LUMO - E HOMO

8

η=

E - E HOMO ΔE = LUMO 2 2

(7)

9

σ=

1 2 =η E HOMO - E LUMO

(8)

(6)

10

The number of electrons transferred (ΔN) from the epoxy polymer to the surface of metal was

11

determined according to Pearson theory by using to equation 9 [21].

ΔN =

12

χ Fe - χ inh 2  ηFe + ηinh 

(9)

13

Where χ Fe and χ int present the absolute electronegativity of the iron and the DGDCBA epoxy

14

polymer, respectively.

15

ηFe and ηint present the absolute hardness of the iron and the DGDCBA, respectively.

16

2.7. Molecular dynamics simulations

17

Molecular dynamic simulation of the DGDCBA epoxy polymer tested was performed in a

18

simulation box with periodic boundary conditions using materials studio version 6.0 [22]. The

19

first step was to import the iron crystal, its cleaved surface along the plane (110) with a

20

thickness of 15.5 Å. Their mesh parameters a=b=40.537 Å and c=4.753 Å. Furthermore, the

21

surface of the Fe (110) was relaxed by minimizing its energy using an intelligent

22

minimization method. The second step was to create a supercell (10×10) to increase the

23

surface area of Fe (110) and change its periodicity. Moreover, the optimized structure of the

24

DGDCBA epoxy polymer was used in this simulation. The third step, is a supercell having a

25

size of a=b= 40.537 Å, c=4.753 Å, contains 50 molecules of water (H2O) and polymer tested

26

was created. Finally, the layer builder was used to create the entire model with a size of

27

a=b=40.537 Å and c=4.753 Å. The molecular dynamic simulation was performed in a

28

simulation box (40.537x40.537x4.753 Å3) using the discovery module with a time step of 1 fs

29

and a simulation time of 500 ps done at 298 K, set NVT and force field COMPASS [23-24].

5

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3. Results and discussion

2

3.1. Gravimetric measurement

3

3.1.1. Effect of concentration

4

The corrosion rate, the inhibition efficiency and the surface coverage in the absence and in the

5

presence of different concentrations of the DGDCBA epoxy polymer after 6 hours of

6

immersion of the E24 carbon steel in 1.0 M HCl at 298 K are mentioned in Table 2.

7

Table 2. Corrosion rate, inhibition efficiency and surface coverage without and with different

8

concentrations of the DGDCBA at 298 K. Inhibitor Blank DGDCBA

Concentration (M) 1.0 10-6 10-5 10-4 10-3

Cr (mg cm2 h1) 1.53 0.245 0.214 0.168 0.137

EI (%) 84 86 89 91

Φ 0.84 0.86 0.89 0.91

9

Figure 2 present the variation of the corrosion rate and the surface coverage in the absence

10

and in the presence of different concentrations of the DGDCBA epoxy polymer of the E24

11

carbon steel in 1.0 M HCl at 298K. From this figure, we observed that the inhibition power of

12

the DGDCBA epoxy polymer increases when the concentration of the inhibitor increases in

13

the corrosive solution. Furthermore, this power affected a maximum value of the order of 0.91

14

for the 10-3 M concentration. Thus, the corrosion rate decreases with concentration, indicating

15

that the DGDCBA epoxy polymer is adsorbed on the surface of the E24 carbon steel.

16

Moreover, this inhibitor DGDCBA adsorbs more on the surface of the E24 carbon steel and

17

covers the active sites which cause the formation of a protective layer which reduces the

18

reactivity of the metal. Finally, the adsorption of this epoxy polymer studied can be attributed

19

to the heteroatoms of oxygen and sulfur which provide their electronic pairs to the metal by

20

forming bonds with the latter [25].

6

ACCEPTED MANUSCRIPT 0,26

0,92 0,91

0,24

0,90 -1 -2

0,89

0,20

0,88

0,18

0,87 0,86

0,16

0,85 0,14

0,84

0,12

0,83

0,0000

0,0002

0,0004

0,0006

0,0008

0,0010

C (mole/L)

1 2



Cr (mg cm h )

0,22

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

3

3.1.2. Effect of temperature

4

The stability of a corrosion inhibitor in an aggressive environment and at temperatures data

5

usage is very important for its application. Furthermore, increasing the temperature would

6

promote desorption of the inhibitor DGDCBA and rapid dissolution of the epoxy polymer

7

studied, thereby weakening the corrosion resistance of the E24 carbon steel. Moreover, we

8

examined the influence of temperature on the evolution of the corrosion rate and on the

9

inhibition efficiency in a temperature range of 25 °C to 55 °C (Table 3). Finally, Figure 3

10

shows the corrosion rate and the inhibition efficiency for the 10-3 M of the DGDCBA

11

inhibitor in the presence of different temperatures. From this figure, we remarked that the

12

corrosion rate increases with the increase of temperature, contrariwise the inhibition

13

efficiency decreases with the increase of the latter [25].

