# Study of Temperature Effect on the Corrosion Inhibition of C38 Carbon Steel Using Amino-tris(Methylenephosphonic) Acid in Hydrochloric Acid Solution

Authors: Najoua Labjar; Fouad Bentiss; Mounim Lebrini; Charafeddine Jama; Souad El hajjaji
Journal: International Journal of Corrosion
 (2011)

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## Abstract

Tafel polarization method was used to assess the corrosion inhibitive and adsorption behaviours of amino-tris(methylenephosphonic) acid (ATMP) for C38 carbon steel in 1 M HCl solution in the temperature range from 30 to60∘C. It was shown that the corrosion inhibition efficiency was found to increase with increase in ATMP concentration but decreased with temperature, which is suggestive of physical adsorption mechanism. The adsorption of the ATMP onto the C38 steel surface was found to follow Langmuir adsorption isotherm model. The corrosion inhibition mechanism was further corroborated by the values of kinetic and thermodynamic parameters obtained from the experimental data.


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## Body

## 1. Introduction

Corrosion inhibition of steel in acid solutions by different types of inhibitors has been extensively studied. The use of environmentally acceptable inhibitors is favoured. Phosphonates are known to be environmentally friendly corrosion inhibitors, which form adsorbed layers on oxide- or hydroxide-covered metal surfaces [1–4]. Many works can be found in the literature about the interactions between phosphonates and iron or steels. In particular, Ochoa and al. [2, 4] studied the interaction between phosphonocarboxylic acid salts (monophosphonates) and carbon steel. Their environmental impact at usual concentrations for corrosion inhibition is negligible [5, 6]. Moreover, in contrast to inorganic phosphorous compounds, they do not cause eutrophication. Their high stability to hydrolysis and resistance to degradation is also beneficial. It was found that few inhibitors with acid-metal systems have specific reactions that are still effective at high temperatures as (or more) they are at low temperatures [7, 8]. A large number of investigations have studied the temperature effects on acidic corrosion and corrosion inhibition of iron and steel in HCl and H2SO4 solutions [9–17].In previous work [1], the improving of the corrosion resistance of C38 carbon steel in 1 M HCl solution using ATMP has been investigated at 30°C by means of gravimetric and electrochemical (ac impedance and Tafel polarisation) methods. We have found that this compound is efficient inhibitor in 1 M HCl and the corrosion inhibition is mainly controlled by a physisorption process. The antibacterial activity investigations have been shown that the ATMP has an antibacterial effect against both Gram-positive and Gram-negative bacteria [1]. A great limitation of the inhibitor application is the fall down of their efficiencies at high temperatures. The effect of temperature on the inhibited acid- metal reaction is highly complex because many charges occur on the metal surface such as rapid etching and desorption of the inhibitor, and the inhibitor itself, in some cases, may undergo decomposition and/or rearrangement [18]. However, it provides the ability of calculating many thermodynamic functions for the inhibition and/or the adsorption processes which contribute in determining the type of adsorption of the studied inhibitor. The aim of this work is then to study the effect of temperature on C38 carbon steel corrosion process in 1 M HCl both in the absence and in the presence of amino-tris(methylenephosphonic) acid (ATMP) using Tafel polarisation method. The thermodynamic parameters for both activation and adsorption processes were calculated and discussed.


