Benzimidazole ligands in the corrosion inhibition for carbon steel in acid medium: DFT study of its interaction on Fe30 surface

Article abstract of DOI:10.1016/j.molstruc.2016.04.057

The corrosion inhibition of N,N′-bis(benzimidazole-2-yl-methyl)amine (L¹) and N, N′-bis(benzimidazole-2-yl-methyl)hydroxyethylamine (L²) was analyzed by electrochemical and theoretical methods. The data show that ligands form an adsorption layer over an iron surface, obeying the Langmuir isotherm of -32.96 kJ mol^-1); the value are higher than -20 kJ mol^-1 but less than -40 kJ mol^-1, belonging to a conversion stage of physical adsorption to chemical adsorption or a comprehensive adsorption. This is consistent with fractal dimension of the electrode surface, estimated by an impedance depression angle of a semicircle that the surface is homogeneously covered by the formation of an inhibitor film. Furthermore, the electronic parameters of the ligands were analyzed by DFT, showing that L¹ and L² possesses corrosion inhibition properties that give up its p orbital electron density through its HOMO orbital to the metal LUMO to form an adsorption layer, and this has been proved theoretically by the interaction of ligands with Fe₃₀. In addition, we have collected corrosion inhibition data for around 70 organic compounds reported in the literature, and the inhibition data plotted against different inhibitors, showing that amine ligands are good corrosion inhibitors.

Full text of DOI:10.1016/j.molstruc.2016.04.057

Accepted Manuscript
Benzimidazole ligands in the corrosion inhibition for carbon steel in acid medium: DFT
study of its interaction on Fe surface
30
E. Garcia-Ochoa, S.J. Guzmán-Jiménez, J. Guadalupe Hernández, Thangarasu
Pandiyan, José M. Vásquez-Pérez, Julián Cruz-Borbolla
PII:
S0022-2860(16)30380-5
10.1016/j.molstruc.2016.04.057
MOLSTR 22471
DOI:
Reference:
To appear in: Journal of Molecular Structure
Received Date: 8 March 2016
Revised Date: 18 April 2016
Accepted Date: 19 April 2016
Please cite this article as: E. Garcia-Ochoa, S.J. Guzmán-Jiménez, J.G. Hernández, T. Pandiyan, J.M.
Vásquez-Pérez, J. Cruz-Borbolla, Benzimidazole ligands in the corrosion inhibition for carbon steel in
acid medium: DFT study of its interaction on Fe surface, Journal of Molecular Structure (2016), doi:
30
10.1016/j.molstruc.2016.04.057.
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ACCEPTED MANUSCRIPT
Benzimidazole ligands in the corrosion inhibition
for carbon steel in acid medium: DFT study of its
interaction on Fe30 surface
E. Garcia-Ochoa1, S.J. Guzmán-Jiménez1, J. Guadalupe Hernández2, Thangarasu
Pandiyan3*, José M. Vásquez-Pérez4, Julián Cruz-Borbolla5
1 Centro de Investigación en Corrosión, Universidad Autónoma de Campeche, Av.
Agustín Melgar s/n, Col. Buenavista, CP 24039, Campeche, Cam, México.
2 Centro Tecnológico de la Escuela Nacional Profesionales, Universidad, Nacional
Autónoma de Mexico (UNAM), Aragon, Estado de Mexico, Mexico.
3Facultad de Química, Universidad Nacional Autónoma de México, Ciudad
Universitaria, México D.F. 04510, México.
4 Cátedra CONACyT, Universidad Autónoma del Estado de Hidalgo, Unidad
Universitaria, km 4.5 Carretera Pachuca-Tulancingo, C.P. 42184, Pachuca-Hidalgo,
México.
5Área Académica de Química, Universidad Autónoma del Estado de Hidalgo,
Unidad Universitaria, km 4.5 Carretera Pachuca-Tulancingo, C.P. 42184, Pachuca-
Hidalgo, México.
* Author to correspondence: pandiyan@unam.mx
1

