Organic coatings silane-based for AZ91D magnesium alloy

Thin Solid Films 519 (2010) 1361–1366

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Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f

Organic coatings silane-based for AZ91D magnesium alloy Junying Hu, Qing Li ⁎, Xiankang Zhong, Longqin Li, Liang Zhang School of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China

a r t i c l e

i n f o

Article history: Received 29 October 2009 Received in revised form 31 August 2010 Accepted 6 September 2010 Available online 21 September 2010 Keywords: Magnesium Electrochemical Organic coatings DFT

a b s t r a c t Organic coatings silane-based containing electron withdrawing group or electron donating group have been synthesized and evaluated as prospective surface treatments for AZ91D magnesium alloy by hydrolysis and condensation reaction of the different silanes. Electrochemical tests were employed to confirm the corrosion resistance ability of the two kinds of organic coatings. The results showed that the coating with electron donating group had better corrosion protection performance. On the basis of the spatial configuration and the density of charge of those silanes molecules which was obtained through Gaussian 03 procedure based on B3LYP and density functional theory, combining experiment results, the rational explanation was provided. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Magnesium and magnesium alloys exhibit an attractive combination of low density and high strength/weight ratio making them ideal candidates for light-weight engineering applications. However, the high chemical activity of magnesium alloys has greatly limited its application especially in the automotive and aerospace industries, where exposure to harsh service conditions is unavoidable [1,2]. So the development of effective corrosion protection systems for magnesium and magnesium alloys is an issue of prime importance for their industrial applications. Several coating techniques have been adopted to improve the corrosion resistance of magnesium alloys. These include anodizing [3], chemical conversion [4], electrochemical plating [5], organic polymer deposition [6] and sol–gel method [7,8], etc., each with their own advantages and disadvantages. At present two main approaches, an active and a passive one are used for corrosion protection. Usually the passive corrosion protection is achieved by deposition of the barrier layer preventing contact of the material with the corrosive environment [9]. One of these ways to provide a passive protection of metals is the application of the sol–gel technology. The sol–gel process is a commonly used method for coating fine particles. The coating is performed in an organic solvent and the process is based on the hydrolysis of the precursors and subsequent condensation on the surface metal hydroxyls. Take tetraethyl orthosilicate (TEOS) for example, with controllable hydrolysis of TEOS, an M–O–Si chemical linkage is established between surface

⁎ Corresponding author. Tel.: + 86 023 68252360; fax: + 86 02368367675. E-mail address: [email protected] (Q. Li). 0040-6090/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2010.09.014

metallic atoms and TEOS, followed by later polymerization, and finally the formation of a three-dimensional network via siloxane bond formation (Si–O–Si) with increasing TEOS concentration and degree of hydrolysis [10]. Adhesion of sol–gel coatings to metal or metal oxide surfaces is especially favorable, because covalent bonds are formed between the substrate surface and the coating film. Various sol–gel procedures for magnesium were reported in the literature [11–13]. Furthermore, surface treatments based on organofunctional solutions became an attractive method to reduce the corrosion rate of metallic substrates and to enhance adhesion. Organofunctional silane [14] and self-assembled monolayer [15] have been tested as pretreatments for magnesium alloys. These treatments provide good corrosion protection in addition to surface functionality, improving the compatibility of the metallic substrate with the painting systems, which offer a linkage between a metal surface and a polymer primer through covalent bonding of a hydrolysable silicate group. The chemical structure of a crosslinking agent may affect coating properties. For example, aminosilanes are unique crosslinkers, which not only can be involved in the conventional chemistry of bonding epoxy groups, but they can also undergo sol–gel hydrolysis and condensation reactions and simultaneously act as coupling agents interacting with the surface of a substrate. Khramov and co-authors [16] have demonstrated that self-assembled nanophase particle systems based on the use of amino-silane as crosslinking agents are promising, which provide improved corrosion protection for aluminum alloys. Literature [17] disclosed that stable hybrid coatings with phosphonate functionalities could be synthesized through the sol–gel route of co-condensation of phosphonato-silane with tetraethyl orthosilicate, which also provided an excellent anti-corrosion ability for magnesium alloys. The comparison of the effect of various functional groups on the anti-corrosion performance of the film as a special objective is however not investigated.