## 2. Experimental Details

The material used in this study is a C38 carbon steel with a chemical composition (in wt %) of 0.370% C, 0.230% Si, 0.680% Mn, 0.016% S, 0.077% Cr, 0.011% Ti, 0.059% Ni, 0.009% Co, 0.160% Cu, and the remainder iron (Fe). The C38 carbon samples were pretreated prior to the experiments by grinding with emery paper SiC (120, 600, and 1200), rinsed with distilled water, degreased in acetone in an ultrasonic bath immersion for 5 min, washed again with bidistilled water, and then dried at room temperature before use. The tested compound, namely amino-tris(methylenephosphonic)acid (N[CH2P(O)(OH)2]3), (ATMP),obtained from Sigma-Aldrich (50 wt.% in H2O), was tested without further purification. The molecular structure of the ATMP is shown in Figure 1.The acid solutions (1 M HCl) were prepared by dilution of an analytical reagent grade 37% HCl with doubly distilled water.Figure 1
Molecular structure of the amino-tris(methylenephosphonic) acid(ATMP).Polarisation curves were conducted using an electrochemical measurement system Tacussel-Radiometer model PGZ 301 potentiostat controlled by a PC and supported by Voltamaster 4.0 software. Electrochemical measurements were carried out in a conventional three-electrode cylindrical Pyrex glass cell. The temperature is thermostatically controlled. The working electrode (WE) in the form of disc cut from steel has a geometric area of 1 cm2 and is embedded in polytetrafluoroethylene (PTFE). A saturated calomel electrode (SCE) and a platinum electrode were used, as reference and auxiliary electrodes, respectively. A fine Luggin capillary was placed close to the working electrode to minimize IR drop. All test solutions were deaerated in the cell by using pure nitrogen for 10 min prior to the experiment. During each experiment, the test solution was mixed with a magnetic stirrer, and the gas bubbling was maintained. The mild steel electrode was maintained at corrosion potential for 30 min and thereafter prepolarised at −800 mVSCE for 10 min. The potentiodynamic current potential curves were obtained by changing the electrode potential automatically from −800 to −200 mVSCE with a scan rate of 0.5 mV s−1.