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Abstract
The corrosion inhibition of N,N´-bis(benzimidazole-2-yl-methyl)amine (L1) and N,
N´-bis(benzimidazole-2-yl-methyl)hydroxyethylamine (L2) was analyzed by
electrochemical and theoretical methods. The data show that ligands form an
adsorption layer over an iron surface , obeying the Langmuir isotherm (ꢀG°ads of -
32.96 kJ mol-1); the value are higher than -20 kJ mol-1 but less than -40 kJ mol-1,
belonging to a conversion stage of physical adsorption to chemical adsorption or a
comprehensive adsorption. This is consistent with the fractal dimension of the
electrode surface, estimated by an impedance depression angle of a semicircle that
the surface is homogeneously covered by the formation of an inhibitor film.
Furthermore, the electronic parameters of the ligands were analyzed by DFT,
showing that L1 and L2 possesses corrosion inhibition properties that give up its p
orbital electron density through its HOMO orbital to the metal LUMO to form an
adsorption layer, and this has been proved theoretically by the interaction of ligands
with Fe30. In addition, we have collected corrosion inhibition data for around 70
organic compounds reported in the literature, and the inhibition data plotted against
different inhibitors, showing that amine ligands are good corrosion inhibitors.
Keywords: Corrosion inhibition, benzimidazole, DFT, iron cluster, electrochemical
1. Introduction
Corrosion problems represent a serious problem in industries, especially petroleum
industry where acids are being used to stimulate the carbonate reservoir or for
dissolving fines. Although acids such as hydrochloric, hydrofluoric, acetic, or formic
acids are common to be injected into the well during the acidizing stimulation
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process, mostly HCl at concentrations of 5–28% is being employed in acidizing
treatments [1] because sulphate, nitrate, and phosphate salts have lower solubility
than chlorides in aqueous media [2]. Thus the corrosion problem in the industries is
unavoidable, and the general Corrosion rate is extremely high (>100 mm/y) and it
can increase exponentially with increasing temperatures and acid concentrations[3].
To control the corrosion damage of well tubulars, mixing tanks, coiled tubings, and
other metallic surfaces, the corrosion process need to be inhibited by the use of an
effective corrosion inhibitor[4, 5]. The study of corrosion inhibition of mild steel
using organic inhibitors mainly in acidic media is one of the most important subjects
in the current industrial research [6-8]. It is common to use organic compounds
having π-electrons and hetero-atoms like nitrogen, sulfur, and oxygen as inhibitors
in order to impart resistance towards the aggressive [9-12] and they can interact to
get adsorbed on to the metal surface [13-15]. The efficiency and suitability of the
inhibitors are mainly depend on the nature and surface charge on metal, the type of
aggressive electrolyte and the chemical structure of inhibitor. Most of these
inhibitors possesses at least one functional group which is considered to be the
reaction centre for the adsorption process as the relationship between the inhibitive
properties and the their molecular structures is crucial for the corrosion inhibition
efficiency. Sometimes, one inhibitor works in one well may not suitable in another
well [16] because the mechanism of the inhibition is usually not known, in spite of
some proposed models for forecasting corrosion inhibition[17-19]. Thus, there is a
great need to investigate the influence of substituent on the inhibitive performance
inhibitors; for example, long chain organic compounds are believed to be stronger
corrosion inhibitors due to the good hydrophobicity, but they are also poor water-
solubility.
In the context, several following compounds were tested as corrosion inhibitors:
benzoin and benzil compounds [20]; sodium N-alkylphthalamates (alkyl = n-C6H13,
n-C10H21, n-C14H29)[21]; tributylamine, some alcohols, aniline, n-octylamine,
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diphenylamine, dodecylamine, di-n-butylamine, cyclohexylamine, and 1,3-dibutyl-
2-thiourea [4]; furfuryl alcohol[22]; octyl alcohol and propargyl alcohol[23]; 2-
butyn-1-ol, 3-butyn-1-ol, 3-pentyn-1-ol, and 4-pentyn-1-ol[24]; benzimidazole, 2-
aminobenzimidazole, 2-mercaptobenzimidazole, 1-benzylbenzimidazol, and 1,2-
dibenzylbenzimidazole and different azole [25]; 3-(4-amino-2-methyl-5-pyrimidyl
methyl)-4-methylthiazoliumchloride[26]; 2-(alkyl(CnHn+1)dimethylamonio)butanol
bromides (n = 11–15)] [27]; 1-(2-pyridylazo)-2-naphthol[28]; 1-(2-ethylamino)-2-
methylimidazoline-N-[3-(2-aminoethylaminoethyl)]-acetamide,
and
1-(2-
ethylamino)-2-methylimi[29]; pyridoin
cinnamylidine-3-thiocarbohydrazide
thiocarbohydrazide[30].
and
and
2,20-pyridil [28];
and 1-
1,10-dicinnamylidine-3-
Although the above compounds were studied for the corrosion inhibition, The
benzimidazole containing inhibitors could be effective due to the following
properties: (i) its hydrophobic nature, (ii) the planarity of benzimidazole moiety; (iii)
delocalized π- electrons in the aromatic ring, (iv) hetero-atoms like nitrogen. In
previous studies [31-34], compounds containing benzimidazole/imidazole groups
have been shown as competent corrosion inhibitors in acid medium [3-5, 22-25].
Thus, in this paper, we evaluate the inhibition effectiveness of N,N´-
bis(benzimidazole-2-yl-methyl)amine and N, N´-bis(benzimidazole-2-yl-methyl)-
hydroxyethylamine on the corrosion of mild steel in 0.5 M HCl solution; to analyze
their structural nature for the corrosion inhibition, the interaction studies with
different metal clusters Fe15, Fe16 and Fe30 is performed by DFT which has been
proved as an efficient theoretical method to probe the inhibitor /surface interaction.
2. Experimental Section
2.1 Synthesis of ligands
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The ligand has been prepared as reported elwhere indicated in literature [35-37].
N,N-bis(benzimidazole-2-yl-methyl)amine (L1): Iminodiacetic acid (13.6 g 100 mM)
and 1,2-phenylenediamine (21.6 g, 200 mM) were refluxed for 24 hours in 4N HCl
(80 mL), the resulting solution was cooled to isolate the hydrochloride of the
compound, then it was neutralized using aqueous ammonia. The product obtained
was re-crystallized from aqueous methanol. Yield: 72%, M.P 248 ± 2°C. Elemental
analysis for C16H15N5; Calc C 69.30, H 5.45, N.25.30; found: C 69.18; H, 5.32, N.
25.24. MS (IE, m/z %): 275 [M]+, 276 [M+1], 132 (100) [C8H8N2]+, 118 (8.9)
[C7H6N2]+ , 146 (24.6%) [C8H8N3]+: 1H NMR (300, MHz, CD3OD): δ= 3.310-4.111
(m, 4H, bzim-CH2-N.), 4.917 (s, H, -CH2-NH-CH2-) and 7.200-7.550 (m, 8H, bzim-
13
rings). C NMR (300, MHz, CD3OD): δ= 48.860-49.428 (CH2-N-) and 123.628-
155.124 (bzim-rings).
N,N- bis (benzimidazole-2yl-methyl) hydroxyethylamine (L2): The above procedure
was adopted to prepare N,N- bis (benzimidazole-2yl-methyl) hydroxyethylamine
(L2) using N-(2-hidroxyethyl) iminodiacetic acid (2.65 g, 15 mmol) and 1,2-
phenylenediamine (3.24 g, 30 mmol). Yield: Yield: 87%, M.P 198 ± 2 °C:
Elemental analysis: Calc. (%) for C18H19N5O.H2O: C, 63.79; H, 6.19; N, 20.64.
Found (%): C 64.27, H 6.43, N 20.64%. MS, (IE, m/z (%)): 322 [M]+, 132 (100)
1
[C8H8N2]+, 77 (8.5%) [C3H9NO]+, 160 (42.5%) [C9H10N3]+. H NMR (300, MHz,
CD3OD): δ = 2.736-4.058 (s, 4H, -N-CH2-CH2-OH), 4.930 (m, 4H, bzim-CH2-N-)
13
and 7.208-7.563 (m, 8H, bzim-rings). C NMR (300, MHz, CD3OD): δ= 48.858-
49.427 (CH2-N-), 53.891-60.494 (-CH2-CH2-OH) and 123.759-154.180 (bzim-
rings).
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2.2 Electrochemical Procedure
A standard electrochemical Princeton Applied Research (PARC) cell (1.0 L)
assembled by a carbon steel working electrode (WE) and two-graphite counter
electrodes (CE), and a saturated calomel electrode (SCE) as the reference electrode,
was used in the experiment. The carbon steel working electrode (WE) was a flat
specimen with an exposure area of 1.0 cm2 and then it was mechanically polished
using different grades of emery paper (120-1200). The specimens must be degreased
with acetone and then washed with bi-distilled water to avoid carbon pollution. The
composition of the carbon steel was: w%: 0.18 C, 0.35 Mn, 0.17 Si, 0.025 S, 0.03 P
and the remaining composition content was Fe. The cell was connected Solartron
1280Z controlled through a Computer having CorrWare and Zplot program. The
organic inhibitor was added to the aggressive HCl medium (0.5M) which was first
purged with nitrogen gas for 45 min to eliminate dissolved oxygen in the medium.
The electrochemical tests were carried out at room temperature under static
conditions. All the experiments were performed after dipping the working electrode
into a HCl (0.5 M) containing the inhibitor at the open-circuit potential, Ecorr, with
respect to a SCE reference electrode. Two independent experiments were carried out
for each concentration and the data were collected.
The same arrangement was employed for both electrochemical polarization curves
and impedance faradaic spectroscopy. In order to apply the electrochemical Tafel
extrapolation, polarization curves were recorded by the potential-dynamical method
at a rate of 1.0 mV/s from -400 mV to + 400 mV versus the open circuit potential;
the scan rate (1.0 mV/seg) allows the quasi-stationary state measurements.
Electrochemical impedance spectroscopy (EIS) was carried from 20 kHz to 50 mHz,
with a 15 mV peak-to-peak.
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2.3 Computational details
To study the adsorption mechanism of ligands L1 and L2, the iron surface was
modeled with finite cluster of 30 Fe atoms as this contain more than 25 atoms bulk –
like form an electronic point of view[38]. The ground state geometry of the cluster
was optimized through Born-Oppenheimer Molecular Dynamics (MD) simulations
as indicated previously for other metal clusters[39, 40]. To test the accuracy of our
methodology, the ground state geometries of two smaller iron clusters Fe15, and Fe16
were optimized[41]. The molecular dynamics were performed for 150 ps with a time
step of 1 fs at the DFTB-SCC spin polarized level of theory using the DFTB+
software [42]. Linear cooling of the system was performed from 1200 K to 10 K
using the Nosé-Hoover chain thermostat, following the annealing technique.
Multiplicity of 49, 51, and 91 were selected for the optimization of the clusters Fe15,
Fe16, Fe30, respectively, in order match the experimental magnetic moments[42].
To determine the interaction energy of the Fe30 cluster accurately with the inhibitor
molecules L1 and L2, multiple configurations for the interaction of Fe30 with the
inhibitors were determined from Born-Oppenheimer molecular dynamics at the
DFTB-SCC spin polarized level of theory. The simulations were run for 50 ps with a
time step of 2.0 fs, cooling the system linearly from 600 K to 10 K. Then local
optimizations were performed for both systems with a quasi-Newton root search
method at the DFT VWN/DZVP/GEN-A2 [43] level of theory using the deMon2k
software [44].
In order to understand the reactivity of the ligands, HOMO and LUMO energies,
ionization potential, electron affinity, electronegativity, hardness, electrophilicity,
electroaccepting and electrodonating powers, Fukui functions, condensed Fukui
functions and electrostatic potential of L1 and L2 inhibitors were calculated at the
[56]
DFT B3LYP/cc-pVDZ level of theory using the Gaussian 09
and MultiWFN
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software [45]. For calculation of condensed Fukui functions Hirshfeld charges were
employed to define the atomic electron populations.
3. Results and Discussion
3.1Corrosion inhibition studies
The electrochemical inhibition properties of
N,N´-bis(benzimidazole-2-yl-
methyl)amine (L1) and N,N´-bis(benzimidazole-2-yl-methyl)hidroxyethylamine
(L2) were analyzed by the polarization Tafel extrapolation and Faradaic impedance
spectroscopy [9, 10, 46-48]. The polarization experiments were carried at different
concentrations of compounds in order to estimate the corrosion rate in the electrode
surface. The Tafel extrapolation was applied to determine the rate of corrosion or
corrosion inhibition. The data show that in the presence of the inhibitor, the
polarization current is considerably decreased, meaning that the intensity of
corrosion is decreased. For instance, for the curve before the addition of L1 or L2 to
the corrosive medium (0.0 mM), the current density was 5.89 ×10-4 A/cm2, and it
was considerably reduced to 2.40 ×10-4 A/cm2 for L1 (0.2 mM), and for L2, it was
reduced to 1.81 ×10-4 A/cm2, observing that the current density is decreased in both
cathodic and anodic branches (Fig.1). It shows that the compounds perform as a
mixed inhibitor. The corrosion rates (Table 1) were measured after the metal surface
exposure to corrosive medium for 4.0 hours in the presence of compounds at
different concentrations, manifesting that with the increasing inhibitor concentration,
the corrosion rate continuously decreases; particularly, the corrosion potential does
not suffer significantly. It indicates that the mechanism of corrosion inhibition in the
metal surface is merely presenting an adsorption phenomenon that hampers both
anodic and cathodic reactions.
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Fig.1. Polarization curves of carbon steel immersed in HCl (0.5 M) at
different concentrations: a) L1; b) L2
Table 1. Electrochemical polarization data of the inhibitors
Inhibitor L1
(mM)
0.0
Ecorr (V)
Icorr (A/cm2)
%E
-
βa(mV dec-1) βc(mV dec-1)
θ
194
211
241
229
176
133
135
133
115
91
-0.5340
-0.5284
-0.5470
-0.5472
-0.5433
5.89x10-4
-
0.01
5.194x10-4
3.977x10-4
3.577x10-4
2.399x10-4
0.1183 11.83
0.3249 32.49
0.3928 39.28
0.5927 59.27
0.03
0.07
0.2
Inhibitor L2
0.0
194
133
-0.5340
5.89x10-4
-
-
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0.01
0.03
0.07
0.2
151
153
171
166
117
112
119
95
-0.5214
-0.5309
-0.5332
-0.5296
3.46x10-4
3.29x10-4
2.881x10-4
1.813x10-4
0.4126 41.26
0.4415 44.15
0.5109 51.09
0.6922 69.22
The degree of inhibitor coating over the metal surface at different concentrations,
which is directly related to the efficiency of the inhibitor [49, 50] is determined as
follows:
icorr −icorr(inhi)
θ
=
icorr
%E =
θ
x100
θ = degree of inhibitor coating over the metalic surface; icorr = corrosion rate without
inhibitor and icorr(inh) = rate of corrosion with inhibitor.
Furthermore, it is found that the adsorption process of L1 and L2 over the metal
surface follows Langmuir isotherm model [49, 51] with yielding a straight line
Cinh
1
=
+Cinh
θ
Kads
for the plot of Cinh/θ vs. Cinh (Fig. 2). The slope of the plot was nearly 1.0,
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Fig.2. Adsorption isotherms of inhibitor on mild steel surface in 0.5 M HCl.; a) L1; b) L2
indicating that the L1 or L2 molecule interacts significantly with metallic surface to
form an inhibitor film over the iron surface that corresponds to single layer[52].
Furthermore, with using this model (Langmuir isotherm adsorption), the Gibbs free
energy (ꢀGo ads), which can be used to describe the stability of the adsorption bond
between compound and metal, was determined by using Kads in the following
equation.
∆Gaods = −RT ln(55.5Kads )
Generally, if the ꢀG value is resulted around -20.0 kJ mol-1, the ligand-metal
interaction is classified as physisorption, i.e., there is an electrostatic interaction of
the inhibitor molecule with the metal surface; otherwise, if the ꢀG is around -40.0
kJ mol-1 or above, there is presence of chemisorptions between ligand and metal,
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where a covalent bond is formed between the donor atom of the inhibitor and iron
[53]. The ꢀGo
value resulted for the adsorption of inhibitor (L1) was -33.75 KJ
ads
mol-1 and its adsorption constant was 14887 M-1, indicating that a strong bond
formed between L1 and metal through chemisorption. Similarly, for L2, the values
were, ꢀGo ads= -36.20 KJ mol-1 and adsorption constant= 39988 M-1. This suggests
that the ligand L2 is stronger than L1 due to the difference of -2.45 Kj M-1
.
The impedance diagram (Fig. 3) describes the behavior of inhibitors at different
concentrations in the corrosive medium and it is seen that there is present a single
capacitive semicircle, corresponding to one time constant (τ),
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Fig. 3. Impedance diagram of carbon steel in HCl (0.5 M) at different inhibitor
concentrations a) L1; b) L2.
equivalent to an electric circuit, (Rs(Rt CPE)) (Fig 4) of corrosion process, which is
similar to the proposal of many researchers[54, 55]. For the inhibitors (L1 and L2),
Fig. 4. Circuit electrical equivalent with one CPE.
there exists an agreement between capacitance and time constant to determine the
amount of substance that reacts in a unit of time. For example, the resistance transfer
increases with the increasing concentrations, consequently, decreases the
capacitance and increases the time constant (see Table 2). In the electric circuit,
constant phase element (CPE) represents the electrochemical metal interface.
corresponding to the solution resistance (Rs) and Rt represents the resistance
transfer. The CPE is determined by the following equation[56, 57]:
1
n
= Q( jω)
Z(cpe)
½
Z(cpe) = impedance of CPE; Q corresponds to a proportionality factor, j is (-1) ;
frequency. n = surface irregularity estimation [25, 57, 58]
ω
= angular
.
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The CPE is considered to be a surface irregularity of the electrode[59] and it causes
a depression in the Nyquist semicircle diagram for the inhibitor presence in the
corrosive medium [60]; thus, we could not draw a conclusion that the metal solution
interface performs as a capacitor, for which the metal surface should be flat and
homogeneous. If the electrode surface is considered as homogeneous and plane, the
exponential value (n) becomes equal to 1.0 and the metal-solution interface acts as a
capacitor with regular surface. The time constant (τ) and the capacitance value (C)
of the CPE can be calculated by the following equations [61, 62].
τ n
Q =
Rp
1
C = (QRp1−n )n
τ = time constant, C = capacitance of double layer associated with one CPE.
Table 2. Electrochemical impedance data of the inhibitors
L1 (mM)
0.0
n
0.815
0.766
0.724
0.773
0.685
Ds
C (F cm-2)
Rs (Ω)
3.83
3.65
3.63
3.90
3.09
Q(Ω-1cm-2sn)
1.061 x 10-3
1.020 x 10-3
9.805 x 10-4
8.495 x 10-4
1.578 x 10-3
Rt (Ω)
42
τ (s)
2.22
2.30
2.38
2.29
2.46
5.296 x 10-4 0.023
4.173 x 10-4 0.025
3.310 x10-4 0.025
3.661 x 10-4 0.030
5.456 x 10-4 0.049
0.01
60
0.03
72
0.07
79
0.20
87
L2 (mM)
0.0
3.83
3.12
1.061 x 10-3
1.054 x 10-3
0.815
0.785
2.22
2.27
42
62
5.296 x 10-4 0.023
4.805 x 10-4 0.030
0.01
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0.03
0.07
0.20
3.32
3.97
3.91
1.215 x 10-3
9.588 x 10-4
8.778 x 10-3
0.789
0.787
0.772
2.26
2.27
2.29
66
6.037 x 10-4 0.040
4.715 x 10-4 0.040
4.227 x 10-4 0.051
84
117
The resistance transfer (Rt) at different concentrations of inhibitor during the period
of 4.0 hours is shown in Fig 5, observing clearly that the resistance was minimum
value in the absence of the compound in the corrosive medium, the speed of
corrosion is high without inhibitor over metal surface. However, in the presence of
the inhibitor, the Rt value increases steadily, suggesting that L1 or L2 form a
protective layer over the metal surface immediately and it stabilizes within a
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Fig. 5. Resistance variations (Rt) of charge transfer over 6 hours at different
concentrations: a) L1; b) L2
short period of time; this is an agreement with the results obtained from the
polarization curves.
The behavior of resistance transfer (Rt) led to a study of the performance of the
double layer caused by CPE. Thus the Rt values were plotted against time over
perioiod of 4.0 hours (Fig. 5) and it shows that the capacitance is maximum in the
absence of inhibitor (Table 2) and it steeply decreases in the presence of inhibitor
until its concentration to 0.2 mM. The time constant CPE (τ) against time, over
period of 4.0 hours shows that there is a continuous decrease in the speed of loading
and unloading of the capacitor when increasing the inhibitor (L1 or L2 )
concentration, manifesting that since the τ value is high, the charge transfer of
electrochemical corrosion reaction is continuously delayed.
What is more, by using the depression angle of the impedance semicircle of the
impedance diagram, the fractal dimension of the electrode surface can also be
estimated [64] with the following equation:
1
n =
Ds −1
Ds= fractional dimension of metallic surface
The Ds data show that the fractional dimension is lower in the absence of inhibitor
in the corrosive medium and it suggests that the high energy regions are caused by
the roughness of the surface of the electrode. This is entirely logical because on a
rough surface, the surface peaks are high-energy points which preferably dissolve
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into the solution to give a more homogeneous surface. On the other hand, in the
presence of inhibitors, a high fractal dimension (Ds) value was obtained, suggesting
that the inhibitors are being covered the electrode surface uniformly, and it inhibits
the corrosion process in the acid medium. Furthermore, in the study, compound L2
inhibits strongly by forming a uniform film over metal surface, because of its
addition functional groups. Thus a higher Ds value resulted for L2 than L1.
The corrosion inhibition efficiency of different compounds reported in the literature
was analyzed (Table 3 and Fig. 6), and it show that amine compounds are generally
more efficient for the corrosion inhibition than other compounds; however, some
benzimidazoles exhibit high corrosion inhibition efficiency, for example, 1,8-bis (1-
chlorobenzyl-benzimidazolyl)–octane or 2,2´-bis(benzimidazole) are good corrosion
inhibitors.
4.42E-04
3.92E-04
3.42E-04
Amine
Pyridine
2.92E-04
Benzimidazole
Present work L1, L2
2.42E-04
1.92E-04
1.42E-04
9.20E-05
4.20E-05
-8.00E-06
0
5
10
15
20
25
30
Number of inhibitors reported in the literature
Fig. 6. The current density of compounds for the range of 0.1-0.2 mM plotted
against different inhibitors.
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Table 3. Efficiency of corrosion inhibition of different organic compounds (0.1 –
0.2 mM) reported in the literature
Compounds
Ref.
Conc. Icorr
(mM) (A/cm2)
Rp
%
ƞ
(ꢀ cm2)
Amines
0.2
0.2
0.2
0.1
0.220 x10-4
0.156 x10-4
0.110 x10-4
1.22 x10-4
58
35
54
67
87
Benzylidene-pyridine-2-yl-amine
4-Methyl-benzylidene)-pyridine-2-yl-amine
4-Chloro-benzylidene)-pyridine-2-yl-amine
[63]
[63]
[63]
[64]
19
18
547
Methyl-1-[((methylphenyl){[3-methoxycarbonyl)-5-
methyl-1H-pyrazol-1-yl]methyl}
amino)methyl]-5-methyl-1H-pyrazole-3carboxilate
0.1
2.72 x10-4
273
71
N,N-bis[3,5-dimethyl-1H-pyrazol-1-yl)methyl]-N-(4-
methylphenyl)amine
[64]
0.1
0.1
0.47 x10-4
3.27 x10-4
679
339
89
65
N,N,N-tris[(3,5-dimethyl-1H-pyrazol-1-yl)methyl] amine
[65]
[65]
N,N,bis(methyl 1-[({[3-(methoxycarbonyl)-5-methyl-1H-
pyrazol-1 yl]methyl}amino)methyl])-5-methyl-1H-
pyrazole-3-carboxylate
0.1
0.1
0.1
0.1
3.48 x10-4
0.25 x10-4
0.26 x10-4
0.28 x10-4
72
90
89
88
2-[{2-[bis-(2-hydroxyethyl)amino]-ethyl}(2-
hydroxyethyl)amino]ethanol
[66]
[67]
[67]
[67]
758
748
743
4-(N,N,N-dimethyldodecylammonium
bromide)benzylidene-4-methoxybenzene-2-yl-amine
4-(N,N,N-dimethyldodecylammonium
bromide)benzylidene-4-aminobenzene-2-yl-amine
4-(N,N,N-dimethyldodecylammonium
bromide)benzylidene-4-hydroxybenzene-2-yl-amine
0.1
0.1
0.1
0.29 x10-4
0.32 x10-4
0.369 x10-4
734
693
220
88
87
91
4-(N,N,N-dimethyldodecylammonium
bromide)benzylidene-4-chlorobenzene-2-yl-amine
[67]
[67]
4-(N,N,N-dimethyldodecylammonium
bromide)benzylidene-4-nitrobenzene-2-yl-amine
N-[(Z)-1-phenylemethyleidene]-N-{2-[(2-{[(Z)-1phenyl-
[68]
18

