Table 3 - Free



The influence of some new 2,5-disubtituted 1,3,4-thiadiazoles on the corrosion behaviour of mild steel in 1 M HCl solution: electrochemical study and theoretical approach

F. Bentiss a,*, M. Lebrini b, M. Lagrenée c, M. Traisnel b, A. Elfarouk d, H. Vezin e

a Laboratoire de Chimie de Coordination et d'Analytique, Faculté des Sciences, Université Chouaib Doukkali, B.P. 20, M-24000 El Jadida, Morocco

b Laboratoire des Procédés d'Elaboration des Revêtements Fonctionnels, PERF-LSPES UMR-CNRS 8008, ENSCL, BP 90108, F-59652 Villeneuve d'Ascq Cedex, France

c Unité de Catalyse et de Chimie du Solide, UMR- CNRS 8181, ENSCL, BP. 90108, F-59652 Villeneuve d’Ascq Cedex, France

d Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral-Côte d’Opale,

C.U. de la Mi-Voix, 50 rue F. Buisson, B.P. 699, F-62228 Calais, Cedex, France.

eLaboratoire de Chimie Organique et Macromoléculaire, UMR- CNRS 8009, USTL Bât C4, F-59655 Villeneuve d’Ascq Cedex, France

* Corresponding author. Tel.: +33-320-337-746; Fax: +33 3 20436814.

E-mail address: f.bentiss@pop.ensc-lille.fr (F. BENTISS).

Abstract

The new 2,5-disubtituted 1,3,4-thiadiazoles were investigated as corrosion inhibitors of mild steel in 1 M HCl using ac impedance technique. Four of these compounds exhibit good inhibition properties, while two of them, 2,5-bis(4-nitrophenyl)-1,3,4-thiadiazole and 2,5-bis(4-chlorophenyl)-1,3,4-thiadiazole, stimulate the corrosion process especially at low concentrations. The experimental data obtained from this method show a frequency distribution and therefore a modelling element with frequency dispersion behaviour, a constant phase element (CPE) has been used. Possible correlations between experimental inhibition efficiencies and quantum chemical parameters such as dipole moment (μ), highest occupied (EHOMO) and lowest unoccupied (ELUMO) molecular orbitals were investigated. The models of the inhibitors were optimized with the Density Functional Theory formalism (DFT) using B3LYP/6-31G as a higher level of theory. The Quantitative Structure Activity Relationship (QSAR) approach has been used and composite index of some quantum chemical parameters were constructed in order to characterize the inhibition performance of the tested molecules.

Keywords: Thiadiazole derivatives; Acid corrosion inhibitors; Mild steel; Ac impedance; DFT; Quantitative structure-activity relationship

1. Introduction

Acid solutions are generally used for the removal of rust and scale in industrial processes. Inhibitors are generally used in these processes to control the metal dissolution. Hydrochloric acid is widely used in the pickling of steel and ferrous alloys. Most of the well-known acid inhibitors are organic compounds containing nitrogen, sulphur and oxygen atoms. There has been a growing interest in the use of organic compounds as inhibitors for the aqueous corrosion of metals. The study of corrosion processes and their inhibition by organic compounds is a very active field of research [1–5]. Some quantum mechanical studies have successfully linked the corrosion inhibition efficiency with molecular properties for different kinds of organic compounds [6–8]. Despite the large numbers of organic compounds, the choice of an appropriate inhibitor for a particular system is very limited due to the specificity of the inhibitors and the great variety of corrosion systems [9].

The relationships between descriptors characterizing the structure properties of chemicals on quantitative basis are structure–activity relationships (QSAR). It correlates and predicts physical and chemical properties of chemicals, plays an important role in effective assessment of organic compounds. The application of QSAR in corrosion research has been reported [10–15].

Attempts have been made to predict corrosion inhibition efficiency with a number of individual parameters obtained via various quantum chemical calculation methods as a tool for studying corrosion inhibitors [16–23]. These trials were aimed to find possible correlations between corrosion inhibition efficiency and a number of quantum molecular properties such as dipole moment (μ), highest occupied (EHOMO) and lowest unoccupied (ELUMO) molecular orbitals and the differences between them (HOMO–LUMO gap) as well as some structural parameters.