## 3. Results and Discussion

### 3.1. Corrosion Kinetic Study

In order to gain more information about the type of adsorption and the effectiveness of the ATMP inhibitor at higher temperature, polarisation experiment was conducted in the range of 30–60°C without and with selected concentrations of the inhibitor. Representative Tafel polarisation curves for C38 steel electrode in 1 M HCl without and with 0.1 M of ATMP at different temperatures are shown in Figure2.Similar polarisation curves were obtained in the case of the other concentrations of ATMP (not given). The analysis of these figures reveals that raising the temperature increases both anodic and cathodic current densities, and consequently the corrosion rate of C38 steel increases.Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl and 1 M HCl+0.1 M of ATMP.
(a)(b)Electrochemical kinetic parameters (corrosion potential (Ecorr), corrosion current density (Icorr), and cathodic Tafel slope (bc)), determined from these experiments by extrapolation method [19–23], are reported in Table 1. The Icorr was determined by Tafel extrapolation of only the cathodic polarization curve alone, which usually produces a longer and better defined Tafel region [24]. The inhibition efficiencies,E(%), are calculated from Icorr values as described elsewhere [18]. The surface coverage θ was calculated from the following equation [25]:(1)θ=Icorr-Icorr(inh)Icorr-Isat⁡,
where Icorr, Icorr(inh),  and Isat are the corrosion current density values in the absence, the presence of ATMP, and in an entirely covered surface, respectively, (Isat=Icorrfor the most elevated concentration of inhibitor).Table 1
Electrochemical parameters and the corresponding inhibition efficiencies at various temperatures studied of C38 steel in 1 M HCl containing different concentrations of ATMP.
Temperature (C°)Conc. (M)Ecorr versus SCE mVIcorr (μAcm-2)bc  (mV dec-1)E(%)θ301 M HCl−482569.8188——5 × 10−5−482477.818616.10.165 × 10−3−473175.414669.20.695 × 10−2−471109.312880.80.811 × 10−1−46476.712286.50.87401 M HCl−464800.7190——5 × 10−5−470700.318912.50.135 × 10−3−452478.715440.20.405 × 10−2−471308.313261.50.611 × 10−1−462235.312970.60.71501 M HCl−461999.1191——5 × 10−5−455875.918812.30.125 × 10−3−463737.216626.20.265 × 10−2−464572.714542.70.431 × 10−1−454407.913459.20.59601 M HCl−4651314.7194——5 × 10−5−4561195.51919.00.095 × 10−3−4611046.918720.40.205 × 10−2−453788.016740.10.401 × 10−1−445651.115250.50.50AsIsat≪Icorr,   thus(2)θ=Icorr-Icorr(inh)Icorr.Analyse of the results in Table1 indicates that in the presence of ATMP molecules, the Icorr of C38 steel decreases at any given temperature as inhibitor concentration increases compared to the uninhibited solution, due to the increase of the surface coverage degree. In contrast, at constant ATMP concentration, the Icorr increases as temperature rises, but this increase is more pronounced for the blank solution. Hence we can note that the E(%) depends on the temperature and decreases with the rise of temperature from 30 to 60°C. This can be explained by the decrease of the strength of the adsorption process at elevated temperature and would suggest a physical adsorption mode.The activation parameters for the corrosion reaction can be regarded as an Arrhenius-type process, according to the following equation:(3)Icorr=Aexp⁡⁡(-EaRT),
where Ea is the apparent activation corrosion energy, R is the universal gas constant, and A is the Arrhenius preexponential factor. The apparent activation energies (Ea) in the absence and in the presence of various concentrations of ATMP are calculated by linear regression between ln (Icorr) and 1/T (Figure 3), and the results are given in Table 2. All the linear regression coefficients are close to 1, indicating that the steel corrosion in hydrochloric acid can be elucidated using the kinetic model. As observed from Table 2, the Ea increased with increasing concentration of ATMP, but all values of Ea in the range of the studied concentration were higher than that of the uninhibited solution. The increase in Ea in the presence of ATMP may be interpreted as physical adsorption. Indeed, a higher energy barrier for the corrosion process in the inhibited solution is associated with physical adsorption or weak chemical bonding between the inhibitor species and the steel surface [14, 26]. 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 carbon steel surface with the increase in temperature. A corresponding increase in the corrosion rate occurs because of the greater area of metal that is consequently exposed to the acid environment [27].Table 2
Corrosion kinetic parameters for C38 steel in 1 M HCl in absence and presence of different concentrations of ATMP.
Concentration (M)Ea(kJ mol-1)ΔHa (kJ mol−1)ΔSa(J mol−1 k−1)Ea-ΔHa (kJ mol−1)Blank22.9220.28−125.222.645 × 10−524.9822.34−119.842.645 × 10−348.9046.26−48.052.645 × 10−255.2552.62−31.042.631 × 10−158.7556.11−22.432.64Figure 3
Arrhenius plots for C38 steel corrosion ratesln Icorr versus 1/T in 1 M HCl in absence and in presence of different concentrations of ATMP.The enthalpy of activation (ΔHa) and the entropy of activation (ΔSa) for the intermediate complex in the transition state for the corrosion of C38 steel in 1 M HCl in the absence and in the presence of different concentrations of ATMP were obtained by applying the alternative formulation of Arrhenius equation [28]:(4)Icorr=RTNhexp⁡(ΔSaR)exp⁡(-ΔHaRT),
where h is the Plank’s constant and N is the Avogadro’s number. Figure 4 shows a plot of ln(Icorr/T) versus 1/T. A straight lines are obtained with a slope of (-ΔHa/R) and an intercept of (lnR/Nh+ΔSa/R) from which the values of ΔHaand ΔSawere calculated (Table 2). The positive values of ΔHain the absence and the presence of ATMP reflect the endothermic nature of the C38 steel dissolution process. One can also notice that Ea and ΔHa values vary in the same way as shown in Table 2, indicating that the corrosion process is a unimolecular reaction [29]. This result permits verifying the known thermodynamic equation between theEaand ΔHa [29](5)Ea-ΔHa=RT.Figure 4
Transition-state plots for C38 steel corrosion rateslnIcorr versus 1/T in 1 M HCl in absence and in presence of different concentrations of ATMP.The values of activation entropy (ΔSa) are higher for inhibited solutions than that for the uninhibited solution and increase gradually with increasing ATMP concentrations (Table 2). The positive increment of ΔSa suggests that an increase in randomness occurred on going from reactants to the activated complex [30]. This observation is in agreement with the findings of other workers [30, 31].