ACCEPTED MANUSCRIPT
methylidene]amino}phenyl)disulfanyl]phenyl} amine
0.1
0.1
1.004 x10-4
0.795 x10-4
123.5
145.8
87
86
2-[({2-[(2-{[(Z)-1-(2-hydroxyphenyl)methylidene] amino}
phenyl) disulfanyl]phenyl} imino)methyl]phenol
[68]
[68]
N-[(Z)-1-(4-methylphenyl)methylidene]-N-{2-[(2-{[(Z)-1-
(4-methylphenyl) methylidene]amino}phenyl)
disulfanyl]phenyl} amine
0.1
0.655 x10-4
759.4
91
(E,E)-N,N'-dibenzo[b,d]thiene-2,8-diylbis[1-(thiophen-2-
yl)methanimine]
[69]
0.1
1.067 x10-4
0.1972 x10-4
0.5705 x10-4
0.4082x10-4
0.2815x10-4
0.2345x10-4
0.76x10-4
499.9
427
85
60
71
79
86
88
70
Dibenzo[b,d]thiophene
Decylamine ethoxylate
Decylamine ethoxylate
[69]
[70]
[70]
[70]
[70]
[70]
[71]
0.2
0.13
0.17
0.19
0.18
0.1
601
840
1243
1505
230
Decylamine ethoxylate
Hexadecylamine ethoxylate
N-benzyl-N,N-bis[(3,5-dimethyl-1H-pyrazol-1-
yl)methyl]amine
pyridines
0.1
0.1
0.79 x10-4
0.91 x10-4
4.04 x10-4
453
315
74
70
69
(5-methyl-1-pyridin-2-yl-1H-pyrazol-3-yl)methanol
ethyl 5-methyl-1-pyridin-2-yl-1H-pyrazol-3-carboxylate
[72]
[72]
[73]
0.91
x10-4
(2Z)-3-imino-4-methyl-2-(pyridin-3-ylhydrazono)
pentanenitrile
0.1
0.1
0.1
3.34 x10-4
2.37 x10-4
1.19 x10-4
75
82
91
4-(3,4-dichlorophenyl)-2,6-dimethyl-1,2-dihydropyridine-
3,5-dicarbonitrile
[73]
[73]
[73]
1,4-diamino-5-cyano-2-(4-methoxyphenyl)-6-oxo-1,6-
dihydropyridine-3-carboxylic acid
Ethyl 4-amino-5-cyano-2-(dicyanomethylene)-6-phenyl-
1,2-dihydropyridine-3-carboxylate
0.1
0.2
0.2
3.319 x10-4
0.22 x10-4
0.156 x10-4
56
58
19
75
35
54
Bis-2,6-(3,5-dimethylpyrazolyl)pyridine
Benzylidene-pyridine-2-yl-amine
(4-benzylidene)-pyridine-2-ylamine
[74]
[63]
[63]
19