In continuation of our work on development of thiadiazole derivatives as corrosion inhibitors in acidic [24-29], we have studied the corrosion inhibiting behaviour of some new thiadiazole derivatives on mild steel in 1 M HCl solutions using the electrochemical impedance spectroscopy (EIS). The impedance spectra obtained from this study are analyzed to show the equivalent circuit that fits the corrosion data, also the adsorption behaviour of these series is examined. The objective of the present work is to correlate the experimentally determined corrosion inhibition data for studied thiadiazoles using the semi-empirical approach of QSAR. In this respect, inhibition performance of the six thiadiazole compounds was subjected to correlation analysis with the calculated quantum chemical parameters using linear and non-linear models to see if any clear links exist between the two.

2. Experimental detail

The tested inhibitors, namely 2,5-bis(phenyl)-1,3,4-thiadiazole (DPTH), 2,5-bis(4-methoxyphenyl)-1,3,4-thiadiazole (4-MTH), 2,5-bis(4-dimethylaminophenyl)-1,3,4-thiadiazole (4-DATH), 2,5-bis(4-methylphenyl)-1,3,4-thiadiazole (4-MPTH), 2,5-bis(4-nitrophenyl)-1,3,4-thiadiazole (4-NPTH) and 2,5-bis(4-chlorophenyl)-1,3,4-thiadiazole (4-CPTH) were synthesised according to a previously described experimental procedure [30]. The molecular structures of these thiadiazole derivatives are shown in Figure 1. The concentration range of thiadiazole derivatives employed was 0.25×10-4 M to 1.5×10-4 M. Corrosion tests have been carried out on electrodes cut from sheets of mild steel. Steel strips containing 0.09% P, 0.38% Si, 0.01% Al, 0.05% Mn, 0.21% C, 0.05% S and the remainder iron were used for the measurement of weight loss and electrochemical studies. The surface preparation of the specimens was carried out using emery paper grade 600 and 1200; they were degreased with ethanol under ultrasound and dried at room temperature before use. The solutions (1 M HCl) were prepared by dilution of an analytical reagent grade 37% HCl with doubly distilled water.

Electrochemical experiments were conducted using an impedance equipment (Tacussel-Radiometer PGZ 3O1) and controlled with Tacussel corrosion analysis software model Voltamaster 4. The electrochemical cell used has been described in a previous paper [31]. The reference electrode was a saturated calomel electrode. All the reported potential values are referred to this type of electrode. Electrochemical impedance spectroscopy measurements were performed using Tacussel Radiometer PGZ 3O1 Frequency Response Analyser in a frequency range of 105 Hz to 10-2 Hz with ten points per decade. Square sheets of mild steel of size (5 cm × 5 cm × 0.06 cm), which exposed a 7.55 cm2 surface to the aggressive solution, were used as the working electrode. Experiment temperature was 30°C. After the determination of steady-state current at a given potential, sine wave voltages (10 mV) peak to peak were superimposed on the rest potential. Nyquist plots were made from these experiments. The best semicircle can be fit through the data points in the Nyquist plot using a non-linear least square fit so as to give the intersections with the x-axis [32].

The thiadiazole derivatives have been fully optimised at the using B3LYP Density Functional Theory formalism (DFT) with 6-31G (d,p) basis set with Gaussian 03 code. The following quantum chemical indices were considered: the energy of the highest occupied molecular orbital (EHOMO), the energy of the lowest unoccupied molecular orbital (ELUMO), energy band gap, ΔΕ = EHOMO – ELUMO and the dipole moment (μ). Non-linear regression analyses were performed by the MATLAB Toolbox software for windows.

|[pic] |[pic] |

|2.5-Bis(4-dimethylaminophenyl)-1.3.4-thiadiazole (4-DATH) |2.5-Bis(4-methoxyphenyl)-1.3.4-thiadiazole (4-MTH) |

|[pic] |[pic] |

|2.5-Bis(4-methylphenyl)-1.3.4-thiadiazole (4-MPTH) |2.5-Bis(phenyl)-1.3.4-thiadiazole (DPTH) |

|[pic] |[pic] |

|2.5-Bis(4-nitrophenyl)-1.3.4-thiadiazole (4-NPTH) |2.5-Bis(4-chlorophenyl)-1.3.4-thiadiazole (4-CPTH) |

Fig. 1. Molecular structures of the studied thiadiazole derivatives.