14

Table 3: Corrosion rate and inhibition efficiency without and with 10-3 M of the DGDCBA

15

inhibitor epoxy polymer at different temperatures. Inhibitor

Blank

DGDCBA

Temperature (K) 298 308 318 328 298 308 318 328

Cr (mg cm-2 h-1) 1.53 2.94 5.86 9.76 0.137 0.441 1.523 3.220 7

EI (%) 91 85 74 67

θ 0.91 0.85 0.74 0.67

ACCEPTED MANUSCRIPT 5

95 90

-1 -2

85 3 80 2 75 1

70

0 295

65 300

305

310

315

320

325

330

Temperature (K)

1 2

%

Cr (mg cm h )

4

Figure 3: Corrosion rate and inhibition efficiency for the 10-3 M at different temperatures.

3

3.1.3. Thermodynamic parameters

4

The Arrhenius-type dependence observed between the corrosion rate and the temperature,

5

allowed us to calculate the value of the activation energy at different temperatures, in the

6

absence and in the presence of the inhibitor epoxy polymer, according to equation 10 [26].

7

The standard activation enthalpy ΔHa and the standard activation entropy G 0ads are

8

determined according to equations 11 and 12 [27].

9

Cr =Aexp

-E a RT

(10)

ΔS° -ΔH °a RT exp a exp Nh R RT

(11)

Cr R ΔS°a -ΔH °a =Ln + + T Nh R RT

(12)

10

Cr =

11

Ln

12

Where Cr is the corrosion rate, Ea is the activation energy, R is the constant of the perfect gas,

13

T is the temperature, h is the Planck constant and N is the Avogadro number.

14

Figure 4 present the variation in the logarithm of the corrosion rate of the E24 carbon steel in

15

1.0 M HCl in the absence and in the presence of the inhibitor epoxy polymer as a function of

16

fraction 1000/T for the 10-3 M concentration.

8

ACCEPTED MANUSCRIPT

1.0 M HCl DGDCBA

2,5 2,0

-1

0,5

Ln (Cr) (mg cm h )

1,0

-2

1,5

0,0 -0,5 -1,0 -1,5 -2,0 -2,5 3,00 3,05 3,10 3,15 3,20 3,25 3,30 3,35 3,40 -1

1000/T (K )

1 2

Figure 4: Ln (Cr) according to fraction 1000/T without and with 10-3 M.

3

Figure 5 present the variation of Ln (Cr/T) as a function of the fraction 1000/T. From this

4

figure we obtained straight lines with a slope equal to (- ΔH a /1000R) and extrapolating these

5

lines gives the values of the (Ln(R/Nh) + ΔSa /R). -3,0

1.0 M HCl DGDCBA

-3,5 -4,0 -4,5

Ln (Cr/T)

-5,0 -5,5 -6,0 -6,5 -7,0 -7,5 -8,0 -8,5 3,00

3,05

3,10

3,15

3,20

3,25

3,30

3,35

3,40

-1

1000/T (K )

6 7 8

Figure 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

Ea (kJ mol-1)

ΔH a (kJ mol-1)

ΔSa (J mol-1 K-1)

Blank 10-3 M for DGDCBA

50.82 87.13

48.22 84.55

-79.56 22.78

9

ACCEPTED MANUSCRIPT 1

From Table 4, the value of the activation energy obtained in the presence of the 10-3 M of the

2

DGDCBA epoxy polymer is greater than that of the 1.0 M HCl (without DGDCBA). This

3

behavior is related to the phenomenon of physisorption of inhibitor on the surface of the metal

4

substrate [28-29]. The positive sign of these standards activations enthalpies reflects the

5

endothermic nature of the dissolution process of E24 carbon steel [30-31]. The large negative

6

value of standard activation entropy in the presence of HCl (without inhibitor) indicates that

7

the activation state is more organized than the resting-state. In other words, the corrosion

8

reaction occurs on the surface of the E24 carbon steel. However, the result in the presence of

9

10-3 M of the DGDCBA shows a positive value of standard activation entropy, indicating an

10

entropic activation state. This result shows that the DGDCBA is preventing the corrosion of

11

the E24 carbon steel surface as a protective layer [32].