ACCEPTED MANUSCRIPT
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.111 x10-4
0.21 x10-4
1.241 x10-4
1.194 x10-4
1.08 x10-4
2.62 x10-4
1.76 x10-4
1.25 x10-4
18
67
73
85
85
70
51
67
77
(4-chloro-benzylidene)-pyridine-2-yl-amine
2-(3-methyl-1H-pyrazol-5-yl) pyridine
2-phenylimidazo[1,2-a]pyridine
[63]
[75]
[76]
[76]
[77]
[78]
[78]
[78]
420
147.4
157.7
90
2-(m-methoxy phenyl) imidazo[1,2- a] pyrimidine
3-bromo-2-phenylimidazol[1,2- α] pyridine
2,6-bis-(hydroxy)-pyridine
2,6-bis-(chloro)-pyridine
Diethyl 1,1’-(pyridine-2,6-diyl)bis(5-methyl-1H-pyrazol2-
3-carboxylate
imidazoles
0.1
4.63 x10-4
1.87 x10-4
1.48 x10-4
1.77 x10-4
1.96 x10-4
28.5
53.7
102
77
2-(2-trifluoromethyl-4,5-dihydro-imidazol-1-yl)-
ethylamine
49
79
74
69
65
[73]
[73]
[79]
[79]
[79]
2-(2-trichloromethyl-4,5-dihydro-imidazol-1-yl)-
ethylamine
0.1
N´-(phenylmethylidene)-2-(2-methyl-1H-benzimidazol-1-
yl) acetohydrazides
0.17
0.17
0.16
N´-(4-methylphenylmethylidene)-2-(2-methyl-1H-
benzimidazol-1-yl)acetohydrazides
N´-(4-methoxyphenylmethylidene)-2-(2-methyl-1H-
benzimidazol-1-yl)acetohydrazides
74
Benzimidazoles
2,2´-bis(benzimidazole)
0.1
6.0×10-4
1.17×10-4
1.40×10-4
0.31×10-4
2.88×10-4
2.57×10-4
7.14×10-4
2.21×10-4
96
87
85
98
80
82
58
84
[80]
[11]
[11]
[81]
[82]
[82]
[83]
[83]
tris(benzimidazole-2-ylmethyl)amine
tris(benzimidazole-2-ylmethyl)amine
1,8-bis (1-chlorobenzyl-benzimidazolyl) -octane
2-(4-pyridyl)-benzimidazole
0.1
150
0.15
0.13
0.1
146
639
48.63
52.12
46.6
148.9
2-(4-pyridyl)-benzimidazole
0.25
0.1
2-aminomethyl benzimidazole
Bis (2-benzimidazolylmethyl) amine
0.1
20

