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The inhibition action of Formazan Derivatives on the corrosion of mild steel in hydrochloric acid medium B. Anand1*, M.Jayandran1, V.Balasubramanian2 1 Department of Chemistry, Mahendra Engineering College, Namakkal-637 503, India 2 Department of Chemistry -AMET UNIVERSITY, Chennai -603112, India Fax: +91-4288-238888 Email: email@example.com Abstract The effect of Formazan derivative of p-dimethyl amino benzaldehyde (FD) on the corrosion of mild steel in acidic media (1M HCl and 2 M HCl) have been investigated using weight loss measurements, electrochemical impedance spectroscopy, potentiodynamic polarization and FT-IR spectroscopic techniques. Potentiodynamic polarization studies have shown that compound FD suppress both the anodic and cathodic process and they behave as mixed-type inhibitors. Changes in impedance parameters are indicative of the adsorption of these compounds on the metal surface and the inhibition efficiency was found to mainly depend on the nature of the investigated compounds. It was found from the experimental evidences that the adsorption on the mild steel surface follows the Langmuir isotherm model in all acidic media. These studies have also shown that Formazan of pdimethyl amino benzaldehyde is a good inhibitor for mild steel in 1 M HCl and 2 M HCl acid solutions at room temperature in 2 hrs. In 1 M HCl the inhibition efficiency was high when compared to 2 M HCl acid solutions. The surface analysis study also confirms the corrosion inhibition of the mild steel by the inhibitor (FD). 1 Keywords: Mild steel, Corrosion Inhibitors, Weight loss method, AC impedance; potentiodynamic polarization. 1. Introduction The utility of Mild steel in a vast area of applications has intensified the research in terms of corrosion resistance of it in various aggressive environments [1-3]. Several researchers have devoted their attention to develop more effective and non-toxic inhibitors to reduce both acid attack and protection aspects in Mild steel. Amongst the various methods available, the use of inhibitors is one of the most practical methods for protection against corrosion especially in acidic media [4-9]. The use of organic compounds based corrosion inhibitors against metal dissolution is often associated with chemical and/or physical adsorption, involving a variation in the charge of adsorbed substance and a transfer of charge from one phase to other [9-14]. Special attention was paid to the effect of electron donating on the atom, electron withdrawing or groups responsible for adsorption mainly depends on steric factors, aromaticity, the structural properties of the organic compounds studied such as the presence of - electrons and heteroatoms, which induce greater adsorption of the inhibitor molecules onto the surface of mild steel [14-18]. Therefore, in this investigation, the corrosion inhibition of mild steel in 1 M HCl and 2 M HCl solution is studied in the absence and presence of Formazan of p-dimethyl amino benzaldehyde (FD) for two hours at room temperature. 2 2. Experimental 2.1 Material preparation According to ASTM method as reported already , mild steel strips were cut into pieces of 5 cm × 1 cm having the following composition (in percentage) % C=0.017; Si=0.007; Mn=0.196; S=0.014; P=0.009; Ni=0.013; Mo=0.015; Cr=0.043 and Fe=99.686 was used. The samples were polished, drilled a hole at one end and numbered by punching. During the study the samples were polished with various grades of SiC abrasive papers (from grits 120 to 1200) and degreased using Acetone. 2.2 Preparation of Solutions: All the solutions were prepared using NICE brand analar grade chemicals in double distilled water and bubbling purified by nitrogen gas for 30 minutes to carry out de-aeration of the electrolytes. 