12

3.2. Polarization curves

13

Figure 6 (a, b) shows the cathodic and anodic polarization curves of the E24 carbon steel

14

traced after one hour of immersion in 1.0 M HCl, in the absence and in the presence of

15

different concentrations of the DGDCBA epoxy polymer studied as inhibitor. This shows that

16

the addition of the inhibitor results in a displacement of the free potential to higher values and

17

a decrease in the current density in the cathodic and anodic domains [33-34]. However, the

18

inhibition efficiency of the corrosion current is a maximum at 10-3 M of the inhibitor tested.

19

The values of the electrochemical parameters are grouped in Table 5. 3

1.0 M HCL -6 10 of DGDCBA -5 10 of DGDCBA -4 10 of DGDCBA -3 10 of DGDCBA

(a) 2

0

0

1.0 M HCl -6 10 of DGDCBA -5 10 of DGDCBA -4 10 of DGDCBA -3 10 of DGDCBA

2

-1 -2 -3

-1 -2 -3 -4

-4 -5

-5 -0,8

20

(b)

1

log i (mA/cm )

2

log i (mA/cm )

1

2

-0,7

-0,6

-0,5

-0,4

-0,6

-0,5

-0,4

-0,3

-0,2

-0,1

E (V/Ag/AgCl)

E (V/Ag/AgCl)

21

Figure 6: Cathodic (a) and anodic (b) polarization curves of the E24 carbon steel in 1.0 M

22

HCl in the absence and in the presence of different concentrations of the DGDCBA inhibitor.

23 24

10

ACCEPTED MANUSCRIPT 1

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

Concentration M 1.0 10-6 10-5 10-4 10-3

- Ecorr mV 457.7 461 557 582 561

icorr µA cm-2 550 114 93 21.8 9.26

Tafel slopes (mV dec-1) - βc βa 114 102 48 46 55 53 63 57 49 80

EI (%) 79 83 96 98

2

From the analysis of the parameters regrouped in Table 5, we observed that increasing of the

3

inhibitor concentration decreases the corrosion current density to lower values. Thus, the

4

inhibition efficiency increases with the addition of the DGDCBA epoxy polymer inhibitor

5

concentration. The different concentrations of the polymer studied reduce the values of the

6

slope of Tafel, compared with that obtained for the acid alone. Furthermore, this phenomenon

7

suggests that the addition of the DGDCBA inhibitor to the electrolyte has an effect on the

8

mechanism of hydrogen reduction [35-36]. Moreover, the inhibition efficiency affected 98%

9

at 10-3 M for DGDCBA, because the benzene rings are rich in electrons which vent to the

10

increase of the electron density of these. This facilitates its adsorption on the E24 carbon steel

11

and consequently the improvement of inhibition efficiency [37-38]. Finally, these results were

12

confirmed by the plot of the electrochemical impedance diagrams.

13

3.3. Electrochemical impedance spectroscopy

14

The corrosion behavior of the E24 carbon steel in 1.0 M HCl in the absence and in the

15

presence of the DGDCBA is also examined by the EIS technique after one hour immersion at

16

298 K. The Nyquist diagrams obtained are given in Figure 7. The impedance spectra have a

17

single capacitive loop whose size increases with the DGDCBA inhibitor concentration, this

18

loop means that a phenomenon occurs. Furthermore, this phenomenon indicates that the

19

corrosion is controlled by a process of charge transfer, which acts on the variation of the

20

double layer capacity. Moreover, the addition of the DGDCBA inhibitor to the corrosive

21

solution leads to the increase of the size of the capacitive loops as the epoxy polymer

22

concentration increases in comparison with the witness impedance diagram. As a

23

consequence, the inhibition efficiency increases caused by adsorption of the epoxy polymer

24

on the surface of the E24 carbon steel [39-40]. Then, the planar geometry of the DGDCBA

25

promotes adsorption on the surface as a protective layer. Additionally, the double-layer

26

capacities are best described by a charge-transfer function with constant phase elements

27

(CPE) to obtain a more adjustment accurate of the experimental data set. Finally, the

28

electrochemical parameters are given in Table 6. 11

ACCEPTED MANUSCRIPT 900

20

Blank

18

800

16

-Im(Z)/Ohm

14

700

10 8 6 4

600

-Im(Z)/Ohm

12

2

1.0 M HCl -6 10 M of DGDCBA -5 10 M of DGDCBA -4 10 M of DGDCBA -3 10 M of DGDCBA

0 0

500

5

10

15

20

25

30

35

40

Re(Z)/Ohm

400 300 200 100 0 0

1

100 200 300 400 500 600 700 800 900 1000 1100 1200

Re(Z)/Ohm

2

Figure 7: Nyquist impedance diagram for the E24 carbon steel in 1.0 M HCl in the absence

3

and in the presence of different DGDCBA concentrations at 298 K.

