# Adsorption Properties and Inhibition of C38 Steel Corrosion in Hydrochloric Solution by Some Indole Derivates: Temperature Effect, Activation Energies, and Thermodynamics of Adsorption

Authors: M. Lebrini; F. Robert; C. Roos
Journal: International Journal of Corrosion
 (2013)

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## Abstract

The corrosion rates in the presence of some indole derivates, namely, 9H-pyrido[3,4-b]indole (norharmane) and 1-methyl-9H-pyrido[3,4-b]indole (harmane), as inhibitors of C38 steel corrosion inhibitor in 1 M HCl solution, were measured by potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) techniques, in the range of temperatures from 25 to 55∘C. Results obtained revealed that the organic compounds investigated have inhibiting properties for all temperatures. The inhibition was assumed to occur via adsorption of the indole molecules on the metal surface. Adsorption of indole derivates was found to follow the Langmuir isotherm. The apparent activation energies, enthalpies, and entropies of the dissolution process and the free energies and enthalpies for the adsorption process were determined by potentiodynamic polarization and electrochemical impedance. The fundamental thermodynamic functions were used to collect important information about indole inhibitory behaviour.


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## Body

## 1. Introduction

The effect of temperature on the inhibited acid-metal reaction is highly complex, because many changes occur on the metal surface such as rapid etching and desorption of inhibitor and the inhibitor itself may undergo decomposition and/or rearrangement. Temperature effects on acidic corrosion and corrosion inhibition of iron and steel most often in HCl and H2SO4 solutions had been the object of a large number of investigations [1–12]. However, it was found that few inhibitors with acid-metal systems have specific reactions which are effective (or more) at high temperature as they are at low temperature [13–15]. Thermodynamic parameters such as adsorption heat, adsorption entropy, and adsorption free energy can be obtained from experimental data of the studies of the inhibition process at different temperatures. The kinetic data such as apparent activation energy and preexponential factor at different inhibitor concentrations are calculated, and the effects of the activation energy and preexponential factor on the corrosion rate of steel were discussed [16–20].Our earlier results obtained for 9H-pyrido[3,4-b]indole (norharmane) and 1-methyl-9H-pyrido[3,4-b]indole (harmane) as corrosion inhibitors of C38 steel demonstrated that correlation exists between the inhibition efficiency and the chemical structure [21]. It was found that these compounds are good inhibitors in acidic solutions and the inhibition efficiency of these indole-type organic compounds may be explained in terms of electronic properties (the energy of the highest occupied molecular orbital (EHOMO) and the energy of the lowest unoccupied molecular orbital (ELUMO)). The aim of this paper is to extend these investigations in order to obtain a better understanding of the mode of inhibitory action of the harmane and norharmane by calculating thermodynamic parameters for both C38 steel dissolution and inhibitor adsorption process in hydrochloric acid solution using potentiodynamic polarization and electrochemical impedance spectroscopy (EIS).


## 2. Experimental

Electrode and Solution. Corrosion tests have been carried out on electrodes cut from sheets of C38 steel. Steel strips contained 0.36 wt% C, 0.66 wt% Mn, 0.27 wt% Si, 0.02 wt% S, 0.015 wt% P, 0.21 wt% Cr, 0.02 wt% Mo, 0.22 wt% Cu, 0.06 wt% Al, and the remainder iron. The specimens were embedded in epoxy resin leaving a working area of 0.78 cm2. The working surface was subsequently ground with 180 and 1200 grit grinding papers, cleaned by distilled water and ethanol. The solutions (1 M HCl) were prepared by dilution of an analytical reagent grade 33% HCl with doubly distilled water. All the tests were performed in the range of temperatures from 25 to 55°C. The tested inhibitors are 9H-pyrido[3,4-b]indole (norharmane) and 1-methyl-9H-pyrido[3,4-b]indole (harmane); their molecular structures are shown in Figure 1. The investigated compounds were commercial products: norharmane (Aldrich, P99%), harmane (Sigma, P98%), the concentration range of inhibitor employed was 0.2 mM M to 1.2 mM. The concentration of inhibitor was determined in accordance with its solubility. Varela et al. reports the solubility of norharmane and harmane in water at 20°C, at pH 7 and 13, using the absorbance at the maxima in the absorption spectra of saturated solutions [22]. The solubility of norharmane was 1.86 mM (pH = 7) and 1.81 mM (pH = 13). For harmane, the solubility was 1.61 mM (pH = 7) and 0.786 mM (pH = 13). At lower pH (Our experimental conditions, pH = 0), where the cationic form is the predominant species, all the compounds present a very high solubility, and it was not possible to obtain data with this technique at lower pH.Chemical formulas of the tested inhibitors (a) norharmane and (b) harmane.
(a)
(b)Electrochemical Measurements. Electrochemical measurements, including potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS), were performed in a three-electrode cell. C38 steel specimen was used as the working electrode, a platinum wire as the counter, and a saturated calomel electrode (SCE) as the reference. Before potentiodynamic test and EIS experiments, the electrode was allowed to corrode freely and its open circuit potential (OCP) was recorded as a function of time during 3 h, the time necessary to reach a quasi-stationary value for the open-circuit potential. This steady-state OCP corresponds to the corrosion potential (Ecorr) of the working electrode. The anodic and cathodic polarisation curves were recorded by a constant sweep rate of 20 mV min−1. Electrochemical impedance spectroscopy (EIS) measurements were carried out, using ac signals of amplitude 5 mV peak to peak in the frequency range of 100 kHz to 10 mHz. Electrochemical measurements were performed through a VSP electrochemical measurement system (Bio-Logic). The above procedures were repeated two times with success for each concentration of the two tested inhibitors. The Tafel fit and EIS data were analysed using graphing and analyzing impedance software, version EC-Lab V9.97.


## 3. Results and Discussion

### 3.1. Effect of Concentration

The corrosion rates of metals and alloys in aggressive solutions can be determined using different electrochemical methods. Electrochemical impedance spectroscopy and polarisation curves were thus employed in the present work to study the effect of indole derivates concentration. The percentages of inhibition efficiency and values of associated electrochemical parameters are listed in Table1. Inspections of the obtained data reveal that the Icorr values decrease considerably in the presence of harmane and norharmane with increasing inhibitor concentration. The Ecorr values shifted to more positive potentials in the presence of indole derivates concentration, although there was not a specific relation between Ecorr and inhibitors concentration. This effect may be related to the adsorption of the organic compound at the active sites of the electrode surface, retarding the corrosion reaction. The data also reveal that the addition of harmane or norharmane causes a significant increase in Rct in the additive-free solution and diminishes the value of Cdl. The decrease in Cdl could be attributed to the adsorption of the inhibitors forming a protective layer on the metal surface [23]. The inhibition efficiencies, calculated from ac impedance study, show the same trend as these obtained from polarization measurements. However, IE (%) increases with inhibitor concentrations for both inhibitors, reaching a maximum value at 1.2 mM. It was found that these compounds are good inhibitors in acidic solutions and the inhibition efficiency of these indole-type organic compounds may be explained in terms of electronic properties. The detailed study of 1 M HCl at 25°C is reported in [21].Table 1
Corrosion parameters obtained from electrochemical measurements of C38 steel in 1 M HCl containing various concentrations of indole derivates at 25°C.
Inhibitor
Polarisation curves
EIS
E
corr versus SCE (mV)
I
corr (μA·cm−2)
IE (%)
R
ct (Ω·cm2)
C
dl (μF·cm−2)
IE (%)
1 M HCl
-
529
284
—
49 ± 0.02
546
Norharmane
0.2 mM
-
467
67
76
148 ± 0.91
183
67
0.4 mM
-
476
61
79
238 ± 1.65
120
79
0.8 mM
-
494
52
82
514 ± 1.18
55
90
1.2 mM
-
455
28
90
641 ± 1.73
44
92
Harmane
0.2 mM
-
476
65
77
181 ± 0.10
330
73
0.4 mM
-
489
55
81
321 ± 0.97
270
85
0.8 mM
-
479
34
88
537 ± 0.17
188
91
1.2 mM
-
492
24
91
735 ± 0.68
148
93


