Corrosion Science 72 (2013) 82–89

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Corrosion Science

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2-Mercaptobenzimidazole as a copper corrosion inhibitor:Part I. Long-term immersion, 3D-profilometry, and electrochemistry

0010-938X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.corsci.2013.03.011

⇑ Tel.: +386 2 2294 447.E-mail address: matjaz.finsgar@um.si

Matjaz Finšgar ⇑University of Maribor, Faculty of Chemistry and Chemical Engineering (UM FKKT), Smetanova ulica 17, 2000 Maribor, Slovenia

a r t i c l e i n f o a b s t r a c t

Article history:Available online 18 March 2013

Keywords:A. CopperB. EISB. PolarizationB. Weight lossC. Neutral inhibition

The high corrosion inhibition effectiveness of 2-mercaptobenzimidazole (MBIH) in 3 wt.% aqueous NaClsolution is reported using long term immersion tests, 3D-profilometry, electrochemical impedance spec-troscopy, and potentiodynamic curve measurements. The high corrosion inhibition performance was pro-ven after 180 days of immersion. The impedance spectra were characterized by two time constantsrelating to charge transfer and finite layer thickness or semi-infinite diffusion of copper ions throughthe surface layer, therefore Cu corrosion in solution containing MBIH follows kinetic-controlled and dif-fusion-controlled processes. Moreover, it is shown that MBIH is a mixed-type inhibitor.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Copper is one of the most important nonferrous materials hav-ing a wide range of uses. Copper-based alloys are used in manyenvironments and applications due to their desirable properties,such as electrical and thermal conductivity, ease of fabricationand joining, mechanical properties, and resistance to biofouling[1]. Copper-based materials are frequently intentionally or unin-tentionally exposed to chloride solutions. However, Cu is suscepti-ble to corrosion in chloride media [2,3]. One approach topreventing Cu corrosion is the use of corrosion inhibitors. Amongthe corrosion inhibitors used in practice, benzotriazole (BTAH)was found to be widely employed for Cu protection in variousmedia [2,4–7] (and the refs. therein). Mercapto compounds are alsopotentially effective Cu corrosion inhibitors [6,8,9]. Different stud-ies using various experimental setups contribute to an understand-ing of how and why organic compounds inhibit the corrosionprocess [2,6]. However, inhibitor action is frequently reported onlyempirically without detailed examination.

Mercapto-imidazole compounds are particularly worth investi-gating as they are potential Cu corrosion inhibitors. One of them is2-mercaptobenzimidazole (MBIH) [10–20], for which some corro-sion studies already exist wherein the research was mainly focusedon the polymerized MBIH surface layer (see below). However, sci-entific interest in the MBIH compound and consequently detailedexamination of its action is still far less than for BTAH [2]. MBIHaction remains relatively unexamined, even though this compoundis a very effective Cu corrosion inhibitor in chloride media, as will

be shown in this work. This study presents new insights into theMBIH corrosion inhibition ability, corrosion processes (especiallyby including diffusion analysis), and the manner of inhibitor action.In order to make a comprehensive investigation, the surfacechemistry of MBIH adsorbed on Cu from 3 wt.% NaCl solution usingX-ray photoelectron spectroscopy will be studied in Part II [21] togain further insight into the molecular binding and models ofadsorption. The acronyms BTAH or BTA and MBIH or MBI are usedto emphasize the N–H hydrogen removal from BTAH or MBIH mol-ecules. This is especially needed for the designation of complexeswith Cu(I) (e.g. Cu(I)–MBIH or Cu(I)–MBI) [2].