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In our previous experiments, SiO2 oxide film with certain corrosion resistance was studied [18]. In order to expand the application of silane sol on the magnesium alloys, the effect of two organic coatings silane-based with different functional groups on the anti-corrosion performance of AZ91D magnesium alloy was investigated in the present paper. The surface morphology and the corrosion resistance of coatings were characterized by using scanning electron microscope (SEM) and electrochemistry impedance spectroscopy (EIS) as well as potentiodynamic polarization measurements. The results show that the silane molecular configuration spatial and functional groups have a great effect on the preparation and anti-corrosion properties of the silane coatings. 2. Experimental details 2.1. Synthesis and deposition of sol–gel coatings In order to provide a comparative study of the effect of the silane functional group on the corrosion protection performance of the sol– gel coatings, the following composite coatings were synthesized: (i) coating A with ethylene functional groups; and (ii) coating B with glycidoxypropyl groups. The sols were obtained by two-step process (i) acid catalysisbased hydrolysis and (ii) alkaline catalysis-based condensation. Sol A was prepared by hydrolyzing TEOS and triethoxyvinylsilane (VTEO) (1.16 mol/L Si in ethanol and TEOS:VTEO in a 1:3 molar ratio) by the addition of acetic acid acidified water (pH b 6) to the mixture drop by drop. Then a drop of ammonia (0.5 M) was added to accelerate the condensation reaction after hydrolysis for 1 h at 60 °C, the mixture was agitated for 1 h. Sol B was obtained by hydrolyzing TEOS and 3-glycidoxypropyltrimethoxysilane (GPTMS) (1.16 mol/L Si in ethanol and TEOS:GPTMS in a 1:3 molar ratio) through the same preparation procedures as the sol A described above. Two sols were aged for 1 day at room temperature before deposition on the magnesium alloy. The substrate material used for the present investigation was AZ91D ingot-cast magnesium alloy. The chemical composition of the alloy is given in Table 1. The substrates with dimensions of 18 mm × 22 mm × 4 mm were polished with 1500 grit SiC paper and degreased in an ultrasonic bath of acetone. Then the samples were rinsed with distilled water as well as ethanol and dried in warm air. The coating was prepared via spin-coating method using a homemade coater with a speed of 1000 r/min. Then, all samples were cured at 100 °C for 1 h in dry oven for crosslinking and gelatin of sol–gel and solvent evaporation.

Fig. 1. The FT-IR spectrum of silane sol (a) sol A, and (b) sol B.

acetone before coating deposition. The samples have been not sputtered any conductor such as Au or C before the SEM test. The coating thicknesses are measured by Ellipseometer M-2000V (J.A. Woollam, America). The potentiodynamic polarization curves and electrochemical impedance spectroscopy were performed using a PS-268B system (Zhongfu, Beijing, China) and an IM6e (ZAHNER, elektrick. Co. Germany), respectively. A three-electrode cell, with the sample as the working electrode, a saturated calomel electrode (SCE) as reference and a platinum sheet as counter electrode, was employed in those tests. The area of the working electrode was 1 cm2. All the electrochemical measurements were carried out in 3.5 wt.% neutral NaCl aqueous solution which the pH value was adjusted to 7 with HCl

2.2. Experimental methods The structure of silane coatings was characterized by Fourier Transform Infrared (FT-IR) spectrum. The measurements were performed on TENSOR-27 (Germany) spectrophotometer with incidence angle of 80° normal to the surfaces of the specimens, spectral resolution of 4 cm−1, number of scans of 120. The gel power which was cured at 100 °C was used in FT-IR test. The microstructure and surface morphology of the sol–gel coatings were observed by a SEM S-4800 (HITACHI, Tokyo, Japan). The energy used for analysis was 20 kV. The specimens used for SEM with a dimension of 5 mm × 5 mm × 3 mm were polished sequentially with 800, 1200 and 3000 grade sand paper in water and then cleaned in

Table 1 Chemical composition of AZ91D magnesium alloy (in wt.%). Al

Zn

Mn

Ni

Cu

Ca

Fe

Mg

8.77

0.74

0.18

0.001

0.001

b0.01

b0.001

Bal.