4

The analysis of the Table 6 shows that the charge transfer resistance value Rct increases with

5

increasing concentration of the epoxy polymer and reaches a maximum value of 944.4 Ω cm2

6

at 10-3 M of the DGDCBA inhibitor. Furthermore, this increase in charge transfer resistance

7

leads to metal protection and decreases the numbers of active sites that are created by

8

adsorption against chloride ions on the E24 carbon steel surface that is positively charged

9

[41]. Moreover, the values of the double layer capacity Cdl calculated in the presence of the

10

DGDCBA epoxy polymer inhibitor are lower in comparison with the witness value. This can

11

be attributed to the adsorption of the DGDCBA used on the surface of the E24 carbon steel

12

leading to the formation of a protective layer [42]. For example, the value of the double layer

13

capacity is 114 μF cm-2 in the witness and 85.42 μF cm-2 in the presence of the epoxy polymer

14

inhibitor at 10-3 M of the concentration. In addition, this behavior means that the charge rate

15

at the metal-solution interface is greatly reduced and that this inhibitor is well adsorbed on the

16

surface of the electrode. Finally, the inhibition efficiency of the DGDCBA increases with the

17

increase of the inhibitor studied and reaches at 96% for the 10-3 M concentration.

18

The Bode diagrams of 1.0 M HCl of the E24 carbon steel in the absence and in the presence

19

of the epoxy polymer at different concentrations are illustrated in Figure 8. From this figure,

20

we observed increasing phase angles with increasing of the DGDCBA inhibitor. This increase

21

in phase angles confirms higher protection by increasing the epoxy polymer concentration.

22

From the Bode diagram we have found that there are three frequency domains: low

23

frequencies, high frequencies and intermediate frequencies. Furthermore, for low frequencies 12

ACCEPTED MANUSCRIPT 1

increase in absolute values of impedance confirm the greatest protection with increase the

2

concentration of the DGDCBA on the E24 carbon steel. Moreover, at high frequency, the

3

values of log |Z| and the phase angle are close to zero. This indicates that the behavior of the

4

electrode that corresponds to the resistance of the solution (Rs). Then, for intermediate

5

frequencies a linear relation between log |Z| as a function of log (frequency) with a slope close

6

to -1 and the phase angle is close to 72° has been observed. This indicates that the capacitive

7

behavior at intermediate frequencies [43-44].

2,5 2

60

2,0 40

1,5 1,0

20

Phase (Z)/deg

log |Z|(Ohm cm )

80

1.0 M HCl -6 10 M of DGDCBA -5 10 M of DGDCBA -4 10 M of DGDCBA -3 10 M of DGDCBA

3,0

0,5 0

0,0

-2

-1

0

1

2

3

4

5

6

log (frequency) Hz

8 9

Figure 8: Bode diagram for the metal/DGDCBA/HCl.

10

The curves presented in the Bode and Nyquist diagrams show the existence of an equivalent

11

electrical circuit that contains a constant phase element on the metal/solution interface in all

12

the frequencies examined (Figure 9). The equivalent electrical circuit used is composed of the

13

solution resistance (Rs), the charge transfer resistor (Rct) and the constant phase element

14

(CPE).

CPE

Rs Rct

15 16

Figure 9: Equivalent electrical circuit of the metal/DGDCBA/HCl.

17

13

ACCEPTED MANUSCRIPT 1

Table 6: Parameters of EIS and inhibition efficiency of the E24 carbon steel in 1.0 M HCl

2

without and with different DGDCBA concentrations. Inhibitor Blank DGDCBA

Concentrations M 1.0 10-6 10-5 10-4 10-3

Rs Ω cm2 1.22 1.426 2.681 2.817 5.298

Q µF 308 128.5 108 28.37 24.77

ndl 0.823 0.837 0.810 0.860 0.895

Cdl µF cm-2 114 85.42 57.11 15.35 15.31

Rct Ω cm2 40 599.1 642.2 804.6 944.4

EI (%) 93 94 95 96

3 4

3.4. Immersion time

5

Electrochemical impedance spectroscopy is a useful technique for testing the long-time

6

immersion inhibition process. These experiments are conducted to observe the evolution of

7

the phenomena that occur at the interface of the metal substrate at different immersion times

8

from ½ h to 48 h. Figure 10 shows the evolution of the impedance diagrams at different

9

immersion times in 1.0 M HCl in 10-3 M of the DGDCBA inhibitor. From the results of this

10

figure, the charge transfer resistance increases with increasing immersion time after 6 h and