### 3.2. Effect of Temperature

#### 3.2.1. Potentiodynamic Polarisation

In order to get more information about the performance of indole derivates, the nature of adsorption isotherm, and thereafter to evaluate the adsorption and activation processes, the influence of temperature is studied by potentiodynamic polarisation. Some of the polarisation curves for C38 steel electrode in 1 M HCl in the absence and in the presence of 0.2 mM of norharmane and harmane in the temperature range 25–55°C are given in Figures2, 3, and 4, respectively. As it can be seen, raising the temperature increases both anodic and cathodic reactions of C38 steel electrode both in the absence and in the presence of inhibitors. Polarisation curves of the C38 steel electrode in 1 M HCl without and with addition of various concentrations of harmane at 45°C are shown in Figure 5, representative example. As it can be seen, the anodic and cathodic reactions are affected by the addition of inhibitor. Similar observations were found for all concentrations studied in the presence of both inhibitors. Accurate evaluation of Tafel slopes by Tafel extrapolation is often impossible, simply because an experimental polarization curve does not exhibit linear Tafel regions [24–27]. Our experimental polarization curves presented here do not display the expected log/linear Tafel behaviour with anodic branches exhibiting curvature over the complete applied potential range. The curvature of the anodic branch may be attributed to the deposition of the corrosion products or impurities in the steel (e.g., Fe3C) to form a nonpassive surface film [24]. The various electrochemical parameters were calculated from Tafel plots and summarized in Table 2. The inhibition efficiency and the surface coverage degree (θ) values for steel are also shown in the same table. The surface coverage θ was calculated from (1) [28]. It has been observed from Table 2, that the corrosion current density (Icorr) increased with increasing temperature in both uninhibited and inhibited solutions. The addition of norharmane or harmane to the HCl solution shifts the Ecorr towards more negative values at all of the studied temperatures, although there was not a specific relation between Ecorr and inhibitors concentration. The IE (%) values decrease with increasing temperature; a decrease in inhibition efficiencies with the increase in temperature might be due to weakening of physical adsorption. Consider
(1)θ=Icorr-Icorr(inh)Icorr,
where Icorr and Icorr(inh) are the corrosion current density values in the absence and presence of indole derivates, respectively.Table 2
Electrochemical parameters calculated from Tafel plots and the corresponding inhibition efficiencies at various temperatures studied of C38 steel in 1 M HCl containing different concentrations of indole derivates.
Norharmane
Harmane
Temp. (°C)
Con. (mM)
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
1 M HCl
-
460
232
106
89
—
—
—
—
—
—
—
—
0.2
-
467
67
107
125
76
0.7641
−476
65
110
124
77
0.7711
25
0.4
-
476
61
116
122
79
0.7852
−489
55
98
107
81
0.8063
0.8
-
494
52
97
118
82
0.8169
−479
34
113
119
88
0.8803
1.2
-
455
28
93
112
90
0.9014
−492
24
87
107
91
0.9155
1 M HCl
-
454
843
111
109
—
—
—
—
—
—
—
—
0.2
-
473
236
112
144
72
0.7200
−465
212
118
133
75
0.7485
35
0.4
-
472
195
109
126
77
0.7687
−470
182
116
136
78
0.7841
0.8
-
470
165
102
131
80
0.8043
−456
154
109
128
82
0.8173
1.2
-
479
98
103
135
88
0.8837
−464
101
103
118
88
0.8802
1 M HCl
-
451
1192
120
109
—
—
—
—
—
—
—
—
0.2
-
501
512
130
146
57
0.5705
−496
413
117
134
65
0.6535
45
0.4
-
509
472
112
115
60
0.6040
−488
389
112
125
67
0.6737
0.8
-
505
443
135
135
63
0.6284
−487
335
113
126
72
0.7190
1.2
-
485
352
107
140
70
0.7047
−484
245
110
118
79
0.7945
1 M HCl
-
450
1982
131
116
—
—
—
—
—
—
—
—
0.2
-
509
1023
142
150
48
0.4839
−504
983
136
148
50
0.5040
55
0.4
-
497
954
114
156
52
0.5187
−496
852
123
140
57
0.5701
0.8
-
566
867
117
127
56
0.5626
−564
715
110
146
64
0.6393
1.2
-
494
651
109
139
67
0.6715
−515
574
107
132
71
0.7104Figure 2
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl.Figure 3
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of norharmane.Figure 4
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of harmane.Figure 5
Polarisation curves for C38 steel in 1 M HCl containing different concentrations of harmane at 45°C.In order to calculate activation parameters for the corrosion process, Arrhenius (2) and an alternative formulation of Arrhenius (3) were used:
(2)Icorr=Kexp(-EaRT),(3)Icorr=RTNhexp(ΔSaR)exp(-ΔHaRT),
where Icorr is the corrosion current density, K the Arrhenius preexponential constant, Ea is the activation energy for the corrosion process, h is the Plank’s constant, N is the Avogadro’s number, the enthalpy of activation (ΔHa), and the entropy of activation (ΔSa).Arrhenius plots for the corrosion density of C38 steel in the case of harmane are given in Figure6, representative example. Similar plots are obtained in the case of norharmane. The apparent activation energies (Ea) at different concentrations of indole derivates were determined by linear regression between lnIcorr and 1/T and the result is shown in Table 3. All the linear regression coefficients were close to 1, indicating that the C38 steel corrosion in hydrochloric acid can be elucidated using the kinetic model. Inspection of Table 3 showed that the values of Ea determined in 1 M HCl containing indole derivates are higher than that for uninhibited solution. The increase in the apparent activation energy may be interpreted as physical adsorption that occurs in the first stage [29]. Moreover, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. Szauer and Brand explained that the increase in activation energy can be attributed to an appreciable decrease in the adsorption of the inhibitor on the steel surface with increase in temperature [30]. Figure 7 showed a plot of ln (Icorr/T) versus 1/T with a slope of (-ΔHa/R) and an intercept (lnR/Nh+ΔSa/R) from which the values of ΔHa and ΔSa were calculated, respectively. All estimated kinetic-thermodynamic parameters were tabulated also in Table 3. Inspection of these data revealed that the thermodynamic parameters (ΔHa and ΔSa) for dissolution reaction of C38 steel in 1 M HCl in the presence of both inhibitors are higher than that of in the absence of inhibitors. The positive signs of ΔHa reflect the endothermic nature of the steel dissolution process suggesting that the dissolution of steel is slow in the presence of inhibitors [31]. Furthermore, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. One can notice that Ea and ΔHa values vary in the same way for both inhibitors (Table 3). The values of ΔSa were negative both in the absence and presence of inhibitors, implying that the activated complex represented the rate-determining step with respect to the association rather than the dissociation step. It means that a decrease in disorder occurred when proceeding from the reactants to the activated complex [30]. Also, the ΔSa shift can be explained as a result of the replacement process of water molecules during adsorption of organic inhibitor on the steel surface.Table 3
Thermodynamic parameters calculated from Tafel plots for the adsorption of indole derivates in 1 M HCl on the C38 steel at different temperatures.
Con. (mM)
Norharmane
Harmane
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
HCl
24.42
23.29
−119.48
—
—
—
0.2
31.73
30.60
−99.81
31.20
30.07
-
101.88
0.4
32.38
31.25
−98.12
31.80
30.67
-
100.43
0.8
33.40
32.27
−95.27
35.18
34.05
-
90.53
1.2
37.99
36.85
−81.97
36.89
35.76
-
86.63Figure 6
Arrhenius plots of corrosionln(Icorr) versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 7
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl and at different concentrations of harmane.