Electrochemical polymerization of MBIH is possible under ano-dic potentials, as shown by Perrin and Pagetti [11]. This surfacefilm can successfully protect the Cu surface. If this film is formedin an alkaline water–methanol solution it can subsequently protectCu in 0.5 M NaCl well. Moreover, this poly(MBI) film formed onCu–40Zn by anodic polarization in methanol alkaline solution, pro-tects brass well when it is subsequently immersed in 3% NaCl [22].Trachli et al. [12] showed that polymerization of MBIH on Cu startsat potentials more positive than 0.4 V vs. SCE in a methanol solu-tion of 0.1 M NaOH. However, they also showed that this polymer-ized MBIH layer (pMBIH) had the same protection effectiveness asMBIH without anodic pre-treatment (directly added to the 0.5 MNaCl solution). Zhang et al. [23] studied the corrosion behaviourof Cu in 0.5 M HCl containing MBIH, MBOH and BTAH. Theyshowed that MBIH was the most effective, followed by MBOH,and BTAH. The authors claim that BTAH is less effective in acidicsolutions due to the protonation of the molecule leading toBTAHþ2 . Guo et al. [24] demonstrated that the two-component sys-tem containing MBIH and polybenzimidazole is a coupling agentfor epoxy resin and polyimide coating. They suggested that MBIH

M. Finšgar / Corrosion Science 72 (2013) 82–89 83

fills the surface islands uncovered by polybenzimidazole. Thesecoatings are used as effective Cu corrosion protection layers, whichhave high thermal stability. Synergistic corrosion inhibition effectof polybenzimidazole with MBIH for Cu was also reported by Car-ron et al. [25]. Moreover, synergistic corrosion inhibition effect ofMBIH with sodium dodecylbenzenesulphonate (SDBS) for Cu in0.5 M H2SO4 was reported by Hosseini et al. [26]. The literatureconcerning the MBIH surface structure on the Cu substrate is re-viewed in Part II [21].

The aim of this work is to demonstrate the long-term stabilityand effectiveness of the MBIH compound in 3 wt.% aqueous NaClsolution, i.e. 180 days. Next, topographic analysis of the corrodedsurfaces after the immersion tests is performed. Hitherto, to thebest of the author’s knowledge, no such analysis for MBIH has beenperformed (see above). Moreover, the literature concerning corro-sion analysis using electrochemical impedance spectroscopy (EIS)for MBIH-treated Cu is scarce. Due to this reason, the mechanismof Cu corrosion in solution containing MBIH will be explored by de-tailed analysis of the EIS spectra. Finally, an inhibitor type will beproposed by means of potentiodynamic curve measurements. Allcorrosion tests for inhibited solution will be performed in compar-ison with the non-inhibited solution. The findings in this studyencouraged the author to examine the surface structure of MBIHadsorbed on Cu from 3 wt.% aqueous NaCl solution using X-rayphotoelectron spectroscopy, which is presented in Part II [21].

2. Experimental

2.1. Preparation of solutions and samples

MBIH was dissolved to 1 mM in 3 wt.% aqueous NaCl solution(prepared with Milli-Q water, resistivity 18.2 MO cm). The pH ofthe solution was 5.5. Chadwick and Hashemi [10] reported thatMBIH is only slightly soluble in 0.5 M aqueous NaCl solution. Inthis work a 1 mM concentration of MBIH was employed, which isalready difficult to dissolve and it is close to its solubility limit.Similar was also reported by Popova et al. [27] for 1 M HCl solution.MBIH was purchased from Sigma Aldrich, USA (with a purity98 wt.%) and NaCl from Carlo Erba, Italy (pro analysis). Cu samples(with a 99.999 wt.% Cu) were cut out from 2-mm thick copperplate, temper Half Hard, (Goodfellow, Cambridge, UK) in the shapeof discs 15 mm in diameter (for electrochemical analysis) or rect-angle (for immersion tests and profilometry). Using a circulatingdevice the specimens were ground under a stream of water, start-ing with 1000-grit SiC paper and continued with 2400 and 4000-grit papers (provided by Struers). Between each paper change thesample was rinsed with deionized water to remove the particlesresulting from grinding. Samples were ground in one direction un-til all imperfections were removed and the surface was coveredwith a uniform pattern of scratches. The grinding direction waschanged four times by turning the sample through 90� to minimizeabrasion. Before each analysis, surfaces were checked under themicroscope and if any scratches were still present the preparationprocedure was repeated. After polishing the samples were cleanedultrasonically in a bath of 50% ethanol/50% Milli-Q water (by vol-ume) and afterwards thoroughly rinsed with Milli-Q water [3,28–31].