3. Results and discussion

3.1. AC impedance studies

Impedance measurements were carried out under potentiostatic conditions after 24 h of immersion at 30°C. Nyquist plots of uninhibited and inhibited solutions containing different concentrations of 4-PMTH in 1 M HCl are shown in Fig. 2 (representative example). The Nyquist plots are significantly changed on addition of inhibitors, and the impedance of the inhibited system increased with inhibitor concentration. The most pronounced effect and highest charge-transfer resistance is for 4-MTH (Fig. 3), while 4-CPTH and 4-NPTH actually shows a simulating effect at law concentrations.

[pic]

Fig. 2. Nyquist diagrams for mild steel in 1 M HCl containing different concentrations of 4-MPTH.

[pic]

Fig. 3. Nyquist diagrams for mild steel in 1 M HCl without and with 1.5×10-4 M of different thiadiazoles tested.

The impedance analysis of mild steel in 1 M HCl shows one depressed capacitive loop (one time constant in the Bode-phase representation). All experimental plots have a depressed semicircular shape in the complex impedance plane, with the center under the real axis (Fig. 2). This behaviour is typical for solid metal electrodes that show frequency dispersion of the impedance data [33] and has been attributed to roughness and other inhomogeneities of the solid surface [33–38]. In these cases the parallel network charge transfer resistancedouble layer capacitance (Rt─Cdl) is usually accepted as a poor approximation [33], especially for systems where an efficient inhibitor is present. When a non-ideal frequency response is present, it is commonly accepted to employ distributed circuit elements in an equivalent circuit. The most widely used is the constant phase element (CPE), which has a non-integer power dependence on the frequency [39]. Often a CPE is used in a model in place of a capacitor to compensate for non-homogeneity in the system. The impedance of a CPE is described by the expression:

[pic] (1)

where A is a proportionality coefficient, ( is the angular frequency (in rad s-1), i2 = -1 is the imaginary number and n has a meaning of a phase shift and can be used as a measure of the surface inhomogeneity [37,40]. For n =/0, ZCPE represents a resistance with R = A-1, for n = 1 a capacitance with C = A, for n = 0.5 a Warburg element and for n = -1 an inductance with L = A-1 [41].

Figure 4 shows the electrical equivalent circuit employed to analyze the impedance spectra with one capacitive loop [41,42]. Excellent fit with the model was obtained for all experimental data. As an example, the Nyquist and Bode plots for DPTH at 10-4 M in 1 M HCl are presented in Fig. 5a and b, respectively. The simulated and measured results fit very well. It is observed that the fitted data follow almost the same pattern as the original results along the whole diagrams, with an average error of about 3% in all cases. The high frequency part of the impedance and phase angle describes the behaviour of an inhomogeneous surface layer, while the low frequency contribution shows the kinetic response for the charge transfer reaction [43]. The fitted parameter results for thiadiazole derivatives, using Zview impedance modelling software, are presented in Table 1.

[pic]

Fig. 4. Structural model of the interface mild steel/1 M HCl + thiadiazoles.

[pic]

Fig. 5. EIS Nyquist (a) and Bode (b) plots for mild steel / 1 M HCl + 10-4 M DPTH interface: (···) experimental data; (—) calculated.

Table 1

Impedance parameters for the corrosion of mild steel in 1 M HCl containing different concentrations of thiadiazole derivatives.