Fig. 2. SEM micrographs for (a) coating A and (b) coating B.

J. Hu et al. / Thin Solid Films 519 (2010) 1361–1366

Fig. 3. Potentiodynamic polarization curves tested in 3.5 wt.% NaCl solution for (a) the bare substrate; (b) coating A and (c) coating B.

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Fig. 4. EIS plots for the coating A during 120 h of immersion in 3.5 wt.% NaCl solution.

3.2. SEM or NaOH. After initial delay of 10 min in NaCl solution, potentiodynamic polarization curves were scanned from −1.7 V at a rate of 1 mV/s. EIS was also performed to determine the corrosion resistance at 25 °C. The samples were immersed in 3.5 wt.% NaCl aqueous solution for 20 min before impedance measurements. The measuring frequency ranged from 106 Hz down to 50 mHz, with ac excitation amplitude of 10 mV. All the experiments were performed at the corrosion potential. In order to check the reproducibility of results, at least three samples were measured for each coating. The error range of different samples was controlled in 25%. 3. Results and discussion 3.1. FT-IR spectrum

The corrosion resistance of sol–gel films is closely related to their microstructure. So SEM technique was used to evaluate the effect of the two sols on the morphology of the magnesium alloy substrate in 3.5 wt.% NaCl solution. It can be seen that the microstructure of the coating A is loose and porous as shown in Fig. 2(a). So it is very easy to permit electrolyte to pass through. However, the SEM image of coating B (Fig. 2(b)) is smoother than that of coating A. Besides, the surface of the coating B has no obvious cracks or holes. It is obviously that the sample treated by sol B would have better corrosion resistance than the samples treated by the sol A, which can be proved by the following electrochemical tests. The coating thicknesses was 587 nm obtained by Ellipseometer M-2000V. 3.3. Potentiodynamic polarization measurements

Fourier transform infrared spectroscopy is a well-established characterization tool offering a ‘fingerprint’ for chemical compounds. Fig. 1 shows the FT-IR spectra of sol A and sol B. It is known that the Si– O–Si has an asymmetric stretching mode in a wide region [19–21], the location depending upon the nature of the bonding associated with it. Based on our previews study, the νas (Si–O–Si) in Si sol prepared by only TEOS was observed at the 1100 cm−1 [18]. In Fig. 1(a) there is an obvious absorption peak at about 1077 cm−1 which is attributed to νas (Si–O–Si) in sol A. However, from the Fig. 1(b) the peak of νas (Si–O– Si) appears at the 1106 cm−1 shift to high wave number in the sol B. Also, the peak at the 1106 cm−1 is broader and stronger maybe due to the asymmetric stretching of the C–O–C in the GPTMS. Afterwards, compare the absorption peak of νas (Si–O–Si) in the two sols, it can be known that with the presence of electron withdrawing group (CH2=CH–) made the IR absorption shift to shorter wave number (the νas at 1077 cm−1 in sol A) whereas electron donating group made the peak shift to high wave number (the νas at 1106 cm−1 in sol B). This indicated that the functional group existed in the silane molecules can influence the Si–O asymmetric stretching, and then further have an effect on the sol structure.