2.2. Evaluation of corrosion resistance

2.2.1. Immersion tests and 3-D profilometryThe specimens for the immersion tests and topography mea-

surements had dimensions of 50 mm � 20 mm � 2 mm. They wereexposed for 180 days to the stationary non-stirring medium at24 ± 2 �C (laboratory conditions) in 100 mL closed glass vials

containing 3 wt.% NaCl or 3 wt.% NaCl + 1 mM MBIH. A volume of100 mL is commonly used in industrial practice for screeningcorrosion inhibitor effectiveness. On the other hand, for the elec-trochemical measurements a volume of 1 L was employed, whichis a standard amount for electrochemical tests [32]. The specimenswere aligned in such a way that they contacted the glass vial onlyby the four edges to avoid crevice corrosion effect. After exposure,the specimens were rinsed with Milli-Q water, light brushed withfibre-bristle brush (non-metallic bristle) to remove tightly adher-ent corrosion products, rinsed again with Milli-Q water, driedunder a stream of nitrogen and weighed. Six repetitions were madeand as a result an average mass-loss was calculated (outliers werediscarded by Grubbs statistical test) [33]. The error of the balancewas ±1 mg. After the immersion test corroded surface was exam-ined by the profilometer.

A profilometer, model Form Talysurf Series 2 (Taylor-HobsonLtd.) was employed for surface analysis. The instrument has alateral resolution of 1 lm and vertical resolution of about 5 nm.It measures the surface profile in one direction. The topographyof the surface is acquired by combining several measurements inparallel directions 1 lm apart. The data are processed withTalyMap gold 4.1 software to calculate the mean surface roughnessand to create a surface profile. To level the profile, corrections weremade to exclude general geometrical shape and possible measure-ment-induced misfits [3,29].

2.2.2. Electrochemical measurementsPrepared specimens were embedded in a Teflon holder, so that

the area exposed to the solution was 1 cm2. Experiments were per-formed in a three-electrode cell (volume 1 L) closed to air understagnant conditions at 25 �C, controlled by a thermostat. A workingelectrode was embedded in a Teflon holder (PAR) using a Teflon o-ring, in which the area exposed to the solution was 1 cm2. A satu-rated calomel electrode (i.e. SCE, 0.2444 V vs. SHE) was used as areference electrode, along with a platinum mesh as a counter elec-trode. The reference electrode was inserted in the Luggin capillary.All potentials in this work refer to the SCE scale. Measurementswere carried out with a Gamry 600™ potentiostat/galvanostat con-trolled by electrochemical program.

Impedance spectra were obtained in the frequency range from100 kHz to 5 mHz with 10 points per decade and a 10 mV (peakto peak) amplitude of the excitation signal. The impedance spectrawere collected at different immersion times at the open circuit po-tential, Eoc. The impedance data were interpreted on the basis ofequivalent electrical circuits, EEC, by fitting the measured datausing the downhill Simplex procedure to minimize v2 (definedbelow). The electrochemical process was modelled by electricalcircuit elements, such as resistors, capacitors, and Warburgelements.

Potentiodynamic curve measurements were performed after100 h of immersion. Measurements started at �250 mV vs. theopen circuit potential Eoc, and progress with increasing potentialin the anodic direction with a potential scan rate of m = 0.1 mV/s.