ACCEPTED MANUSCRIPT
1.95×10-4
0.1
Tri (2-benzimidazolylmethyl) amine
2,6-Bis-(2-benzimidazolyl) pyridine
Bis-(2-benzimidazolyl methyl) sulphide
Bis-(2-benzimidazolyl methyl) oxide
1,2-Bis-(2-benzimidazolyl) ethylene
Benzimidazole
212.7
40.5
32.5
25
88
79
71
63
50
36
[83]
[84]
[84]
[84]
[84]
[85]
[85]
2.47×10-4
0.1
3.49×10-4
0.1
4.53×10-4
0.1
5.99×10-4
0.1
17.5
90
0.42
0.38
1.30×10-4
1.15×10-4
2-Methylbenzimidazole
98
44
2-Mercaptobenzimidazole
0.33
0.1
0.56×10-4
0.288×10-4
0.484×10-4
0.520×10-4
0.390×10-4
3.700×10-4
2.399x10-4
213
464
196
262
372
73
87
79
82
87
75
59
[85]
[86]
[86]
[87]
[87]
[88]
2-mercaptobenzimidazole
2-mercaptobenzoxazole
0.1
1, 4-bis-benzimidazolyl-butane
1, 4-bis-benzimidazolyl-butane
1-Butyl-2-(4-methylphenyl)benzimidazole
0.1
0.2
0.19
0.2
87
Present
work
L1
0.2
1.813x10-4
117
69
Present
work
L2
3.2 Theoretical studies
The geometries of Fe15, Fe16 and Fe30 clusters are fully optimized (Fig. 7) with the
total multiplicity of M = 49, 51, and 91 respectively (M = 2S + 1, S = total spin),
and the global minimum energy of Fe15 and Fe16 clusters data derived from our
methodology matches with the reported in the literature[41]. The global reactivity
descriptors, i.e HOMO and LUMO energies, ionization potential, electron affinity,
electronegativity, hardness, electrophilicity, electroaccepting and electrodonating
21