### 3.2. Adsorption Isotherm and Thermodynamic Parameters

The values of surface coverageθcorresponding to different concentrations of AMTP in the temperature range from 30 to 60°C have been used to explain the best isotherm to determine the adsorption process. As it is known that the adsorption of an organic adsorbate onto metal-solution interface can be presented as a substitutional adsorption process between the organic molecules in the aqueous solution Org(sol) and the water molecules on the metallic surface H2O(ads),(6)Org(sol)+nH2O(ads)⟷Org(ads)+nH2O(sol),
where Org(sol) and Org(ads) are the organic molecules in the aqueous solution and adsorbed on the metallic surface, respectively, H2O(ads) is the water molecules on the metallic surface, and n is the size ratio representing the number of water molecules replaced by one molecule of organic adsorbate. When the equilibrium of the process described in this equation is reached, it is possible to obtain different expressions of the adsorption isotherm plots, and thus the surface coverage degree (θ) can be plotted as a function of the concentration of the inhibitor under test [32]. The Langmuir adsorption isotherm was found to give the best description of the adsorption behaviour of ATMP. In this case, the surface coverage (θ) of the inhibitor on the steel surface is related to the concentration of inhibitor in the solution according to the following equation:(7)θ1-θ=KadsCinh.
Rearranging this equation gives(8)Cinhθ=1Kads+Cinh,
where θ is the surface coverage degree, Cinh is the inhibitor concentration in the electrolyte, and Kads is the equilibrium constant of the adsorption process. The Kads values may be taken as a measure of the strength of the adsorption forces between the inhibitor molecules and the metal surface [33]. To calculate the adsorption parameters, the straight lines were drawn using the least squares method. The experimental (points) and calculated isotherms (lines) are plotted in Figure 5. The results are presented in Table 3. A very good fit is observed with a regression coefficient (R2) up to 0.99 and the obtained lines have slopes very close to unity, which suggests that the experimental data are well described by Langmuir isotherm and exhibit single-layer adsorption characteristic [18]. This kind of isotherm involves the assumption of no interaction between the adsorbed species and the electrode surface. From the intercepts of the straight lines Cinh/θ-axis, the Kads values were calculated and given in Table 3. As can be seen from Table 3, Kads values decrease with increasing temperature from 30 to 60°C. Such behaviour can be interpreted on the basis that the increase in temperature results in desorption of some adsorbed inhibitor molecules from the metal surface [18].Table 3
Thermodynamic parameters for the adsorption of ATMP on the C38 steel in 1 M HCl at different temperatures.
Temperature (K)R2Kads (M−1)ΔGadsο(kJ mol−1)ΔHadsο (kJ mol−1)ΔSadsο(J mol−1 K−1)300.99666.7−26.50−54.87−95.00400.99222.2−24.52500.99138.9−24.04600.9886.9−23.49Figure 5
Langmuir’s isotherm adsorption model of ATMP on the C38 steel surface in 1 M HCl at different temperatures.The well-known thermodynamic adsorption parameters are the free energy of adsorption (ΔGadsο), the standard enthalpy of adsorption (ΔHadsο), and the entropy of adsorption (ΔSadsο). These quantities can be calculated depending on the estimated values of Kads from adsorption isotherms, at different temperatures. The constant of adsorption,Kads, is related to the standard free energy of adsorption, ΔGadsο, with the following equation [34]:(9)Kads=155.5exp⁡⁡(-ΔGadsοRT),