#### 3.2.2. Impedance Measurements

The corrosion behaviour of C38 steel in 1 M HCl solution in the presence of indole derivates was also investigated by EIS in the temperature range 25–55°C. The EIS of C38 steel electrode in 1 M HCl solution in the absence and in the presence of of 0.2 mM of noharmane and harmane, at different temperatures, are shown in Figures8, 9, and 10; representative example. Figure 11 shows the impedance plots of C38 steel electrode in 1 M HCl solution in the absence and presence of different concentrations of norharmane at 35°C. It can be seen that, the size of the capacitive loop increased by increasing the concentration of norharmane. All the impedance spectra were measured at the corresponding open-circuit potentials. After analyzing the shape of the Nyquist plots, it is concluded that the curves obtained up to 45°C approximated by a single capacitive semi-circles, showing that the corrosion process was mainly charge transfer controlled. The general shape of the curves is very similar for all concentrations studied. The diameter of Nyquist plots (Rct) decreases with increasing temperature for both inhibitors. For the most temperatures 45 and 55°C, an inductive loop appeared at low-frequency values. Similar observations were found for all concentrations studied. The presence of the LF inductive loop may be attributed to the relaxation process obtained by adsorption species like Clads- and Hads+ on the electrode surface [32–35]. It may also be attributed to the adsorption of inhibitor on the electrode surface [36] or to the redissolution of the passivated surface at low frequencies [37]. The above impedance diagrams (Nyquist) contain depressed semicircles with the center under the real axis; such behaviors characteristic for solid electrodes and often referred to as frequency dispersion have been attributed to roughness and inhomogeneities of the solid surfaces, impurities [38–41]. Therefore, a constant phase element (CPE) instead of a capacitive element is used to get a more accurate fit of experimental data set. For analysis of the impedance spectra exhibiting one capacitive loop, the equivalent circuit (EC) given in Figure 12(a) was used to fit the experimental spectra while the EC shown in Figure 12(b) was used for the impedance spectra containing one capacitive loop and an inductive loop. Simulation of Nyquist plots with above models shows excellent agreement with experimental data (Figures 12(a) and 12(b); representative example).Figure 8
Nyquist diagrams for C38 steel in 1 M HCl at different temperatures.Figure 9
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of norharmane at different temperatures.Figure 10
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of harmane at different temperatures.Figure 11
Nyquist diagrams for C38 steel in 1 M HCl containing different concentrations of noharmane at 35°C.Nyquist plots: (□) experimental data and (—) fit data, together with the equivalent circuit used to fit the impedance data, recorded for a C38 electrode (a) in 1 M HCl solution + 0.2 mM harmane at 35°C and (b) in 1 M HCl solution + 0.2 mM norharmane at 55°C.
(a)
(b)The parameters calculated with the application of these models are summarized in Tables4 and 5. The values discussed show that the organic compounds investigated have inhibiting properties for all temperature values. This conclusion is based on the values of Rct in inhibitors presence. They are greater than those in 1 M HCl. The temperature rise leads to a decrease of Rct values. This is due, on one hand, to the increase of the rate of metal dissolution and, on the other hand, to the shift of the adsorption/desorption equilibrium towards the inhibitor’s desorption and hence to the decrease of surface coverage degree. The n value almost decreases with temperature increase and this is interpreted as an evidence for surface inhomogeneity increase. The latter is attributed to the accelerated corrosion and the developed metal surface. At lower temperatures the inhibitors adsorb on the most active surface sites; this results in a decrease of surface inhomogeneity. The desorption, which is favored by high temperatures, will increase with this effect. The Cdl value was calculated using (4) [42–44]:
(4)Cdl=(A·Rct1-n)1/n.
It is clear that the addition of harmane or norharmane causes a significant increase in Cdl in the additive-free solution for all temperatures studied. As the double layer capacitance can be connected with the thickness of the layer of adsorbed inhibitor molecules at the interface and this dependence is of reverse proportionality; it follows that the thickness of the adsorption layer will decrease with temperature increase. Similar tendency was found for CPE constant (A) for all temperatures studied. It can be seen from Tables 2, 4, and 5 that the inhibition efficiencies calculated by both methods show the same trend. The IE (%) values decrease with increasing temperature and no difference of numerical values of inhibition efficiencies was observed at 25 and 35°C. However the results obtained at 45 and 55°C show a difference in numerical values obtained by both methods. This variation may be due to the difference between methods, which each method is realised differently with some conditions and assumptions.Table 4
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of norharmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
148 ± 0.91
2.91 ± 0.02
0.871 ± 0.008
183
—
—
67
0.6689
35
53 ± 0.43
4.37 ± 0.25
0.836 ± 0.053
209
—
—
60
0.6038
45
30 ± 0.35
10.88 ± 3.65
0.765 ± 0.059
380
25 ± 4.61
9 ± 1.78
50
0.5000
55
10 ± 0.65
13.35 ± 1.75
0.815 ± 0.120
501
2 ± 0.40
2 ± 1.37
50
0.5000
0.4 mM
25
238 ± 1.65
1.89 ± 0.19
0.872 ± 0.005
120
—
—
79
0.7941
35
95 ± 0.89
3.53 ± 0.14
0.829 ± 0.052
175
—
—
78
0.7789
45
55 ± 3.04
6.19 ± 0.94
0.790 ± 0.032
252
10 ± 1.20
15 ± 1.60
73
0.7273
55
14 ± 0.93
8.84 ± 2.31
0.831 ± 0.054
362
3 ± 0.21
2 ± 0.32
64
0.6429
0.8 mM
25
514 ± 1.18
0.84 ± 0.03
0.883 ± 0.012
55
—
—
90
0.9047
35
180 ± 1.04
3.18 ± 0.13
0.825 ± 0.045
173
—
—
82
0.8235
45
85 ± 1.56
5.01 ± 0.30
0.814 ± 0.023
244
7 ± 0.27
14 ± 0.90
79
0.7857
55
22 ± 1.55
7.13 ± 0.47
0.809 ± 0.251
267
6 ± 1.60
2 ± 1.10
77
0.7727
1.2 mM
25
641 ± 1.73
0.66 ± 0.02
0.887 ± 0.010
44
—
—
92
0.9236
35
245 ± 0.55
2.3 ± 0.78
0.803 ± 0.072
114
—
—
91
0.9143
45
123 ± 0.81
2.9 ± 0.57
0.802 ± 0.140
127
—
—
88
0.8780
55
25 ± 0.41
4.46 ± 0.17
0.804 ± 0.023
149
6 ± 0.50
3 ± 1.43
80
0.8000Table 5
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of harmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
181 ± 0.10
4.82 ± 0.19
0.866 ± 0.042
330
—
—
73
0.7293
35
73 ± 0.61
6.92 ± 0.44
0.816 ± 0.501
353
—
—
71
0.7123
45
50 ± 1.23
9.73 ± 0.27
0.805 ± 0.062
468
25 ± 8.41
8 ± 3.02
70
0.7000
55
16 ± 0.81
19.5 ± 4.03
0.719 ± 0.501
503
11 ± 0.34
3 ± 0.8
69
0.6875
0.4 mM
25
321 ± 0.97
3.71 ± 0.37
0.870 ± 0.036
270
—
—
85
0.8474
35
129 ± 0.65
5.29 ± 0.09
0.804 ± 0.074
275
—
—
84
0.8372
45
82 ± 1.54
7.95 ± 1.02
0.784 ± 0.128
375
25 ± 1.74
9 ± 1.5
82
0.8171
55
21 ± 2.31
10.31 ± 2.13
0.824 ± 0.054
455
21 ± 0.58
4 ± 1.3
76
0.7619
0.8 mM
25
537 ± 0.17
2.52 ± 0.27
0.873 ± 0.051
188
—
—
91
0.9088
35
218 ± 0.56
3.96 ± 0.72
0.795 ± 0.104
211
—
—
90
0.9037
45
136 ± 1.53
4.37 ± 0.73
0.811 ± 0.091
226
—
—
89
0.8897
55
27 ± 1.20
8.64 ± 2.03
0.780 ± 0.035
299
5 ± 0.12
2 ± 0.76
81
0.8148
1.2 mM
25
735 ±  0.68
1.92 ± 0.12
0.883 ± 0.036
148
—
—
93
0.9333
35
293 ± 0.54
3.28 ± 0.27
0.814 ± 0.037
192
—
—
93
0.9283
45
182 ± 0.53
4.33 ± 0.07
0.826 ± 0.051
254
—
—
92
0.9176
55
32 ± 0.66
7.36 ± 1.91
0.783 ± 0.102
260
11 ± 1.54
5 ± 0.8
84
0.8438To obtain the activation parameters from the impedance technique, values ofRct and those of βa and βc obtained at different temperatures were used to calculate values of Icorr according to Stern-Geary [45] equation:
(5)Icorr=βaβc2.303(βa+βc)(1Rct).
Figures 13 and 14 show the Arrhenius plot for the results obtained in 1 M HCl solutions in the presence of harmane, representative example. Similar plots are obtained in the case of norharmane. The results are in good agreement with those obtained from polarization studies and show the same trend. The difference of numerical values of ΔSa determined from the two techniques may be attributed to the different methods that have been used for the determination of the corrosion rates.Figure 13
Arrhenius plotslnIcorr versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 14
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl at different concentrations of harmane.


### 3.3. Adsorption Isotherm

Inhibition by organic compounds is, mainly, due to their ability to adsorb onto a metal surface to form a protective film. The establishment of isotherms that describe the adsorption behaviour of corrosion inhibitor is important as they provide important information about the nature of metal-inhibitor interaction. It has been reported that the adsorption of the inhibitor molecules depends on a variety of factors such as the presence of functional groups (either electron donating or withdrawing), charge distribution at the donor atom, theπ orbital character of donating electrons, the nature of substrate metal and the type of interaction between organic molecules and the metallic surface as well.The most frequently used isotherms are Langmiur (6), Temkin (7), and Frumkin (8). All these isotherms are tested. In all cases, the degree of surface coverage (θ) is plotted as a function of the inhibitor concentration (Cinh). In the present study, values of θ are obtained from Icorr and Rct. The significance of the adsorption isotherm was obtained by calculating the correlation coefficients (R2). As an example, Figures 15, 16, and 17 represent fitting of impedance and polarization data obtained for C38 electrode in 1 M HCl containing various concentrations of norharmane at 55°C to Langmuir, Temkin, and Frunkin isotherms. The best correlation between the experimental results, obtained from the three tested isotherm functions, was obtained using Langmuir isotherm (the strong correlation R2=0.999 for both methods). Similar observations were found for all temperatures studied. The simplest, being the Langmuir isotherm, is based on assumption that all adsorption sites are equivalent and that particle binding occurs independently from nearby sites being occupied or not [46]. Consider
(6)Cinhθ=1K+Cinh(Langmuirisotherm),(7)(θ1-θ)exp(-2aθ)=KCinh(Frumkinisotherm),(8)exp(-2aθ)=KCinh(Temkinisotherm),
where “K” is the binding constant of the adsorption reaction and “a” is the lateral interaction term describing the molecular interactions in the adsorption layer and the heterogeneity of the surface.Figure 15
Langmuir adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.Figure 16
Frumkin adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.Figure 17
Temkin adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.The well known thermodynamic adsorption parameters are the standard free energy of adsorption (ΔGads0), the heat of adsorption (ΔHads0), and the standard entropy of adsorption (ΔSads0). These quantities can be calculated depending on the estimated values of K from adsorption isotherms at different temperatures.The constant of adsorption,K, is related to the standard free energy of adsorption, ΔGads0, with the following equation:
(9)K=155.5exp(-ΔGads0RT).
The value 55.5 in the above equation is the concentration of water in solution in mol L−1 [47]. The ΔGads0 values at all studied temperatures can be calculated. Then, the obtained ΔGads0 values plotted versus T (Figures 18 and 19) gave the heat of adsorption ΔHads0 and the standard adsorption entropy ΔSads0 in accordance with the basic equation:
(10)ΔGads0=ΔHads0-TΔSads0.
All thermodynamic adsorption parameters estimated from both methods for indole derivates on C38 steel from 1 M of HCl solution are listed in Tables 6, 7, and 8. The entire values of thermodynamic adsorption obtained by both methods are in good agreement and follow the same trend. The negative values of ΔGads0 ensure the spontaneity of the adsorption process and stability of the adsorbed layer on the steel surface. The calculated ΔGads0 values indicate the physical nature of adsorption of norharmane and harmane. The dependence of ΔGads0 on experimental temperature can be summarized in two cases as follows.Table 6
Thermodynamic parameters calculated from IES for the adsorption of indole derivates in 1 M HCl on the C38 steel at different temperatures.
Con. (mM)
Norharmane
Harmane
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
HCl
28.00
26.87
-
131.04
—
—
—
0.2
32.78
31.65
-
120.35
29.03
27.91
-
131.68
0.4
33.34
32.22
-
116.44
32.82
31.69
-
121.55
0.8
38.00
36.87
-
105.77
34.05
32.92
-
119.20
1.2
38.77
37.64
-
104.36
37.05
35.92
-
110.91Table 7
Thermodynamic parameters calculated from IES for the adsorption of indole derivates on C38 steel in 1 M HCl at different temperatures.
Temp. (°C)
Norharmane
Harmane
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
25
−18.00
−14.63
35
−14.46
−8.18
20.2
−15.03
−3.94
36
45
−14.50
−15.44
55
−14.90
−15.69Table 8
Thermodynamic parameters calculated from LP for the adsorption of indole derivates on C38 steel in 1 M HCl at different temperatures.
Temp. (°C)
Norharmane
Harmane
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
25
−14.59
−14.71
35
−14.84
−8.45
20.7
−15.04
−7.43
24.5
45
−15.06
−15.23
55
−15.21
−15.46Figure 18
Variation ofΔGads0, evaluated from IES, versus T on C38 steel in 1 M HCl containing indole derivates.Figure 19
Variation ofΔGads0, evaluated from LP, versus T on C38 steel in 1 M HCl containing indole derivates.(a) Value ofΔGads0 becomes less negative with increasing temperature indicating the occurrence of exothermic process at which adsorption was unfavourable with increasing reaction temperature as the result of the inhibitor desorption from the steel surface [48].(b) Value ofΔGads0 becomes more negative with increasing temperature indicating the occurrence of endothermic process at which increasing temperature facilitates inhibitor adsorption.The first case (a) is observed for the adsorption of the studied inhibitor species on C38 steel surface from HCl solution depending on the applied temperature range (Tables7 and 8), indicating the occurrence of exothermic adsorption processes. Also, it is noteworthy feature that the calculated value of ΔGads0 at 25°C in the case of harmane is greater than that in the case of norharmane, which means that the electrostatic interaction between the harmane and the steel surface is stronger. This is in good agreement with the range of the inhibition efficiency values obtained at 25°C from both impedance and polarisation measurements. However in the temperature range 35–55°C, there is an observable contradiction between the results of inhibition efficiency values and the finding of the calculated value of ΔGads0. The negative sign of (ΔHads0) reveals that the adsorption of inhibitor molecules is an exothermic process. Generally, an exothermic adsorption process suggests either physisorption or chemisorption while endothermic process is attributed to chemisorption [17]. Moreover, the values obtained for harmane are somewhat higher than those obtained for norharmane. This result indicated that harmane is more strongly adsorbed on the steel surface. This is in good agreement with the results obtained from impedance and polarisation measurements. The results show a great difference between the value of ΔHads0 for harmane obtained from EIS (−3.88 kJ mol−1) and from LP (−7.40 kJ mol−1). This difference may be due to the accuracy of linear regression between ΔGads0 and T, where the linear regression coefficient (R2) obtained from EIS is 0.9905 and from LP is 0.9254. The ΔSads0 values in the presence of indole derivates are large and positive, meaning that an increasing in disordering takes place in going from reactants to the metal-adsorbed species reaction complex [49].The integrated version of the Van’t Hoff equation expressed by (11) can be also deduced the ΔHads0 value [50]:
(11)lnK=-ΔHads0RT+constant.
Figures 20 and 21 show the plot of lnK versus 1/T from both methods which gives straight lines with slopes of (-ΔHads0/R) and intercepts of (-ΔSads0/R+ln1/55.5). The calculated ΔHads0 using the Van’t Hoff equation are −8.25 (from IES) and −8.41 (from LP) kJ mol−1 for norharmane. For harmane, the calculated ΔHads0 are −3.88 (from IES) and −7.40 (from LP) kJ mol−1. These results confirm the exothermic behaviour of the adsorption of the inhibitors on the steel surface, therefore, the physisorption process. Values of ΔHads0 obtained by both (9) and (10) are in good agreement. Moreover, the deduced ΔSads0 values (−20.01 J mol−1 K−1 from IES and −20.82 J mol−1 K−1 from LP) and (−36.14 J mol−1 K−1 from IES and −24.63 J mol−1 K−1 from LP) for norharmane and harmane, respectively, are very close to those obtained in Tables 7 and 8.Figure 20
Van’t Hoff plots for the C38 steel/indoles/1 M HCl system evaluated from LP.Figure 21
Van’t Hoff plots for the C38 steel/indoles/1 M HCl system evaluated from IES.