1 M HCl and 2 M HCl solutions were prepared by double distilled water while the inhibitor solution of 0.1% Formazan benzaldehyde was prepared by dissolving 0.1 gms of Formazan of p-dimethyl amino benzaldehyde (FD) in 100ml of test solution. Various milli molar (mM) concentration solutions of FD were also prepared. The structure of the inhibitor is shown in Figure-1. CH3 N NH2 C O NH HN N C NH CH3 Figure 1- Formazan of p-dimethyl amino benzaldehyde (FD) 3 2.3 Weight loss measurement: Mild steel specimens were immersed 1 M HCl and 2 M HCl for 2 h at room temperature (28 ± 2 ºC) for each inhibitor concentration. Then the specimens were removed, rinsed in double distilled water, acetone and the loss in weight of the specimen was determined. From this, the inhibiton efficiency (IE %) was calculated using the formula, IE % = WoWi x 100 Wo (1) Where, WO and Wi (in g) are the values of the weight loss observed of mild steel in the absence and presence of inhibitor respectively. 2.4 Electrochemical Studies: All the electrochemical measurements were performed using the Electrochemical Workstation (Model No: CHI 600D, CH Instruments, USA) at a constant temperature of 28 ± 2 ºC maintained with 1 M HCl and 2 M HCl as an electrolyte. A platinum electrode and a saturated calomel electrode (SCE) were used as auxiliary and reference electrodes, respectively, while the working electrode comprised of mild steel specimen with 1cm2 exposed area. The tip of the reference electrode was carefully positioned very close to the surface of the working electrode by the use of a fine Luggin capillary in order to minimize the ohmic potential drop. The remaining uncompensated resistance was also reduced by the electrochemical workstation. Potentiodynamic polarization studies were carried out at a scan rate of 0.01mV s-1 and at a potential range of -800 to -200 mV for optimum concentration of the inhibitors. The electrochemical impedance studies were carried out in the same setup as that of potentiodynamic polarization studies and the applied ac perturbation signal was about 10 mV within the frequency range 1Hz to 1 KHz. All the electrochemical impedance measurements were carried out at open circuit potential. 4 The percentage of the inhibition efficiency is calculated from the values of the current density (Icorr) with aid of the following formula, IE% = Icorr I corr - I corr (i ) I corr × 100 (2) = Corrosion current density in the absence of inhibitor Icorr(i) = Corrosion current density in the presence of inhibitor. 2.5 Scanning Electron Microscope (SEM analysis): The mild steel specimens were immersed in the blank (1 M HCl and 2 M HCl) containing the inhibitor Formazan of p-dimethyl amino benzaldehyde (FD)for 2 h after which they were taken out, washed with distilled water and then the specimens was observed under Scanning Electron Microscope (SEM- HITACHI S3000H, Japan). 2.6 FT-IR Studies: The corrosion products formed on the steel surface during weight loss measurement was removed by scrapping and was used for recording FT-IR spectra. This study reveals the possibility of the adsorption of the inhibitor on the metal surface. The Fourier transform infrared (FT-IR) spectra of the scraped films were recorded using a (Perkin Elmer-1400) FT-IR spectrophotometer. 3. Results and Discussion 3.1 Weight loss method The comparison graph of corrosion behaviour and inhibitor efficiency of mild steel in 1M HCl and 2 M HCl with Formazan of p-dimethyl amino benzaldehyde (FD) which was studied by weight loss method at 2 h at room temperatures was given in Figure 2 (a) & (b). From the graph, it was observed that the weight loss of mild steel in the acid decreases with increasing concentration of additives and the values were tabulated in Table 1 from which it was clear that the corrosion rate has 5 decreased with increasing concentration of inhibitor and inhibition efficiency increased with increasing the concentration of the inhibitor. In addition, the maximum corrosion inhibition efficiency of Formazan of p-dimethyl amino benzaldehyde (FD) was 74.29 % at 1M HCl and 71.95 % at 2M HCl respectively at 31.70 mM concentration of the inhibitor solution for two hours at room temperature. Table 1- Corrosion parameters in absence and presence of Formazan of p-dimethyl amino benzaldehyde (FD) with 1M HCl and 2M HCl. Inhibitor Conc. of inhibitor (mM) Corrosion Rate (mm/y) Inhibitor Efficiency (%) 1M HCl 35.5526 29.5343 23.9618 18.6122 13.0396 9.1389 2M HCl 36.5557 30.4259 25.5221 20.1725 15.0458 10.2534 1M HCl --16.92 32.60 47.64 63.32 74.29 2M HCl --16.76 30.18 44.81 58.84 71.95 Blank