2-(2-Pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol as a sustainable inhibitor for copper corrosion in molten hydrated phase change materials

Article abstract of DOI:10.1016/j.molliq.2020.113927

An imidazoline derivatives, 2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol (PDIE) was synthesized with the help of microwave radiation and its inhibiting effect on copper corrosion was investigated in phase change materials (PCM) melts by using gravimetric measurements, electrochemical techniques and quantum chemical calculations. Results show that the addition of PDIE inhibitor greatly decreases the mass transportation at Cu/PCM interface and reduces the corrosion rate of copper by adsorbing on the copper surface. As the concentration of studied inhibitor reaches to the optimal 0.5 mM, the inhibition efficiency is maximized, reaching over 70percent at 333 K. Thermodynamic analysis indicates that the adsorption process of PDIE molecule is a mixed physisorption and chemisorption obeying Langmuir isotherm. Surface screening shows that the inhibited copper remains almost morphologically intact and the presence of PDIE compounds on copper surface are confirmed by XPS, EDS and FTIR detections. Local reactivity analysis reveals that the imidazoline ring and heteroatoms are the active sites of PDIE molecule. The corrosion inhibition mechanism is provided through both experimental tests and theoretical studies.

Full text of DOI:10.1016/j.molliq.2020.113927

Journal Pre-proof
2-(2-Pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol as a
sustainable inhibitor for copper corrosion in molten hydrated
phase change materials
Tianyu Zhao, Adnan Munis, Maosheng Zheng, Jun Hu, Haipeng
Teng, Liping Wei
PII:
S0167-7322(20)32146-2
DOI:
https://doi.org/10.1016/j.molliq.2020.113927
MOLLIQ 113927
Reference:
To appear in:
Journal of Molecular Liquids
Received date:
Revised date:
Accepted date:
8 April 2020
23 July 2020
25 July 2020
Please cite this article as: T. Zhao, A. Munis, M. Zheng, et al., 2-(2-Pentadecyl-4,
5-dihydro-1H-imidazol-1-yl)ethanol as a sustainable inhibitor for copper corrosion in
molten hydrated phase change materials, Journal of Molecular Liquids (2020),
https://doi.org/10.1016/j.molliq.2020.113927
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2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol as a sustainable
inhibitor for copper corrosion in molten hydrated phase change materials
First Author
Tianyu Zhao [Given Name: Tianyu, Family Name: Zhao]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China
Email: tianyu@stumail.nwu.edu.cn
Second Author
Adnan Munis [Given Name: Adnan, Family Name: Munis]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China
Email: adnanmunis@stumail.nwu.edu.cn
Third Author(*corresponding author)
Maosheng Zheng* [Given Name: Maosheng, Family Name: Zheng]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China.
Tel: +86-29-88303216, Email: mszheng2@yahoo.com
Fourth Author
Jun Hu [Given Name: Jun, Family Name: Hu]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China
Email: hujun32456@163.com
Fifth Author
Haipeng Teng [Given Name: Haipeng, Family Name: Teng]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China
Email: tenghp@nwu.edu.cn
Sixth Author
Liping Wei [Given Name: Liping, Family Name: Wei]
School of Chemical Engineering, Northwest University, Xi’an, 710069, P.R. China
Email: weiliping@nwu.edu.cn
1

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2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol as a sustainable
inhibitor for copper corrosion in molten hydrated phase change materials
Abstract
An imidazoline derivatives, 2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol (PDIE)
was synthesized with the help of microwave radiation and its inhibiting effect on copper
corrosion was investigated in phase change materials (PCM) melts by using gravimetric
measurements, electrochemical techniques and quantum chemical calculations. Results show
that the addition of PDIE inhibitor greatly decreases the mass transportation at Cu/PCM
interface and reduces the corrosion rate of copper by adsorbing on the copper surface. As the
concentration of studied inhibitor reaches to the optimal 0.5mM, the inhibition efficiency is
maximized, reaching over 70% at 333K. Thermodynamic analysis indicates that the
adsorption process of PDIE molecule is a mixed physisorption and chemisorption obeying
Langmuir isotherm. Surface screening shows that the inhibited copper remains almost
morphologically intact and the presence of PDIE compounds on copper surface are confirmed
by XPS, EDS and FTIR detections. Local reactivity analysis reveals that the imidazoline ring
and heteroatoms are the active sites of PDIE molecule. The corrosion inhibition mechanism is
provided through both experimental tests and theoretical studies.
Keywords: phase change material; corrosion inhibition; electrochemistry; imidazoline;
quantum chemical calculation;
1 Introduction
In order to narrow the gap between the alternative energy technologies and the increasing
energy demands, finding the efficient and economical energy storage buffer has become an
urgent issue. Among various thermal energy storage techniques, latent heat storages,
particularly hydrated salt phase change materials (PCM), have drawn much attention due to
their low phase change temperature and high thermal energy storage density. Researches
show that the capacity and stability of different energy systems can be considerably improved
with the addition of PCM [1-6]. Nevertheless, most hydrated salt melts are corrosive to
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metals and therefore the durability of container materials needs to be specially concerned
during the storage and transportation of PCM. Due to the high thermal conductivity and good
formability, copper as well as its alloys are widely applied in industries where massive heat
exchange is needed. However, the compatibility of copper has been found relatively less with
most hydrated salt PCM as compared to stainless steel[7-12]. Up till now very limited
work[7-15] has been devoted to evaluate the corrosive effects of hydrated salt PCM on metals
and the available information for corrosion protection of container materials is very scanty.
It is well accepted that heterocyclic compounds, especially nitrogen contained molecules,
are effective anticorrosive agents for metal protection [16, 17]. As one of the most promising
green inhibitors, imidazoline derivatives are favourable due to their good thermal stability,
easy accessibility and low toxicity and have been widely applied for metal protection [18].
Imidazoline derivatives is featured by three substructures, i.e., a five-membered ring with
nitrogen, a long alkyl chain and a pendant side chain possessing an active functional group.
Generally, the nitrogen-contented imidazoline ring prefers to attach and then efficiently
interact with metal surface by means of electrons sharing process, meanwhile the pendant
functional group favors the creation of coordination bonds at the metal/inhibitor interface and
the long alkyl tail potentially stretches up against metal surface or parallel lie on it[19]. These
combined efforts lead to the excellent inhibitive performance of imidazoline derivatives
against metal corrosion.