## 3.1. Effect of Concentration

The corrosion rates of metals and alloys in aggressive solutions can be determined using different electrochemical methods. Electrochemical impedance spectroscopy and polarisation curves were thus employed in the present work to study the effect of indole derivates concentration. The percentages of inhibition efficiency and values of associated electrochemical parameters are listed in Table1. Inspections of the obtained data reveal that the Icorr values decrease considerably in the presence of harmane and norharmane with increasing inhibitor concentration. The Ecorr values shifted to more positive potentials in the presence of indole derivates concentration, although there was not a specific relation between Ecorr and inhibitors concentration. This effect may be related to the adsorption of the organic compound at the active sites of the electrode surface, retarding the corrosion reaction. The data also reveal that the addition of harmane or norharmane causes a significant increase in Rct in the additive-free solution and diminishes the value of Cdl. The decrease in Cdl could be attributed to the adsorption of the inhibitors forming a protective layer on the metal surface [23]. The inhibition efficiencies, calculated from ac impedance study, show the same trend as these obtained from polarization measurements. However, IE (%) increases with inhibitor concentrations for both inhibitors, reaching a maximum value at 1.2 mM. It was found that these compounds are good inhibitors in acidic solutions and the inhibition efficiency of these indole-type organic compounds may be explained in terms of electronic properties. The detailed study of 1 M HCl at 25°C is reported in [21].Table 1
Corrosion parameters obtained from electrochemical measurements of C38 steel in 1 M HCl containing various concentrations of indole derivates at 25°C.
Inhibitor
Polarisation curves
EIS
E
corr versus SCE (mV)
I
corr (μA·cm−2)
IE (%)
R
ct (Ω·cm2)
C
dl (μF·cm−2)
IE (%)
1 M HCl
-
529
284
—
49 ± 0.02
546
Norharmane
0.2 mM
-
467
67
76
148 ± 0.91
183
67
0.4 mM
-
476
61
79
238 ± 1.65
120
79
0.8 mM
-
494
52
82
514 ± 1.18
55
90
1.2 mM
-
455
28
90
641 ± 1.73
44
92
Harmane
0.2 mM
-
476
65
77
181 ± 0.10
330
73
0.4 mM
-
489
55
81
321 ± 0.97
270
85
0.8 mM
-
479
34
88
537 ± 0.17
188
91
1.2 mM
-
492
24
91
735 ± 0.68
148
93


## 3.2. Effect of Temperature

### 3.2.1. Potentiodynamic Polarisation

In order to get more information about the performance of indole derivates, the nature of adsorption isotherm, and thereafter to evaluate the adsorption and activation processes, the influence of temperature is studied by potentiodynamic polarisation. Some of the polarisation curves for C38 steel electrode in 1 M HCl in the absence and in the presence of 0.2 mM of norharmane and harmane in the temperature range 25–55°C are given in Figures2, 3, and 4, respectively. As it can be seen, raising the temperature increases both anodic and cathodic reactions of C38 steel electrode both in the absence and in the presence of inhibitors. Polarisation curves of the C38 steel electrode in 1 M HCl without and with addition of various concentrations of harmane at 45°C are shown in Figure 5, representative example. As it can be seen, the anodic and cathodic reactions are affected by the addition of inhibitor. Similar observations were found for all concentrations studied in the presence of both inhibitors. Accurate evaluation of Tafel slopes by Tafel extrapolation is often impossible, simply because an experimental polarization curve does not exhibit linear Tafel regions [24–27]. Our experimental polarization curves presented here do not display the expected log/linear Tafel behaviour with anodic branches exhibiting curvature over the complete applied potential range. The curvature of the anodic branch may be attributed to the deposition of the corrosion products or impurities in the steel (e.g., Fe3C) to form a nonpassive surface film [24]. The various electrochemical parameters were calculated from Tafel plots and summarized in Table 2. The inhibition efficiency and the surface coverage degree (θ) values for steel are also shown in the same table. The surface coverage θ was calculated from (1) [28]. It has been observed from Table 2, that the corrosion current density (Icorr) increased with increasing temperature in both uninhibited and inhibited solutions. The addition of norharmane or harmane to the HCl solution shifts the Ecorr towards more negative values at all of the studied temperatures, although there was not a specific relation between Ecorr and inhibitors concentration. The IE (%) values decrease with increasing temperature; a decrease in inhibition efficiencies with the increase in temperature might be due to weakening of physical adsorption. Consider
(1)θ=Icorr-Icorr(inh)Icorr,
where Icorr and Icorr(inh) are the corrosion current density values in the absence and presence of indole derivates, respectively.Table 2
Electrochemical parameters calculated from Tafel plots and the corresponding inhibition efficiencies at various temperatures studied of C38 steel in 1 M HCl containing different concentrations of indole derivates.
Norharmane
Harmane
Temp. (°C)
Con. (mM)
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
1 M HCl
-
460
232
106
89
—
—
—
—
—
—
—
—
0.2
-
467
67
107
125
76
0.7641
−476
65
110
124
77
0.7711
25
0.4
-
476
61
116
122
79
0.7852
−489
55
98
107
81
0.8063
0.8
-
494
52
97
118
82
0.8169
−479
34
113
119
88
0.8803
1.2
-
455
28
93
112
90
0.9014
−492
24
87
107
91
0.9155
1 M HCl
-
454
843
111
109
—
—
—
—
—
—
—
—
0.2
-
473
236
112
144
72
0.7200
−465
212
118
133
75
0.7485
35
0.4
-
472
195
109
126
77
0.7687
−470
182
116
136
78
0.7841
0.8
-
470
165
102
131
80
0.8043
−456
154
109
128
82
0.8173
1.2
-
479
98
103
135
88
0.8837
−464
101
103
118
88
0.8802
1 M HCl
-
451
1192
120
109
—
—
—
—
—
—
—
—
0.2
-
501
512
130
146
57
0.5705
−496
413
117
134
65
0.6535
45
0.4
-
509
472
112
115
60
0.6040
−488
389
112
125
67
0.6737
0.8
-
505
443
135
135
63
0.6284
−487
335
113
126
72
0.7190
1.2
-
485
352
107
140
70
0.7047
−484
245
110
118
79
0.7945
1 M HCl
-
450
1982
131
116
—
—
—
—
—
—
—
—
0.2
-
509
1023
142
150
48
0.4839
−504
983
136
148
50
0.5040
55
0.4
-
497
954
114
156
52
0.5187
−496
852
123
140
57
0.5701
0.8
-
566
867
117
127
56
0.5626
−564
715
110
146
64
0.6393
1.2
-
494
651
109
139
67
0.6715
−515
574
107
132
71
0.7104Figure 2
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl.Figure 3
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of norharmane.Figure 4
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of harmane.Figure 5
Polarisation curves for C38 steel in 1 M HCl containing different concentrations of harmane at 45°C.In order to calculate activation parameters for the corrosion process, Arrhenius (2) and an alternative formulation of Arrhenius (3) were used:
(2)Icorr=Kexp(-EaRT),(3)Icorr=RTNhexp(ΔSaR)exp(-ΔHaRT),
where Icorr is the corrosion current density, K the Arrhenius preexponential constant, Ea is the activation energy for the corrosion process, h is the Plank’s constant, N is the Avogadro’s number, the enthalpy of activation (ΔHa), and the entropy of activation (ΔSa).Arrhenius plots for the corrosion density of C38 steel in the case of harmane are given in Figure6, representative example. Similar plots are obtained in the case of norharmane. The apparent activation energies (Ea) at different concentrations of indole derivates were determined by linear regression between lnIcorr and 1/T and the result is shown in Table 3. All the linear regression coefficients were close to 1, indicating that the C38 steel corrosion in hydrochloric acid can be elucidated using the kinetic model. Inspection of Table 3 showed that the values of Ea determined in 1 M HCl containing indole derivates are higher than that for uninhibited solution. The increase in the apparent activation energy may be interpreted as physical adsorption that occurs in the first stage [29]. Moreover, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. Szauer and Brand explained that the increase in activation energy can be attributed to an appreciable decrease in the adsorption of the inhibitor on the steel surface with increase in temperature [30]. Figure 7 showed a plot of ln (Icorr/T) versus 1/T with a slope of (-ΔHa/R) and an intercept (lnR/Nh+ΔSa/R) from which the values of ΔHa and ΔSa were calculated, respectively. All estimated kinetic-thermodynamic parameters were tabulated also in Table 3. Inspection of these data revealed that the thermodynamic parameters (ΔHa and ΔSa) for dissolution reaction of C38 steel in 1 M HCl in the presence of both inhibitors are higher than that of in the absence of inhibitors. The positive signs of ΔHa reflect the endothermic nature of the steel dissolution process suggesting that the dissolution of steel is slow in the presence of inhibitors [31]. Furthermore, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. One can notice that Ea and ΔHa values vary in the same way for both inhibitors (Table 3). The values of ΔSa were negative both in the absence and presence of inhibitors, implying that the activated complex represented the rate-determining step with respect to the association rather than the dissociation step. It means that a decrease in disorder occurred when proceeding from the reactants to the activated complex [30]. Also, the ΔSa shift can be explained as a result of the replacement process of water molecules during adsorption of organic inhibitor on the steel surface.Table 3
Thermodynamic parameters calculated from Tafel plots for the adsorption of indole derivates in 1 M HCl on the C38 steel at different temperatures.
Con. (mM)
Norharmane
Harmane
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
HCl
24.42
23.29
−119.48
—
—
—
0.2
31.73
30.60
−99.81
31.20
30.07
-
101.88
0.4
32.38
31.25
−98.12
31.80
30.67
-
100.43
0.8
33.40
32.27
−95.27
35.18
34.05
-
90.53
1.2
37.99
36.85
−81.97
36.89
35.76
-
86.63Figure 6
Arrhenius plots of corrosionln(Icorr) versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 7
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl and at different concentrations of harmane.