Formazan of p-dimethyl amino benzaldehyde (FD) 6.34 12.68 19.02 25.36 31.70 It was also concluded that the inhibitor was very efficient for mild steel corrosion in 1M HCl and 2M HCl and when comparing with acids, the inhibitor efficiency was maximum in 1M HCl than 2M HCl. Figure 2(a) revealed the comparison of corrosion rate (CR) with concentration of Formazan of p-dimethyl amino benzaldehyde (FD) (in %) in 1M HCl and 2M HCl solution at two hour at room temperature. Comparison of inhibition efficiency (IE) with concentration of (FD) (in %) in 1M HCl and 2M HCl solution for two hours at room temperature is shown in Figure 2(b). 6 3.2 Adsorption Isotherm: Basic information on the interaction between the inhibitor and the mild steel surface can be proved by the adsorption isotherm and in general, inhibitors can function either by physical (electrostatic) adsorption or chemisorption with the metal. To obtain more information about the interaction between the inhibitor molecules and the metal surface, different adsorption isotherms were 7 tested. The fractional surface coverage at different concentrations of inhibitors 1M HCl and 2M HCl solutions were determined from the weight loss measurements data  using the formula, () = Wo - Wi Wo (3) where, Wo and Wi are the values of weight loss of uninhibited and inhibited specimens, respectively. Kc = 1- -------------- (4) where, c is the concentration of the inhibitor, is the fractional surface coverage. The Langmuir isotherm, Eq. (4), which is based on the assumption that all adsorption sites are equivalent and that molecular binding, occurs independently from the fact whether the nearby sites are occupied or not, was verified for all the studied inhibitors. The adsorption equilibrium constant K is related to the free energy of adsorption Gads as, K = - G ads exp RT C solvent 1 ---------------- (5) Where, Csolvent represents the molar concentration of the solvent, which in the case of water is 55.5 mol dm-3, R is the gas constant and T is the thermodynamic temperature in K. The Langmuir isotherm, Eq. (5), can be rearranged to obtain the following expression, c = 1 + c ------------------------K (6) so that a linear-relationship can be obtained on plotting c/ as a function of c, with a slope of unity. The thermodynamic parameters K and Gads for the adsorption of the studied inhibitors on mild steel is obtained by Langmuir's adsorption isotherm are plotted in Figure 3 and the obtained values are given in Table 2. It was found that the linear correlation coefficients clearly prove that the adsorption of the Formazan of p-dimethyl amino benzaldehyde (FD) from 1M HCl and 2M HCl solutions on the 8 mild steel corrosion obeys the Langmuir adsorption isotherm. The negative values of G0ads for the addition of inhibitors indicate that the process of adsorption of studied inhibitors is spontaneous in nature . The free energy of adsorption of (Gads), in 1M HCl was found to be -17.612 kJmol-1while for 2M HCl it was found to be -18.687 kJmol-1, respectively. It is well known that the values of Gads in the order of -20 kJ mol-1 or lower indicate a physisorption while those about -40 kJ mol-1 or higher involve charge sharing or transfer from the inhibitor molecules to the metal surface to form a co-ordinate type of bond . The calculated adsorption values for all the studied inhibitor show that the adsorption is of physical in nature, and there is no chemisorption between the inhibitor molecule and the metal surface. This indicates that the adsorption of FD at 2 h takes place through electrostatic interaction between the inhibitor molecule and the metal surface. Hence it indicates that the interaction between the inhibitor molecule and metal surface is physisorption. Figure 3 - Langmuir isotherm for adsorption of FD on mild steel surface studied at (1M HCl and 2M HCl). 9 Name of the Acid 1M HCl 2M HCl Concentration in (mM) 31.70 31.70 Surface coverage () 0.7429 0.7195 Gads KJ / mol-1 -17.612 -18.687 Kx (10-2 M-1) 1.79 1.79 Table 2- Thermodynamic parameters for the adsorption of FD in (1M HCl and 2M HCl) on the mild steel. 