11

decreases after 24 h of immersion time. Furthermore, this behavior indicates that this is

12

attributed to an increase in the strength of the protective film over time up to 6 h. Therefore,

13

the protective properties of the film formed on the surface of the E24 carbon steel are

14

enhanced for the immersion time. In addition, the developed passive film is likely to dissolve

15

in a high immersion time [45]. 1000

1/2 h 5h 6h 24 h 48 h

900 800

-Im(Z)/Ohm

700 600 500 400 300 200 100 0 0

16

200 400 600 800 1000 1200 1400 1600 1800 2000

Re(Z)/Ohm

17

Figure 10: Impedance spectroscopy obtained after different immersion times in 1.0 M HCl in

18

10-3 M of the DGDCBA. 14

ACCEPTED MANUSCRIPT 1

3.5. Adsorption isotherm

2

The corrosion inhibitor of the E24 carbon steel by the DGDCBA epoxy polymer is explained

3

by their adsorption on the surface of this metal. There are two main types of adsorption:

4

adsorption physisorption and chemisorption. It depends on the charge of the metal, the

5

chemical structure of the epoxy polymer studied and the type of the electrolyte. Furthermore,

6

the physical adsorption requires the presence of an electrically charged metal surface and

7

charged species in the solution. Moreover, the chemical adsorption involves an electron

8

transfer between the inhibition epoxy polymer and the unsaturated orbitals of the metal

9

surface making it possible to form coordinate bonds and covalent bonds. Then, the adsorption

10

phenomenon of the DGDCBA epoxy polymer on the metal surface follows the Langmuir

11

adsorption isotherm. Finally, the recovery rate of the metal surface is given by equation 13

12

[46-47]. θ =K ads .Cinh 1-θ

13

(13)

14

With K denotes the equilibrium constant of the adsorption process and C is the concentration

15

of the epoxy polymer inhibitor. The rearrangement of the equation 13 gives the relation 14.

16

The value of the adsorption coefficient (Kads) is related to the standard free energy ΔG ads of

17

adsorption by equation 15.

18

Cinh 1 = +Cinh θ K ads

(14)

20

-ΔG °ads 1 exp( ) (15) 55.5 RT Where R is the constant of perfect gases (J mol-1 K-1) and T is the temperature (K), the value

21

55.5 is the concentration of water in solution (mol L-1).

22

The variation of C/θ as a function of the concentration the DGDCBA epoxy polymer inhibitor

23

at 298K is presented in Figure 11. The adsorption isotherm value is regrouped in Table 7.

19

K ads =

15

ACCEPTED MANUSCRIPT 0,0012

DGDCBA 0,0010

Cinh/

0,0008

1

0,0006 0,0004 0,0002 0,0000 0,0000

0,0002

0,0004

0,0006

0,0008

0,0010

Cinh(M)

1 2

Figure 11: Langmuir adsorption isotherm of the DGDCBA epoxy polymer inhibitor on the

3

surface of the E24 carbon steel at 298 K.

4

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

Kads

R2

DGDCBA

2261062

1

ΔG °ads (KJ mol-1) - 46.201

5

The value of the variation of free energy G 0ads is negative, which indicates the stability of the

6

adsorbed layer on the metal surface. Furthermore, the calculated value G 0ads of the

7

DGDCBA epoxy polymer inhibitor in an acid medium is greater than - 40 KJ mol-1. This

8

involves electron transfer between the epoxy polymer inhibitor and the metal surface to form

9

a bond. Then, according to the data of the literature, it is a physisorption [48]. Finally, the

10

linear correlation coefficient R2 is equal to 1, which shows that the adsorption on the surface

11

of the steel obeys the Langmuir isotherm.

12

3.6. Quantum chemistry descriptors calculation

13

To confirm the sites of adhesion of the DGDCBA epoxy polymer to the substrate, we

14

proceeded to the quantum chemistry calculation using the Gaussain software 09W [49-50].

15

Then, the different quantum discriptors were performed by the density functional theory

16

(DFT) method on the 6-31G (d,p) basis sets. The optimized geometric structure and density

17

distribution electrons of EHOMO and ELUMO are illustrated in Figure 12.

16

ACCEPTED MANUSCRIPT

Optimized structure

HOMO

LUMO

1 2

Figure 12: Optimized structure, HOMO and LUMO orbitals of the DGDCBA epoxy polymer.

3

The electron density (HOMO) is located on the aromatic ring surface, on the methylene group

4

bonded to the quaternary carbon and on the epoxy group of the difunctional DGDCBA epoxy

5

polymer, respectively (Figure 12). Furthermore, the electron density (LUMO) is located on

6

the epoxy group and on the C=S group linked to the epoxy, respectively. Then, the Table 8

7

groups the different quantum chemistry descriptors calculation of the DGDCBA epoxy

8

polymer.