Researches reveal that factors as the length of the alkyl chain, the location and the
polarity of functional group on the imidazoline ring have considerable effects on the
inhibitive behavior [20]. It has been realized that[21, 22] the diffusion coefficient of corrosive
species including Cl-, HS- and H2O in imidazoline derivatives self-assembly film decreases as
the length of alkyl chain of imidazoline molecule increases, resulting in the increment of
inhibition efficiency. An effective imidazoline-based corrosion inhibitor owns attributes of
hydrocarbon chain attached on the ring nitrogen atom or on a relatively small organic radical
and the length of chain C longer than 12[23, 24]. Based on these findings, an imidazoline
derivatives was synthesized from hexadecanoic acid and aminoethylethanolamine in the
present work and its inhibition performance towards copper corrosion was evaluated in
composite hydrated salt PCM media. The studied hydrated salt PCM (Na2HPO4·12H2O -
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Na2SO4·10H2O) has been reported as an effective energy storage buffer in conjunction with
solar heating system[6, 25]. The imidazoline derivatives was synthesized，characterized and
then tested in the Cu-PCM system. The inhibitive performance of the imidazoline derivatives
was investigated using electrochemical measurements including potentiodynamic
polarization (PDP) and electrochemical impedance spectroscopy (EIS). Scanning electron
microscope (SEM), energy dispersivespectrometer (EDS) and X-ray photoelec-tron
spectroscopy (XPS) were employed to characterize the specimen surface. The inhibition
mechanism was further revealed by quantum chemical calculations.
2 Materials and methods
2.1 Synthesis and characteristic of inhibitor
The imidazoline compounds were prepared by using multimode microwave technology in
free solvent condition followed the synthesis route reported by Palou et. al[26]. The reaction
scheme is simplified in Fig.1. Raw materials of hexadecanoic acid (20mM) and
aminoethylethanolamine (20mM) were measured according to 1:1 molar quantities and
mixed together with the support of calcium oxide (10 g) in an open Pyrex vessel. The mixture
was then subjected to 8.5 min irradiation in a domestic microwave oven under 800W output
power. After that, the reactants were dissolved in ethyl acetate, and the yellowish solution
was heated to boiling and filtered while it was hot. The filtrate was dried later and the
purified cream-colored products were obtained.
The synthetic was then characterized by a FTIR Spectrometer (IRAffinity-1S, Shimadzu)
with records shown in Fig.2. There are adsorption peaks detected at 2916 and 2847 cm-1of
wavelength reflecting the stretching of C-H and -CH3 and the peak appeared at 722 cm-1 is
attributed to the [CH2]n skeleton of long alkyl tail. The peaks featured as C=N and C-N bond
(imidazoline ring) are detected at 1638 and 1315 cm-1 from the spectrum, respectively. The
N-H stretching which represents secondary amine is identified at 3293 cm-1. Additionally, the
O-H bending mode is visible at 1463 cm-1. These characteristic peaks are identical with those
reported in literatures [22, 27-29] indicating the successful derivation of the target
imidazoline derivatives.
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Fig. 1 Synthesis route of 2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol.
Fig.2 FTIR spectrum of 2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol.
2.2 Preparation of PCM and working electrodes
The hydrated PCM salts comprised of Na2HPO4·12H2O and Na2SO4·10H2O which has been
reported as an efficient thermal energy storage [6, 25] were chosen as the corrosive media
and prepared in analytical grade at a ratio (wt%) of 9:1. The prepared PCM salts were mixed
and melted at 333K by utilizing magnetic stirring in a thermostat water bath with a measured
pH value of 9. The inhibited medias were prepared by adding 0.1, 0.25, 0.5 and 1.0 mM of
2-(2-pentadecyl-4, 5-dihydro-1H-imidazol-1-yl)ethanol (PDIE) in the blank PCM,
respectively. After the addition of inhibitor, the measured pH value of PCM media remains
the same as 9, indicating the presence of PDIE did not affect the overall chemical property of
the electrolyte.
The working electrodes used for electrochemical tests were round copper coupons in
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14mm diameter machined from 3mm thick commercial copper sheet with Cu (wt%) >95%.
These coupons were subject to partially encapsulate in araldite leaving a 1.540 cm2 circular
surface area exposed to PCM media. Before commencing measurement, the exposed copper
surface was abraded using successive grades of emery paper up to 1500 grit, then degreased
in ethanol and cleaned through sonication in deionized water.
2.3 Weight loss measurement
The copper coupon of 2×1.5×0.3 cm3 was first abraded successively to 1500 grit SiC, later
degreased in ethanol, cleaned in deionized water and finally dried in air. The PCM melts were
prepared in five 100 mL bottles separately with various concentrations of the studied PDIE
additive (0.0, 0.1, 0.25, 0.5 and 1.0 mM). The prepared copper coupon was weighed by an
analytical balance with precision ±0.1 mg and then carefully placed in each reaction bottle
with the help of a thread maintaining fully immersed in the corrosive medium. All the
reaction bottles were suspended in a thermostatic water bath under a fixed temperature of
333K. An immersion duration of 72 hours was chosen according to ASTM G31-72 (2004),
item 8.11.4.2[30]. After 72h immersion, coupons were retrieved, cleaned with a brush,
washed thoroughly in deionized water, rinsed in ethanol, dried in air and then re-weighed.
The difference between the measured mass before immersion test W0 and after immersion
test W1 is designated as the weight loss (Eq.1).
∆푊 (푚푔) = 푊 − 푊
(1)
0
1
2.4 Electrochemical measurements
Electrochemical measurements were performed by using
a
PARSTAT 2273
Potentiostat/Galvanostate (Princeton Applied Research, US) equipped with a standard
three-electrode system in a sealed electrolytic cell with a capacity of 150 ml. A 10mm×
10mm Pt spade was employed as the auxiliary electrode and a saturated calomel electrode
(SCE) held by Luggin capillary was served as the reference electrode. All potentials recorded
in the present paper were referred to SCE scale. Prior to commencing each test, the
electrochemical cell is maintained for 30min at open circuit potential (Eocp) to attain the
system equilibrium. In order to diminish the disturbance of charging current meanwhile
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acquiring reliable response of electrode process, a scan rate of 1 mV s-1 was applied in the
DC polarization which has also been well reported [31,32]. The polarization curve is recorded
by anodically polarizing working electrode at a scan rate of 1 mV s-1 from -250 mV (SCE)
versus Eocp towards anodic direction. The electrochemical impedance spectroscopy (EIS)
measurements are investigated by applying potential perturbation signal of 5mV amplitude at
Eocp with frequency ranging from 10-3 Hz to 105 Hz. During tests, the electrochemical cell was
suspended in a thermostatic water bath with temperature controlled in ±1 K accuracy. All the
measurements were performed in triplicate to guarantee the data reproducibility.