3. Results and discussion

3.1. Immersion tests and topography measurements

In order to check the spontaneous corrosion reaction and MBIHcorrosion inhibition effectiveness for Cu in 3 wt.% NaCl, immersiontests were performed for a period of 180 days in non-inhibited andMBIH-inhibited (1 mM) solutions. The inhibitory property of MBIHis indicated by the lower mass loss after the immersion test in theinhibited solution compared to exposure in non-inhibited solution.The inhibition effectiveness, g, was calculated from the average

84 M. Finšgar / Corrosion Science 72 (2013) 82–89

mass loss measured for six Cu samples in pure 3 wt.% NaCl and insolution containing 1 mM MBIH according to Eq. (1) (Dm is theaverage mass loss, where outliers were discarded). The g of theMBIH at 1 mM concentration was calculated to be 87.5%.

g ¼ 100Dmðnon-inhibitedÞ � DmðinhibitedÞ

Dmðnon-inhibitedÞ ð1Þ

After the immersion tests the topography measurements of thetreated Cu specimens were performed by stylus profilometer. Themost valuable information provided by the profilometer is themean surface roughness Sa, which is based on the general surfaceroughness and is calculated according to Eq. (2). Lx and Ly are theacquisition lengths of the surface in the x and y directions, z(x,y)is the height [3,29]. The samples were measured with a 1 mm2 spotsize. The same profile corrections were applied for all measure-ments, using the TalyMap Gold 4.1 software. Two examples ofthe 3D- (left) and 2D-profiles (right) of the treated Cu specimensin non-inhibited and MBIH-inhibited solution are shown in Fig. 1.Measurements were performed for each sample after the immer-sion test and the average Sa values were calculated. For the non-inhibited and MBIH-inhibited 3 wt.% NaCl solutions the averageSa values were calculated to be 1.21 lm and 0.125 lm, respec-tively. This significant difference in the average Sa value clearlyshows that the corrosion action of the chloride ions is much morepronounced in non-inhibited compared to MBIH-inhibited solution(also clearly seen in Fig. 1), indicating high corrosion inhibitioneffectiveness.

Sa ¼1LX

1LY

Z Lx

0

Z Ly

0jzðx; yÞjdxdy ð2Þ

3.2. Electrochemical analysis

3.2.1. Electrochemical impedance spectroscopy (EIS) measurementsEIS measurements of Cu were performed after 10, 50, and 100 h

of immersion at open-circuit potential in 3 wt.% NaCl (Fig. 2) and inthe same solution containing 1 mM MBIH (Figs. 3 and 4). Thepurpose of the quite long immersion time is the need to achievea steady-state condition for the impedance spectra to be valid.

EIS measurements for the non-inhibited solution in Fig. 2 aregiven only for comparison with the MBIH-inhibited solution dueto numerous published EIS data concerning Cu. Recently, VanIngelgem et al. [34] concluded that the best equivalent electricalcircuit (EEC) – a model – to fit the EIS response for Cu in NaCl

Fig. 1. Side and top view of profiles obtained by profilometer of Cu specimens after immMBIH. The centred height scale is shown on the right side (±5 lm).

solution is RX(Q1(R1(Q2(R2(QdlRct)))) or RX(Q1(R1(Qdl(RctW))), whereRX is the uncompensated resistance, Q is the constant phaseelement, R is the resistance, ct and dl stand for the charge transferand double layer, subscripts 1 and 2 represent the two surfacelayers, and W represents the Warburg element for the diffusionprocess (all of which are described below). These models corre-spond to an electrode coated by a porous layer, which includes dif-fusion [35]. To use these models the authors were encouraged bythe literature data concerning Cu in different solutions [36–47]and by the three clearly distinguished relaxation processes seenon the Bode plot (phase angle) [34]. These relaxation processesare also seen in the present case and are designated by the threegrey rectangles in Fig. 2c, therefore the explanation of the Cu cor-rosion process in NaCl solution in Fig. 2 is the same as previouslygiven by Van Ingelgem et al. [34].