### 3.2.2. Impedance Measurements

The corrosion behaviour of C38 steel in 1 M HCl solution in the presence of indole derivates was also investigated by EIS in the temperature range 25–55°C. The EIS of C38 steel electrode in 1 M HCl solution in the absence and in the presence of of 0.2 mM of noharmane and harmane, at different temperatures, are shown in Figures8, 9, and 10; representative example. Figure 11 shows the impedance plots of C38 steel electrode in 1 M HCl solution in the absence and presence of different concentrations of norharmane at 35°C. It can be seen that, the size of the capacitive loop increased by increasing the concentration of norharmane. All the impedance spectra were measured at the corresponding open-circuit potentials. After analyzing the shape of the Nyquist plots, it is concluded that the curves obtained up to 45°C approximated by a single capacitive semi-circles, showing that the corrosion process was mainly charge transfer controlled. The general shape of the curves is very similar for all concentrations studied. The diameter of Nyquist plots (Rct) decreases with increasing temperature for both inhibitors. For the most temperatures 45 and 55°C, an inductive loop appeared at low-frequency values. Similar observations were found for all concentrations studied. The presence of the LF inductive loop may be attributed to the relaxation process obtained by adsorption species like Clads- and Hads+ on the electrode surface [32–35]. It may also be attributed to the adsorption of inhibitor on the electrode surface [36] or to the redissolution of the passivated surface at low frequencies [37]. The above impedance diagrams (Nyquist) contain depressed semicircles with the center under the real axis; such behaviors characteristic for solid electrodes and often referred to as frequency dispersion have been attributed to roughness and inhomogeneities of the solid surfaces, impurities [38–41]. Therefore, a constant phase element (CPE) instead of a capacitive element is used to get a more accurate fit of experimental data set. For analysis of the impedance spectra exhibiting one capacitive loop, the equivalent circuit (EC) given in Figure 12(a) was used to fit the experimental spectra while the EC shown in Figure 12(b) was used for the impedance spectra containing one capacitive loop and an inductive loop. Simulation of Nyquist plots with above models shows excellent agreement with experimental data (Figures 12(a) and 12(b); representative example).Figure 8
Nyquist diagrams for C38 steel in 1 M HCl at different temperatures.Figure 9
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of norharmane at different temperatures.Figure 10
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of harmane at different temperatures.Figure 11
Nyquist diagrams for C38 steel in 1 M HCl containing different concentrations of noharmane at 35°C.Nyquist plots: (□) experimental data and (—) fit data, together with the equivalent circuit used to fit the impedance data, recorded for a C38 electrode (a) in 1 M HCl solution + 0.2 mM harmane at 35°C and (b) in 1 M HCl solution + 0.2 mM norharmane at 55°C.
(a)
(b)The parameters calculated with the application of these models are summarized in Tables4 and 5. The values discussed show that the organic compounds investigated have inhibiting properties for all temperature values. This conclusion is based on the values of Rct in inhibitors presence. They are greater than those in 1 M HCl. The temperature rise leads to a decrease of Rct values. This is due, on one hand, to the increase of the rate of metal dissolution and, on the other hand, to the shift of the adsorption/desorption equilibrium towards the inhibitor’s desorption and hence to the decrease of surface coverage degree. The n value almost decreases with temperature increase and this is interpreted as an evidence for surface inhomogeneity increase. The latter is attributed to the accelerated corrosion and the developed metal surface. At lower temperatures the inhibitors adsorb on the most active surface sites; this results in a decrease of surface inhomogeneity. The desorption, which is favored by high temperatures, will increase with this effect. The Cdl value was calculated using (4) [42–44]:
(4)Cdl=(A·Rct1-n)1/n.
It is clear that the addition of harmane or norharmane causes a significant increase in Cdl in the additive-free solution for all temperatures studied. As the double layer capacitance can be connected with the thickness of the layer of adsorbed inhibitor molecules at the interface and this dependence is of reverse proportionality; it follows that the thickness of the adsorption layer will decrease with temperature increase. Similar tendency was found for CPE constant (A) for all temperatures studied. It can be seen from Tables 2, 4, and 5 that the inhibition efficiencies calculated by both methods show the same trend. The IE (%) values decrease with increasing temperature and no difference of numerical values of inhibition efficiencies was observed at 25 and 35°C. However the results obtained at 45 and 55°C show a difference in numerical values obtained by both methods. This variation may be due to the difference between methods, which each method is realised differently with some conditions and assumptions.Table 4
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of norharmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
148 ± 0.91
2.91 ± 0.02
0.871 ± 0.008
183
—
—
67
0.6689
35
53 ± 0.43
4.37 ± 0.25
0.836 ± 0.053
209
—
—
60
0.6038
45
30 ± 0.35
10.88 ± 3.65
0.765 ± 0.059
380
25 ± 4.61
9 ± 1.78
50
0.5000
55
10 ± 0.65
13.35 ± 1.75
0.815 ± 0.120
501
2 ± 0.40
2 ± 1.37
50
0.5000
0.4 mM
25
238 ± 1.65
1.89 ± 0.19
0.872 ± 0.005
120
—
—
79
0.7941
35
95 ± 0.89
3.53 ± 0.14
0.829 ± 0.052
175
—
—
78
0.7789
45
55 ± 3.04
6.19 ± 0.94
0.790 ± 0.032
252
10 ± 1.20
15 ± 1.60
73
0.7273
55
14 ± 0.93
8.84 ± 2.31
0.831 ± 0.054
362
3 ± 0.21
2 ± 0.32
64
0.6429
0.8 mM
25
514 ± 1.18
0.84 ± 0.03
0.883 ± 0.012
55
—
—
90
0.9047
35
180 ± 1.04
3.18 ± 0.13
0.825 ± 0.045
173
—
—
82
0.8235
45
85 ± 1.56
5.01 ± 0.30
0.814 ± 0.023
244
7 ± 0.27
14 ± 0.90
79
0.7857
55
22 ± 1.55
7.13 ± 0.47
0.809 ± 0.251
267
6 ± 1.60
2 ± 1.10
77
0.7727
1.2 mM
25
641 ± 1.73
0.66 ± 0.02
0.887 ± 0.010
44
—
—
92
0.9236
35
245 ± 0.55
2.3 ± 0.78
0.803 ± 0.072
114
—
—
91
0.9143
45
123 ± 0.81
2.9 ± 0.57
0.802 ± 0.140
127
—
—
88
0.8780
55
25 ± 0.41
4.46 ± 0.17
0.804 ± 0.023
149
6 ± 0.50
3 ± 1.43
80
0.8000Table 5
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of harmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
181 ± 0.10
4.82 ± 0.19
0.866 ± 0.042
330
—
—
73
0.7293
35
73 ± 0.61
6.92 ± 0.44
0.816 ± 0.501
353
—
—
71
0.7123
45
50 ± 1.23
9.73 ± 0.27
0.805 ± 0.062
468
25 ± 8.41
8 ± 3.02
70
0.7000
55
16 ± 0.81
19.5 ± 4.03
0.719 ± 0.501
503
11 ± 0.34
3 ± 0.8
69
0.6875
0.4 mM
25
321 ± 0.97
3.71 ± 0.37
0.870 ± 0.036
270
—
—
85
0.8474
35
129 ± 0.65
5.29 ± 0.09
0.804 ± 0.074
275
—
—
84
0.8372
45
82 ± 1.54
7.95 ± 1.02
0.784 ± 0.128
375
25 ± 1.74
9 ± 1.5
82
0.8171
55
21 ± 2.31
10.31 ± 2.13
0.824 ± 0.054
455
21 ± 0.58
4 ± 1.3
76
0.7619
0.8 mM
25
537 ± 0.17
2.52 ± 0.27
0.873 ± 0.051
188
—
—
91
0.9088
35
218 ± 0.56
3.96 ± 0.72
0.795 ± 0.104
211
—
—
90
0.9037
45
136 ± 1.53
4.37 ± 0.73
0.811 ± 0.091
226
—
—
89
0.8897
55
27 ± 1.20
8.64 ± 2.03
0.780 ± 0.035
299
5 ± 0.12
2 ± 0.76
81
0.8148
1.2 mM
25
735 ±  0.68
1.92 ± 0.12
0.883 ± 0.036
148
—
—
93
0.9333
35
293 ± 0.54
3.28 ± 0.27
0.814 ± 0.037
192
—
—
93
0.9283
45
182 ± 0.53
4.33 ± 0.07
0.826 ± 0.051
254
—
—
92
0.9176
55
32 ± 0.66
7.36 ± 1.91
0.783 ± 0.102
260
11 ± 1.54
5 ± 0.8
84
0.8438To obtain the activation parameters from the impedance technique, values ofRct and those of βa and βc obtained at different temperatures were used to calculate values of Icorr according to Stern-Geary [45] equation:
(5)Icorr=βaβc2.303(βa+βc)(1Rct).
Figures 13 and 14 show the Arrhenius plot for the results obtained in 1 M HCl solutions in the presence of harmane, representative example. Similar plots are obtained in the case of norharmane. The results are in good agreement with those obtained from polarization studies and show the same trend. The difference of numerical values of ΔSa determined from the two techniques may be attributed to the different methods that have been used for the determination of the corrosion rates.Figure 13
Arrhenius plotslnIcorr versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 14
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl at different concentrations of harmane.


