Computational, MD simulation, SEM/EDX and experimental studies for understanding adsorption of benzimidazole derivatives as corrosion inhibitors in 1.0 M HCl solution

Article abstract of DOI:10.1016/j.jallcom.2020.155842

The adsorption and corrosion inhibition performance of two benzimidazole derivatives, namely:2-(allylthio)-1H-benzo[d]imidazole (SHA) and bis((1H-benzo[d]imidazole-2-yl)thio)methane (BB1C) were studied as a corrosion inhibitors for mild steel (MS) in 1.0 M HCl solution using Weight Loss (WL) measurements, Potentiodynamic Polarization (PDP), Electrochemical Impedance Spectroscopy (EIS), Scanning Electron Microscopy(SEM) and Energy Dispersive X-ray (EDX) analysis. The kinetics of corrosion retardation were inspected by polarization studies, and the respective achievements declared that both compounds could retard corrosion reactions via cathodic/anodic (mixed) inhibition mechanism. The adsorption process on MS surface obeyed Langmuir isotherm. Adsorption and thermodynamic parameters were also evaluated. SEM/EDX analysis strongly supports the obtained results and confirms the existence of a barrier film on the metal surface. Our findings provide deeper insights into understanding the interaction mechanisms of SHA and BB1C with MS surface. Experimental outcomes support the outcomes obtained from DFT and Molecular dynamic (MD) simulation.

Full text of DOI:10.1016/j.jallcom.2020.155842

Journal Pre-proof
Computational, MD simulation, SEM/EDX and experimental studies for understanding
adsorption of benzimidazole derivatives as corrosion inhibitors in 1.0￿ M HCl solution
E. Ech-chihbi, A. Nahlé, R. Salim, F. Benhiba, A. Moussaif, F. El-Hajjaji, H. Oudda, A.
Guenbour, M. Taleb, I. Warad, A. Zarrouk
PII:
S0925-8388(20)32206-4
DOI:
https://doi.org/10.1016/j.jallcom.2020.155842
JALCOM 155842
Reference:
To appear in: Journal of Alloys and Compounds
Received Date: 20 January 2020
Revised Date: 24 May 2020
Accepted Date: 27 May 2020
Please cite this article as: E. Ech-chihbi, A. Nahlé, R. Salim, F. Benhiba, A. Moussaif, F. El-Hajjaji,
H. Oudda, A. Guenbour, M. Taleb, I. Warad, A. Zarrouk, Computational, MD simulation, SEM/EDX
and experimental studies for understanding adsorption of benzimidazole derivatives as corrosion
inhibitors in 1.0￿ M HCl solutio nJ ,ournal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/
j.jallcom.2020.155842.
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Credit Author Statement
E. Ech-chihbi: Methodology; A. Nahlé: Writing-Reviewing and Editing; R.
Salim: Validation; F. Benhiba: Data curation; A. Mousaif: Investigation; F. El-Hajjaji:
Writing-Reviewing
and
Editing;
H.
Oudda: Data
curation;
A.
Guenbour: Conceptualization; M. Taleb: Formal analysis; I. Warad: Visualization; A.
Zarrouk: Supervision, Writing- Original draft preparation, Writing-Reviewing and Editing.
All authors have read and approved the manuscript.