For the MBIH-treated Cu in Fig. 3, three distinctive segments areshown in the log |Z| vs. log f and phase angle vs. log f spectra (f isfrequency in Hz, Z is impedance in O cm2). In the higher f region,log |Z| vs. log f reaches a horizontal amplitude and the phase angletends towards 0� with increasing f (Fig. 3b and c). This behaviour istypical of a resistor and corresponds to an uncompensatedresistance RX. The second segment is in the middle f region, wherea linear relationship between log |Z| vs. log f with a slope close to�1 (Fig. 3b) and with the phase angle approaching �90� (Fig. 3c)is observed. This behaviour is typical of a capacitor. A thirdsegment lies in the low f region, where Z is almost independentof f in the log |Z| vs. log f spectrum, reaching the so-called dclimit, when |Z| � Rp � polarization resistance (Fig. 3b),

because jZj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ2

real þ Z2img

qand limf!0ðZrealÞE¼Eoc

¼ Rp þ RX and

limf?0 (Zimg) = 0. Zreal and Zimg are the real and imaginary compo-nents of the impedance. However, the horizontal amplitude atlow f was not completely reached due to the very resistive behav-iour of Cu in inhibited solution or due to the diffusion process(Fig. 3b). In the case of MBIH-treated Cu compared to the uninhib-ited solution, the low f resistive region is transferred by approxi-mately three orders of magnitude to the higher |Z| in the log |Z|vs. log f spectrum, showing high MBIH corrosion inhibition effec-tiveness (Fig. 2b vs. Fig. 3b).

Two relaxations for the MBIH-treated Cu can be identified inFig. 3 and are indicated by the numbered grey squares in theNyquist (Fig. 3a) and Bode phase angle vs. log f spectra (Fig. 3c).To better represent the first relaxation process in the Nyquist plot,related to the charge transfer resistance and double layer capaci-tance in series with the uncompensated resistance (described

ersion for 180 days in 3 wt.% NaCl solution without or with 1 mM concentration of

Fig. 2. (a) Nyquist and (b and c) Bode plots for a Cu in 3 wt.% NaCl measured after 10, 50, and 100 h of immersion. Frequency regions for the three relaxation processes arerepresented by rectangles 1, 2, and 3 in the Figure c.

Fig. 3. (a) Nyquist and (b and c) Bode plots for the Cu in 3 wt.% NaCl containing 1 mM MBIH measured after 10, 50, and 100 h of immersion. EIS data were fitted by employingRX(RctQdl)(RfWQf) EEC, W represents the Warburg element for the semi-infinite diffusion. Frequency regions for the relaxation processes of RctCdl and diffusion are representedby rectangles 1 and 2, respectively.

Fig. 4. (a) Nyquist and (b) Bode plot for the Cu in 3 wt.% NaCl containing 1 mM MBIH measured after 10, 50, and 100 h of immersion. EIS data were fitted by employingRX(RctQdl)(RfOQf) EEC, O represents an element for finite layer diffusion.

Table 1Impedance parameters for Cu in 3 wt.% NaCl containing 1 mM MBIH at 10 h, 50 h, and 100 h of immersion obtained by using the EECs in Fig. 5.

EEC model used forfitting:

v2 RX

(X cm2)Rct

(MX cm2)Qdl

(lX�1 cm�2 sn)n(dl)

Cdl

(lF cm�2)Rf

(MX cm2)Qf

(lX�1 cm�2 sn)n(f)

W(lX�1 cm�2 s1/2)

YO for O(lX�1 cm�2 s1/2)

B(s�1/2)

10 h ImmersionRX(RctQdl)(RfWQf) 3.33 � 10�4 7.8 0.33 55 0.84 – 0.52 1.00 1 2.3 – –RX(RctQdl)(RfOQf) 3.37 � 10�4 7.8 0.33 53 0.84 – 0.51 1.00 1 – 2.3 1.7 � 106