9

The energy of the highest occupied molecular orbital (EHOMO) shows the ability of the

10

DGDCBA epoxy polymer to donate electrons. Moreover, the higher energy value of the

11

HOMO orbital facilitates the tendency of the epoxy polymer to give up electrons to electron17

ACCEPTED MANUSCRIPT 1

accepting species having unoccupied molecular orbitals whose energy level is low. Then, the

2

energy of lower unoccupied molecular orbital (ELUMO) is related to the ability of the epoxy

3

polymer to accept electrons, a low value of energy LUMO means that the DGDCBA epoxy

4

polymer accepts electrons [51]. In addition, the adsorption of the DGDCBA epoxy polymer

5

inhibitor on the surface of the substrate increases when the gap energy is lower [52].

6

The highest hardness value (1.396 eV) and the lowest softness value (0.716 eV-1) of the

7

DGDCBA epoxy polymer have a very good chemical reactivity with the surface of the E24

8

carbon steel.

9

The value of the number of electrons transferred (0.891) is less than 3.6 indicates the tendency

10

of the epoxy polymer to give electrons to the surface of the substrate [53]. Then, this result

11

shows that the quality of the protective film is well formed. The latter is in agreement with

12

Lukovit's study [54].

13

Table 8: Different quantum chemistry descriptors of the DGDCBA epoxy polymer. Quantum descriptors Values

EHOMO eV -3.026

ELUMO eV -0.234

ΔE gap eV 2.792

η eV 1.396

σ eV-1 0.716

ΔN eV 0.891

14

3.7. Electrostatic potential

15

The determination of the electrostatic potential is very interesting for the studies of epoxy

16

polymer interactions. Furthermore, the negative regions of electrostatic potential are favorable

17

for electrophilic attack. While, positive regions are more sensitive to nucleophilic attacks [55].

18

3.7.1. Mulliken atomic load distribution and dipole moment

19

Figure 13 shows the dipole moment and the distribution of the Mulliken atomic charges on

20

the atoms of the DGDCBA, respectively. Then, we have observed that the oxygen atoms and

21

some carbon atoms of the epoxy polymer studied have negative charges. Finally, we conclude

22

that these atoms are responsible for a nucleophilic attack towards the surface of the E24

23

carbon steel.

18

ACCEPTED MANUSCRIPT

1 2

Figure 13: Mulliken atomic charge distribution of the DGDCBA epoxy polymer with the

3

dipole moment vector.

4

3.7.2. Molecular electrostatic potential

5

The representation of the molecular electrostatic potential of the DGDCBA epoxy polymer

6

studied was determined to identify the electron density regions (Figure 14). This strong

7

electron density is presented by a red color, however the low electron density is presented by

8

a blue color. The electronic density decreases in the following order: red> orange> yellow>

9

green> blue [56-57]. Furthermore, the highest electron density is located on the oxygen

10

atoms. Then, the low electron density is located on the sulfur atom and the some carbon

11

atoms. -3.710e-2

3.710e-2

12 13

Figure 14: Molecular electrostatic potential of the DGDCBA epoxy polymer.

19

ACCEPTED MANUSCRIPT 1

Figure 15 shows the contour of the molecular electrostatic potential of the epoxy polymer

2

DGDCBA. In addition, we observed that the surface of the contour of the molecular

3

electrostatic of the epoxy polymer studied present on the surface of two benzene groups. This

4

indicates that these benzene groups are adsorbed plane way on the surface of the metal

5

substrate.

6 7

Figure 15: Contour of the molecular electrostatic potential of the DGDCBA epoxy polymer.

8

3.8. Molecular dynamics simulations

9

The adsorption of the DGDCBA on the iron surface has been optimized using a molecular

10

dynamics simulation to understand the interactions between the epoxy polymer inhibitions

11

studied and the iron surface. Molecular dynamics simulation can reasonably predict the most

12

favorable configuration at the Fe(110)/DGDCBA/50 H2O interface. Furthermore, Figure 16

13

shows the energy curve of the DGDCBA epoxy polymer inhibitor in its optimized neutral and

14

isolated forms before being placed on the surface of the metal substrate using the

15

DMol3/GGA/DNP basis sets. According to this figure, the DGDCBA polymer inhibitor has an

16

optimal energy (-2784.186 Ha) [58].