2.5 Surface characterizations
After 72 h exposure in the PCM media in the absence and presence of 0.5mM inhibitors at
333K, copper coupons were separated from the melts and gently cleaned in distilled water in
order to remove the attached salts to better observe the surface damage. Surface
morphologies and elemental analyses of samples were recorded with the help of a JEOL JSM
6610- LV scanning electron microscopy (SEM) coupled with an energy dispersive
spectrometer (EDS) under an acceleration voltage of 20 kV. An X-ray photoelectron
spectrometer (PHI-5000 Versaprobe III, ULVAC-PHI) with the monochromatized Al Kɑ
(photoelectron energy, 1486.6 eV) X-ray source was employed to determine the surface
composition of the inhibited copper sample. The XPS detection was operated at a pressure
below 6×10−12 torr and a take-off angle of 45°was applied from surface. XPS data analysis
was carried out through software. The Fourier Transform Infrared Spectrometer device
mentioned in Section 2.4 was also applied to characterize the films extracted from the
inhibited copper surface.
2.6 Quantum chemical calculations
Quantum chemical calculations were performed with Materials Studio 2017 package via
DMol3 [33] programming based on density functional theory (DFT) [34,35]. The structure of
PDIE molecule was geometrically optimized at fine quality by employing the electronic
exchange-correlation functional GGA and BLYP basis[36,37], in conjunction with a
double-zeta basis set plus polarization (DNP) with 0.005 Ha Fermi smearing and a 3.7 orbital
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cutoff to enhance computing performance. The solvent effect was considered in the
computational calculations by applying conductor-like screening model (COSMO) with
defining water as the solvent. The corresponding quantum chemical indices, such as the
energy of frontier orbitals (the highest occupied molecular orbital, HOMO and the lowest
unoccupied molecular orbital, LUMO), the energy gap ΔE = ELUMO - EHOMO, and the dipole
moment (μ) were derived and discussed. Fukui functions of f (+) nucleophilicity and f (−)
eletrophilicity were also evaluated in order to analyze the local reactivity of the PDIE
molecule when interacting with copper atom.
3 Results and discussion
3.1 Open circuit potential
Fig.3 displays the monitored open circuit potential of Cu in PCM media as a function of
immersion time in the absence and presence of PDIE inhibitor. It is seen from the
commencement of curve that the initial open circuit potential of Cu electrode in blank PCM
media lies on more negative value than that recorded in PDIE contained PCM systems,
elucidating the corrosive nature of bare PCM media. In comparison, the revealed
ennoblement of Eocp in the presence of inhibitor is likely indicative of the retardation of
anodic process at the metal/electrolyte interface [38]. With the increasing of immersion time,
the measured Eocp of blank system displays a positive shift before reaching the
pseudo-stability status, while the Eocp of PDIE contained system shifts to negative direction.
The resultant variation of open circuit potential with time elapsing is highly associated with
the activation or the transformability changes of the metal surface film. Commonly, the
observed negative displacement of Eocp in the inhibited system is attributed to the adsorption
effect of inhibitor molecules on the electrode surface [16].
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Fig. 3 Open circuit potentials of copper electrode in blank and inhibited PCM melts with
various inhibitor concentrations
3.2 EIS measurements
The corrosion kinetics at Cu/PCM interface can be revealed from EIS technique. Fig. 4
displays the Nyquist and Bode diagrams at Eocp of Cu surface immersed in the PCM media
with and without PDIE additive. In the inhibitor free system, the Nyquist response of Cu in
the PCM media (Fig. 4 (a)) shows two time constants behavior, characterized by a small
capacitive loop at high frequency (HF) range and followed by a long linear portion between
Zre and Zim at low frequency (LF) range, namely Warburg impedance. The origin of HF
capacitive loop is mainly ascribed to the interfacial charge transfer process occurs at Cu/PCM
interface which designates copper dissolution [39, 40]. During the electrochemical process,
copper anodic dissolution can be considered as two steps including the first oxidation of Cu
to Cu(Ⅰ) and the follow-up oxidation of Cu(Ⅰ) to Cu(Ⅱ) [40-42]. Meanwhile, based on the
hydrolysis nature of the major PCM species HPO42− (Eq.2), Cu ions are able to combine with
hydroxide ions and subsequently to create a porous Cu2O scale (Eq.3 and Eq.4)[41, 42].
HPO42− + H2O ⇌ H2PO4− +OH−
Cu + OH− → Cu(OH) + e−
2Cu(OH) → Cu2O + H2O
(2)
(3)
(4)
Consequently, the electrons generated from the overall anodic process will be consumed
immediately by cathodic process mainly through water reduction (Eq. 5).
3H2O + 3e− → 3/2 H2 + 3OH−
(5)
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The appearance of Warburg impedance at LF (the inserted in Fig. 4 (a)) region can be
related to the diffusion process of oxidants from the bulk PCM into the scale and the scale/Cu
interface. Different from aqueous solutions, the interfacial charge transfer process of active
metals in concentrated salt medium can massively happen, and possibly are not rate
limiting[43, 44]. Instead, the transportation of oxidants in the porous scale may become
rate-limiting process [43, 44]. Therefore, the overall electrochemical process of copper in
bulk PCM is dominated by the diffusion of oxidants. By contrast, as PDIE compounds are
added to the PCM media, the Nyquist spectrum of copper changes significantly in both the
shape and the size of curve; the Warburg impedance at LF range vanished; the overall
response is dominant by one depressed semicircular capacitor loop; and the diameter of loop
grows multiply. These characteristics suggest that the overall copper corrosion is controlled
by the charge transfer process. Besides, the diameter of the capacitor loop that represents the
value of the interfacial charge transfer resistance (Rct) reaches the maximum as the addition
of PDIE compounds is 0.5mM, which is an indication of the most retarded interfacial mass
transportation.
The same is true of the Bode-phase angle response. As shown in (Fig. 4 (b)), the phase
angle against frequency spectrum of Cu displays initially two time constants in the case of
PDIE compounds free medium changed into one time constant in the presence of PDIE
inhibitor. As the concentration of inhibitor increases, the phase angle peak shows the
tendency to grow higher and broader, suggesting the growth of a protectable film on the
electrode surface[13]. The phase angle peak achieves the maximum (around 60) and covers
the widest frequency range (from 105 Hz to 10-1 Hz) when the concentration of PDIE reaches
0.5mM. However, at additive amount doubled into 1mM, the width of phase angle peak
reduces a little suggesting the adsorption ability of PDIE molecules is weakened as compared
to that in the 0.5mM PDIE containing system. Slight shrinking of Nyquist loop (Fig. 4 (a))
and a decrement of Bode-log |Z| value at LF range (Fig. 4 (c)) are also detected in the case of
high concentration (1mM) of additive, indicating that the studied PDIE compounds remains
the most inhibitory active in the PCM media only at particular range of concentration.