50 h ImmersionRX(RctQdl)(RfWQf) 1.18 � 10�3 7.9 1.30 22 0.87 – 0.61 0.68 1 2.0 – –RX(RctQdl)(RfOQf) 1.11 � 10�3 7.9 1.50 22 0.87 – 0.61 0.67 1 – 2.0 6.9

100 h ImmersionRX(RctQdl)(RfWQf) 1.41 � 10�3 7.7 1.20 19 0.83 – 0.53 0.50 1 1.4 – –RX(RctQdl)(RfOQf) 1.28 � 10�3 7.7 1.20 17 0.83 – 0.50 0.50 1 – 1.4 4.1RX(Qf(Rf(Cdl(RctW)))) 1.31 � 10�3 7.5 0.19 – – 1.6 0.18 0.67 0.96 7.1 – –

M. Finšgar / Corrosion Science 72 (2013) 82–89 85

86 M. Finšgar / Corrosion Science 72 (2013) 82–89

below), a simulation was performed using the RX, Rct, and Qdl datafor 10 h of immersion in Table 1 (the simulated RX(QdlRct) curve inthe grey rectangle 1, Fig. 3a). Simulation was performed for the fre-quency region from 100 kHz to 1 mHz. In the lower frequency re-gion of the Nyquist plot, the �Zimg vs. Zreal curves deviate fromthe Zreal axis (Fig. 3a), indicating that a diffusion process shouldbe taken into account. Moreover, the phase angle at the lowest fre-quencies does not approach 0� (Fig. 3c). Such behaviour indicatesthe diffusion process especially for the curves measured after 50and 100 h of immersion. The EEC model was constructed on thatbasis and is given in Fig. 5a. Two diffusion cases were taken intoaccount, i.e. diffusion through a finite layer thickness (representedby the O element, sometimes named Porous bounded Warburg)and semi-infinite diffusion (represented by the W element, some-times named Infinite Warburg). The same models have beenemployed before by Metikoš-Hukovic et al. [48,49], Babic et al.[50,51], and Hayon et al. [52] for Cu (or its alloys) treated withdifferent inhibitors. For the sake of confidence, beside this model,the following EECs were also used for fitting: R(Q(R(QR))),R(Q(RW)), R(Q(RO)), R(QR(QR)), R(QR(QR)(QR)), R(Q(R(Q(R(QR))))),R(Q(R (Q(RO)))), R(QR)W, R(QR)O, R(QR)(QR), R(QR)(QR)W, R(QR)(QR)O, R(Q(R(QR)))(QR), R(Q(R(Q(RW)))), R(Q(R(Q(RW))))(QR),R(Q(R(Q (R(Q(RW)))))), and R(Q(R(Q(RQ)))). However, the fittingprocedure using these models reported higher error judged bythe goodness of fit, v2 (Eq. (3)), compared to the model in Fig. 5a.

Goodness of fit is defined as:

v2 ¼XN

i¼1

½ðai � Z0iÞ2 þ ðbi � Z00i Þ

2�r2

i

ri ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

i � b2i

q ð3Þ

where the experimental data point is [xi, ai, bi], the calculated datapoint is [xi, Z0i, Z00i ], r is a fraction of the modulus and determined asv2

min � r2, and N is the number of the data points. A lower v2 valuerepresents a better fit.

As mentioned above, the model in Fig. 5a consists of two timeconstants in series with the uncompensated resistance RX. A largepart of RX comes from solution resistance. The first time constantin the high frequency region (RctQdl) represents the charge-transferprocess of copper dissolution, where Rct describes thecharge-transfer resistance and Qdl the constant phase element(CPE) relating to the double layer capacitor. The impedance ofthe CPE is described as:

ZðCPEÞ ¼ ðQðjxÞnÞ�1 ð4Þ

where Q is the frequency-independent real constant, j is the imag-inary number (j2 = �1), x is the angular frequency (x = 2pf), and n

Fig. 5. RX(RctQdl)(RfO(or W)Qf) and RX(Qf(Rf(Cdl(RctW)))) models used to fit imped-ance spectra.