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Computational, MD simulation, SEM/EDX
and experimental studies for understanding adsorption of
benzimidazole derivatives as corrosion inhibitors in 1.0 M
HCl solution.
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E. Ech-chihbi , A. Nahlé , R. Salim , F. Benhiba , A. Moussaif , F. El-
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Hajjaji , H. Oudda , A. Guenbour , M. Taleb , I. Warad , A. Zarrouk
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Laboratory of Separation Processes, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco.
Laboratory of Engineering, Electrochemistry, Modeling and Environment (LIEME), Faculty of
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Sciences, University sidi Mohamed Ben Abdellah, Fez, Morocco.
Department of Chemistry, College of Sciences, Sciences, University of Sharjah, Sharjah, P.O.Box:
27272, United Arab Emirates.
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National Center of Energy Sciences and Nuclear Techniques, Rabat, Morocco.
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Laboratory of Materials, Nanotechnology and Environment, Faculty of Sciences, Mohammed V
University, Av. Ibn Battouta, PO Box 1014 Agdal-Rabat, Morocco.
Department of Chemistry and Earth Sciences, PO Box 2713, Qatar University, Doha, Qatar.
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* Corresponding author. Tel.: +971-6-5166 771 Fax: +971-6-5053820
E-mail address: anahle@sharjah.ac.ae.
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Abstract
The adsorption and corrosion inhibition performance of two benzimidazole derivatives,
namely:2-(allylthio)-1H-benzo[d]imidazole
(SHA)
and
bis((1H-benzo[d]imidazol-2-
yl)thio)methane (BB1C) were studiedas a corrosion inhibitors for mild steel (MS) in 1.0 M
HCl solution using Weight Loss (WL) measurements, Potentiodynamic Polarization (PDP),
Electrochemical Impedance Spectroscopy (EIS), Scanning Electron Microscopy(SEM) and
Energy Dispersive X-ray (EDX) analysis. The kinetics of corrosion retardation were inspected
by polarization studies, and the respective achievements declared that both compounds could
retard corrosion reactions via cathodic/anodic (mixed) inhibition mechanism. The adsorption
process on MS surface obeyed Langmuir isotherm. Adsorption and thermodynamic
parameters were also evaluated. SEM/EDX analysis strongly supports the obtained results and
confirms the existence of a barrier film on the metal surface. Our findings provide deeper
insights into understanding the interaction mechanisms of SHA and BB1C with MS surface.
Experimental outcomes support the outcomes obtained from DFT and Molecular dynamic
(MD) simulation.
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Keywords: Benzimidazole; Mild steel; EIS; SEM/EDX; DFT; MD Simulation.
(Approx. 9500 words, 11 Tables, 17 Figures, 25 Equations, and 82 References).
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1.Introduction
Acid pickling treatment of metals and alloys in an effectively method to eliminate unfavorable
dirt, oxides, and rusts on metal to obtain the clean metal surface [1-4]. Mild Steel (MS) has
attracted much attention in a wide range of industrial applications because of its unique
mechanical properties and its low cost [5]. The use of organic compounds as corrosion
inhibitors is one of the effective and economical methods to reduce corrosive attacks on
metallic materials [6]. The organic molecules containing heteroatoms (e.g., N, S, O, and P),
π–electrons of aromatic moiety and conjugated double bonds, which can endow inhibitors
mighty adsorption capacity on metal as many researchers reported [7-9]. The adsorption
process of the organic inhibitors depends mainly on certain physico-chemical and electronic
properties, such as electron density of atomic orbitals, functional groups, steric factors, and
the electronic structure of the molecules [9, 10]. The adsorbed inhibitor molecule can slow
down the corrosion of metals by blocking the active corrosion sites or by the formation of a
protective film between the metal surface and the aggressive medium [12-14]. The toxic
properties and the environmental impact of some organic corrosion inhibitors have tended
to limit their application. As a result, current researches have focused on synthesizing and
using new environmentally friendly inhibitors. Azole compounds such as
thiazole, thiadiazole, imidazole, benzimidazole, etc. can be pointed out as the most eco-
friendly compounds, which provide corrosion inhibition properties and moreover act as non-
toxic and relatively cheap [15-18]. Benzimidazole derivatives has gained considerable
attention in the field of medicinal chemistry. The moiety is of substantial importance because
of its wide array of pharmacological activities. This nitrogen containing heterocycle is a part
of a number of therapeutically used agents [19]. Similarly, benzimidazole derivatives are the
most widely used class of fungicides in agriculture as they are highly active against
pathogenic and non-pathogenic fungi [20]. Recently imidazole derivatives were reported also
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as a new class of corrosion inhibitors of metals in different studies due to the availability of
their π-electrons of -C=N azomethine double bond which can coordinate with metals to form
a barrier between the metal and corrosive elements [21].
The use of benzimidazole bases as corrosion inhibitor is widely undertaken by several