## 3.2.1. Potentiodynamic Polarisation

In order to get more information about the performance of indole derivates, the nature of adsorption isotherm, and thereafter to evaluate the adsorption and activation processes, the influence of temperature is studied by potentiodynamic polarisation. Some of the polarisation curves for C38 steel electrode in 1 M HCl in the absence and in the presence of 0.2 mM of norharmane and harmane in the temperature range 25–55°C are given in Figures2, 3, and 4, respectively. As it can be seen, raising the temperature increases both anodic and cathodic reactions of C38 steel electrode both in the absence and in the presence of inhibitors. Polarisation curves of the C38 steel electrode in 1 M HCl without and with addition of various concentrations of harmane at 45°C are shown in Figure 5, representative example. As it can be seen, the anodic and cathodic reactions are affected by the addition of inhibitor. Similar observations were found for all concentrations studied in the presence of both inhibitors. Accurate evaluation of Tafel slopes by Tafel extrapolation is often impossible, simply because an experimental polarization curve does not exhibit linear Tafel regions [24–27]. Our experimental polarization curves presented here do not display the expected log/linear Tafel behaviour with anodic branches exhibiting curvature over the complete applied potential range. The curvature of the anodic branch may be attributed to the deposition of the corrosion products or impurities in the steel (e.g., Fe3C) to form a nonpassive surface film [24]. The various electrochemical parameters were calculated from Tafel plots and summarized in Table 2. The inhibition efficiency and the surface coverage degree (θ) values for steel are also shown in the same table. The surface coverage θ was calculated from (1) [28]. It has been observed from Table 2, that the corrosion current density (Icorr) increased with increasing temperature in both uninhibited and inhibited solutions. The addition of norharmane or harmane to the HCl solution shifts the Ecorr towards more negative values at all of the studied temperatures, although there was not a specific relation between Ecorr and inhibitors concentration. The IE (%) values decrease with increasing temperature; a decrease in inhibition efficiencies with the increase in temperature might be due to weakening of physical adsorption. Consider
(1)θ=Icorr-Icorr(inh)Icorr,
where Icorr and Icorr(inh) are the corrosion current density values in the absence and presence of indole derivates, respectively.Table 2
Electrochemical parameters calculated from Tafel plots and the corresponding inhibition efficiencies at various temperatures studied of C38 steel in 1 M HCl containing different concentrations of indole derivates.
Norharmane
Harmane
Temp. (°C)
Con. (mM)
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
E
corr versus SCE (mV)
I
corr (μA·cm−2)
b
a (mV·dec−1)
b
c (mV·dec−1)
IE (%)
θ
1 M HCl
-
460
232
106
89
—
—
—
—
—
—
—
—
0.2
-
467
67
107
125
76
0.7641
−476
65
110
124
77
0.7711
25
0.4
-
476
61
116
122
79
0.7852
−489
55
98
107
81
0.8063
0.8
-
494
52
97
118
82
0.8169
−479
34
113
119
88
0.8803
1.2
-
455
28
93
112
90
0.9014
−492
24
87
107
91
0.9155
1 M HCl
-
454
843
111
109
—
—
—
—
—
—
—
—
0.2
-
473
236
112
144
72
0.7200
−465
212
118
133
75
0.7485
35
0.4
-
472
195
109
126
77
0.7687
−470
182
116
136
78
0.7841
0.8
-
470
165
102
131
80
0.8043
−456
154
109
128
82
0.8173
1.2
-
479
98
103
135
88
0.8837
−464
101
103
118
88
0.8802
1 M HCl
-
451
1192
120
109
—
—
—
—
—
—
—
—
0.2
-
501
512
130
146
57
0.5705
−496
413
117
134
65
0.6535
45
0.4
-
509
472
112
115
60
0.6040
−488
389
112
125
67
0.6737
0.8
-
505
443
135
135
63
0.6284
−487
335
113
126
72
0.7190
1.2
-
485
352
107
140
70
0.7047
−484
245
110
118
79
0.7945
1 M HCl
-
450
1982
131
116
—
—
—
—
—
—
—
—
0.2
-
509
1023
142
150
48
0.4839
−504
983
136
148
50
0.5040
55
0.4
-
497
954
114
156
52
0.5187
−496
852
123
140
57
0.5701
0.8
-
566
867
117
127
56
0.5626
−564
715
110
146
64
0.6393
1.2
-
494
651
109
139
67
0.6715
−515
574
107
132
71
0.7104Figure 2
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl.Figure 3
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of norharmane.Figure 4
Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl + 0.2 mM of harmane.Figure 5
Polarisation curves for C38 steel in 1 M HCl containing different concentrations of harmane at 45°C.In order to calculate activation parameters for the corrosion process, Arrhenius (2) and an alternative formulation of Arrhenius (3) were used:
(2)Icorr=Kexp(-EaRT),(3)Icorr=RTNhexp(ΔSaR)exp(-ΔHaRT),
where Icorr is the corrosion current density, K the Arrhenius preexponential constant, Ea is the activation energy for the corrosion process, h is the Plank’s constant, N is the Avogadro’s number, the enthalpy of activation (ΔHa), and the entropy of activation (ΔSa).Arrhenius plots for the corrosion density of C38 steel in the case of harmane are given in Figure6, representative example. Similar plots are obtained in the case of norharmane. The apparent activation energies (Ea) at different concentrations of indole derivates were determined by linear regression between lnIcorr and 1/T and the result is shown in Table 3. All the linear regression coefficients were close to 1, indicating that the C38 steel corrosion in hydrochloric acid can be elucidated using the kinetic model. Inspection of Table 3 showed that the values of Ea determined in 1 M HCl containing indole derivates are higher than that for uninhibited solution. The increase in the apparent activation energy may be interpreted as physical adsorption that occurs in the first stage [29]. Moreover, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. Szauer and Brand explained that the increase in activation energy can be attributed to an appreciable decrease in the adsorption of the inhibitor on the steel surface with increase in temperature [30]. Figure 7 showed a plot of ln (Icorr/T) versus 1/T with a slope of (-ΔHa/R) and an intercept (lnR/Nh+ΔSa/R) from which the values of ΔHa and ΔSa were calculated, respectively. All estimated kinetic-thermodynamic parameters were tabulated also in Table 3. Inspection of these data revealed that the thermodynamic parameters (ΔHa and ΔSa) for dissolution reaction of C38 steel in 1 M HCl in the presence of both inhibitors are higher than that of in the absence of inhibitors. The positive signs of ΔHa reflect the endothermic nature of the steel dissolution process suggesting that the dissolution of steel is slow in the presence of inhibitors [31]. Furthermore, the values obtained for norharmane are somewhat higher than those obtained for harmane and confirm the fact that the inhibitor efficiency of norharmane is slightly lower than that of harmane. One can notice that Ea and ΔHa values vary in the same way for both inhibitors (Table 3). The values of ΔSa were negative both in the absence and presence of inhibitors, implying that the activated complex represented the rate-determining step with respect to the association rather than the dissociation step. It means that a decrease in disorder occurred when proceeding from the reactants to the activated complex [30]. Also, the ΔSa shift can be explained as a result of the replacement process of water molecules during adsorption of organic inhibitor on the steel surface.Table 3
Thermodynamic parameters calculated from Tafel plots for the adsorption of indole derivates in 1 M HCl on the C38 steel at different temperatures.
Con. (mM)
Norharmane
Harmane
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
HCl
24.42
23.29
−119.48
—
—
—
0.2
31.73
30.60
−99.81
31.20
30.07
-
101.88
0.4
32.38
31.25
−98.12
31.80
30.67
-
100.43
0.8
33.40
32.27
−95.27
35.18
34.05
-
90.53
1.2
37.99
36.85
−81.97
36.89
35.76
-
86.63Figure 6
Arrhenius plots of corrosionln(Icorr) versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 7
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl and at different concentrations of harmane.