|Inhibitor |Conc. |Erest potential |Rt |A |C |n |E |

| |(10-4 M) |vs SCE (mV) |(( cm2) |(sn Ω-1 cm-2 × 10-3) |(μF cm-2) | |(%) |

|Blank |0 |-510 |16.00 |2.74 |1862.82 |0.82 | |

| | | | | | | | |

|4-DATH |0.25 |-490 |175.69 |0.127 |88.27 |0.89 | 90.9 |

| |0.5 |-476 |316.95 |0.0835 |80.46 |0.90 | 95.0 |

| |1.0 |-475 |578.86 |0.0682 |50.61 |0.88 | 97.2 |

| |1.5 |-473 |619.18 |0.0756 |44.63 |0.87 | 97.4 |

| | | | | | | | |

|4-MTH |0.25 |-454 |292.34 |0.133 |94.69 |0.90 | 94.5 |

| |0.5 |-485 |483.12 |0.118 |89.67 |0.91 | 96.7 |

| |1.0 |-478 |733.94 |0.0732 |60.75 |0.92 | 97.8 |

| |1.5 |-479 |755.75 |0.0784 |57.10 |0.92 | 97.9 |

| | | | | | | | |

|4-MPTH |0.25 |-484 |116.12 |0.166 |118.98 |0.92 | 86.2 |

| |0.5 |-475 |243.03 |0.101 |70.69 |0.89 | 93.4 |

| |1.0 |-489 |244.77 |0.129 |62.28 |0.85 | 93.5 |

| |1.5 |-489 |360.74 |0.110 |62.01 |0.85 | 95.6 |

| | | | | | | | |

|DPTH |0.25 |-486 |44.68 |0.377 |283.25 |0.93 | 64.2 |

| |0.5 |-488 |48.46 |0.271 |202.15 |0.94 | 67.0 |

| |1.0 |-500 |85.47 |0.168 |121.18 |0.93 | 81.3 |

| |1.5 |-498 |175.76 |0.0835 |58.69 |0.92 | 90.9 |

| | | | | | | | |

|4-NPTH |0.25 |-482 |13.32 |2.473 |1735.06 |0.90 |-20.1 |

| |0.5 |-476 |17.68 |2.171 |1442.16 |0.89 | 9.5 |

| |1.0 |-479 |22.75 |1.0859 |753.72 |0.91 | 29.7 |

| |1.5 |-475 |35.41 |0.452 |220.67 |0.85 | 54.8 |

| | | | | | | | |

|4-CPTH |0.25 |-473 |11.48 |3.026 |2059.26 |0.90 |-39.4 |

| |0.5 |-475 |13.32 |2.474 |1735.32 |0.91 |-20.1 |

| |1.0 |-475 |17.67 |2.167 |1441.36 |0.89 | 9.5 |

| |1.5 |-470 |22.72 |1.0802 |752.64 |0.91 | 29.6 |

It is obvious from Table 1 that the value of the charge-transfer resistance, Rt increases with the concentration of thiadiazole derivatives and reached a maximum value of 755.75 Ω cm2 at 1.5×10-4 M in the case of 4-MTH. A large charge-transfer resistance is associated with a slower corroding system [44]. On the other hand, the Rt values for 4-NPTH and 4-CPTH at low concentrations are weaker than that of 1 M HCl, showing that the corrosion of the steel electrode is accelerated in these cases. This behaviour was observed by many authors, for example in the case of 2,5-bis(4-nitrophenyl)-1,3,4-oxadiazole [45], 3,5-bis(4-chloro)-4H-1,2,4-triazole [46] and 4-nitropyrazole [47]. That was explained in the case of the 4-nitropyrazole (NOP) by the diffusion, along with desorption of NOP with partially involved adsorption of water [48] or electrochemical reduction of nitro group [49].

The value of the parameter A of the ZCPE varies in a regular manner with concentration. Its recalculation in terms of capacitor, i.e. in F cm-2, could serve as a basis of comparison, although roughly. The capacitances were calculated from A and R, using the following equation [50–52]

[pic] (2)

A tendency can be seen for decreasing of the capacitance with the concentration of thiadiazole derivatives. The double layer between the charged metal surface and the solution is considered as an electrical capacitor. The decrease of C with increasing thiadiazole derivatives concentrations may be attributed to the formation of a protective layer at electrode surface. The increase of the values of n when compared with 1 M HCl and with concentration can be explained by some decrease of the surface heterogeneity, due to the adsorption of the inhibitor on the most active adsorption sites [38].

In the case of impedance study, E(%) is calculated by Rct as described elsewhere [31]. The efficiency values are given in Table 1. It is found that E(%) increases with the inhibitor concentration and depends on the substituent of the thiadiazole derivatives. E(%) of thiadiazole derivatives tested decreases in the order 4-MTH ( 4-DATH ( 4-MPTH ( DPTH ( 4-NPTH ( 4-CPTH.