researchers. Recent studies have shown that the benzimidazole derivatives displayed excellent
inhibition performance for steel in acidic solution [17, 22-26].
The aim of this paperis to evaluate the inhibition effectiveness of two synthesized
benzimidazole derivatives namely 2-(allylthio)-1H-benzo[d]imidazole (SHA) and bis((1H-
benzo[d]imidazol-2-yl)thio)methane (BB1C) on the MS corrosion in 1.0 M HCl solution. The
inhibition effectiveness of these organic compounds was examined successively via WL, PDP
curves, EIS, isotherm calculationsand SEM/EDX analysis. DFT calculations and dynamics
molecular (MD) simulations has been also conducted in order to determine the correlation
between the corrosion inhibition properties of the investigated derivatives and their molecular
structures. The adsorption mechanism of was also proposed and discussed. In addition,
Adsorption and thermodynamic parameters were calculated. The molecular structures of the
examined SHA and BB1C are shown in Table 1.
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2. Experimental
2.1. Synthesis Procedure of inhibitors
The investigated compounds SHA and BB1C were synthesized following the reported
procedure (Figure 1). The synthesis reaction of SHA was carried out for 1h in a sodium
hydroxide solution (2.5 wt. %) at room temperature: a mixture of benzimidazole-2-thione
(0.007 moles) and allyl bromide (0.0072 moles) in the sodium hydroxide solution. The
reaction led, in each case, to a product corresponding to an S-alkylation.
For BB1C, 0.014 moles of KHCO , 0.0001 moles of bromotetrabutlammonuim (TBAB) and
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0.0034 moles of 1,1-dibromomethane are added to a solution of 0.007 moles of
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benzimidazole-2-thione in 20 mL of dimethyllformamide (DMF). The reaction mixture is
stirred at room temperature for 4 h (Figure 1).
SHA: Yield 80.0%; m.p. 146-148 °C (Ethanol);RMN 1H (CDCl ): 3.43 ppm (d, 2H, J = 6.5
3
Hz, -CH -S), 5.30 ppm (m, 2H, CH =), 6.30 ppm (m, 1H, CH=), 7.40 ppm (m, 4H, ArH). MS;
2
2
+
M m/z = 190.
BB1C: Yield 75.0%; m.p. 180-182 °C (Ethanol); RMN 1H (CDCl3) : 3.53 ppm (s, 2H, S-
+
CH2-S), 7.40 ppm (m, 8H, ArH), 11.20 ppm (s, 2H, N-H) ; M m/z = 312.
2.2. Materials
HCl solution was prepared by dilution of analytical grade (37 %) HCl with distilled water.
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The concentration of SHA and BB1C rangedfrom1.0×10 M to 1.0×10 M. MS specimens
has elemental composition (wt. %): 99.21% Fe, 0.38% Si, 0.21% C, 0.05% Mn, 0.05% S,
0.09% P, and 0.01% Al. The specimens used in the present study were polished with different
grades of SiC abrasive papers (grit #180, #600, and #2000), degreased with acetone, rinsed
with distilled water, and then dried at room temperature.
2.3. Weight loss experiments
WL experiments were carried out by immersing MS specimens (2.5ꢀcm in diameter and
1.5ꢀcm in thickness with a hole of 0.2ꢀcm diameter) in uninhibited and inhibited solutions for
6h at 298 K [27]. To insure the reproducibility of the WL results, each experiment was triply
performed and means values were reported at each concentration. The corrosion rate (CR) can
be estimated according to the following equation [28]:
w
2
1
CR=
(1)
S×t
2
2
2
2
3
4
Where, w is the weight loss of steel sample, S is the total surface area of sample and t is the
immersion time.
The inhibition efficiency, η %, was determined as follows [29]:
CR
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CR-CRinh
CR
1
η %=
×100
(2)
CR
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Where CR and CR are the corrosion rate without and with inhibitors, respectively.
inh
2.4. Electrochemical techniques
Electrochemical study was carried out in a three-electrode cell which was composed of a MS
sample as a working electrode (Exposed area: 1cm²), a platinum counter-electrode (CE),
andan Ag/AgCl as a reference electrode (RE). All the electrochemical tests were executed
using a potentiostat/galvanostat/PGZ100 controlled by analysis software VoltaMaster 4. The
electrochemical parameters were extracted owing to EC-Lab V10.02 software. Prior to each
electrochemical experiment, the working electrode (WE) was immersed in the electrolyte for
30 min to reach a steady open circuit potential (stable open circuit potential: EOCP).
EIS measurements was carried out in the frequency range of 100 KHz to 100 mHz at an Open
Circuit Potential (OCP) with 10 points per decade. The amplitude of the applied alternative
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current signal was 10 mV ms .The inhibition efficiency (ηimp%) can be computed using
equation (3) and the fractional surface coverage using equation (4) [30] :
inh
R - R
(
P
)
×100
P
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5
η %=
(3)
(4)
imp
inh
RP
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θ= ηimp 100
inh
WhereR and R are the polarization resistance of MS in the absence and presence of the
P
P
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inhibitor, respectively. The electrochemical measurements were performed in triplicates in
order to ensure reproducibility of the analysis.
Potentiodynamic polarization plots were obtained by sweeping the working electrode
-1
potential from -900 mV to -100 mV with respect to the RE, at a slow scan rate of 0.5 mV s .
The inhibition efficiency (ηPDP%) is calculated according to the following equation (5) [31] :
°