20

ACCEPTED MANUSCRIPT

1 2

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

3

The study of the fluctuating interaction energies between the DGDCBA epoxy polymer, the

4

metallic surface of Fe(110) and the water molecule was calculated by molecular dynamics

5

simulation, optimizing the whole Fe(110)/DGDCBA/50H2O system. Furthermore, the

6

adsorption energy distribution for the Fe(110)/DGDCBA/50 H2O pair in hydrochloric acid as

7

a solution by the adsorption locator model is shown in Figure 17. The latter shows that the

8

adsorption energy of the epoxy polymer studied has reached a value of -268 Kcal/mol. This

9

indicates that the adsorption power on the metal surface is appropriate.

21

ACCEPTED MANUSCRIPT

1 2

Figure 17: Adsorption energy distribution for Fe(110)/DGDCBA/50 H2O system using

3

adsorption locator model.

4

Figure 18 shows the interaction energies fluctuant curves calculated by optimizing the whole

5

Fe(110)/DGDCBA/50 H2O system. Moreover, the calculation of the energies namely: the

6

total energy, the average total energy, the van der Waals energy, the electrostatic energy and

7

the intramolecular energy between the DGDCBA epoxy polymer and the surface of the

8

metallic substrate converge in the adsorption process [59].

22

ACCEPTED MANUSCRIPT

1 2

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

3

Molecular dynamics simulation was performed to better understand the interaction between

4

the DGDCBA epoxy polymer and the surface of Fe (110). Then, the simulations were carried

5

out in the system containing 50 molecules of water and one molecule of the DGDCBA.

6

Furthermore, the radial distribution function (RDF) (or pair correlation function) g (r) can be

7

obtained after this analysis. The RDF is used as a useful method to estimate the length of the

8

link. The peak occurs from 1 Å up to 3.5 Å, it is an indication of the length of small bonds,

9

which is correlated with chemisorption. While physical interactions are associated with peaks

10

greater than 3.5 Å. Moreover, the RDF of the epoxy polymer atoms shows that the bond

11

length of iron is less than 3.5 Å (Figure 19) [60]. Finally, the results obtained confirm the

12

greater adsorption capacity of the DGDCBA inhibitor tested and, consequently, the protection

23

ACCEPTED MANUSCRIPT 1

of the metal against dissolution, because of their greater ability to give and to accept electrons

2

on the surface of the metal through these active sites.

3 4

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

5

Molecular dynamics simulations are performed to study the adsorption behavior of the

6

DGDCBA epoxy polymer on the Fe(110) surface in solution. Furthermore, the side and top

7

views of stable adsorption configuration of the best low-energy of the DGDCBA adsorbed on

8

the surface of Fe(110) with the presence of the water molecule (Fe(110)/DGDCBA/50 H2O)

9

obtained using the adsorption locator module are shown in Figure 20. Finally, we can

10

conclude that the studied epoxy polymer can be adsorbed plane way on the surface of the

11

Fe(110) and offers a larger surface area to stop the dissolution of the metal surface.

12

Top

Side

13

Figure 20: Side and top views of stable adsorption configuration for

14

Fe(110)/DGDCBA/50H2O system obtained using the adsorption locator module. 24

ACCEPTED MANUSCRIPT 1

The parameters presented in Table 9 include the total energy in Kcal mol-1 of the

2

substrate/adsorbate system. Then, the total energy is defined as the sum of the adsorption

3

energy and the internal energy of the sorbate. Furthermore, the adsorption energy (EAds) of the

4

DGDCBA epoxy polymer on the surface of the Fe(110) in the presence of the water molecule

5

was corrected by the basic superposition error (BSSE). Indeed, the adsorption energy is given

6

by formula 16.

7

E

Ads

=E

(Fe(110)/DGDCBA/50H O) 2

-(E

DGDCBA

-E

Fe(110)

-E

50H O 2

)

(16)

8

The adsorption energy is defined as the algebraic sum of the rigid adsorption energy (R.A.E)

9

and the deformation energy (DE) for the adsorbed components. Furthermore, the rigid

10

adsorption energy therefore reports the energy released (Kcal mol-1) when the DGDCBA

11

epoxy polymer of adsorbate not released before the step of optimizing the geometry, that is

12

adsorbed on the surface of the Fe(110) in presence of 50 molecules of water. Contrariwise, the

13

deformation energy reports the released energy (Kcal mol-1) when the adsorbed epoxy

14

polymer inhibitor is released on the surface of the Fe(110). Then, the Table 9 also gives the

15

desorption energy (dEads/dNi) which reports the energy of the substrate-adsorbate

16

configuration where one of the adsorbed components has been removed. In addition, the

17

negative adsorption energy values mean that the adsorption of the epoxy polymer studied

18

could occur spontaneously [61].