The ability of the molecule to adsorb on the steel surface was dependent on the group in para position in phenyl substituent. Indeed, it appears that replacement of hydrogen atom in para position in phenyl substituent of DPTH molecule by an electron-releasing group such as –CH3, –N(CH3)2 and –OCH3 group arises an enhancement in the inhibition efficiency. The same effect has been observed for 2,5-disubstituted-1,3,4-oxadiazole derivatives [45] and 3,5-disubstituted-4H-1,2,4-triazole derivatives [1]. On the other hand, the difference in inhibition efficiency between 4-MTH, 4-DATH and 4-MPTH can be explained by the presence of –OCH3 group in 4-MTH. In order to gain more information about the mode of adsorption of these compounds on the steel surface, the experimental data have been tested with several adsorption isotherms. In order to obtain the isotherm, coverage θ calculated from the capacitance measurements as described elsewhere [53]. The plots of Cinh/( versus Cinh yielded a straight line with nearly unit slope and the best fit was obtained with Langumir adsorption isotherm as in Fig. 6. It is found that all the linear correlation coefficients are very closed to 1.00, clearly proving that the adsorption of these thiadiazole derivatives from 1 M HCl solution on the mild steel obeys the Langmuir adsorption isotherm. From the intercepts of the straight lines Cinh/( – axis, K values were calculated and are given in Table 2. The constant of adsorption, K, is related to the standard free energy of adsorption, (G0ads, with the following equation [29]:

[pic] (3)

where R is the universal gas constant and T is the absolute temperature. The standard free energy of adsorption ((G0ads) can be calculated (Table 2). The negative values of (G0ads ensure the spontaneity of the adsorption process and stability of the adsorbed layer on the steel surface. Its well known that values of ─(G0ads of the order of 20 kJ mol-1 or lower indicate a physisorption; those of order of 40 kJ mol-1 or higher involve charge sharing or transfer from the inhibitor molecules to the metal surface to form a coordinate type of bond (chemisorption) [54,55]. The calculated (G0ads values of slightly more negative than -40 kJ.mol-1 indicate, therefore, that the adsorption mechanism of the investigated thiadiazoles (DPTH, 4MPTH, 4-MTH and 4-DATH) on steel in 1 M HCl solution is typical of chemisorption (Table 2). The large negative value of (G0ads in the case of 4-MTH indicated that this inhibitor was strongly adsorbed on the steel surface [56]. Moreover, |(G0ads| of this family decreases in the order 4-MTH ( 4-DATH ( 4-MPTH ( DPTH. This is in good agreement with the values of inhibition efficiency obtained from the ac impedance study (Table 1).

[pic]

Fig. 6. Langmuir’s isotherm for adsorption of electron-releasing thiadiazoles family on the mild steel surface in 1 M HCl.

Table 2

The values of K and (G0ads of electron-releasing thiadiazoles family for mild steel in 1 M HCl at 30°C

|Inhibitor |K (104 M-1) |R2 |(G0ads (kJ mol-1) |

|4-MTH |111.11 |1 |-45.22 |

|4-DATH |102.04 |1 |-45.00 |

|4-MPTH |98.04 |1 |-44.90 |

|DPTH |19.12 |0.998 |-40.78 |

Whereas, the significantly decrease in the inhibition efficiency are obtained by replacing the hydrogen atom in para position in phenyl substituent of DPTH molecule by the electron-withdrawing group, –NO2 and –Cl in 4-NPTH and 4-CPTH. In this case, E(%) values were found to be negative at weak concentrations (Table 1). The acceleration of corrosion by 4-NPTH and 4-CPTH may be attributed to the following factors: (i) the lowering of overpotential for the cathodic process; (ii) stimulation through preferential paths of partial electrochemical reactions in corrosion processes; (iii) stimulation caused by inhibitor participation in the metal dissolution process [57]. According to Donahue et al., the acceleration of corrosion in the presence of organic compounds is related to the oxidative propensity of the surface chelates. It takes place until the chelate is adsorbed. If charge transfer comes about with desorption of the complex ion according to the reaction:

[(FeOH) . Inh n]ads = [(FeOH) . Inh n]+sol + e – (4)

the additive will undoubtedly act as stimulator [58]. In the same way, Hackerman et al. explained this phenomenon, in the case of 4-nitropyrazole (NOP), to the formation of a soluble [FeClx-(OH)y(NOP)z]n complex that is readily removed from the metal surface [47]. This removal of a soluble complex results in exposure of fresh surface and facilitates continued corrosion.