3.3 Potentiodynamic polarization studies: Potentiodynamic polarization results obtained for the inhibitory effect of Formazan of pdimethyl amino benzaldehyde (FD) on mild steel corrosion in 1M HCl and 2M HCl are depicted clearly in Figure 4(a) & (b). The various polarization parameters such as corrosion current (Icorr), corrosion potential (Ecorr), anodic and cathodic Tafel slopes (-ba and -bc) were derived from potentiodynamic polarization studies on mild steel in both acid media. Figure 4 (a) Potentiodynamic polarization curves of mild steel in 1M HCl in the absence and presence of the inhibitor. 10 Figure 4 (b) Potentiodynamic polarization curves of mild steel in 2M HCl in the absence and presence of the inhibitor. It could be observed from the Table that the Ecorr values have shifted slightly towards negative side in presence of inhibitors suggesting that the inhibitors inhibit the corrosion of mild steel in acids solution by controlling cathodic reactions due to the blocking of active sites on the metal surface. It is evident that inhibitors bring about considerable polarization of the cathode. It was, therefore inferred that the inhibitive action of FD is of mixed type. The corresponding results of potentiodynamic polarization parameters are represented in Table 3. Table 3 - Polarization parameters of mild steel electrode immersed in the absence and presence of the optimum concentration of the inhibitors. Name of the Acid 1M HCL c (V dec-1) 5.026 5.905 4.809 5.905 a (V dec-1) 10.632 9.103 6.088 9.103 ECorr (V) -0.493 -0.514 -0.553 -0.514 ICorr x10-4 (A) 3.913 0.9472 3.332 0.9472 Corrosion Inhibition Rate Effeciency (mmpy) (%) 18.810 --4.552 16.010 4.552 75.79 --71.57 Inhibitors Blank FD Blank 2M HCL FD 11 The non-constancy of Tafel slopes for different inhibitor at optimum concentration reveals that the inhibitor action due to the interference in the mechanism of the corrosion processes at cathode. The Icorr values have decreased when comparing with different inhibitors at optimum concentration. The inhibition efficiencies were determined from the values of corrosion current density and the inhibition efficiency values were found to show good agreement with those obtained from weight loss measurements. FD shows the maximum inhibition efficiency of 75.79 % in 1M HCl and 71.57 % in 2M HCl. This result suggests that the addition of inhibitors retards the hydrogen evolution reaction . Hence the FD acts as good inhibitor system due to the higher electrostatic attraction of FD and metal surface by the high electron density of the nitrogen (N-H group) atom in the inhibitor molecule. 3.4 Electrochemical impedance spectroscopy (EIS) The corrosion of mild steel in 1M HCl and 2M HCl solution in the absence and presence of Formazan of p-dimethyl amino benzaldehyde (FD) was investigated by EIS measurements at open circuit potential condition. Nyquist plots for mild steel obtained at the interface of electrode and electrolyte in the absence and presence of optimum concentration of inhibitors is given in Figure 5(a) & (b). The Nyquist diagram obtained with 1M HCl and 2M HCl shows only one capacitive loop and the diameter of the semicircle increases on the increasing the electrostatic attraction of the inhibitor suggesting that the formed inhibitive film was strengthened by the addition of such inhibitors. All the obtained plots show only one semicircle and they were fitted using one time constant equivalent model (Randle's model) with capacitance(C) and charge transfer resistance (Rct). The main parameters deduced from the impedance technique are given Table 4. 12 Figure 5 (a) -A.C. Impedance curves of mild steel electrode immersed in 1M HCl in the absence and presence of the inhibitors. Figure 5 (b) - A.C. Impedance curves of mild steel electrode immersed in 2M HCl in the absence and presence of the inhibitors. 