is the CPE power. The phase angle of the CPE, a, is calculated asn = a/(p/2). The factor n is an adjustable parameter in the fittingprocedure. When n – 1, the behaviour of the system has beenattributed to the surface heterogeneity [53,54] or to continuouslydistributed time constants for the charge-transfer reactions [55–59]. The CPE only describes an ideal capacitor when n = 1. Moreover,on real cells the ‘‘double layer capacitor’’ often behaves like a CPE,not a capacitor and its n is usually less than 1. It is probably bestto treat n as an empirical constant with no real physical basis de-spite the proposed theories of CPE origin, which account for thenon-ideal behaviour. In many cases, the CPE element is employedonly for fitting impedance data.

The impedance of the first time constant Z1 is thus:

Z1 ¼Rct

1þ Q dlðjxÞnRctð5Þ

The process describing the first time constant occurs on thesubstrate-electrolyte interface covered by the MBIH, where thesurface layer comprises pockets filled with an electrolyte solution(Fig. 5a). This electrolyte solution can be very different than thebulk solution outside of the MBIH surface layer. The interface be-tween this pocket of solution and the metal is modelled as a doublelayer capacitance (using Qdl) in parallel with a kinetically con-trolled charge transfer reaction (Fig. 5a).

The second time constant in the low frequency region (Rf(O orW)Qf) results from the diffusion of copper ions through the surfacelayer. Qf represents the CPE of the surface layer (as in a very thincoating), Rf is the resistance of the ion conducting paths that devel-oped in the surface layer (the electrolyte which is different fromthat in the bulk solution), and O or W are the elements for the finiteand semi-infinite (unrestricted) layer thickness diffusion, respec-tively. O in Table 1 is given in the admittance representation(YO). The impedance response for finite length diffusion is:

ZD ¼ ZOðjxÞ�0:5 tanh½BðjxÞ0:5� ð6Þ

where

B ¼ dffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=Df Þ

pð7Þ

Impedance ZO = 1/YO (Y � admittance), Df is the diffusion coeffi-cient of Cu ions and d the surface layer thickness [49]. B character-izes the time it takes for ions to diffuse through the surface layer.On the other hand, the impedance for semi-infinite diffusion canbe described by Eq. (4) when n = ½.

The impedance of the second time constant in the case of finitelength thickness layer diffusion is thus:

Z2 ¼Rf

1þ Rf Q fðjxÞn þ Rf YOðjxÞ0:5 coth½BðjxÞ0:5�ð8Þ

And the total impedance for the RX(RctQdl)(RfOQf) model is de-fined as:

Ztotal ¼ RX þRct

1þ Q dlðjxÞnRct

þ Rf

1þ Rf Q f ðjxÞn þ Rf YOðjxÞ0:5 coth½BðjxÞ0:5�ð9Þ

On the other hand, the impedance of the second time constantincluding semi-infinite diffusion is:

Z2 ¼Rf

1þ Rf Q fðjxÞn þ Rf WðjxÞ0:5ð10Þ

And the total impedance for the RX(RctQdl)(RfWQf) model is de-fined as:

Ztotal ¼ RX þRct

1þ Q dlðjxÞnRctþ Rf

1þ Rf Q fðjxÞn þ Rf WðjxÞ0:5ð11Þ

M. Finšgar / Corrosion Science 72 (2013) 82–89 87

Measured and simulated plots obtained from a computer-basedequivalent electrical circuit are given in Fig. 3a and c for the RX

(RctQdl)(RfWQf) model and in Fig. 4a and c for the RX

(RctQdl)(RfOQf) model. The fitting procedure gave quantitative re-sults of the impedance data collected in Table 1 for the models con-structed in Fig. 5a.