(i -i )

corr corr
2
3
ηPDP %=
×100
(5)
°




i
corr
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Where,
i
and icorr are the corrosion current densities without and with addition of inhibitor,
corr
respectively.
2.5. Surface investigation by SEM/EDX
Surface morphologies of the specimens, which were exposed to the blank acid medium and
−
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the solution with 1.0x10 ꢀM of SHA BB1C and for 6 h at room temperature, respectively,
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were analyzed. SEM images were acquired by Quanta FEG 450 typically operated with an
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acceleration voltage of 10 KV coupled with an EDX unit. For EDX analysis, the acceleration
voltage used in the present study was 15 kV. These analyses were performed in MAScIR-
Rabat Foundation.
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2.6. Quantum chemical calculations
Quantum chemical methods have proved to be very useful in predicting the optimized
molecular structure, electronic parameters, and reactivity of these molecules by analyzing the
different possibilities of electron exchange with the metal surface [32]
.
All calculations were done with DFT at B3LYP/6-31G (d, p) level of theory using Gaussian
software 09 [33]. Theoretical descriptors such as the energies of the highest occupied and
lowest unoccupied molecular orbital (EHOMO and ELUMO), energy gap (ΔEgap), dipole moment
(
μ χ (Absolute electronegativity), ΔN (Fraction of electrons transferred from single inhibitor
),
molecule to metallic surface), ΔEb–d (Back donation), and report of electron transferred
ΔN110) were calculated according the following equation [15, 34-35]
(
.
∆E (eV ) = E
− EHOMO
LUMO
(6)
(7)
gap
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χ =
(
EHOMO + ELUMO
)
2
1
η
=
(
EHOMO -ELUMO
)
(8)
(9)
2
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Δ
E = (E
-ELUMO )
HOMO
b-d
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Φ- χinh
1
2
ΔN=
(10)
2
η
Fe110
+ ηinh
(
)
For the computation of ΔN, the metal work function was instead of χ Fe which is equal to
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4.82eV for iron (110) plan. In this case we have only considered Fe (110) surface for the
reasons of its packed surface and higher stabilization energy. The value of ηFe(110) is equal to
zero electron-volt which corresponds to the metallic bulk [36]
.
The Fukui indices indicate a tendency of the molecule to either donate or receive electrons.
Thus, these functions have been modeled to distinguish the most nucleophilic interactions in a
-
k
+
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molecule [37]. Usually electrophilic (
P
) and nucleophilic ( Pk ) attacks are calculated using
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equations (11) and (12) as follow [38]:
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For nucleophilic attack:
+
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P = P (N +1)- P (N)
(11)
(12)
k
k
k
For electrophilic attack:
-
k
P = P
(
N
)
- Pk
(
N -1
)
k
1
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Where (+) and (-) signs show nucleophilic and electrophilic attack, respectively. is the
P
k
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atomic charge (estimated through using the natural population analysis NPA) in neutral (N),
anionic (N + 1), and cationic (N - 1) species.
2.7. Computational details for MD simulations
The molecular dynamics (MD) simulations were performed using the Forcite code of Material
Studio 8.0 software package [39]. In the simulation, the study of the interactions of the
molecule with the surfaces of Fe (110) was carried out in a simulation box (32.27 Å
×32.27
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2
2
1
2
3
Å×30.13 Å) (13×13) unit cell and 40 Å vacuum with periodic boundary condition.The choice
of the Fe(110) surface is based on the stability, as indicated in the literature [40]. The
structures of the studied molecules are pre-optimized using Generalized Gradient
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Approximation (GGA) with the double numeric polarized (DNP). The Andersen
thermostat providing an NVT set (constant number of particles, volume, and temperature)
followed by the total simulation time of 400 ps with time step = 1 fs, spline width 1 Å, cutoff
distance of 15.5 Å, and a buffer width of 0.5 Å [41].Geometry optimizations of the studied
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structures were performed with an energy convergence tolerance of 1.0x10 kcal mol using
fine quality. MD simulation was performed by using COMPASS force field [42]. Our
+
-
supercell contains 5H O ions, 5 Cl ions, 500 H O molecules, and1 molecule of SHA or
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BB1C.
The interaction (E ) and the binding (Ebinding
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energies of the studied system were
int
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determined using equations (13) and (14) [43]:
Einteraction =E Total -Esurface+solution -Einhibitor
(13)
(14)
1
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Ebinding = - Einteraction
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Where ETotal is the total energy of the simulation system, Esurface+solution referred to the total
energy of Fe(110) surface together with solution inhibitor, and Einhibitor is the energy of free
inhibitor molecule.
3. Results and discussion
3.1. WLmeasurements
Corrosion parameters of MS in 1.0 M HCl solution in the absence and presence of different
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concentrations of inhibitor (1.0×10 M to 1.0×10 M) were carried out using WL
measurements at 298 K and the results are encapsulated in Table . The observed weight loss
values of triplicate measurements are highly reproducible giving standard deviations. The
results presented in Table shows that the corrosion rate (CR) decreases while the inhibition
efficiency ηWL) increases with increasing the concentration of the inhibitors reaching a
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(
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maximum value of 94% and 97.3% at optimum concentration of 1.0×10 M for SHA and
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BB1C, respectively. This result is due to the greater adsorption ability of these compounds
onto the surface of the mild steel and consequently, the higher inhibition concentration [44]
.
3.2. Electrochemical studies
3.2.1. Open circuit potential
The Figure
2 shows variation of the potential of MS with time (monitored for 30min) during
the attainment of an open circuit potential (OCP) in 1.0 M HCl solution in the absence and
presence of different concentrations of SHA and BB1C.It was noticed that the addition of the
studied molecules induces shift in OCP (i.e., E ). Based on the plots (Figure 2), it can be
corr
observed that the MS sample could attain a quasi–stable open circuit potential under 30min.
Thus, 30 min OCP measurement was adopted prior to performing all electrochemical
measurements in this work.
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3.2.2. PDP measurements
Potentiodynamic polarization (PDP) curves for MSwithout and with different concentrations
of SHA and BB1C in 1.0 M HCl at 298 K are shown in Figure
3.
As it can been seen from Figure , it is clear that both anodic and cathodic reactions of
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corrosion process were inhibited when the bienzimidazole derivatives were added to the acid
solution, and this effect became more pronounced as the concentration of studied compounds
increased.The cathodic branches of Tafel curves decreased markedly to lower values in
comparison to the blank and all curves give rise to parallel lines indicating that the inhibitor
does not modify the hydrogen evolution mechanism and this reaction is activation controlled
[45, 46]. In other words, the investigated molecules can hinder the reduction of hydrogen ions
by covering the active reaction sites at the mild steel surface with a protective barrier. Tafel
parameters such as corrosion current density (icorr), corrosion potential (Ecorr),
Tafel slope for anodic
and
cathodic
branches
(
βa
,
βc),
and
.
the
percentage inhibition efficiencies (ηPDP
%) are calculated and are shown in Table
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Some papers reported that the displacement in Ecorr is larger than 85ꢀmV with corresponding
to that of the blank solution, implying that the inhibitor in the solution is regarded as a
cathodic or anodic type inhibitor, and if the displacement is smaller than 85ꢀmV, the inhibitor
is considered as a mixed type [45, 46]. It can be shown from Table
displacements were 43 mV (SHA), 46 mV (BB1C), suggesting that both inhibitors behave as
mixed type with a cathodic tendency. The cathodic slope ( ) values are not significantly
3 that the maximum Ecorr
β
c
changed with increasing the inhibitor concentration which indicates that the hydrogen
reduction reaction on the MS surface is performed according to a pure activation mechanism
[46]
.
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3.2.2. EIS measurements
In order to acquire more information on corrosion mechanisms and improve previous results
obtained from WL and PDP measurements, Nyquist plots (experimental and fit) of MS in
1.0 M HCl without and with different concentrations of SHA and BB1C at 298 K are
shown in Figure 4. It is clear from Figure 4 that all Nyquist fitted diagrams display a single
capacitive loop in both the absence and presence of the inhibitors. This finding
indicates that the corrosion reaction in 1.0 M HCl is mainly controlled by charge transfer
process [47]. The size of the impedance diagram increases as the concentration rises and
consequently the protection efficiency increases. These results fully demonstrate that these
compounds can form a dense anti-corrosion film on the electrode surface, thereby
efficaciously restrain the MS corrosion [48]. Furthermore, these Nyquist diagrams are not
perfect semicircles. The deviation of semicircles from perfect circular shape is often referred
to the frequency dispersion of interfacial impedance [49]. This behavior is usually attributed
to the inhomogeneity of the metal surface arising from surface roughness or interfacial
phenomena [49, 50]. The Bode representation displays the logarithm of the impedance
modulus log|Z| and phase angle α° versus the frequency in a logarithmic scale log f (Figure
1
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3
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5). The phase angle plots become significantly wider at the high frequency range with the
concentration of SHA and BB1C increases. In all cases, it is clear that the Bode phase
angle plots have only one maximum i.e. one-time constant corresponds to a corrosion process
by adsorbing on MS/solution interface [50]. CPE/n is used instead of the capacitor to
dl
consider the non-idealities coming from the inhomogeneity of the electrode surface [51]. The
CPE is defined in impedance representation as:
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n