## 3.2.2. Impedance Measurements

The corrosion behaviour of C38 steel in 1 M HCl solution in the presence of indole derivates was also investigated by EIS in the temperature range 25–55°C. The EIS of C38 steel electrode in 1 M HCl solution in the absence and in the presence of of 0.2 mM of noharmane and harmane, at different temperatures, are shown in Figures8, 9, and 10; representative example. Figure 11 shows the impedance plots of C38 steel electrode in 1 M HCl solution in the absence and presence of different concentrations of norharmane at 35°C. It can be seen that, the size of the capacitive loop increased by increasing the concentration of norharmane. All the impedance spectra were measured at the corresponding open-circuit potentials. After analyzing the shape of the Nyquist plots, it is concluded that the curves obtained up to 45°C approximated by a single capacitive semi-circles, showing that the corrosion process was mainly charge transfer controlled. The general shape of the curves is very similar for all concentrations studied. The diameter of Nyquist plots (Rct) decreases with increasing temperature for both inhibitors. For the most temperatures 45 and 55°C, an inductive loop appeared at low-frequency values. Similar observations were found for all concentrations studied. The presence of the LF inductive loop may be attributed to the relaxation process obtained by adsorption species like Clads- and Hads+ on the electrode surface [32–35]. It may also be attributed to the adsorption of inhibitor on the electrode surface [36] or to the redissolution of the passivated surface at low frequencies [37]. The above impedance diagrams (Nyquist) contain depressed semicircles with the center under the real axis; such behaviors characteristic for solid electrodes and often referred to as frequency dispersion have been attributed to roughness and inhomogeneities of the solid surfaces, impurities [38–41]. Therefore, a constant phase element (CPE) instead of a capacitive element is used to get a more accurate fit of experimental data set. For analysis of the impedance spectra exhibiting one capacitive loop, the equivalent circuit (EC) given in Figure 12(a) was used to fit the experimental spectra while the EC shown in Figure 12(b) was used for the impedance spectra containing one capacitive loop and an inductive loop. Simulation of Nyquist plots with above models shows excellent agreement with experimental data (Figures 12(a) and 12(b); representative example).Figure 8
Nyquist diagrams for C38 steel in 1 M HCl at different temperatures.Figure 9
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of norharmane at different temperatures.Figure 10
Nyquist diagrams for C38 steel in 1 M HCl containing 0.2 mM of harmane at different temperatures.Figure 11
Nyquist diagrams for C38 steel in 1 M HCl containing different concentrations of noharmane at 35°C.Nyquist plots: (□) experimental data and (—) fit data, together with the equivalent circuit used to fit the impedance data, recorded for a C38 electrode (a) in 1 M HCl solution + 0.2 mM harmane at 35°C and (b) in 1 M HCl solution + 0.2 mM norharmane at 55°C.
(a)
(b)The parameters calculated with the application of these models are summarized in Tables4 and 5. The values discussed show that the organic compounds investigated have inhibiting properties for all temperature values. This conclusion is based on the values of Rct in inhibitors presence. They are greater than those in 1 M HCl. The temperature rise leads to a decrease of Rct values. This is due, on one hand, to the increase of the rate of metal dissolution and, on the other hand, to the shift of the adsorption/desorption equilibrium towards the inhibitor’s desorption and hence to the decrease of surface coverage degree. The n value almost decreases with temperature increase and this is interpreted as an evidence for surface inhomogeneity increase. The latter is attributed to the accelerated corrosion and the developed metal surface. At lower temperatures the inhibitors adsorb on the most active surface sites; this results in a decrease of surface inhomogeneity. The desorption, which is favored by high temperatures, will increase with this effect. The Cdl value was calculated using (4) [42–44]:
(4)Cdl=(A·Rct1-n)1/n.
It is clear that the addition of harmane or norharmane causes a significant increase in Cdl in the additive-free solution for all temperatures studied. As the double layer capacitance can be connected with the thickness of the layer of adsorbed inhibitor molecules at the interface and this dependence is of reverse proportionality; it follows that the thickness of the adsorption layer will decrease with temperature increase. Similar tendency was found for CPE constant (A) for all temperatures studied. It can be seen from Tables 2, 4, and 5 that the inhibition efficiencies calculated by both methods show the same trend. The IE (%) values decrease with increasing temperature and no difference of numerical values of inhibition efficiencies was observed at 25 and 35°C. However the results obtained at 45 and 55°C show a difference in numerical values obtained by both methods. This variation may be due to the difference between methods, which each method is realised differently with some conditions and assumptions.Table 4
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of norharmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
148 ± 0.91
2.91 ± 0.02
0.871 ± 0.008
183
—
—
67
0.6689
35
53 ± 0.43
4.37 ± 0.25
0.836 ± 0.053
209
—
—
60
0.6038
45
30 ± 0.35
10.88 ± 3.65
0.765 ± 0.059
380
25 ± 4.61
9 ± 1.78
50
0.5000
55
10 ± 0.65
13.35 ± 1.75
0.815 ± 0.120
501
2 ± 0.40
2 ± 1.37
50
0.5000
0.4 mM
25
238 ± 1.65
1.89 ± 0.19
0.872 ± 0.005
120
—
—
79
0.7941
35
95 ± 0.89
3.53 ± 0.14
0.829 ± 0.052
175
—
—
78
0.7789
45
55 ± 3.04
6.19 ± 0.94
0.790 ± 0.032
252
10 ± 1.20
15 ± 1.60
73
0.7273
55
14 ± 0.93
8.84 ± 2.31
0.831 ± 0.054
362
3 ± 0.21
2 ± 0.32
64
0.6429
0.8 mM
25
514 ± 1.18
0.84 ± 0.03
0.883 ± 0.012
55
—
—
90
0.9047
35
180 ± 1.04
3.18 ± 0.13
0.825 ± 0.045
173
—
—
82
0.8235
45
85 ± 1.56
5.01 ± 0.30
0.814 ± 0.023
244
7 ± 0.27
14 ± 0.90
79
0.7857
55
22 ± 1.55
7.13 ± 0.47
0.809 ± 0.251
267
6 ± 1.60
2 ± 1.10
77
0.7727
1.2 mM
25
641 ± 1.73
0.66 ± 0.02
0.887 ± 0.010
44
—
—
92
0.9236
35
245 ± 0.55
2.3 ± 0.78
0.803 ± 0.072
114
—
—
91
0.9143
45
123 ± 0.81
2.9 ± 0.57
0.802 ± 0.140
127
—
—
88
0.8780
55
25 ± 0.41
4.46 ± 0.17
0.804 ± 0.023
149
6 ± 0.50
3 ± 1.43
80
0.8000Table 5
Values of the elements of equivalent circuit required for fitting the EIS for C38 steel immersed in the presence and absence of harmane at different temperatures.
Temp (°C)
R
ct (Ω cm2)
A104 (Ω−1 sn cm−2)
n
C
dl (μF cm−2)
L (H cm−2)
R
L (Ω cm2)
IE (%)
θ
25
49 ± 0.02
9.5 ± 0.73
0.853 ± 0.014
546
—
—
—
—
Blank
35
17 ± 0.64
20.5 ± 4.21
0.795 ± 0.421
863
18 ± 1.87
6 ± 1.26
—
—
45
12 ± 0.94
43.5 ± 3.56
0.745 ± 0.362
1583
15 ± 2.35
3 ± 0.87
—
—
55
3 ± 0.96
72.8 ± 5.64
0.735 ± 0.093
1834
10 ± 8.54
2 ± 1.25
—
—
0.2 mM
25
181 ± 0.10
4.82 ± 0.19
0.866 ± 0.042
330
—
—
73
0.7293
35
73 ± 0.61
6.92 ± 0.44
0.816 ± 0.501
353
—
—
71
0.7123
45
50 ± 1.23
9.73 ± 0.27
0.805 ± 0.062
468
25 ± 8.41
8 ± 3.02
70
0.7000
55
16 ± 0.81
19.5 ± 4.03
0.719 ± 0.501
503
11 ± 0.34
3 ± 0.8
69
0.6875
0.4 mM
25
321 ± 0.97
3.71 ± 0.37
0.870 ± 0.036
270
—
—
85
0.8474
35
129 ± 0.65
5.29 ± 0.09
0.804 ± 0.074
275
—
—
84
0.8372
45
82 ± 1.54
7.95 ± 1.02
0.784 ± 0.128
375
25 ± 1.74
9 ± 1.5
82
0.8171
55
21 ± 2.31
10.31 ± 2.13
0.824 ± 0.054
455
21 ± 0.58
4 ± 1.3
76
0.7619
0.8 mM
25
537 ± 0.17
2.52 ± 0.27
0.873 ± 0.051
188
—
—
91
0.9088
35
218 ± 0.56
3.96 ± 0.72
0.795 ± 0.104
211
—
—
90
0.9037
45
136 ± 1.53
4.37 ± 0.73
0.811 ± 0.091
226
—
—
89
0.8897
55
27 ± 1.20
8.64 ± 2.03
0.780 ± 0.035
299
5 ± 0.12
2 ± 0.76
81
0.8148
1.2 mM
25
735 ±  0.68
1.92 ± 0.12
0.883 ± 0.036
148
—
—
93
0.9333
35
293 ± 0.54
3.28 ± 0.27
0.814 ± 0.037
192
—
—
93
0.9283
45
182 ± 0.53
4.33 ± 0.07
0.826 ± 0.051
254
—
—
92
0.9176
55
32 ± 0.66
7.36 ± 1.91
0.783 ± 0.102
260
11 ± 1.54
5 ± 0.8
84
0.8438To obtain the activation parameters from the impedance technique, values ofRct and those of βa and βc obtained at different temperatures were used to calculate values of Icorr according to Stern-Geary [45] equation:
(5)Icorr=βaβc2.303(βa+βc)(1Rct).
Figures 13 and 14 show the Arrhenius plot for the results obtained in 1 M HCl solutions in the presence of harmane, representative example. Similar plots are obtained in the case of norharmane. The results are in good agreement with those obtained from polarization studies and show the same trend. The difference of numerical values of ΔSa determined from the two techniques may be attributed to the different methods that have been used for the determination of the corrosion rates.Figure 13
Arrhenius plotslnIcorr versus 1/T of 1 M HCl and at different concentrations of harmane.Figure 14
Arrhenius plots of corrosionln(Icorr/T) versus 1/T of 1 M HCl at different concentrations of harmane.