More quantitative information is extracted from the impedance curve by using the
electrochemical equivalent circuit (EEC) illustrated in Fig. 5. Herein, the constant phase
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element (CPE) was employed rather than an ideal capacitor so as to compensate the deviation
induced by the inhomogeneity/porosity of film formed on the electrode surface which is
characterized by twisted semicircles observed from Nyquist response with their centers below
the real axis of complex plan (Zre). The impedance of a CPE is defined through Eq. (6) [45].
1
−푛
(
)
푍퐶푃퐸
=
푖휔
(6)
푌
0
where Y0 represents the modulus, i is the imaginary root, ω is the angular frequency (ω = 2πf)
and n is the deviation parameter relating to the defective surface film. The ideal capacitor
behavior is regarded as n=1.
Accordingly, the inhibitor free system is analyzed by the EEC elucidated in Fig. 5(a) in
which a Warburg impedance (W) is involved, while the inhibited systems are analyzed in
term of the EEC shown in Fig. 5(b). In both models, Rs represents the electrolyte resistance
between the WE and SCE; R1 and CPE1 stand for the surface film resistance and the dielectric
nature of the film, respectively; Rct represents the charge transfer resistance at film/Cu
interface and CPE2 imitates the interfacial double layer capacitance. From CPE2 components
Y0 and n, the value of double layer (Cdl) can be derived through Eq.(7) [31].
1−푛
퐶푑푙 = 푌1 푅푐푡
⁄
⁄
푛
푛
( )
7
0
The inhibition efficiency (ηR) of PDIE compounds is evaluated as follows [45]:
푅푐푡 − 푅푐0푡
( )
휂푅 % = (
) × 100
(8)
푅푐푡
where 푅c0t and 푅ct are charge transfer resistance yielded in the absence and presence of
inhibitor, respectively.
All the calculated EIS parameters are gathered in Table 1. It is noticed that both values
of surface film resistance R1 and charge transfer resistance Rct of the inhibited copper
electrode increase with the increasing of PDIE dosage from 0.1mM to 0.5mM, especially Rct
which is approximate 2-4 times enlarged, as compared to the bare one. This is in accordance
with the observation of large and wide phase angle peaks born in the presence of PDIE
compounds, indicating the strong inhibitory activities of the studied PDIE compounds at
Cu/PCM interface which potentially cover the active copper substrate and thus block the
interfacial mass transportation. The value of Cdl also shows decreasing as the concentration of
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additive increasing up to 0.5mM. The decrement of double layer capacitance in inhibited
system is attributed to the formation of adsorbed film due to the adsorption of inhibitors
which in return reduces the dielectric constant between the metal and electrolyte [46].
Generally, organic inhibitors own less dielectric constant as compared to water molecules.
Therefore a gradual replacement of water molecules by the adsorption of the PDIE molecules
at Cu/PCM interface is highly likely, thus leading to the creation of protective layer on the
copper surface[47,48]. The more PDIE molecules are adsorbed, the more thicker the barrier
layer is formed in terms of the expression of Helmholtz model where the value of Cdl is
inversely proportional to the film thickness d, as shown in Eq.(9) [35].
휀휀0퐴
퐶푑푙
=
(9)
푑
where A is the surface area of electrode, ε0 is the vacuum permittivity and ε is the local
dielectric constant.
The highest Rct as well as ηR and the lowest Cdl are noted at PDIE concentration of
0.5mM, reflecting the most corrosion resistant copper surface and the most compact surface
film formed by PDIE molecules. It is clear that the inhibition efficiency of the studied PDIE
is concentration dependent and follows the order: 0.5mM > 1mM > 0.25mM > 0.1mM. As
the addition dosage exceeds the optimal value (>0.5mM), the inhibition efficiency ηR shows
the tendency to decrease about 5% inferring that the maximum surface coverage ability of
PDIE molecules has been reached in the Cu-PCM system. This phenomenon can be further
explained by the CMC (critical micelle concentration) theory [49] that the surfactant inhibitor
molecules in the electrolyte remain an ordered structure and subsequent form an adsorption
surfactant monolayer or bilayer on the metal surface at specific concentration range. Once the
inhibitor addition is exceeds the critical value, the electrolyte turns to be saturated and the van
der Waals force induced interaction between PDIE molecules become prominent,
subsequently resulting in the desorption of adsorbed molecules from metal surface[50-52].
The excess inhibitor molecules will further gather together and form a micelle which is in
spherical shape configurated by all alky tails pointing to the center of the sphere and
imidazoline rings pointing to the outside[49]. By suspending in the electrolyte, the micelle
lost the inhibitive ability and therefore the inhibition efficiency of PDIE shows decline when
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they are added beyond the optimal dosage.
Fig. 4 Impedance diagrams for copper in PCM media in the absence and presence of different
concentrations of PDIE additives at 333K: (a) Nyquist diagram; (b) Bode-phase angle
diagram; (c) Bode- impedance diagram; symbols represent experimental data and solid lines
are fitting curves
Fig. 5 Equivalent circuit model applied to fit impedance data (a) without and (b) with the
presence of inhibitor
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Table 1 Electrochemical impedance parameters derived for copper in PCM melts in the
absence and presence of different concentration of PDIE inhibitor at 333K.
Concentration
Rs
CPE1
(Y0/Ω-1 Sn cm-2)
4.765E-4
n1
R1
CPE2
(Y0 /Ω-1 Sn cm-2)
8.353E-3
n2
Cdl
(μF cm-2)
14.80
3.59
Rct
(Ω cm2)
472
W
Chi-Sqr
ηR (%)
mM
blank
0.1
(Ω cm2)
1.791
2.026
2.621
1.863
2.916
(Ω cm2)
6.895
(Ω-1 cm-2 S-1/2
)
0.869
0.925
0.913
0.996
0.892
0.706
0.516
0.535
0.499
0.504
4.308E-3
1.423 E-2
7.411 E-3
2.212 E-2
7.384 E-3
7.327 E-3
-
5.179E-5
10.915
11.570
16.385
13.901
1.931E-3
1003
1342
1864
1531
-
-
-
-
51.15
64.83
74.68
69.17
0.25
0.5
4.143E-5
1.295E-3
2.09
2.367E-5
7.987E-4
1.26
1
4.631E-5
1.220E-3
2.26
3.3 Potentiodynamic polarization measurements
Fig.6 displays the recorded potentiodynamic polarization (PDP) curves for copper electrode
immersed in blank and inhibited PCM media. It can be seen that the polarization curves
exhibit Tafel-type behavior in both anodic and cathodic region. Thereby, the corrosion current
densities (icorr) are derived by extrapolating the anodic and cathodic Tafel branches of PDP
curves [13,18,35]. Polarization parameters including corrosion potential (Ecorr), corrosion
current density (icorr), cathodic Tafel slope (βc), anodic Tafel slope (βa) and the standard
deviation of icorr are listed in Table 2 with inhibition efficiency (ηi) calculated from
Eq.(10)[31].