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ZCPE = Q
(
jω
)
(15)


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where,
number, and
ofsurface inhomogeneity. For ideal electrodes, the CPE is equal to an ideal capacitor
when = 1.
Q
represents the CPE constant,
ω
is the angular frequency;
j
represents the imaginary
n
is an exponent related to the phase shift and can be used as a measure
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
n
The appropriate circuit which is required to analyze the electrode/solution interface system by
fitting the experimentally graphs are composed from various electrical elements: electrolyte
resistance (Rs) series with the parallel combination of the constant phase elements (CPE
and the polarization resistance ( p). This equivalent electrical circuit model used to fit the
EIS data is shown in Figure . The parameters obtained from EIS studies are presented in
Table . It is found that Rp values increases with the increase in the concentration of inhibitor
/ndl),
R
6
4
whereas the Cdl values show the reverse dependence. This is probably due to the increase of
surface coverage on the MS surface by the adsorption of inhibitor molecules. The decrease of
Cdl is related to the increase in the double-layer thickness resulting from the replacement of
water molecules at the steel/solution interface by these organic compounds through adsorption
process. The slight deviation of the value of ndl from the unity can be related to the deviation
of CPE from the ideal capacitive behavior due to inhomogeneity on metal surface resulting
2
from porous layer formation [52-54]. The highest value of Rp (1205 Ω cm ) and the lowest
-2
-3
value of Cdl (28.8 µF cm ) have been found for BB1C at optimum concentration (1.0x10
1
2

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
M). This result shows that the inhibitive performance of BB1C is better than that of SHA. The
obtained value of ηEIS is 93.7% for SHA. This value of inhibition efficiency increases with the
addition of a second segment of benzimidazole in the molecule and reaches a value of 97.1%
for BB1C. This order can be explained by the interaction between several active sites of N, S,
and π-electrons with vacant d-orbitals of iron atoms. Also, the total contact area created by
BB1C is greater than SHA, thus creating a greater surface interaction with the steel surface
[55]. The obtained results are in good agreement with those obtained from PDP and WL
measurements.
3.3.
Adsorption isotherms
1
1
1
1
1
1
In order to understand the adsorption mechanism of SHA and BB1C on to MS surface in HCl
solution, thermodynamic parameters of the adsorption process were calculated using the data
obtained from EIS measurements. The experimental data were fitted by various isotherms
models such as Langmuir, Temkin, Frumkin, and Freundlich. Their corresponding
expressions are as follows [56]
:
Langmuir isotherm:
θ
Cinh
1
6
KC =
;
vs Cinh
(16)
inh
1
-θ
θ
1
1
1
7
8
9
Temkin :
(-2fθ)
e
= KCinh
;
θ vs ln(Cinh
)
(17)
(18)
Freundluich:
n
inh
2
2
0
1
θ = KC
;
ln
(
θ
)
vs ln
(
Cinh
)
Frumkin :
θ


1-θ 
(-2fθ)
2
2
e
= KCinh
;
ln C
vs θ
(19)

inh

1
-θ
θ

1
3

-
1
1
2
3
4
5
6
7
8
9
Where Cinh is the inhibitors concentration (mol L ),
θ
is the degree of surface coverage,
K is
–
1
the adsorptive equilibrium constant (L mol ), and
f is the molecular interaction parameter.
The fitted results are presented in Figure
The fitted linear regression coefficients (
7.
2
R
) indicate that the adsorption of SHA and BB1C on
the MS surface is accord to the Langmuir isotherm, which is explained by a single layer
characteristic.
The values of the adsorption/desorption equilibrium constant
K
in the presence of SHA and
4
BB1C on the MS surface determined by Langmuir adsorption equation were 151.9×10 and
4
236.1×10 , respectively. In the literature, high values of
K allow more adsorption [57-59]. The
0
ads
1
1
1
1
1
1
1
0
1
2
3
4
5
6
standard adsorption free energy ΔG can be determined in order to judge the adsorption type
of the investigated molecules according to the following formula:
0
ads
ΔG = -RT Ln (55.5 K)
(20)
where 55.5 is the concentration of H O, T is the temperature, and
R
is the gas constant.
2
0
ads
−1
Generally, values of ΔG
of ≤ −20 kJ mol correspond to physical adsorption
−
1
(physisorption), while those around −40 kJ mol or more negative assigned to chemisorption
0
ads
-1
-1
[60]. The calculated values of ΔG for SHA and BB1C are -45.2 kJ mol and -46.3 kJ mol ,
0
ads
-1
1
7
respectively. As a result, the ΔG values up to -40 kJ mol declares that strong adsorption
1
1
2
8
9
0
of organic molecules occurs at the MS/solution interface. This adsorption process is due to the
pairs of free electrons on the nitrogen and sulfur atoms as well as the π-electrons of the
benzimidazole aromatic rings.
2
2
1
2
3.4. Thermodynamic activation parameters
The influence of temperature on the corrosion behavior of metals is very complicated because
of the different changes that occur at the electrode/electrolyte interface such as the dissolution
of the adsorbed molecule film [61]. The effect of temperature on the corrosion of MS in 1.0 M
2
2
3
4
1
4