## 3.3. Adsorption Isotherm

Inhibition by organic compounds is, mainly, due to their ability to adsorb onto a metal surface to form a protective film. The establishment of isotherms that describe the adsorption behaviour of corrosion inhibitor is important as they provide important information about the nature of metal-inhibitor interaction. It has been reported that the adsorption of the inhibitor molecules depends on a variety of factors such as the presence of functional groups (either electron donating or withdrawing), charge distribution at the donor atom, theπ orbital character of donating electrons, the nature of substrate metal and the type of interaction between organic molecules and the metallic surface as well.The most frequently used isotherms are Langmiur (6), Temkin (7), and Frumkin (8). All these isotherms are tested. In all cases, the degree of surface coverage (θ) is plotted as a function of the inhibitor concentration (Cinh). In the present study, values of θ are obtained from Icorr and Rct. The significance of the adsorption isotherm was obtained by calculating the correlation coefficients (R2). As an example, Figures 15, 16, and 17 represent fitting of impedance and polarization data obtained for C38 electrode in 1 M HCl containing various concentrations of norharmane at 55°C to Langmuir, Temkin, and Frunkin isotherms. The best correlation between the experimental results, obtained from the three tested isotherm functions, was obtained using Langmuir isotherm (the strong correlation R2=0.999 for both methods). Similar observations were found for all temperatures studied. The simplest, being the Langmuir isotherm, is based on assumption that all adsorption sites are equivalent and that particle binding occurs independently from nearby sites being occupied or not [46]. Consider
(6)Cinhθ=1K+Cinh(Langmuirisotherm),(7)(θ1-θ)exp(-2aθ)=KCinh(Frumkinisotherm),(8)exp(-2aθ)=KCinh(Temkinisotherm),
where “K” is the binding constant of the adsorption reaction and “a” is the lateral interaction term describing the molecular interactions in the adsorption layer and the heterogeneity of the surface.Figure 15
Langmuir adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.Figure 16
Frumkin adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.Figure 17
Temkin adsorption plots for C38 steel in 1 M HCl containing different concentrations of norharmane at 55°C.The well known thermodynamic adsorption parameters are the standard free energy of adsorption (ΔGads0), the heat of adsorption (ΔHads0), and the standard entropy of adsorption (ΔSads0). These quantities can be calculated depending on the estimated values of K from adsorption isotherms at different temperatures.The constant of adsorption,K, is related to the standard free energy of adsorption, ΔGads0, with the following equation:
(9)K=155.5exp(-ΔGads0RT).
The value 55.5 in the above equation is the concentration of water in solution in mol L−1 [47]. The ΔGads0 values at all studied temperatures can be calculated. Then, the obtained ΔGads0 values plotted versus T (Figures 18 and 19) gave the heat of adsorption ΔHads0 and the standard adsorption entropy ΔSads0 in accordance with the basic equation:
(10)ΔGads0=ΔHads0-TΔSads0.
All thermodynamic adsorption parameters estimated from both methods for indole derivates on C38 steel from 1 M of HCl solution are listed in Tables 6, 7, and 8. The entire values of thermodynamic adsorption obtained by both methods are in good agreement and follow the same trend. The negative values of ΔGads0 ensure the spontaneity of the adsorption process and stability of the adsorbed layer on the steel surface. The calculated ΔGads0 values indicate the physical nature of adsorption of norharmane and harmane. The dependence of ΔGads0 on experimental temperature can be summarized in two cases as follows.Table 6
Thermodynamic parameters calculated from IES for the adsorption of indole derivates in 1 M HCl on the C38 steel at different temperatures.
Con. (mM)
Norharmane
Harmane
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
E
a (kJ mol−1)
Δ
H
a (kJ mol−1)
Δ
S
a (J mol−1 K−1)
HCl
28.00
26.87
-
131.04
—
—
—
0.2
32.78
31.65
-
120.35
29.03
27.91
-
131.68
0.4
33.34
32.22
-
116.44
32.82
31.69
-
121.55
0.8
38.00
36.87
-
105.77
34.05
32.92
-
119.20
1.2
38.77
37.64
-
104.36
37.05
35.92
-
110.91Table 7
Thermodynamic parameters calculated from IES for the adsorption of indole derivates on C38 steel in 1 M HCl at different temperatures.
Temp. (°C)
Norharmane
Harmane
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
25
−18.00
−14.63
35
−14.46
−8.18
20.2
−15.03
−3.94
36
45
−14.50
−15.44
55
−14.90
−15.69Table 8
Thermodynamic parameters calculated from LP for the adsorption of indole derivates on C38 steel in 1 M HCl at different temperatures.
Temp. (°C)
Norharmane
Harmane
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
Δ
G
ads
0 (kJ mol−1)
Δ
H
ads
0 (kJ mol−1)
Δ
S
ads
0 (J mol−1 K−1)
25
−14.59
−14.71
35
−14.84
−8.45
20.7
−15.04
−7.43
24.5
45
−15.06
−15.23
55
−15.21
−15.46Figure 18
Variation ofΔGads0, evaluated from IES, versus T on C38 steel in 1 M HCl containing indole derivates.Figure 19
Variation ofΔGads0, evaluated from LP, versus T on C38 steel in 1 M HCl containing indole derivates.(a) Value ofΔGads0 becomes less negative with increasing temperature indicating the occurrence of exothermic process at which adsorption was unfavourable with increasing reaction temperature as the result of the inhibitor desorption from the steel surface [48].(b) Value ofΔGads0 becomes more negative with increasing temperature indicating the occurrence of endothermic process at which increasing temperature facilitates inhibitor adsorption.The first case (a) is observed for the adsorption of the studied inhibitor species on C38 steel surface from HCl solution depending on the applied temperature range (Tables7 and 8), indicating the occurrence of exothermic adsorption processes. Also, it is noteworthy feature that the calculated value of ΔGads0 at 25°C in the case of harmane is greater than that in the case of norharmane, which means that the electrostatic interaction between the harmane and the steel surface is stronger. This is in good agreement with the range of the inhibition efficiency values obtained at 25°C from both impedance and polarisation measurements. However in the temperature range 35–55°C, there is an observable contradiction between the results of inhibition efficiency values and the finding of the calculated value of ΔGads0. The negative sign of (ΔHads0) reveals that the adsorption of inhibitor molecules is an exothermic process. Generally, an exothermic adsorption process suggests either physisorption or chemisorption while endothermic process is attributed to chemisorption [17]. Moreover, the values obtained for harmane are somewhat higher than those obtained for norharmane. This result indicated that harmane is more strongly adsorbed on the steel surface. This is in good agreement with the results obtained from impedance and polarisation measurements. The results show a great difference between the value of ΔHads0 for harmane obtained from EIS (−3.88 kJ mol−1) and from LP (−7.40 kJ mol−1). This difference may be due to the accuracy of linear regression between ΔGads0 and T, where the linear regression coefficient (R2) obtained from EIS is 0.9905 and from LP is 0.9254. The ΔSads0 values in the presence of indole derivates are large and positive, meaning that an increasing in disordering takes place in going from reactants to the metal-adsorbed species reaction complex [49].The integrated version of the Van’t Hoff equation expressed by (11) can be also deduced the ΔHads0 value [50]:
(11)lnK=-ΔHads0RT+constant.
Figures 20 and 21 show the plot of lnK versus 1/T from both methods which gives straight lines with slopes of (-ΔHads0/R) and intercepts of (-ΔSads0/R+ln1/55.5). The calculated ΔHads0 using the Van’t Hoff equation are −8.25 (from IES) and −8.41 (from LP) kJ mol−1 for norharmane. For harmane, the calculated ΔHads0 are −3.88 (from IES) and −7.40 (from LP) kJ mol−1. These results confirm the exothermic behaviour of the adsorption of the inhibitors on the steel surface, therefore, the physisorption process. Values of ΔHads0 obtained by both (9) and (10) are in good agreement. Moreover, the deduced ΔSads0 values (−20.01 J mol−1 K−1 from IES and −20.82 J mol−1 K−1 from LP) and (−36.14 J mol−1 K−1 from IES and −24.63 J mol−1 K−1 from LP) for norharmane and harmane, respectively, are very close to those obtained in Tables 7 and 8.Figure 20
Van’t Hoff plots for the C38 steel/indoles/1 M HCl system evaluated from LP.Figure 21
Van’t Hoff plots for the C38 steel/indoles/1 M HCl system evaluated from IES.


## 4. Conclusion

Norharmane and harmane were found to be inhibitors for C38 steel corrosion in 1 M HCl solution and their inhibition efficiency increased with increasing concentration. Indole derivates are found to affect both the anodic and cathodic processes and their inhibition efficiencies decrease with increasing temperature. Impedance measurements show that the interface studied (in presence of the compounds investigated) is described by a relatively simple structural model, which shows the presence of one time constant and dispersed capacitance. For the most temperatures 45 and 55°C, an inductive loop appeared at low-frequency values. The structural parameters calculated show decrease of the resistanceRct and increase of the capacitance. The inhibition is attributed to physisorption of the heterocyclic compound on the steel surface and blocking its active sites. The activation parameters of corrosion process such as activation energy, Ea, activation enthalpy, ΔHa, and activation entropy, ΔSa, were calculated from the dependence of corrosion rates on the temperature from polarization and impedance measurements. Also, the thermodynamic adsorption parameters were calculated and commented on from polarization and impedance measurements. The adsorption of indole derivates on the mild steel surface in 1 M HCl obeyed the Langmuir adsorption isotherm model at all studied temperatures.



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*Source: 139798-2013-06-05.xml*