3.2. Quantum chemical studies

Quantum structure–activity relationships (QSAR) has been used to study the effect of molecular structure on inhibition efficiency of some 2,5-disubtituted 1,3,4-thiadiazoles. The calculated quantum chemical indices of thiadiazole derivatives (Fig. 1) obtained by resorting to DFT method with 6-31G (d,p) basis set with Gaussian 03 code are presented in Table 3. Compounds with electron donating groups, such as CH3, –N(CH3)2 and –OCH3 which increases the electron density on the benzene ring, have high inhibition efficiency probably by increasing the chemical adsorption on the metal surface [45]. On the other hand, acceleration of corrosion activity for 4-CPTH and 4-NPTH may be due to the presence of with-drawing groups (Cl and NO2), which decreases the electron density on the nitrogen atoms in the 1,3,4-thiadiazole moiety. This was reflected on calculated quantum parameter giving low values for EHOMO and ELUMO compared to the other compounds (Table 3).

An attempt to correlate some quantum chemical parameters with experimental inhibition efficiencies, Table 3 shows that no simple relation or direct trend relationship can be derived from the inhibition performance of this class of heterocyclic compounds. The difficulty in obtaining a direct relation between quantum chemical parameters and corrosion inhibition efficiency provides confirmation of the complex nature of interactions that are involved in the corrosion inhibition process. Therefore, there could be a composite index of more than one parameter, which might affect the inhibition efficiency of the molecules. Though, a number of satisfactory correlations have been recorded by other investigators between the inhibition efficiency of various inhibitors used and some selected quantum chemical parameters [16(23].

The linear resistance model (LR) proposed by Bentiss and all. for the study of interaction of corrosion organic inhibitors with metal surface in acidic solution has been used in this work according to the following equation [59].

[pic] (LR) (5)

where Rt is the charge transfer resistance, A, B, and C are the regression coefficients of the calculated quantum chemical parameters for the molecule j and Cinh,i denotes the concentration of the inhibitor in experiment i.

Table 3

Calculated quantum chemical indices of thiadiazole derivatives

|Compound |EHOMO |ELUMO |µ |ΔE |

| |(eV) |(eV) |(Debye) |(eV) |

|4-DATH |-4.73 |-1.14 |3.25 |-3.59 |

|4-MTH |-5.85 |-1.74 |2.6 |-4.11 |

|4-MPTH |-5.38 |-2.77 |0.58 |-2.61 |

|DPTH |-6.06 |-1.87 |2.56 |-4.19 |

|4-NPTH |-7.04 |-3.23 |1.29 |-3.81 |

|4-CPTH |-6.25 |-2.2 |2.059 |-4.05 |

The linear approach was not found to be satisfactory for correlating the present results of all the studied thiadiazole derivatives. This can be explained by the presence of two much different structural and electronic effects in the thiadiazole derivatives. Accordingly, in order to improve the correlation between experimental and calculated efficiencies, it is recommended to avoid the overlapping of these structural effects, by studying each family one at a time. Hence, the electron-releasing effect in the three compounds 4-MPTH, 4-DATH and 4-MTH was chosen to be analyzed in the first part of the work. In this case, a highly significant correlation between experimental and calculated values of resistance-transfer charges (Rt) was obtained and the best rational equation, using a composite index of EHOMO, ELUMO and µ, was:

Rt = 139.7 + (-3.01 106 EHOMO + 5.11 106 ELUMO – 1.57 106 µ) Cinh (6)

N = 12 R = 0.95 Fobs = 27 F(0.99)=7.59

where R denotes the multiple correlation coefficient and N is the total number of experimental impedances. The significance of the regression equation was obtained by calculating the Fischer's number [74]. Calculated Rt using the LR model, for concentration range of inhibitor 0.25 ( 10-4 M to 1.5 ( 10-4 M., illustrates the very good agreement (R ( 0.95) between the experimental Rt and the calculated ones of the electron-releasing thiadiazoles family as it is presented in Fig. 7.