19

The high adsorption energy (-6471.63 Kcal mol-1) of the DGDCBA epoxy polymer indicates

20

that the adsorption of the inhibitor on the surface of Fe(110) is adsorbed by involving the

21

displacement of H2O molecules on the iron surface and sharing of electrons between the

22

heteroatoms in the polymer inhibitor and the surface of Fe(110). This gives the possibility of

23

bond formation (Π-Π) resulting from the overlap of electrons (3d) of the iron atom and free

24

doublet of sulfur and oxygen atoms.

25

The high values of the adsorption energies of DGDCBA epoxy polymer are due to the flatness

26

and the presence of a pair of electrons on the heteroatoms (-S- and -O-), favoring a greater

27

adsorption on the surface of the Fe(110). Then, the protection of the metal surface is obtained

28

by a forte adsorption of the macromolecular matrix and avoiding that it is easily corroded.

29

Thus, the Table 9 also shows (dEAds/dNi) which reports the configuration energy of iron

30

component where one of the inhibitor molecules was removed [62-63].

25

ACCEPTED MANUSCRIPT 1 2

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). Structures

ETotal 10+3

EAds

R.A.E 10+3

DE

dEAds/dNi H2O

dEAds/dNi DGDCBA

Fe (110) - 1

-6.25

-6471.63

-6.85

379.204

-12.102

-240.735

Fe (110) - 2

-6.20

-6428.81

-6.79

363.863

-11.906

-266.041

Fe (110) - 3

-6.20

-6424.97

-6.78

358.483

-13.398

-265.294

Fe (110) - 4

-6.20

-6421.35

-6.79

366.398

-11.042

-223.815

Fe (110) - 5

-6.19

-6414.06

-6.78

369.402

-12.188

-180.856

Fe (110) - 6

-6.19

-6412.20

-6.79

378.666

-10.175

-184.083

Fe (110) - 7

-6.19

-6411.85

-6.78

368.394

-9.718

-170.190

Fe (110) - 8

-6.18

-6404.10

-6.77

365.113

-10.317

-262.269

Fe (110) - 9

-6.18

-6402.06

-6.76

360.744

-12.025

-251.483

Fe (110) - 10

-6.17

-6392.02

-6.77

379.531

-10.273

-166.014

3

Conclusion

4

In this work, we investigated the performances of the corrosion inhibition of the difunctional

5

S, S’-diglycidyl O, O'- dicarbonodithioate of bisphenol A (DGDCBA) epoxy polymer in the

6

hydrochloric acid of the E24 carbon steel in the presence of different concentrations (10-3 to

7

10-6 M). Furthermore, the experimental results we obtained in this study concerning the

8

inhibition of the metal substrate in the presence of different concentrations are very

9

interesting. Then, the phenomenon of adsorption of the DGDCBA epoxy polymer on the

10

metal surface is physisorption. In additionally, the potentiodynamic polarization shows that a

11

decrease in the corrosion current density in the cathodic range with an inhibitory efficiency is

12

of the order of 98% at the concentration 10-3M of the DGDCBA. However, the

13

electrochemical impedance spectroscopy has a better inhibitory efficiency of 96% for the

14

concentration 10-3M of the studied epoxy polymer. Moreover, the prediction of the quantum

15

chemistry descriptors, namely: the energy of the highest occupied molecular orbital (EHOMO),

16

the energy of the lowest unoccupied molecular orbital (ELUMO), the gap energy (ΔE), the

17

chemical hardness (σ), the chemical sweetness (ƞ), and the number of electrons transferred

18

(ΔN) confirm the adhesion sites of the difunctional DGDCBA epoxy polymer. Finally, the

19

theoretical (density functional theory and molecular dynamics) and experimental results are in

20

good agreement.

21

Acknowledgments-I would like to thank Professor Ahmed Elharfi, responsible for the Team

22

of Polymers and Organic Chemistry, Department of Chemistry, Faculty of Science, Ibn Tofail 26

ACCEPTED MANUSCRIPT 1

University, Professor Najat HAJJAJI, responsible for the Team of Corrosion, Protection and

2

Environment, Department of Chemistry, Faculty of Science, Ibn Tofail University and Salma

3

Kantouch who collaborated to the success of this paper.

4

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ACCEPTED MANUSCRIPT  The study shows that the DGDCBA epoxy polymer is an excellent corrosion inhibitor for E24 carbon steel in 1.0 M HCl.  Potentiodynamic polarization curves reveal that tested DGDCBA inhibitor acts as a mixed type  The adsorption of the DGDCBA compound obeys Langmuir adsorption isotherm.  DFT and MD stimulation studies have been done.