where R is the universal gas constant, T is the thermodynamic temperature, and the value of 55.5 is the concentration of water in the solution in mol/L. The calculated ΔGadsοvalues, at all studied temperatures, are given in Table 3. The negative values of ΔGadsο indicate the spontaneity of the adsorption process and the stability of the adsorbed layer on the C38 steel surface [16]. Generally, the adsorption type is regarded as physisorption if the absolute value of ΔGadsο is in the range of 20 kJ mol−1 or lower. The inhibition behaviour is attributed to the electrostatic interaction between the organic molecules and steel surface. When the absolute value of ΔGadsο is in the order of 40 kJ mol−1 or higher, the adsorption could be seen as chemisorption. In this process, the covalent bond is formed by the charge sharing or transferring from the inhibitor molecules to the metal surface [35, 36]. The obtained ΔGadsο values in the studied temperature domain are in the range of −23.5 to −26.5 kJ mol−1, indicating, therefore, that the adsorption mechanism of the ATMP onto C38 steel in 1 M HCl solution is mainly due to physisorption (Table 3). This behaviour is in good agreement with that obtained at 30°C using ac impedance technique [1]. On the other hand, the obtained values of ΔGadsο show a regular dependence on temperature, indicating a good correlation among thermodynamic parameters. However, a limited decrease in the absolute value of ΔGadsο with the increase in temperature values is observed. This behaviour is explained by the fact that the adsorption is somewhat unfavourable with increasing experimental temperature, indicating that the physisorption has the major contribution while the chemisorption has a minor contribution in the corrosion inhibition mechanism [37]. The other thermodynamic functions (ΔHadsο and ΔSadsο) can be calculated from the following equation:(10)ΔGadsο=ΔHadsο-TΔSadsο.
Figure 6 shows the plot of ΔGadsο versus T which gives straight lines with slopes of -ΔSadsο and intercepts of ΔHadsο. The obtained values of ΔHadsο and ΔSadsο are given in Table 3. The obtained value of ΔHadsο is negative, reflecting the exothermic nature of the adsorption process on C38 steel surface. The value of ΔHadsο can also provide valuable information about the type of inhibitor adsorption. While an endothermic adsorption process (ΔHadsο>0) is attributed unequivocally to chemisorption [38], an exothermic adsorption process (ΔHadsο<0) may involve either physisorption or chemisorption or a mixture of both the processes. In an exothermic process, chemisorption is distinguished from physisorption by considering the absolute value ofΔHadsο. For the chemisorption process, ΔHadsο approaches 100 kJ mol−1, while for the physisorption process, it is less than 40 kJ mol−1 [37]. In the case of ATMP, the calculated value of ΔHadsο (−56.56 kJ mol−1) is larger than the common physical adsorption enthalpy, but smaller than the common chemical adsorption enthalpy, confirming that the adsorption mechanism of ATMP on carbon steel surface probably involves two types of interactions, predominant physisorption (ionic), and weak chemisorption (molecular). The value of ΔSadsο is negative (Table 3), meaning that the inhibitor molecules move freely in the bulk solution (are chaotic) before adsorption, while as adsorption progresses, the inhibitor molecules adsorbed onto the mild steel surface become more orderly, resulting in a decrease in entropy [39].Figure 6
Variation ofΔGadsο versus T on C38 steel in 1 M HCl containing ATMP.ΔHadsο and ΔSadsο can be also deduced from the integrated version of the Van‘t Hoff equation expressed by [40](11)ln⁡⁡Kads=-ΔHadsοRT+constant.
Figure 7 shows the plot of ln Kads versus 1/T which gives straight lines with slopes of (-ΔHadsο/R) and intercepts of (ΔSadsο/R+ln1/55.5). The calculated ΔHadsο using the Van‘t Hoff equation is −55.55 kJ mol−1 for ATMP, confirming the physisorption process and the exothermic behaviour of the adsorption of the ATMP molecule on the steel surface. Values of ΔHadsο obtained by both methods are in good agreement. Moreover, the deduced ΔSadsο value of −97.16 J mol−1K−1 for ATMP is very close to that obtained in Table 3.Figure 7
Vant’t Hoff plot for the C38 steel/ATMP/1 M HCl.