1
2
3
4
5
6
7
8
9
0
1
2
3
4
HCl without and with different concentrations of SHA and BB1C has been studied in the
temperature range of 298 K - 328 K using PDP technique. Compared with that in blank
-3
solution, the icorr value decreases remarkably with the addition of 1.0×10 M of SHA and
BB1C at each temperature, implying that these compounds considerably inhibit the corrosion
reaction of MS.
The inhibition efficiency decreasedfor BB1C from 97.4% at 298ꢀK to 88.6% at 328ꢀK.Thus,
BB1C still show superior inhibition performance to prevent MS from corrosion by forming a
firm adsorption film on the steel substrate [61, 62]. Arrhenius plots of Ln(icorr) vs. 1000/T and
Ln(icorr/T) vs. 1000/T of MS in 1.0 M HCl solution containing SHA and BB1C are illustrated
1
1
1
1
1
9
in Figure . The corrosion kinetic parameters such as activation energy (Ea), the enthalpy of
activation (ΔHa), and the entropy of activation (ΔSa) for the corrosion of MS in acid medium
-3
without and with the optimum concentration of inhibitors (1.0×10
M) at
temperatures ranging from 298 K to 328 K are estimated from Arrhenius equation (21) and
transition state equation (22) [16, 63]
.

Ea

1
1
5
6
icorr =Aexp -
(21)



RT

icorr
T
R

ΔSa


ΔHa

=
exp
exp -
(22)







Nh
R
RT

1
1
1
2
2
2
2
7
8
9
0
1
2
3
Where,
A
is the Arrhenius factor,
h
is Planck's constant,
N
is Avogadro's number, and R is the
universal gas constant. The values of activation energy Ea were calculated according to the
equation (21) from the slopes of the straight lines (-Ea ). The values of ΔHa and ΔSa can be
computed from the relationship between Ln(icorr ) vs. 1000/ . The straight lines would have
a slope equal to –ΔH /R and an intercept equal to Ln(R/N h)+ –ΔS /R. The activation
/
R
/
T
T
×
a
a
-3
parameters for MS in 1.0 M HCl in the absence and presence of 1.0×10 M of SHA and
BB1C are shown in Table
6
.
1
5

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
The presence of the studied inhibitors increased the energy barrier (Ea) of the inhibiting
solution above that of the blank and hence the inhibition process. This increase can be
explained by the gradual adsorption of these molecules to form a barrier film on MS surface.
These findings suggest a physical adsorption mode of SHA and BB1C on the mild
steel surface [15]. The positive sign of the enthalpy (ΔHa) reflects the endothermic nature of
the MS dissolution process [64, 65]. The negative values of the entropy (ΔSa) indicate a
decrease in the degree of randomness, which occurred when the reactants are transformed to
activated complexes i.e. the association is favorite rather than the dissociation process [66,
67]
.
1
1
1
1
1
1
1
1
3.5. Surface analysis
3.5.1. Energy dispersive X-ray analysis (EDX)
In order to get more information about the composition of MS surface before and after the
formation of the protective film, Energy Dispersive X-ray analysis (EDX) was recorded
for MS samples immersed 6 hours in 1.0 M HCl solution in the absence and presence of the
-3
optimum concentration of benzimidazole derivatives (1.0×10 M). The results obtained from
the EDX spectra are shown in Figure 10. EDX spectra of MS after immersion in 1.0ꢀM HCl
without any inhibitors show the main component of the existence elements on MS surface.
1
8
However, it can be noticed fromthe EDX recorded in the presence of SHA and BB1C (Figure
1
2
2
2
2
2
9
0
1
2
3
4
10) that new peaks appear of Nitrogen (N) and Sulfur (S) atoms which act as active centers of
these inhibitors for adsorption and formation of the film on steel surface. It is also assumed
from Table
7 that the percentage atomic content of Oxygen remarkably reduced from 2.68 %
to 1.14% for SHA and disappeared in the case of BB1C due to the MS surface coverage by
these compounds.
3.5.2. Scanning Electron Microscopy (SEM)
1
6

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
SEM images were taken in order to study the surface morphology of MS specimens
after 6hours of immersion in 1.0 M HCl with and without SHA and BB1C. It can be observed
from Figure 11 that the surface morphology was damaged heavily by exposing the specimen
to 1.0 M HCl (Blank). While, the surface of specimen was smoother and showed less pits
-3
after immersion in acidic solution containing 1.0×10 M of SHA and BB1C. The smoothness
of inhibited MS surface is due to the formation of a protective barrier film created when
inhibitor molecules interact with the corroding surface of MS in acid solution [68]
.
3.5. Quantum chemical calculations
Quantum chemical calculations were used to investigate the adsorption and inhibition effect
of SHA and BB1C using DFT (Density Functional Theory) calculations. The B3LYP/6-31 G
(d, p) basis set in Gaussian 09 program was used in the neutral forms of SHA and BB1C
in both gaseous and aqueous phases. The optimized geometry, HOMOs-LUMOs molecular
orbitals, Molecular Electrostatic Potential (MEP), and the contours maps of the electrostatic
potential are shown in Figure 12. It is clear that the electronic distribution of the HOMO is
mainly delocalized over the benzimidazole moiety for SHA, as well as sulfur atom lone pairs,
whereas the HOMO distributions of BB1C across the entire molecule (Figure 12). Both the
LUMOs of SHA and BB1C have been delocalized over the whole molecule, whereas they are
mainly composed of acceptor moieties. The charge distributions have been shown with the
help of different colors; the negative regions of MEP (red and yellow) were
related to electrophilic reactivity while the positive electron density were occurs in the
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
blue regions [69]. The energy values of the HOMO and LUMO,
), electronegativity ( ), the number of electrons transferred (∆N110), molecular dipole
moments ( ) and Fukui functions are frequently used as descriptors of chemical reactivity.
∆Egap, chemical hardness
(η
χ
µ
The calculated values are grouped in Table 8. Obviously, a high value of EHOMO is consistent
with high chemical reactivity, i.e. high tendency to release electrons to the appropriate
1
7