13 Table 4 - A.C. Impedance parameters of mild steel electrode immersed in 1M HCl in the absence and presence of the inhibitors. Parameters Name of the Acid Inhibitors Rct (ohm cm2) 72.72 274.80 70.12 242.00 Inhibition Cdl Efficiency (µF X10-5) µ (%) 4.118 1.592 4.618 1.534 73.53 71.02 Blank 1M HCl FD Blank 2M HCl FD The lower double layer capacitance (Cdl) value for 1M HCl and 2M HCl mediums indicates that the homogeneity of the surface of the mild steel roughened due to corrosion. The double layer capacitance Cdl values have decreased on the effective addition of different inhibitors at the optimum concentration. The studied system indicates that the reduction of charge accumulated in the double layer due to formation of adsorbed inhibitor layer . The inhibiting efficiencies show that the inhibitory actions may be due to the adsorption of the inhibitors on mild steel surface . The compound investigated FD has been found to give an excellent inhibition due to the electron density on the nitrogen of the N-H group. This leads to the strong electrostatic attraction of FD on the metal surface thereby resulting in the high inhibition efficiency. Generally on the metal side, electrons control the charge distribution whereas on the solution side is controlled by ions. Since ions are much larger than the electrons, the equivalent ions to the charge on the metal will occupy quite a large volume on the solution side of the double layer . It can be obtained from Table 4 that, the capacitance of the electrical double layer (Cdl) decreases in the presence of the inhibitors. Decrease in the (Cdl) which can result from a decrease in local dielectric constant and / or an increase in the 14 thickness of the electrical double layer, suggests that the inhibitor molecule may act by adsorption at the metal/solution interface . 3.5 FT-IR spectral studies: FT-IR analyses of metal surface can be useful for predicting whether organic inhibitors are adsorbed or not adsorbed on the metal surface . FTIR spectra were used to support the fact that corrosion inhibition of mild steel in acid medium is due to the adsorption of inhibitor molecules on the mild steel surface as well as providing new bonding information on the steel surface after immersion in inhibited HCl solution at optimum concentration. Figure 6(a) shows the IR spectrum of the Formazan of p-amino benzaldehyde (FD). In this spectrum the peak appeared at 3367cm-1 corresponds to amide N-H stretching, 1510 cm-1 corresponds to C=0 group, 1417 cm-1 corresponds to C-C stretching and from 1230 cm-1 to 1000 cm-1 the wavenumber indicates the presence of C-O bonding nature. Figure 6 - IR spectrum of the corrosion product showing adsorption in the presence of aqueous extract of Formazan of p-amino benzaldehyde (FD). 15 Figure 6 (b) is similar to Figure 6 (a) which indicates the corrosion products contains Formazan of pamino benzaldehyde. Therefore from the spectra it is revealed that the inhibition is due to the physical adsorption of corresponding organic molecule. Moreover the spectrum shows there is no any coordinate type of metal inhibitor bond. 3.6 SEM Analysis: The polished mild steel specimens were immersed in the acid solution (1M HCl and 2M HCl) and in the acids containing inhibitor Formazan of p-amino benzaldehyde (FD) for 2 h, and then the specimens were taken out, dried and observed under Scanning Electron Microscope (SEM). The micrograph are shown in the Figure 7 & 8 depicts that the polished specimen which was kept in the blank solution of 1M HCl and 2M HCl, associated with polishing scratches. Figure 9 & 10 shows specimen which was kept in the 31.70 mM concentration of inhibitor solution with 1M HCl and 2M HCl depends upon the concentration of the inhibitor solution suggesting that the presence of adsorbed layer of the inhibitor on mild steel surface which impedes corrosion rate of metal appreciably. This is attributed to the involvement of the compounds in the interaction with the active sites of metal surface. This results in enhanced surface coverage of the metal so that there is a decrease in the contact between metal and the aggressive medium . Figure 7- SEM images obtained for the mild steel surfaces immersed for 2 h in 1M HCl (blank acid solution) 16 Figure 8 - SEM images obtained for the mild steel surfaces immersed for 2 h in 2M HCl (blank acid solution) Figure 9 - SEM images obtained for the mild steel surfaces immersed for 2 h in 1M HCl with 31.70 mM inhibitor solution. Figure 10 - SEM images obtained for the mild steel surfaces immersed for 2 h in 2M HCl with 31.70 mM inhibitor solution. 