ACCEPTED MANUSCRIPT
powers of L1 and L2 inhibitors are presented Table 4, showing that both inhibitors
are expected behave almost similar in their interaction with metal surface.
Fig. 7 Optimized geometries of Fe15 (left), Fe16 (center) and Fe30 (right) clusters
obtained by simulated annealing at the DFTB-SCC spin polarized level of theory.
Table 4. HOMO, LUMO, gap, ionization potential (IP), electron affinity (EA),
electronegativity (χ), hardness (η) and electrophilicity (ω) of L1 and L2 inhibitors
calculated at the DFT B3LYP/cc-pVDZ level of theory. All values are given in eV.
Inhibitor
EHOMO
-4.75
-4.78
ELUMO
-0.76
-0.84
ꢀE
IP
EA
χ
Η
ꢁ
ω+
ω−
L1
L2
3.99
3.94
6.21
6.10
0.58
0.47
3.39
3.29
2.81
2.81
2.05
1.92
0.06
0.04
6.85
6.61
To rationalize chemical reactions in analyzing the reactive site in a ligand molecule,
although several local and global descriptors are being considered [89-93], the
condensed-to atom Fukui indexes (CAFI) f(r) was used to identify the local
reactivity of the ligand [90, 94, 95]. In the study, the most suitable descriptor,
Hirshfeld charge was employed to calculate the CAFI as suggested in the previous
reports [96, 97]. The calculation yielded reliable NPA charges at different basis sets
22