1
2
3
4
5
6
7
8
9
0
1
2
3
4
acceptor molecules of low empty molecular orbital [70, 71]. The binding ability of the
inhibitor to the metal surface also increases with the decrease of the ELUMO and energy band
gap (ΔEgap) values. These results showed that BB1C is most reactive in both phases, while
SHA is less reactive. Obviously, a low value of hardness
η is related to high protection ability
[72, 3]. In our case, BB1C with hardness value of 2.593ꢀeV was predictable to have a superior
inhibition efficiency. Generally, molecules that have dipole moment with high value are
connected with polarizability having high value and excellent effective surface area and hence
should be excellent corrosion inhibitors as comparing with other inhibitor with having dipole
moment with low values [38]. The order obtained for dipole moment values: BB1Cꢀꢀ>ꢀꢀSHA
indicates that BB1C has an excellent inhibition performance comparedto SHA. The
theoretical calculations suggested that ∆Eback-donation values follows this order: BB1C (-0.648
eV) > SHA (-0.667 eV), which indicates that back-donation is favored for the BB1C. The
quantum chemical descriptors for benzimidazole derivatives in their neural form are shown in
1
1
1
1
1
Table 8
.
+
−
1
5
The calculated condensed Fukui indices fk and fk derived from natural population analysis
1
1
6
7
(NPA) for the studied inhibitors in their neutral form in both gaseous and aqueous phasesare
regrouped in Table 9. The preferred active sites for electrophilic attack is the atom where the
−
1
1
2
2
8
9
0
1
value of fk the highest value the preferred active site for nucleophilic attacks is the atom
+
where fk has the highest value [38]. According to Fukui indices (Table
9
), the high value of
+
fk is present at S(10), C(13), N(7), C(3), and C(4), indicating the high susceptibility of
+
nucleophilic attack at these sites, while great value of fk is present at S(10), N(7), C(8), and
2
2
2
3
C(1), i.e., these sites are susceptible to electrophilic attack. In the case of BB1C, the sites for
nucleophilic and electrophilic attack are S(12), S(10), C(3), C(8), N(7), and N(14). Therefore,
1
8

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
the benzimidazole-2-thione segment are the most plausible nucleophilic and electrophilic
attack.
3.7. DM simulation studies
3.7.1. Effect of temperature on adsorption species containing in the supercell of Fe (110)
The complexity of understanding the mechanism of corrosion inhibition has prompted many
electrochemists and theorists to search more effective ways to understand this phenomenon.
The simulation of molecular dynamics (MD) is considered to be a very effective and more
common method to explain this mechanism in parallel with experimental studies [74]. For this
reason, it is important to create a system similar to that carried out in experimental part;
+
-
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
indeed, the supercell of Fe (110) contains H O and Cl corrosive ions, water molecules (H O)
3 2
and the inhibitory molecule (SHA or BB1C). In this section, the absorption behavior of the
tested molecules in acidic environment have been studied based on the adsorption
configurations of inhibitor molecules as well as the values of the interaction energies.The
experimental study shows that our inhibitors are effective against corrosion.
BB1Cshowedgreatercorrosioninhibitioneffect than SHA. Therefore, the first mission is to
confirm this result using MD simulation.
After 400 ps, both the temperature and energy reached a balance which explains that the
system acquired the state of equilibrium for both simulated temperatures (Figure 13). The
most stable adsorption configuration for SHA and BB1C on Fe (110) surface for both
temperatures (298 K and 328 K)are shown in Figure 14. It can be noticed from Figure 14 that
the tested molecules are positioned during the process of simulation just above and parallel
with the first layer of superficial iron despite the increase in temperature. For this reason, a
strong interaction between the inhibitor/surface system exists that leads to a greater extent of
inhibition efficiency (See RDF method). The large molecular structure of BB1C covers a
large part of the metal surface, which enhances its inhibitive effectiveness compared to SHA.
1
9

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
The amount of energy that is released when a molecule is adsorbed on the metal surface can
be registered under the name interaction energy (Einteraction) of the studied system.Indeed, the
energy indices such as binding energy (Ebinding) and (Einteraction) make it possible to value the
adsorption capacity of the studied compounds on the iron substrate. Generally, the high
negative values of the adsorption energies indicate a strong, stable and spontaneous
adsorption of inhibitors on Fe(110) surface [75]. Table 10 shows that the values obtained of
-1
the Einteraction at the 298 and 328 K temperatures are -586.785 and -558.499 kJ mol for SHA,
-1
-641.939 and -595.548 kJ mol for BB1C, respectively. The negative values of the E
interaction
reflect the spontaneous adsorption on Fe(110) surfaces. In addition, the BB1C is associated
with more negative interaction energy, which is reflects its strong adsorption on the metal
surface and achieves better corrosion inhibition. Furthermore, the values of binding energy for
both inhibitors are classified according to the following order: BB1C > SHA.This
classification indicates that the adsorption performance of BB1C is higher than SHA. In
addition, it is obvious that the increase in temperature leads to a decrease in the Ebinding values
for both molecules, indicating that the increase in temperature may affect the adsorption
process of these molecules.
1
1
1
1
1
1
1
1
1
1
2
2
2
These results provide strong support for DFT calculations and experimental results, and
further confirm that the formation of the inhibitor-adsorption film on MS substrate.
3.7.2. Radial distribution function (RDF)
The chemical bonds formed between an atom of the inhibitor molecule and the iron atom of
steel are determined using the radial distribution function (RDF) method. The RDF is
determinate as follows:
NX NY
δ
(r − r)
1
1
ij
2
3
gXY (r) =
×
(23)
∑∑
2
〈
ρY 〉local NX
4π r
i∈ X i∈ Y
2
0