푖c0orr − 푖corr
( )
휂 % = (
) × 100
(10)
푖c0orr
where i0corr and icorr are current density in the absence and presence of inhibitor, respectively.
From the E-logi plots, it can been seen that the presence of PDIE compounds shift the
Ecorr of copper in the PCM media to more noble values and the suppression effect on current
densities is evident in both cathodic and anodic branches, which allows to designate the
studied PDIE compounds as a mix type corrosion inhibitor in the Cu-PCM system. However,
the course of each polarization curve remains similar during the whole voltage application
process, indicating the incorporation of PDIE compounds does not change the main corrosion
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mechanism of copper in the PCM media. The remarkable reduction of icorr can be clearly seen
from Table 2 indicating the inhibitory activities of PDIE compounds possibly through
adsorbing on the copper surface and subsequently forming an inhibitive layer which hinders
the further penetration of aggressive ions at Cu/PCM interface, resulting in the reduction of
charge transportation. As the concentration of inhibitor increasing from 0.1mM to 0.5mM, the
overall current density of copper surface shows stepwise decreasing which signifies an
increment of surface coverage area θ (θ =1-icorr/i0corr). The existence of PDIE compounds
considerably slows down the overall electrochemical process at Cu/PCM interface including
both the anodic dissolution of copper and the accompanied cathodic hydrogen evolution
reaction. It is noted that at PDIE concentration of 0.5mM the measured current density of
copper surface is suppressed by an order of magnitude as compared to the bare system and
the inhibition efficiency of PDIE compounds reaches the highest of 77.63%. While as the
addition amount increases to 1mM, the values of icorr slightly rises and induces a decrement
of ηi, which reflects the more frequent electrochemical activities and lager mass transfers
occurred at Cu/PCM interface as compared to the case of halved concentration. These
observations indicate that the corrosion inhibition behavior of studied PDIE compounds in
Cu-PCM system is sensitive to the addition dosage and an over adding may cause negative
effect, which are in good accordance with the EIS results.
Fig. 6 Potentiodynamic polarization plots for copper obtained in PCM melts at 333K with
and without different concentrations of PDIE additives
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Table 2 Polarization parameters derived for copper in PCM melts in absence and presence of
different concentration of inhibitor at 333K
Concentration
Ecorr
(V vs. SCE)
-0.439
βa
(mV dec-1)
87.62
-βc
icorr
(μA cm-2)
112.19
48.51
θ
ηi
(mM)
blank
0.1
(mV dec-1)
134.76
116.94
121.05
133.24
125.40
(%)
Std. Dev. σ
4.87
-
-
-0.415
64.33
3.49
0.57
0.71
0.78
0.74
56.76
70.51
77.63
74.45
0. 25
0.5
-0.418
68.41
33.08
1.86
-0.410
79.27
25.10
1.04
1
-0.422
72.19
28.66
2.11
3.4 Adsorption isotherm study
The interaction between PDIE inhibitors and metallic surface can be expressed by adsorption
isotherms. The adsorption behavior is commonly interpreted by Eq.(11) as a
quasi-substitution process between inhibitor molecules in the electrolyte (Inhaq) and water
molecules adsorbed on the metal surface (H2Oads)[53,54].
Inhaq + 푛H2Oads ↔ Inhads + 푛H2Oaq
(11)
where n accounts for the number of absorbed water molecules substituted by inhibitor
molecules.
Adsorption isotherms can be therefore depicted in the general formula below [55]
(
)
(
)
푓 휃, 푛 exp −2푎휃 = 퐾퐶i
(12)
in which f (θ, n) represents the configurational function related to the applied physical model
and the hypothesis for isotherm derivation; θ is the degree of surface coverage; n has the
same meaning as expressed in Eq.(11); 푎 is the molecular interaction parameter; K is the
equilibrium constant of adsorption and Ci is the inhibitor concentration.
In our case, the isotherm fitting results for both EIS and PDP measurements show a
good obedience to Langmuir adsorption isotherm with regression coefficient (R2) equal to
0.9926 and 0.9959, respectively, as demonstrated in Fig. 7. For Langmuir adsorption
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isotherm, values of n and 푎 in Eq.(12) equal to 1 and 0 respectively. The isotherm can be
interpreted as Eq.(13) where the available adsorption sites on metal surface is assumed to be
constant and each site carries only one adsorbate[54].
퐶i
1
=
+ 퐶i
(13)
휃
퐾ads
where Kads is the equilibrium constant of adsorption/desorption process.
From Fig. 7, the fitting slopes (1.39087 and 1.31078 for EIS and PDP results
respectively) are observed with deviations from unity, indicating the non-ideal Langmuir
behavior which may result from the nonhomogeneous copper surface formed by the
adsorption of PDIE inhibitors [56]. Accordingly, the free adsorption energy of studied PDIE
inhibitor ∆퐺a0ds can be calculated from Eq. (14) [47,54].
1
−∆퐺푎0푑푠
푅푇
퐾ads
=
exp (
)
(14)
55.5
where 55.5 is molar concentration of water in mol per dm−3, R is universal gas constant equal
to 8.3144 J K-1 mol-1 and T is temperature in Kelvin scale.
The computed ∆퐺푎0푑푠 values of the studied PDIE are -37.492 kJ mol-1 and -38.121 kJ
mol-1 for EIS and PDP results, respectively. The negative value of ∆퐺푎0푑푠 implies that the
adsorption process of PDIE compounds happens spontaneously on copper surface[32,56].
Generally, the value of free adsorption energy around -40 kJ mol-1 is deemed as
chemisorption owing to the formation of covalent bond via charge transfer between the
inhibitor molecules and the metal surface, while if the value of free adsorption energy is
around or less negative than -20 kJ mol-1, it corresponds to physisorption driven by
electrostatic interaction[32,50,51]. The computed free adsorption energy of PDIE stands in
the range of −20 and −40 kJ mol-1, therefore indicating the coexistence of chemisorption and
physisorption that occurred during the adsorption process of PDIE molecules on copper
surface.