## 3.1. Corrosion Kinetic Study

In order to gain more information about the type of adsorption and the effectiveness of the ATMP inhibitor at higher temperature, polarisation experiment was conducted in the range of 30–60°C without and with selected concentrations of the inhibitor. Representative Tafel polarisation curves for C38 steel electrode in 1 M HCl without and with 0.1 M of ATMP at different temperatures are shown in Figure2.Similar polarisation curves were obtained in the case of the other concentrations of ATMP (not given). The analysis of these figures reveals that raising the temperature increases both anodic and cathodic current densities, and consequently the corrosion rate of C38 steel increases.Effect of temperature on the cathodic and anodic responses for C38 steel in 1 M HCl and 1 M HCl+0.1 M of ATMP.
(a)(b)Electrochemical kinetic parameters (corrosion potential (Ecorr), corrosion current density (Icorr), and cathodic Tafel slope (bc)), determined from these experiments by extrapolation method [19–23], are reported in Table 1. The Icorr was determined by Tafel extrapolation of only the cathodic polarization curve alone, which usually produces a longer and better defined Tafel region [24]. The inhibition efficiencies,E(%), are calculated from Icorr values as described elsewhere [18]. The surface coverage θ was calculated from the following equation [25]:(1)θ=Icorr-Icorr(inh)Icorr-Isat⁡,
where Icorr, Icorr(inh),  and Isat are the corrosion current density values in the absence, the presence of ATMP, and in an entirely covered surface, respectively, (Isat=Icorrfor the most elevated concentration of inhibitor).Table 1
Electrochemical parameters and the corresponding inhibition efficiencies at various temperatures studied of C38 steel in 1 M HCl containing different concentrations of ATMP.
Temperature (C°)Conc. (M)Ecorr versus SCE mVIcorr (μAcm-2)bc  (mV dec-1)E(%)θ301 M HCl−482569.8188——5 × 10−5−482477.818616.10.165 × 10−3−473175.414669.20.695 × 10−2−471109.312880.80.811 × 10−1−46476.712286.50.87401 M HCl−464800.7190——5 × 10−5−470700.318912.50.135 × 10−3−452478.715440.20.405 × 10−2−471308.313261.50.611 × 10−1−462235.312970.60.71501 M HCl−461999.1191——5 × 10−5−455875.918812.30.125 × 10−3−463737.216626.20.265 × 10−2−464572.714542.70.431 × 10−1−454407.913459.20.59601 M HCl−4651314.7194——5 × 10−5−4561195.51919.00.095 × 10−3−4611046.918720.40.205 × 10−2−453788.016740.10.401 × 10−1−445651.115250.50.50AsIsat≪Icorr,   thus(2)θ=Icorr-Icorr(inh)Icorr.Analyse of the results in Table1 indicates that in the presence of ATMP molecules, the Icorr of C38 steel decreases at any given temperature as inhibitor concentration increases compared to the uninhibited solution, due to the increase of the surface coverage degree. In contrast, at constant ATMP concentration, the Icorr increases as temperature rises, but this increase is more pronounced for the blank solution. Hence we can note that the E(%) depends on the temperature and decreases with the rise of temperature from 30 to 60°C. This can be explained by the decrease of the strength of the adsorption process at elevated temperature and would suggest a physical adsorption mode.The activation parameters for the corrosion reaction can be regarded as an Arrhenius-type process, according to the following equation:(3)Icorr=Aexp⁡⁡(-EaRT),
where Ea is the apparent activation corrosion energy, R is the universal gas constant, and A is the Arrhenius preexponential factor. The apparent activation energies (Ea) in the absence and in the presence of various concentrations of ATMP are calculated by linear regression between ln (Icorr) and 1/T (Figure 3), and the results are given in Table 2. All the linear regression coefficients are close to 1, indicating that the steel corrosion in hydrochloric acid can be elucidated using the kinetic model. As observed from Table 2, the Ea increased with increasing concentration of ATMP, but all values of Ea in the range of the studied concentration were higher than that of the uninhibited solution. The increase in Ea in the presence of ATMP may be interpreted as physical adsorption. Indeed, a higher energy barrier for the corrosion process in the inhibited solution is associated with physical adsorption or weak chemical bonding between the inhibitor species and the steel surface [14, 26]. 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 carbon steel surface with the increase in temperature. A corresponding increase in the corrosion rate occurs because of the greater area of metal that is consequently exposed to the acid environment [27].Table 2
Corrosion kinetic parameters for C38 steel in 1 M HCl in absence and presence of different concentrations of ATMP.
Concentration (M)Ea(kJ mol-1)ΔHa (kJ mol−1)ΔSa(J mol−1 k−1)Ea-ΔHa (kJ mol−1)Blank22.9220.28−125.222.645 × 10−524.9822.34−119.842.645 × 10−348.9046.26−48.052.645 × 10−255.2552.62−31.042.631 × 10−158.7556.11−22.432.64Figure 3
Arrhenius plots for C38 steel corrosion ratesln Icorr versus 1/T in 1 M HCl in absence and in presence of different concentrations of ATMP.The enthalpy of activation (ΔHa) and the entropy of activation (ΔSa) for the intermediate complex in the transition state for the corrosion of C38 steel in 1 M HCl in the absence and in the presence of different concentrations of ATMP were obtained by applying the alternative formulation of Arrhenius equation [28]:(4)Icorr=RTNhexp⁡(ΔSaR)exp⁡(-ΔHaRT),
where h is the Plank’s constant and N is the Avogadro’s number. Figure 4 shows a plot of ln(Icorr/T) versus 1/T. A straight lines are obtained with a slope of (-ΔHa/R) and an intercept of (lnR/Nh+ΔSa/R) from which the values of ΔHaand ΔSawere calculated (Table 2). The positive values of ΔHain the absence and the presence of ATMP reflect the endothermic nature of the C38 steel dissolution process. One can also notice that Ea and ΔHa values vary in the same way as shown in Table 2, indicating that the corrosion process is a unimolecular reaction [29]. This result permits verifying the known thermodynamic equation between theEaand ΔHa [29](5)Ea-ΔHa=RT.Figure 4
Transition-state plots for C38 steel corrosion rateslnIcorr versus 1/T in 1 M HCl in absence and in presence of different concentrations of ATMP.The values of activation entropy (ΔSa) are higher for inhibited solutions than that for the uninhibited solution and increase gradually with increasing ATMP concentrations (Table 2). The positive increment of ΔSa suggests that an increase in randomness occurred on going from reactants to the activated complex [30]. This observation is in agreement with the findings of other workers [30, 31].