17 Conclusions: The present study leads to the following conclusions in controlling the corrosion of mild steel by Formazan of p-amino benzaldehyde (FD) in 1M HCl and 2M HCl. 1. Formazan of p-amino benzaldehyde (FD) was found to be an effective inhibitor in the acidic medium giving inhibition efficiency upto 74.29 % in 1M HCl and 71.95 % in 2M HCl respectively. 2. The adsorption of the compound investigated follows the Langmuir isotherm and the adsorption is physical in nature. 3. Polarization measurements demonstrate that the compound under investigation (FD) inhibit both anodic and cathodic reaction and hence it act as mixed type inhibitor. 4. Impendance measurements indicate that, the presence of electron donating group on the inhibitor increase the charge transfer resistance and decreasing the double layer capacitance. The type of the substitutents group and the type of the functional atoms of the inhibitor molecule are found to play an important role in the inhibition process. 5. Results obtained from weight loss measurements and electrochemical measurements are in good agreement. 6. FT-IR analysis confirm that the inhibiton efficiency of the inhibitor in mild steel through electrostatic attraction of inhibitor molecule and the metal surface. 7. The morphological investigation also confirms the effective protection of mild steel, through the less damaged and minimum pits found in the inhibited surface. Acknowledgement: Helpful discussions with Professor V.Collins Arun Prakash and Professor K.M.Govindaraju from Mahendra Engineering College are gratefully acknowledged and also we thankful to AMET University and Mahendra Engineering College for providing Lab Facilities to bring out this work. 18 Reference 1. 2. Ning SG, Shi ML (1990), J Chin Soc Corros Prot.,10:383 EI Mehdia B, Mernari B,Traisnel M, Bentiss F, Lagrenee M (2002), Mater Chem Phys., 77:489 3. 4. 5. Govindaraju K M, Gopi D, Kavitha L (2009), J Appl Electrochem., 39:269-276 Anand B, Balasubramanian V (2011) ,E-Journal of Chemistry., 8(1), 226-230 Zerga B, Sfaria M, Rasis Z, Ebn Touhami M, Taleb M, Hammouti B, Imelouane B, Elbachiri A (2009), Mater Tech., 97, 297 6. Chaieb E, Bouyanzer A, Hammouti B, Benkadour M (2005), Appl Surf Sci., 246:199 7. 8. 9. 10. Bouklah M, Hammouti B (2006), Port Electrochim Acta., 24,457 Bouyanzer A, Majidi L, Hammouti B (2007), Phys Chem News., 37, 70 Matheswaran P and Ramasamy A K, E-Journal of Chemistry., 7(3), 1090-1094 Ferreira E S, Giacomelli C, Gicomelli FC, Spinelli A (2004), Mater Chem Phys., 83:129 11. Bouklah M, Ouassini A, Hammouti B, EI Idrissi A (2006), Appl Surf Sci 252:2178 12. Anand B, Jayndran M, Balasubramainan V, (2011), Asian Journal of Chemistry., Vol. 23, No. 5, 2106-2108 13. Anand B, Balasubramainan V, International Journal of Advanced Materials Science., Vol. (1), No. 1 (2011), pp. 17 14. Akrout H, Maximovitch S, Bousselmi L, Triki E, Dalard F (2007), Mater Corros., 58:202 19 15. Gopi D, Manimozhi S, Govindaraju KM, Manisankar P, Rajeswari S (2007), JAppl Electrochem., 37:439 16. Aloui S, Forsal I, Sfaira M, Ebn Touhami M, Taleb M, Filali Baba M, Daoudi M (2009), Portugaliae Electrochim Acta., 27,599. 17. 18. 19. Kustu C, Emregul KC, Atakol O (2007), Corros Sci., 49.2800 Zhang QB, Hua YX (2009), Electrochim Acta., 54, 1881 Abiola O K, Oforka N C and Ebenso E E, Bulletin of Electrochemistry., 2004, 20, 409. 20. 21. 22. 23. 24. Moretti G, Guidi F (2002), Corros Sci., 44:1995. Bentiss F, Lebrini M, Lagrene M (2005), Corros Sci., 47:2915. Yurt A, Ulutas S, Dal H (2006), Appl Surf Sci., 253:919 Gunasekaran. G, Chauhan.L.R, Electrochim Acta., 49 (2004) 4387. Govindaraju K M, Gopi. D and Kavitha L, J. Applied Electrochemistry., 10 (2009) 263-269. 25. 26. 27. Ozcan.M, Dehri.J, Erbil.M, Appl Surf Sci., 236 (2004) 155. Ashassi-Sorkhabi.H, Shaabani.B, Seifzadeh.D, Appl Surf Sci., 239 (2005), 154. Lagrenee M, Mernari B, Bouanis M, Traisnel M, Bentiss F, Corros. Sci., 44 (2002) 573. 28. Singh, A., Singh, V.K., Quraishi, M.A., 2010a. Aqueous extract of Kalmegh (Andrographis paniculata) leaves as green inhibitor for mild steel in hydrochloric acid solution. Int. J. Corros., 10 (2010) 275. 29. S.S. Abd El-Rehim, S.A. Rwfaey, F. Taha, M.B. Saleh, R.A. Ahmed, J. Appl. Electrochem., 31 (2001) 429435. 20