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Fig. 7 Langmuir isotherm for the adsorption of studied PDIE compounds on copper surface in
PCM melts
3.5 Weight loss measurements
The weight loss of copper samples were measured after 72h immersion in the PCM media
unprotected and protected by PDIE at 333K. The corrosion rate vcorr (mm per year) of copper
specimen and the inhibition efficiency ηw (%) of studied PDIE are calculated in according to
Eq.(15) and Eq.(16), respectively[50,52]. Results are shown in Table 3.
87.6 × ∆푊
푣corr
=
(15)
(16)
휌퐴푡
푣푐0표푟푟 − 푣푐표푟푟
휂푤
=
× 100
푣푐0표푟푟
where t is the immersion time (h), ρ is the density of the copper (8.94 g cm-3); A is the total
area of specimen (cm2); v0 and vcorr are the corrosion rate of sample in the absence and
corr
presence of inhibitors, respectively. It is observed that the studied PDIE compounds exhibit
efficient inhibitive ability to copper corrosion in the PCM media；even with the addition of
0.1mM PDIE compounds the corrosion rate of copper is considerably reduced from 0.105 to
0.034 mm y-1. This depicts the excellent inhibitory ability of the PDIE compounds which
could be ascribed to the high surface coverage of copper offered by the inhibitor molecules
through adsorption activities where the generation of a strong interaction between the
metallic substrate and PDIE molecule is highly likely. The adsorbed PDIE molecules largely
occupy the active sites of copper surface, in return the penetration of corrodent is obstructed
and the reduction of overall interfacial mass transfer is perceived. It is also noted that
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increasing the concentration of PDIE additives up to 0.5mM in the PCM media results in a
direct decreasing in weight loss of copper specimen and the inhibition efficiency climbs up to
86.91%, while as the addition dosage continues increasing a saturation effect is induced as
can be observed from the saturated inhibition efficiency. These observations are in good
accordance with electrochemical measurements.
Table 3 Parameters calculated from weight loss measurements of copper specimens after 72 h
exposure in PCM media at 333K in the absence and presence of PDIE inhibitor
Concentration (mM)
ΔW(mg)
6.249
2.017
1.046
0.818
0.847
vcorr (mm y-1)
ηw (%)
-
Blank
0.1
0.105
0.034
67.73
83.27
86.91
86.45
0.25
0.5
0.018
0.013
1
0.014
3.6 Effect of temperature
The temperature effects on the corrosion behavior of copper in free and inhibited PCM media
were investigated in the temperature range of 317–341 K. Polarization plots are displayed in
Fig. 8. From both blank and imidazoline-containing system, it is clear that the rise of current
densities is pronounced with the increment of temperature and the shifting of anodic branch is
particularly evident in both cases. Moreover, the course of each polarization curve remains
similar suggesting the corrosion mechanism is barely affected by temperature variation.
Primary polarization parameters are derived and summarized in Table 4. From Table 4, the
observed icorr shows high dependence upon environment temperature as it stepwise increases
with temperature rising, being the largest at 341K in both uninhibited and inhibited systems.
This designates the accelerated corrosion reactions at Cu/PCM interface induced by the
increment of temperature. Notably, at each temperature the PDIE containing system
demonstrates much less current density than the PDIE free one, even though at 341K the
measured icorr of inhibited system is approximate one third of the uninhibited one, reflecting
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the remarkable retardation effect of PDIE compounds on corrosion process of copper in the
PCM media. It is also noticed that the inhibition efficiency of additives drops with
temperature rising, as it falls about 20% as the temperature increases from 317K to 341K.
The same decline of inhibitory behavior with respect to temperature is detected by
impedance response. Fig. 9 depicts the temperature effect on impedance spectrums for copper
electrode in PCM media containing 0.5mM PDIE. Correlating impedance parameters are
derived by the EEC shown in Fig. 5(b) with results listed in Table 5. Inspection of Nyquist
plot shows the prominent shrinking of capacitive loops and the in turn reducing of charge
transfer resistance of copper in the inhibited system with increment of temperature from 317
to 341K, which is an indicative of accelerated corrosion process. In accordance with Nyquist
response, Bode diagram also reveals that the absolute impedance value (Fig.9 (c)) is affected
by temperature variation and both the height and the width of phase angle peak (Fig.9 (b))
decrease with the incremental temperature, signifying the weakening of protection provided
by surface film. This degradation of protection is also confirmed from Table 5 where an
increment of Cdl values is detected as temperature increases, regarding to the thinning of
barrier surface film existed on copper substrate according to the rough estimation (Eq.(9)).
Apparently, from both polarization and impedance results that the inhibitory performance of
PDIE drops with temperature rising. Possibly, this is resulted from the desorption of PDIE
molecules and the consequent degradation of protective film formed on the copper surface
induced by high temperature environment where electrolyte molecules are more activated and
interfacial mass transportations are speeded up.
Fig. 8 Polarization plots of copper in PCM media at different temperatures (a) without PDIE
and (b) with 0.5 mM PDIE.
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Table 4 Polarization parameters for copper corrosion obtained in blank and inhibited PCM
media at various temperatures
Media
blank
T
Ecorr
(V vs. SCE)
-0.420
βa
(mV dec-1)
91.40
78.35
87.62
92.67
80.51
83.71
79.27
81.03
-βc
icorr
(μA cm-2)
65.97
ηi
(%)
-
(K)
(mV dec-1)
130.48
133.01
134.76
122.80
137.02
138.66
133.24
140.32
Std. Dev. σ
3.60
317K
325 K
333 K
341 K
317K
325 K
333 K
341 K
-0.424
82.12
2.59
-
-0.439
112.19
149.12
10.69
4.87
-
-0.448
3.09
-
0.5mM PDIE
-0.386
2.53
83.80
79.23
77.63
63.10
-0.398
17.06
2.66
-0.410
25.10
1.04
-0.430
55.03
3.51
Fig. 9 Effect of temperature on impedance response of copper in PCM media with 0.5mM
PDIE: (a) Nyquist diagram; (b) Bode-phase angle diagram; (c) Bode- impedance diagram;
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symbols represent experimental data and solid lines are fitting curves
Table 5 Impedance parameters for copper corrosion obtained in PCM media with 0.5mM
PDIE at various temperatures
Temperature
(K)
Rs
CPE1
(Y0/Ω-1 Sn cm-2)
8.396 E-5
9.504 E-5
2.367 E-5
5.462 E-5
n1
R1
CPE2
(Y0 /Ω-1 Sn cm-2)
2.017E-4
n2
Cdl
(μF cm-2)
0.14
Rct
(Ω cm2)
2868
2206
1864
1139
Chi-Sqr
(Ω cm2)
3.489
3.067
1.863
1.617
(Ω cm2)
24.680
17.991
16.385
5.495
317
0.993
0.989
0.996
0.890
0.580
0.579
0.499
0.508
2.099 E-3
4.279 E-3
7.384 E-3
1.698 E-3
325
5.777E-4
0.69
333
7.987E-4
1.26
341
2.122E-3
4.98
The relationship between corrosion rate of copper with system temperature can be further
analyzed according to Arrhenius law (Eq.(17))[57].