## 3.2. Adsorption Isotherm and Thermodynamic Parameters

The values of surface coverageθcorresponding to different concentrations of AMTP in the temperature range from 30 to 60°C have been used to explain the best isotherm to determine the adsorption process. As it is known that the adsorption of an organic adsorbate onto metal-solution interface can be presented as a substitutional adsorption process between the organic molecules in the aqueous solution Org(sol) and the water molecules on the metallic surface H2O(ads),(6)Org(sol)+nH2O(ads)⟷Org(ads)+nH2O(sol),
where Org(sol) and Org(ads) are the organic molecules in the aqueous solution and adsorbed on the metallic surface, respectively, H2O(ads) is the water molecules on the metallic surface, and n is the size ratio representing the number of water molecules replaced by one molecule of organic adsorbate. When the equilibrium of the process described in this equation is reached, it is possible to obtain different expressions of the adsorption isotherm plots, and thus the surface coverage degree (θ) can be plotted as a function of the concentration of the inhibitor under test [32]. The Langmuir adsorption isotherm was found to give the best description of the adsorption behaviour of ATMP. In this case, the surface coverage (θ) of the inhibitor on the steel surface is related to the concentration of inhibitor in the solution according to the following equation:(7)θ1-θ=KadsCinh.
Rearranging this equation gives(8)Cinhθ=1Kads+Cinh,
where θ is the surface coverage degree, Cinh is the inhibitor concentration in the electrolyte, and Kads is the equilibrium constant of the adsorption process. The Kads values may be taken as a measure of the strength of the adsorption forces between the inhibitor molecules and the metal surface [33]. To calculate the adsorption parameters, the straight lines were drawn using the least squares method. The experimental (points) and calculated isotherms (lines) are plotted in Figure 5. The results are presented in Table 3. A very good fit is observed with a regression coefficient (R2) up to 0.99 and the obtained lines have slopes very close to unity, which suggests that the experimental data are well described by Langmuir isotherm and exhibit single-layer adsorption characteristic [18]. This kind of isotherm involves the assumption of no interaction between the adsorbed species and the electrode surface. From the intercepts of the straight lines Cinh/θ-axis, the Kads values were calculated and given in Table 3. As can be seen from Table 3, Kads values decrease with increasing temperature from 30 to 60°C. Such behaviour can be interpreted on the basis that the increase in temperature results in desorption of some adsorbed inhibitor molecules from the metal surface [18].Table 3
Thermodynamic parameters for the adsorption of ATMP on the C38 steel in 1 M HCl at different temperatures.
Temperature (K)R2Kads (M−1)ΔGadsο(kJ mol−1)ΔHadsο (kJ mol−1)ΔSadsο(J mol−1 K−1)300.99666.7−26.50−54.87−95.00400.99222.2−24.52500.99138.9−24.04600.9886.9−23.49Figure 5
Langmuir’s isotherm adsorption model of ATMP on the C38 steel surface in 1 M HCl at different temperatures.The well-known thermodynamic adsorption parameters are the free energy of adsorption (ΔGadsο), the standard enthalpy of adsorption (ΔHadsο), and the entropy of adsorption (ΔSadsο). These quantities can be calculated depending on the estimated values of Kads from adsorption isotherms, at different temperatures. The constant of adsorption,Kads, is related to the standard free energy of adsorption, ΔGadsο, with the following equation [34]:(9)Kads=155.5exp⁡⁡(-ΔGadsοRT),
where R is the universal gas constant, T is the thermodynamic temperature, and the value of 55.5 is the concentration of water in the solution in mol/L. The calculated ΔGadsοvalues, at all studied temperatures, are given in Table 3. The negative values of ΔGadsο indicate the spontaneity of the adsorption process and the stability of the adsorbed layer on the C38 steel surface [16]. Generally, the adsorption type is regarded as physisorption if the absolute value of ΔGadsο is in the range of 20 kJ mol−1 or lower. The inhibition behaviour is attributed to the electrostatic interaction between the organic molecules and steel surface. When the absolute value of ΔGadsο is in the order of 40 kJ mol−1 or higher, the adsorption could be seen as chemisorption. In this process, the covalent bond is formed by the charge sharing or transferring