[pic]

Fig. 7. Experimental and calculated Rt values (equation 6) by the LR model of electron-releasing thiadiazole derivatives (4-MTH, 4-DATH and 4-MPTH).

Concerning the electron-withdrawing thiadiazoles family (4-CPTH, 4-NPTH), a highly significant correlation coefficient (R = 0.97) between experimental and estimated values of 1/Rt was also obtained (Eq. 7 and Fig. 8). However, we can see that the correlation is not related to the dipole moment (μ) and EHOMO but only with the strong influence of ELUMO energy giving electron acceptance character. This can be related to the simulation of acid corrosion of mild steel in the case of 4-CPTH and 4-NPTH at low concentrations.

1/Rt = 0.087 + (128.15 ELUMO) Cinh (7)

N = 8 R = 0.97 Fobs = 88 F(0.99) = 8.64

[pic]

Fig. 8. Experimental and calculated 1/Rt values (equation 7) by the LR model of electron-withdrawing thiadiazole derivatives (4-NPTHand 4-CPTH).

In order to correlate the quantum chemical indices for all studied thiadiazoles and their experimental inhibition efficiencies, the non-linear model (LKP), proposed by Lukovits et al. [11], has been used in this part of the study. The LKP model is based on the Langmuir adsorption isotherm, where the surface coverage (θ) characterizes the adsorption of molecule. Coverage by inhibitor molecules is one of the primary causes of corrosion inhibition [11,18]. Applied assumption that θi ≈ Ei look reasonable, although almost linear function exists between θi and Ei [18]. By assuming that θi ≈ Ei, the following proposed relation between inhibition efficiency; obtained from ac impedance measurements; and quantum chemical index can be obtained, Eq. (8):

[pic] (8)

where Ei is the inhibition efficiency, A and B are the regression coefficients determined by regression analysis, xj is a quantum chemical index characteristic of molecule (j) and Ci denotes the experiment’s concentration i. In this work, xj is constructed, as a composite index of quantum chemical parameters; EHOMO, ELUMO and μ.

Using the non linear method analysis, Eq. (9) was obtained for the six thiadiazole derivatives (Fig. 1):

[pic] (9)

Calculated efficiencies, Ecalcd (%), for concentration range of inhibitor 0.5×10−2 to 1.5×10−4 M, illustrate good correlation with experimental efficiencies Eexp (%) (R = 0.96) as it is presented in Fig. 9. This significant correlation, using the non-linear model (LKP), indicated that the variation of the corrosion inhibition with the structure of these compounds may be explained in terms of electronic properties.

[pic]

Fig. 9. Correlation between the experimental and calculated E(%) values (equation 9) by the LKP model for all thiadiazole derivatives.

4. Conclusion

The main conclusions drawn from this study are:

● The process on the interface mild steel/1 M HCl with and without thiadiazole derivatives are described by a simple equivalent circuit including a charge transfer resistance, Rt, a parallel double-layer capacitance which distributed and modelled by a CPE element and ohmic resistance, RΩ.

● The results obtained in this study showed the effectiveness of the investigated thiadiazole derivatives, except 4-NPTH and 4-CPTH, as inhibitors for corrosion of the mild steel in 1 M HCl.

● 4-NPTH and 4-CPTH stimulate the steel corrosion process at law concentration in 1 M HCl.

● The inhibiting efficiency increases with increasing of the inhibitor concentration and depends on the substituent of the thiadiazole derivatives according to order 4-MTH ( 4-DATH ( 4-MPTH ( DPTH ( 4-NPTH ( 4-CPTH.

● The Langmuir adsorption isotherm provides a formal description of the adsorptive behaviour of the electron-releasing thiadiazoles family on mild steel. The (G0ads values reveal that the corrosion inhibition by these compounds is due to the formation of a chemisorbed film on the metal surface.

● Using semi-empirical QSAR approach, significant correlations are obtained between inhibition efficiency with the calculated quantum chemical indexes, indicating that variation of the inhibitor effectiveness with the structure of thiadiazole derivatives may be explained in terms of electronic properties.

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