퐸a
(
)
log 푖corr = −
+ log퐴
(17)
2.303푅푇
where Ea is the apparent activation energy of corrosion, R is the universal gas constant (8.314
J K-1 mol-1), T is the absolute temperature and A is pre-exponential factor. Fig. 10 represents
the Arrhenius plots for copper in free and inhibited PCM melts. From the slopes and
intercepts of the log icorr versus 1/T lines, values of activation parameters can be determined.
Here, a good liner relationship between log icorr and 1/T is reflected by the near unity value of
regression coefficient calculated from each plot as shown in Fig. 10. The derived Ea values
are 30.949 kJ mol-1 and 59.379 kJ mol-1 in the absence and presence of inhibitor, respectively.
The observed higher Ea value of inhibited system as compared to the bare system infers the
more difficulty for charge transportation occurred at Cu/PCM interface in the presence of
PDIE additive. The increment of activation energy is commonly interpreted by the adsorption
phenomenon of inhibitors at corroding interface and the formation of metal-inhibitor complex
[58, 59].
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Fig. 10 Arrhenius plots for copper in PCM melts in the absence and presence of 0.5mM
PDIE.
3.7 Morphological analysis
Fig. 11 exhibits the surface morphologies of freshly prepared and corroded copper coupons
analyzed under SEM after 72 h exposing to the PCM media at 333K with and without 0.5mM
PDIE additive. As compared to the freshly prepared surface (Fig. 11(a)), densely distributed
corrosion deposits are observed adherent to the copper coupon retrieved from blank PCM
media (Fig. 11(b)), referring the massive corrosion attacks. EDS spectrogram further
discloses the existence of considerable amounts of oxygen and phosphorus as well as a little
sulfate on the copper surface indicating the penetration of PCM species and the resultant
corrosion products are the mixture of oxides. By contrast, the copper coupon recovered from
PDIE containing media, as shown in Fig. 11(c), is well protected remaining a clean and
almost intact surface featured by less corrosion products and orderly distributed scratches
which were generated from the initial sample polishing procedure. According to the EDS
detection, this inhibited surface is rich of copper substrate (content about doubled as
compared to the uninhibited one) and lack of phosphorus and sulfate elements (less than 1%
in total) whereas carbon and nitrogen atoms appear, which is indicative of the inhibitory
effect offered by PDIE molecules through adsorbing on copper substrate and the consequent
obstructing and preventing attacks from aggressive electrolyte ions. In this case, the
formation of a composite adsorption layer on the copper surface can be reasonably inferred
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which is in line with the dielectric surface film detected by previous impedance spectrum.
Fig. 11 SEM micrographs of (a) fresh copper specimen and copper specimens immersed for
72h in PCM melts (b) without and (c) with 0.5mM PDIE at 333k.
3.8 FTIR characterization
The existence of adsorbed imidazoline compounds on the copper surface was also confirmed
by FTIR detection. Fig. 12 exhibits the featured FTIR spectrum of films extracted from
copper surface after 72 h immersion in the PCM melts fortified with 0.5mM PDIE. The
obtained IR spectrum is similar to that of pure PDIE (Fig. 2) while the intensity difference of
characteristic peaks is evident. Characteristic bands of N-H and C-N stretching which are
detected from IR spectrum of pure PDIE are also found in Fig. 12 in which they demonstrate
slightly shift and relocate at 3328 and 1305 cm-1, respectively. Interestingly, the featured C=N
stretching peak is invisible from the spectrum of extracted film. The vanishing of C=N
stretching band is indicative of the strong intermolecular reaction between PDIE molecules
and copper surface. Besides, adsorption peaks of C-H stretching including the CH2 skeleton
and –CH3 tip are less affected with no visible displacement, reflecting the non-reactivity
nature of alkyl chain.
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Fig. 12 FTIR spectrum of film recovered from copper surface after 72 h exposure in 0.5mM
PDIE containing PCM melts
3.9 XPS characterization
XPS survey has been applied in this study to detect the composition of inhibited copper
surface. Fig. 13 (a) displays the wide-scan XPS spectrum of the copper sample obtained after
72h immersion in the PDIE-containing PCM media at 333K. Binding energies were
calibrated for charge effects with the reference of C1s line at 284.8 eV. As seen from Fig. 13
(a), elements of C, N, O are clearly traced, which is in good consistent with the previous EDS
detection, proving the incorporation of PDIE compounds on the copper surface during
corrosion process. High resolution peaks of Cu, C, O, N, P are detailed in Fig.13 (b)-(f) with
fitted curves. The Cu2p high resolution spectrum (Fig.13 (b)) is comprised of two energy
bands including Cu2p1/2 and Cu p3/2. According to reference database [22, 60,61], the Cu2p1/2
peak located at 952.47 eV is assigned to the metallic Cu and the Cu2p3/2 peak observed at
932.63 eV is linked to the presence of pure Cu or Cu(I). Observations of the sharpness of
peaks and the absence of typical shake-up satellites at the high binding energy ends of
Cu2p1/2 and Cu2p3/2 edges infers that the sample surface is lack of Cu(II) as compared to Cu
and Cu(I) which contribute to the majority of intensity [60-63]. The oxidation of copper
substrate could also be witnessed from O1s spectrum (Fig.13 (d)) where the signal peak
observed at 530.56 eV may correspond to Cu2O and the signal peak detected at 531.28 eV is
assigned to hydroxides [61]. The C1s (Fig.13 (c)) energy band exhibits peaks at 284.8 eV and
287.94 eV, which are related to C-C and C-O bonds, respectively. In the N1s region (Fig.13
(e)), characteristic peaks at binding energies of 399.39eV and 403.41 eV are associated with
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the protonated amine group of the studied PDIE compounds [24,64]. Moreover, the P2p
(Fig.13 (f)) signal peaked at 132.69 eV is connected with phosphates formation. These results
imply the adsorption of PDIE molecules on the metallic copper and the formation of
inhibitive surface film while this film is not completely compact and some uncovered area is
perceived from where slight corrosion products are detected.