ACCEPTED MANUSCRIPT
(DGDZVP and 6-31G**) in the B3LYP framework. The Fukui function f(r) defines
as the derivative of the electronic density ρ(r) with respect to the number of
electrons N at a constant external potential ʋ(r) and it allows to identify the most
active sites in the ligand:
]
If the effects of relaxation associated with the addition or removal of electronic
charges are not considered, then
ρ
LUMO(r) = density of the first unoccupied molecular orbital; ρHOMO(r) = density of
the highest occupied molecular orbital [98]. The condensed Fukui functions[94] are
found by taking the finite difference approximations from the population analysis of
atoms in molecules, depending on the direction of the electron transfer.
23

ACCEPTED MANUSCRIPT
(qx =charge on atom x in the molecule); are being employed.
The Fukui indices data (Table 5, Fig.8 and Fig. 9) show that the reactive sites are
located over the aromatic rings of the ligands. For all atoms in the ligand, the CAFI
f(r) data calculated for ligand with B3LYP at different basis sets (DGDZVP and 6-
31G**) show that the Hirshfeld Population Analysis and natural population analysis
(NPA) predict positive values; the Fukui Functions indicate that those atoms having
the largest Fukui values are the most reactive site; for instance, the most reactive
ones for L1 are N5, C3, C6, C9, C10, and C11; while that L2 are O1, N4, C5, C8,
C10, C13 and C14. These results indicate that the oxygen atom of L2 inhibitor has
the capacity to donate charge. Moreover the electrostatic potential map shown in
Fig. 8c that the nitrogen (N5) for L1 and (N4) for L2 have the most negative potential
on the isosurface
a
b
c
24

ACCEPTED MANUSCRIPT
Fig.8. a) f+ Fukui function of L1 inhibitor (left) and L2 inhibitor (right); b) f- Fukui
function of L1 inhibitor (left) and L2 inhibitor (right); c) Electrostatic potential
plotted on a 0.0001 electron density isosurface of L1 inhibitor (left) and L2 inhibitor
(right). In the electrostatic potential: blue color= positive electric charge; red color
= negative electric charge; green = potential close to zero. All the plots were
calculated at the DFT B3LYP/cc-pVDZ level of theory.
Fig. 9. Atom numbering of L1 inhibitor (left) and L2 inhibitor (right) corresponding
to the condensed Fukui indices.
Table 5. Condensed Fukui indices calculated with Hirshfeld charges of heavy atoms
in L1 and L2 inhibitors. The electron density was calculated at the DFT B3LYP/cc-
pVDZ level of theory. Note that the largest f+ or f- values of L2 inhibitor are not
located on the oxygen atom.
L1
L2
Atom
C1
f-
f+
0.026
0.010
Atom
C1
f-
f+
0.002
0.023
0.015
0.015
0.009
0.006
C2
C2
25