In order to determine the effectiveness of these coatings on corrosion protection, potentiodynamic polarization measurements were conducted in 3.5 wt.% NaCl solution at 25 °C, open to air. The representative polarization curves for the two organic coatings are exhibited in Fig. 3. The polarization curves for a freshly polished sample of AZ91D magnesium alloy with no coating was also included as a comparison. The corrosion current density icorr, corrosion potential Ecorr were determined by Tafel extrapolation method. The relevant parameters are listed in Table 2. Based on the results in Fig. 3 the anti-corrosion performance of the coatings rank according to bare substrate b coating A b coating B. Corrosion current density (icorr), corrosion potential (Ecorr) are often used to evaluate the corrosion protective property of the

Table 2 The electrochemical parameters of potentiodynamic polarization curves calculated from the Tafel plots. Sample

Ecorr (mV/SCE)

icorr (A/cm2)

The substrate TV coating TG coating

−1614 −1573 −1538

1.29 × 10−5 1.39 × 10−6 1.40 × 10−7

Fig. 5. Equivalent circuits of coating A used for numerical fitting of the EIS data from a to b. (a) before 48 h and (b) after 48 h.

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Table 3 The equivalent circuit used for numerical simulation of the TV coating EIS spectra. TV

1h

48 h

120 h

CPEc(S cm−2 s−n)

1.6 × 10−6 0.77 8491 – – –

6.7 × 10−6 0.97 1890 – – –

4.39 × 10−5 0.98 84.14 3.28 × 10−6 0.96 2410

n

Rpo(ohm cm2) CPEcorr(S cm−2 s−n) n Rcorr(ohm cm2)

coatings. As shown in Table 2, compared with the bare substrate, the coating A has a lower corrosion current density (icorr), and more positive corrosion potential (Ecorr). At the same time, icorr for the coating B is decreased approximately by two orders of magnitude and Ecorr is shifted positively 76 mV in contrast to the bare substrate, respectively. Besides, an onset passive region amounted to 150 mV was observed for the coating B. The presence of long perfect passive region suggests that the coating B is considerably uniform, pore-free and adherent as well as high protective in Cl− containing solution. 3.4. EIS EIS, gives possibility to estimate corrosion protection efficiency of coatings in a more adequate way, which is one of the most intensively used and powerful techniques for investigation and prediction of corrosion protection. Impedance provides indication of changes in coating and metal interface performance long before visual changes can be observed using traditional exposure tests. So EIS measurements were carried out in the course of immersion of different samples in 3.5 wt.% NaCl solution to study the anti-corrosion mechanism. The EIS plots obtained for the coating A during immersion in 3.5 wt.% NaCl are presented in Fig. 4. During the first day of immersion the spectra revealed the presence of a time constant at frequencies around 102 Hz, which was attributed to the silane coating properties (i.e., capacitance and resistance). After 48 h, another one at lower frequency (b1 Hz) began to appear which was ascribed to charge transfer controlled processes at the metal/silane coating interface. By observation of the Logf − Log|Z|, it can be known that the shape of this curve in high frequency is a linear parallel to abscissa, revealing a resistive behaviour. In the middle frequencies, the Logf − Log|Z| is linear with a slope of −1. Furthermore, in the lower frequencies, there is also a linear parallel to abscissa which is the trait of the parallel connection of the resistance and capacitance. So the total characteristic of the coating A EIS can be interpreted by the equivalent circuits

Fig. 7. Equivalent circuits of coating B used for numerical fitting of the EIS data from a to b. (a) before 48 h and (b) after 48 h.

shown in Fig. 5. The related parameters of equivalent circuit used for numerical simulation of the coating A EIS spectra were listed in Table 3. The value of capacitance constant-phase element (CPE) was calculated using the following equation: N−1

C = Q ðωmax Þ

:

Where ωmax was the frequency at which the imaginary impedance reaches a maximum for the respective time constant, Q and N were the components of CPE that characterized the capacitance of coating [22]. An ideal capacitor corresponds to α = 1 while α = 0.5 becomes the CPE in a Warburg component [23]. Fig. 6 depicts the impedance spectra of the coating B. The slope of the Logf − Log|Z| is −1 in the high frequencies, which is the characteristic of the parallel connection of resistance and capacitance. Besides, during the initial stage of immersion, two time constants present in the EIS spectra, one is at the high frequency (≈105 Hz) which is attributed to the coating capacitance (Cc) and micro-porous resistance (Rpo) the other one is resulted from the non-ideal doublelayer capacitance of the interface (Cdl) and the resistance (Rdl). With the immersion time increasing, the time constant at the low frequency moves to a higher frequency. At the same, the shape of the Logf − Log|Z| curve takes obvious change, indicating the occurrences of the obvious corrosion of the substrate. Due to the deposition of corrosion product (arising from the corrosion of magnesium alloy and the degradation of sol–gel coatings) another parallel connection of resistance and capacitance was used to describe the impedance model. The corresponding equivalent circuits for coating B during different immersion time were proposed as shown in Fig. 7. Here, constant-phase elements were used instead of capacitances in order to take into account the dispersive characteristic of the time constants originating from the non-uniformity of the coatings. The related parameters of equivalent circuit used for numerical simulation of the coating B EIS spectra were listed in Table 4. Based on the changes of those numerical simulations, it can be clearly known that coating B Table 4 The equivalent circuit used for numerical simulation of the TG coating EIS spectra. TG

1h

48 h

120 h

CPEc(S cm−2 s−n)

2.1 × 10−8 0.90 936 4.4 × 10−6 0.98 3.67 × 105 – – –

5.74 × 10−8 0.86 730 3.0 × 10−6 0.85 8.55 × 104 – – –

1.0 × 10−7 0.80 44.79 1.76 × 10−6 0.96 8286 1.66 × 10−5 0.69 220.7

n

Fig. 6. EIS plots for the coating B during 120 h of immersion in 3.5 wt.% NaCl solution.

Rpo(ohm cm2) CPEdl(S cm−2 s−n) n Rp(ohm cm2) CPEcorr(S cm−2 s−n) n Rcorr(ohm cm2)

J. Hu et al. / Thin Solid Films 519 (2010) 1361–1366

Fig. 8. The molecular structures of the three silane precursor molecular.

plays a more significant role than coating A in improving the corrosion resistance of AZ91D magnesium alloy. The study of the EIS measurements for the non-treated sample was carried out in our lab previous research [24]. The impedance magnitude (|Z|) of the non-treated sample decreased sharply after 48 h and 120 h immersion in 3.5 wt.% NaCl. These results demonstrate that those organic coatings silane-based play a significant role in improving the corrosion resistance of AZ91D magnesium alloy especially the coating B. 3.5. The theoretical explanation In solution, the hydrolysis and condensation chemical activity of silane mainly depend on the steric hindrance of alkoxide groups and the effective electron density of the atom take place in the

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corresponding reaction. In order to analyze the effect of silane molecular structures on the hydrolysis and condensation process, the Gaussian 03 program [25] based on B3LYP [26] was employed to calculate the three silane precursor molecular structures. The electric density of oxygen atom calculated by the B3LYP method of the density functional theory [27,28] was depicted in Fig. 8. It can be known that the electric charge of the alkoxy in the three kinds of precursor is basically identical. So the major effect on the chemical reaction lies in the steric hindrance. Comparing sols A and B, it can be known that the GPTMS precursor has smaller steric hindrance than VTEO, so the sol B has better hydrolysis and condensation ability. Besides, there is the chemical binding of glycidoxypropyl groups to the metal surface resulting in the enhanced hydrolytic stability of the formed Si–O–Mg bonds [29]. The schematic illustration of the sol–gel processing of coating B is shown in Fig. 9. Through the formation of hydrolytically stable Si–O– Mg bonds at the coating/substrate interface, the coating B would serve as excellent barrier films that can afford both corrosion protection and improved adhesion to magnesium substrate — these two known problems of magnesium materials. However, the chemical bond between coating and magnesium alloy would be hard to take shape in the sol A. In a word, the corrosion resistance ability of the organic silane coating mainly depends on the comprehensive properties of the sol. 4. Conclusions Organic coatings silane-based with different functionality groups have been synthesized and evaluated as prospective surface treatments for AZ91D magnesium alloy. Based on the FT-IR spectra data, it can be known that the functional groups have effects on the sol structure, which can be shown by the νas (Si–O–Si). The electrochemical tests showed that organic coating with glycidoxypropyl group had better corrosion protection ability, which is attributed to the smaller steric hindrance and the easily formed Si–O–Mg bonds in sol B. Based on study the effect of silane precursor on the sol performance, it thus concludes that the structure and some functional groups of sol precursor would have a profound effect on its property.