1
2
The g(r) functions indicate the density probability of finding particle Y at distance (r) around
particle X. Moreover,
ρY 〉local represents the particle density of Y averaged over all shells
〈
3
4
5
6
7
8
9
0
1
2
3
4
5
6
around particle X. The distances of the most active heteroatoms (W) in Ångström (Å) for both
studied inhibitors with iron (Fe) atoms are shown in Figure 15. Generally, when these values
(Fe-W) are in the interval of 1 Å ~ 3.5 Å, the chemistry bonds are formed [76]. The
coordination bonds found are due to the existence of non-binding electrons located on the
nitrogen and sulphur atoms. The chemical nature of the bonds formed is more resistant despite
the increase of temperature, indicating the significant efficiency of SHA and BB1C against
corrosion.
1
1
1
1
1
1
1
3.7.3. Mean Squared Displacement (MSD)
MSD calculation is done for understanding the effectiveness of inhibitors film for preventing
−
+
the migration of corrosive species i.e., Cl and H O . Figure 16 shows the mean squared
3
-
displacement (MSD) plots for the diffusion behavior in the systems containing 3Cl and 3
+
H O ions and 30 molecules of inhibitor (SHA and BB1C). The model created to determine
3
the diffusion coefficient (D) of the corrosive ions. This is achieved by using the Einstein
diffusion law represented by the following equation [77, 78]
:
2
]
1
7
MSD=
[
R (t)- R (0)
(24)
(25)
i
i
Nα
1
d
2
]
1
1
8
9
D
=
lim
[
Ri
(t
) − Ri (0)
∑
Nα x dt i
→∞
6
=1
where Nα is the number of diffusing atoms, Ri(0) and Ri(t) are the position vectors of
corrosive species at time 0 and , respectively.
2
2
2
2
2
0
1
2
3
4
t
The diffusion of benzimidazole molecules were examined by drawing their MSD plots and
the diffusion coefficients were calculated from the slopes of these diagrams. The results are
summarized in Table 11. It can be shown from Table 11 that the minimum values of the
diffusion coefficient of corrosive ions are obtained for BB1C, which implies that this
2
1

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
molecule has a better structural performance to prevent corrosion of metal surface. However,
a comparison of the experimental, computational and SEM/EDX results reveals that the
investigated molecules adsorb strongly on MS surface, subsequently obstructing the active
sites that are responsible for corrosion phenomenon. Thus, the surface area available for
+
H ions reduced. In addition, the two anodic and cathodic processes might be suppressed on
addition of inhibitors. The adsorption process occurs mainly through unshared paired
electrons of heteroatoms (N and S), conjugated double and aromatic rings of benzimidazole,
forming a protective surface film.
3.8. Inhibition mechanism of SHA and BB1C
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
Adsorption behavior of inhibitor molecules depends on on the bonding property between the
inhibitor molecules and metal atoms or ions, as well as the surface situations [79]. Figure 17
shows the schematic depiction for the adsorption of SHA and BB1C on the surface of Fe. the
representation has been elucidated based on the results of experimental analysis and
theoretical calculations. A lot of research has indicated that the mild steel surface is positively
charged in HCl solution, i.e., there are excess positive charges on the steel surface [80, 81]
.
In aggressive acidic media, organic molecules can preferentially protonated, which can
favorite electrostatic interactions (i.e., physisorption) with charged metal surface with chloride
-
ions (Cl ) as intermediates their cationic forms [82]. However, as soon as inhibitor molecules
come onto the metallic surface through physisorption, further oxidation of surface metallic
atoms results into the production of electrons that consume by protonating hydrogen and
eliminate hydrogen gas. Therefore, cationic inhibitor molecules return their neutral form.
Subsequently, in the second adsorption mechanism (i.e., chemisorption), the investigated
molecules that contain heteroatoms (S and N) and
π electrons in their chemical structures can
donate the electrons from their electron-rich sites towards the vacant d orbitals of iron atoms.
This type of electron transfer causes an excessive accumulation of negative charge on the
2
2

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
metal surface, which leads to the formation of back-donation interactions.The BB1C inhibitor
has multiple sites of interaction with the metal, allowing it to create a larger surface area to
protect aginst corrosion. This may be the main reason for the higher higher inhibition
properties of this compound compared to SHA.
Conclusions
In the present study, the corrosion inhibition and adsorption characteristics of two
benzimidazole derivatives in 1.0 M HCl solution were investigated. The results show that the
OCP, WL measurement, PDP, EIS, SEM and EDX studies show that the BB1C can provide
effective corrosion inhibition for MS in 1.0ꢀM HCl solution, with the inhibition efficiency up
-3
1
1
1
1
1
1
1
1
1
1
2
2
to 97.1%at 1.0×10 M. Moreover, the inhibitive performance of the BB1C is better than that
of SHA. The PDP curves showed that these compounds prevents metal dissolution
and hydrogen evolution reactions (mixed-type inhibitors). EIS results indicated that the
resistance (R ) of the MS increased significantly while its capacitance decreased after the
p
addition of SHA and BB1C inhibitors. The effective inhibition is achieved by the adsorption
of SHA and BB1C onto the MS surface, which involves the chemisorption as well
as physisorption. The adsorption of the inhibitors on the MS surface obeys Langmuir
isotherm. DFT calculations provide useful information about the electronic property of the
studied molecules and clarify the difference in inhibition efficiency. Molecular dynamics
simulation indicates that both investigated molecules adsorbed nearly parallel to the Fe (110)
surface.
2
3

1
2
References
3
4
5
6
7
8
9
0
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3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
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