ACCEPTED MANUSCRIPT
C3
0.063
0.017
0.014
0.060
0.013
0.036
0.056
0.075
0.076
0.033
0.023
0.039
0.011
0.022
0.030
0.030
0.013
0.033
0.000
0.044
0.012
0.019
0.023
0.004
0.071
0.035
0.016
0.029
0.025
0.024
0.044
0.067
0.074
0.075
0.001
0.001
0.030
0.008
0.041
0.026
C3
C4
0.020
0.014
0.052
0.011
0.015
0.043
0.003
0.046
0.038
0.029
0.052
0.074
0.018
0.029
0.008
0.018
0.018
0.012
0.083
0.000
0.047
0.013
0.004
0.012
0.018
0.022
0.003
0.073
0.017
0.033
0.019
0.024
0.028
0.045
0.063
0.072
0.074
0.001
0.031
0.003
0.041
0.027
C4
C5
C5
C6
C6
C7
C7
C8
C8
C9
C9
C10
C11
C12
C13
C14
C15
C16
C17
N1
C10
C11
C12
C13
C14
C15
C16
C17
N1
N2
N2
N3
N3
N4
N4
N5
N5
O1
The interaction energies resulted from the adsorption of the inhibitors on the metal
cluster i.e. the energy difference between the cluster—inhibitor system and the
26

ACCEPTED MANUSCRIPT
isolated cluster and inhibitor. In the study, three configurations of L1 inhibitor and
five configurations of L2 inhibitor were adopted for their adsorption on the Fe30
cluster by the simulated annealing technique. The results show that both L1 and L2
inhibitors are adsorbed mainly through π interactions with the cluster. The annealed
geometries were then optimized at the DFTB and VWN levels of theory with spin
multiplicity of 91. The interaction energies of these configurations (Table 6) indicate
that the adsorptions energies of L2 are greater than those of L1 at both levels of
theory, but the magnitude of the difference is significantly smaller with VWN.
These values are comparable to the energies for the adsorption of benzene on iron
oxide surfaces[99]. To quantify the magnitude of the adsorption energy, we chose
the VWN values as DFT is more reliable than DFTB. The interaction energy
resulted for L2 (122.1 kcal/mol) is greater than that for L1 (101.9 kcal/mol) (Table
6). Thus adsorption of L2 over the metal cluster much stronger (around 20 kcal/mol)
than that with L1, agreeing with the experimental results that that L2 inhibitor binds
more efficiently to the Fe surface.
Table 6. Interaction energies of L1 and L2 inhibitors on the Fe30 cluster calculated at the
DFTB-SCC and VWN/DZVP/GEN-A2 levels of theory.
Interaction energy (kcal/mol)
Interaction
Multiplicity
DFTB
-63.6
VWN
-95.9
Fe30—L1
91
91
91
91
91
91
91
91
Fe30—L1
Fe30—L1
Fe30—L2
Fe30—L2
Fe30—L2
Fe30—L2
Fe30—L2
-67.1
-101.9
-100.3
-113.3
-108.5
-96.1
-72.0
-116.1
-116.1
-119.4
-132.8
-132.8
-117.3
-122.1
27

ACCEPTED MANUSCRIPT
The preferred interaction of L1 and L2 inhibitors with the Fe30 cluster is shown
(Fig.10), showing that the interaction occurs through π electrons of the aromatic
rings over the cluster. The additional energy acquired for L2 during the interaction
with the cluster ( L2-Fe30) is believed from the presence of oxygen atom although
this O⋯Fe interaction was not observed in all the five annealed configurations,
reducing significantly the energetic difference between the interaction energies of
L1-Fe30 and L2-Fe30 systems.
b
a
Fig. 10. a) Optimized geometry of most stable L1 inhibitor adsorbed on the Fe30
cluster. b) Optimized geometry of most stable L2 inhibitor adsorbed on the Fe30
cluster. Optimizations were performed at the VWN/DZVP/GEN-A2 level of theory.
Conclusion
Both inhibitors perform as mixed inhibitor as they affect both anodic and cathodic
branches by decreasing current density. The efficiency of inhibitors increases with
increasing their concentration in the corrosion medium. Furthermore, the presence of
additional functional group of the inhibitor L2 conferred greater stability to the film
28

ACCEPTED MANUSCRIPT
(-36.20 Kj M-1) than inhibitor L1 (- 33.75 Kj M-) with the difference of - 2.45 Kj M-
1. This is consistent with the fractal dimension data where a greater value is resulted
for L2 than L1, showing that the former adsorbs uniformly on the metal surface. DFT
and electrochemical studies clearly show that there is a formation of an adsorption
layer over the metallic surface by giving the π-electron density from delocalization
region through its HOMO orbital to the metal LUMO. Thus adsorption of L2 over
the metal cluster much stronger (around 20 kcal/mol) than that with L1, agreeing
with the experimental results that that L2 inhibitor binds more efficiently to the Fe
surface. In addition, the corrosion inhibition data collected for around 70 organic
compound reported in the literature show that amine ligands are mostly good
corrosion inhibitor, and exceptionally some benzimidazoles perform as efficient
inhibitors .
Acknowledgements
The authors acknowledge the Dirección General de Asuntos de Personal Académico
(Project PAPIIT No IN209616) for the economic support; USAII, Faculty of
Chemistry, UNAM for instrumental and DGSCA, UNAM for computation facilities
.
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X. W. Xu, X. P. Cai, B. C. Song, B. L. Zhang, H. L. Ying, Q. B. Xiao, J. Wang, Acta Petrologica
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[2]
Z. H. Yang, Z. Y. Song, X. M. Chen, X. A. Zhang, Y. P. Zhang, Y. T. Zhao, Y. Cui, H. Q. Zhang, X.
Xu, J. X. Shao, D. Y. Yu, X. H. Cai, Acta Physica Sinica 55 (2006) 2221-2227.
[3]
M. Xu, L. H. Li, X. Cai, Y. M. Liu, Q. L. Chen, J. X. Guo, P. K. Chu, Diamond Relat. Mater. 15
(2006) 1580-1584.
[4]
D. A. Jones, Principles and Prevention of Corrosion, second ed.,. Prentice-Hall Inc: New
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29