Fig. 9. Schematic of sol–gel processing of coating B.

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Then catching hold of objective materials according to their characteristics may produce great benefits. Acknowledgements The authors thank the supports of the Natural Science Foundation of Chongqing, China (CSTC. 2005BB4055) and High-Tech Cultivation Program of Southwest Normal University (No. XSGX06). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

J.E. Gray, B. Luan, J. Alloy. Compd. 336 (2002) 88. M. Anik, E. Körpe, Surf. Coat. Technol. 201 (2007) 4702. H. Wu, Y. Cheng, L. Li, Z. Chen, H. Wang, Z. Zhang, Appl. Surf. Sci. 253 (2007) 9387. J.S. Lian, G.Y. Li, L.Y. Niu, C.D. Gu, Z.H. Jiang, Q. Jiang, Surf. Coat. Technol. 200 (2006) 5956. J.L. Luo, N. Cui, J. Alloy. Compd. 264 (1998) 299. A. Bautista, Prog. Org. Coat. 28 (1996) 49. R. Supplit, T. Koch, U. Schubert, Corros. Sci. 49 (2007) 3015. A.L.K. Tan, A.M. Soutar, I.F. Annergren, Y.N. Liu, Surf. Coat. Technol. 198 (2005) 478. M.L. Zheludkevich, D.G. Shchukin, K.G. Yasakau, H. Möhwald, M.G.S. Ferreira, Chem. Mater. 19 (2007) 402. Q. Liu, Z. Xu, J.A. Finch, R. Egerton, Chem. Mater. 10 (1998) 3936. Q. Wang, N. Liu, X. Wang, J. Li, X. Zhao, Macromolecules 36 (2003) 5760. A.R. Phain, F.J. Gammel, T. Hack, Surf. Coat. Technol. 201 (2006) 3299. A.R. Phain, F.J. Gammel, T. Hack, H. Haefke, Mater. Corros. 56 (2005) 77. F. Zucchi, V. Grassi, A. Frignani, C. Monticelli, G. TrabanellI, Surf. Coat. Technol. 200 (2006) 4136.

[15] C.F. Cheng, H.H. Cheng, P.C. Cheng, Y.L. Lee, Macromolecules 39 (2006) 7583. [16] A.N. Khramov, V.N. BAlbyshev, N.N. Voevodin, M.S. Donley, Prog. Org. Coat. 47 (2003) 207. [17] A.N. Khramov, V.N. Balbyshev, L.S. Kasten, R.A. Mantz, Thin Solid Films 51 (2006) 174. [18] J. Hu, Q. Li, X. Zhong, Prog. Org. Coat 63 (2008) 13. [19] X. Wang, Y. Guo, G. Lu, H. Yu, L. Jiang, Catal. Today 126 (2007) 369. [20] J. Hu, L. Liu, J. Zhang, C. Cao, Prog. Org. Coat. 58 (2007) 265. [21] C.M. Bertelsen, F.J. Boerio, Prog. Org. Coat. 41 (2001) 239. [22] C.S. Hsu, F. Mansfeld, Corrosion 57 (2001) 747. [23] U. Retter, A. Widmann, K. Siegler, H. Kahlert, J. Electroanal. Chem. 546 (2003) 87. [24] J. Fan, Q. Li, W. Kang, S.Y. Zhang, B. Chen, Mater. Corros. 60 (2009) 438. [25] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, and J.A. Pople, Gaussian, Inc., Pittsburgh PA, 2003. [26] R.G. Parr, W. Yang, Density-functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. [27] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [28] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B. 37 (1988) 785. [29] M.F. Montemor, M.G.S. Ferreira, Electrochim. Acta 52 (2007) 7486.