Fig.13 XPS survey of the adsorbed films formed on the copper sample surface immersed in
PCM melts containing 0.5mM PDIE for 72 h at 333 K: (a) wide scan spectrum; (b)-(f) high
resolution spectra of Cu2p, C1s, O1s, N1s and P2p, respectively.
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3.10 Quantum chemical analysis
Based on the previous expirment evidence that the PDIE molecules can adsorb on the
copper suface and form an adsorption layer functioning as aniticorrosion barrier, quantum
chemical calculations were thereby carried out in this section to further investigate the
adsorption mechanism of the studied inhibitior. The preferred adsorption sites of inhibitor
molecule can be predicted according to the frontier molecular orbital theory that interactions
between orgainc molecule and metal is a manifestation of electron exchange that only occur
between the frontier molecular orbitals[65,66]. Generally, the power of an orgainc inhibitor
strongly depends on its capability to donate free electron pairs or share vacant orbitals, which
can be evaluated by calculating indices such as frontier orbital energies and fukui
functions[67]. An effecive inhibitor will not solely supply electrons to the vacant orbital of
metal, but also accommodate electrons from metal.
Fig.14 displays the optmized configuration of PDIE molecule with the electronic
distribution of frontier molecular orbitals. Analysis of the frontier molecular orbitals shows
that the distributions of both HOMO and LUMO is principally located around the
five-membered imidazoline ring of the PDIE molecule. This signifies that the adsoprtion of
PDIE on the metallic surface is possibliy achieved in a vertical manner with the imidazoline
head preferentially attached on copper sutafce via coordination bonding meanwhile the long
nonpolar alkyl tail tending to diverge from copper substrate and repel water.
Fig. 14 Electronic properties of PDIE molecule: (a) geometry structure; (b) HOMO; (c)
LUMO
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The electron donating and accepting ability of PDIE molecule are quantified as the
energies of frontier molecular orbitals, i.e., EHOMO and ELUMO, respectively. Molecule with a
higher EHOMO value generally behaves as an electron-donator and more accessible to
nucleophilic attack, wheras a high ELUMO value usually corresponds to electrophilic agent
which is more ready to attract electronegative groups[65,67]. Form Koopmans’ theorem[67],
frontier molecular orbital energies are related to the ionization potential (I) and electron
affinity (A), which are in turn defined as I= -EHOMO and A= -ELUMO. Thus more quantum
chemical parameters including the energy gap ΔE, absolute electronegativity (χ) and global
hardness (η) of PDIE molecule are calculated from Eq.(18)-(20) [68] respectively and
tablated in Table 6.
Δ퐸 = 퐸LUMO − 퐸HOMO
(18)
(19)
1
1
휒 = (퐼 + 퐴) = − (퐸HOMO + 퐸LUMO
)
)
2
1
2
1
휂 = (퐼 − 퐴) = − (퐸HOMO − 퐸LUMO
(20)
2
2
When the bulk metal and organic inhibitor are brought together, the electron transportation
inside is driven by the electronegativity difference, which manifests that electrons will flow
from lower χ(inhibitor) to higher χ(metal) until the chemical potentials achieve equal
status[69]. As an estimation, the fraction of electrons transferred (ΔN) between the organic
inhibitor and metallic surafce can be determined through Eq.(21)[65].
휒Cu − 휒inh
Δ푁 =
(21)
2(휂Cu + 휂inh
)
Herein the copper surface is considered as Lewis acid[34]. The experimental polycrystalline
work function value 4.65eV of bulk copper was applied for χCu [70,71] and the global
hardness ηCu was taken as 0 eV based on I=A rule for metallic bulk [71,72]. The value of ΔN
unveils the inhibitory performance correlated with electrons donations. It is a general criteria
that the inhibitor molecule is more likely to donate electrons to metallic surface if ΔN >0
while vice versa if ΔN <0. The positive value of ΔN as recorded in Table 6 therefore gives the
hint that PDIE molecule inclines to donate its electrons to copper surface facilitating the
adsorption process.
As a local reactivity descriptor, Fukui function [73,74] as defined in Eq.(22) is analyzed
for making comparison among the electronically active sites within the PDIE molecule.
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∂푓휌(→푟 )
푓(→푟 ) = (
)
(22)
→
푉(
)
푟
휕푁
Here, 휌(→푟 ) is the electron density in regard to the total number of electrons N in the system.
+
-
The specific Fukui indices of nucleophic attack (fk ), electrophilic attack (fk ) and radical
0
attack (fk ) are evaluated from Eq.(23)-(25) with results listed in Table 7 (only for
imidazoline ring and hydroxyl pendant group).
→ +
(
)
( )
푓(푟 ) = 푞푖 N + 1 − 푞푖 N
(23)
(24)
→ −
( )
(
)
푓(푟 ) = 푞푖 N − 푞푖 N − 1
1
푓(→푟 )0 = (푞푖 N + 1 − 푞푖 N − 1 )
(25)
(
)
(
)
2
where qi(N+1), qi (N), qi (N−1) stand for the atomic charges of atom i with N, N +1 and N −1
electrons, respectively. Literatures [67,73,74] show that the atom site susceptible to
+
nucleophilic attack is located at where the value of fk reaches a maximum. In contrast, the
-
atom site which possesses the highest absolute value of fk is likely subject to electrophilic
attack.
Table 7 reveals that the adsorption of PDIE molecule on copper surface are most likely
achieved through heterocyclic atoms N(1), N(4) and O(8). The C(5) atom also displays a
greater values of Fukui functions possibly atrributed to the presence of double bond. It
specified that the N(4) from imidazoline ring is prone to suffer electrophilic attack showing
-
a greater absolute value of fk , while the other nitrogen atom N(1) located in imidazoline ring
is considered equally to undergo nucleophilic, electrophilic or radical attack due to the
equivalent strength of Fukui indices. Apart from N(4), the oxygen atom pertaining to
hydroxyl moiety O(8) also displays the inclination of being electrophilic attacked accoding
-
+
to its high fk value. Moreover, the higher fk value of C(5) indicates it is ready be attacked
by nucleophile. By comprehending results of frontier orbitals and Fukui functions, it can be
speculated that imidazoline ring is the reactive center most responsible for the adsobing and
bonding of PDIE molecule with copper surface and it supports PDIE molecule not soley
supplying electrons to vacant Cu obtials, but also readily accommodating electrons from
copper surface, which enable PDIE compounds to behave as a mix-type corrosion inhibitor.
29