from the inhibitor molecules to the metal surface [35, 36]. The obtained ΔGadsο values in the studied temperature domain are in the range of −23.5 to −26.5 kJ mol−1, indicating, therefore, that the adsorption mechanism of the ATMP onto C38 steel in 1 M HCl solution is mainly due to physisorption (Table 3). This behaviour is in good agreement with that obtained at 30°C using ac impedance technique [1]. On the other hand, the obtained values of ΔGadsο show a regular dependence on temperature, indicating a good correlation among thermodynamic parameters. However, a limited decrease in the absolute value of ΔGadsο with the increase in temperature values is observed. This behaviour is explained by the fact that the adsorption is somewhat unfavourable with increasing experimental temperature, indicating that the physisorption has the major contribution while the chemisorption has a minor contribution in the corrosion inhibition mechanism [37]. The other thermodynamic functions (ΔHadsο and ΔSadsο) can be calculated from the following equation:(10)ΔGadsο=ΔHadsο-TΔSadsο.
Figure 6 shows the plot of ΔGadsο versus T which gives straight lines with slopes of -ΔSadsο and intercepts of ΔHadsο. The obtained values of ΔHadsο and ΔSadsο are given in Table 3. The obtained value of ΔHadsο is negative, reflecting the exothermic nature of the adsorption process on C38 steel surface. The value of ΔHadsο can also provide valuable information about the type of inhibitor adsorption. While an endothermic adsorption process (ΔHadsο>0) is attributed unequivocally to chemisorption [38], an exothermic adsorption process (ΔHadsο<0) may involve either physisorption or chemisorption or a mixture of both the processes. In an exothermic process, chemisorption is distinguished from physisorption by considering the absolute value ofΔHadsο. For the chemisorption process, ΔHadsο approaches 100 kJ mol−1, while for the physisorption process, it is less than 40 kJ mol−1 [37]. In the case of ATMP, the calculated value of ΔHadsο (−56.56 kJ mol−1) is larger than the common physical adsorption enthalpy, but smaller than the common chemical adsorption enthalpy, confirming that the adsorption mechanism of ATMP on carbon steel surface probably involves two types of interactions, predominant physisorption (ionic), and weak chemisorption (molecular). The value of ΔSadsο is negative (Table 3), meaning that the inhibitor molecules move freely in the bulk solution (are chaotic) before adsorption, while as adsorption progresses, the inhibitor molecules adsorbed onto the mild steel surface become more orderly, resulting in a decrease in entropy [39].Figure 6
Variation ofΔGadsο versus T on C38 steel in 1 M HCl containing ATMP.ΔHadsο and ΔSadsο can be also deduced from the integrated version of the Van‘t Hoff equation expressed by [40](11)ln⁡⁡Kads=-ΔHadsοRT+constant.
Figure 7 shows the plot of ln Kads versus 1/T which gives straight lines with slopes of (-ΔHadsο/R) and intercepts of (ΔSadsο/R+ln1/55.5). The calculated ΔHadsο using the Van‘t Hoff equation is −55.55 kJ mol−1 for ATMP, confirming the physisorption process and the exothermic behaviour of the adsorption of the ATMP molecule on the steel surface. Values of ΔHadsο obtained by both methods are in good agreement. Moreover, the deduced ΔSadsο value of −97.16 J mol−1K−1 for ATMP is very close to that obtained in Table 3.Figure 7
Vant’t Hoff plot for the C38 steel/ATMP/1 M HCl.


## 4. Conclusion

We studied the inhibitor action of ATMP on corrosion of C38 steel in 1 M HCl depending on effect of temperature. We obtained the following conclusion.(1)
Based on the Tafel polarization results, theE (%) of ATMP is found to decrease with increasing temperature, and its addition to 1 M HCl leads to an increase of apparent activation energy (Ea) of the corrosion process.(2)
The corrosion process is inhibited by the adsorption of ATMP on C38 steel surface. This adsorption fits a Langmuir isotherm model. Thermodynamic adsorption parameters show that ATMP is adsorbed on steel surface by an exothermic and spontaneous process.(3)
The calculated values ofΔGadsο and ΔHadsο corroborate that the adsorption mechanism of ATMP on steel surface in 1 M HCl solution is mainly due to physisorption.(4)
At temperatures higher than 30°C, this inhibitor is not efficient to control the corrosion of steel in 1 M HCl at the concentration range studied.



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*Source: 548528-2011-10-17.xml*