The decrease in double layer capacitance for the inhibited com-pared to non-inhibited solution is usually explained by the dis-placement of water molecules from the surface due to adsorptionof inhibitor molecules [26,60–63]. In the present case, the Qdl valuedecreases from 10 h to 50 h and from 50 h to 100 h, indicating thatthe adsorption of the MBIH molecules is on-going up to 100 h ofimmersion. Moreover, the power of CPE for the double layer (then(dl) value in Table 1) is between 0.83 and 0.87, indicating a non-ideal capacitor at the metal-solution interface. This confirms thestatement above that the ‘‘double layer capacitor’’ often behavesas a CPE, not like a capacitor, when attempting to obtain quantita-tive results.

The value of Rct gives information about the corrosion rate andconsequently inhibitor performance. Charge is transferred whenelectrons enter the metal and metal ions diffuse into the electro-lyte. The higher the Rct value is, the greater the resistive behaviourof the metal, implying a more effective inhibitor. This value in-creased significantly from 10 to 50 h, and was similar for 50 and100 h, indicating the time-dependent inhibition effectiveness ofthe MBIH. This is most likely connected with the time needed tobuild-up a protective surface layer.

The capacitance of the parallel plate condenser is:

C ¼ ee0Ad

ð12Þ

where e is the dielectric constant of the surface layer, e0 is thedielectric constant of the free space, A is the exposed area of the testelectrode, and d is the thickness of the surface layer (coating). Bysupposing that the MBIH surface layer behaves as a parallel platecondenser, the decrease in Qf (C = Q, when n = 1) by increasing theimmersion time from 10 to 100 h would correspond to the thicken-ing of this surface layer. Moreover, the power of the CPE (the n(f)

value in Table 1) representing the surface layer is 1 at 10, 50, and100 h of immersion, which shows that it is an ideal capacitor[48,49].

The diffusion process will be explained on the basis of the good-ness of the fitting procedure. As described above, two elementsrepresenting diffusion were employed for the fitting procedure,i.e. diffusion through finite (O) and semi-infinite (W) layers.Figs. 3a and c and 4a and b show measured and corresponding fit-ted curves by employing RX(RctQdl)(RfWQf) and RX(RctQdl)(RfOQf)models, respectively. Based on these figures it is difficult to judgethe goodness of the fitting procedure because both fitted curvesmatch closely at all immersion times. The B value given in Table 1for 10 h of immersion is high when employing the RX(RctQdl)(RfOQf)model for fitting. This indicates that ionic species have a longdiffusion length or a low diffusion coefficient (Eq. (7)). However,this is less likely to be true and the second diffusion process shouldbe considered by including W. Moreover, the lower v2 value in Ta-ble 1 for the semi-infinite diffusion � (RX(RctQdl)(RfWQf) – showsthat this model describes the corrosion process after 10 h ofimmersion better compared to the finite layer diffusion model.On the other hand, at 50 and 100 h of immersion, by using thefinite layer diffusion model (RX(RctQdl)(RfOQf) the v2 is lower com-pared to v2 for (RX(RctQdl)(RfWQf). These findings could be ex-plained by the initial formation of the surface layer in the periodup to 10 h of immersion, which is porous and the movement ofthe ions (diffusion) through this layer in not aggravated as muchas in the later stage (after 50 and 100 h), when these pores closeand a denser surface layer is formed. This would also confirm the

Rct values which are lower at 10 h compared to at 50 and 100 hof immersion. Therefore, the build-up of the corrosion protectiveMBIH surface layer is time dependent.

The impedance of the diffusion process basically describes thediffusion speed. The higher the impedance is, the slower the diffu-sion process. On the other hand, impedance is inversely propor-tional to admittance – therefore, to the YO and W values. Thehigher these values are, the faster diffusion is. As seen from Table 1,these values decrease with time, indicating the time dependentbuild-up of the more protective surface layer, which decreasesdiffusion speed vs. time, i.e. diffusion at 100 h is slower comparedto at 50 h and 10 h. This is also seen for the B values at 50 h and100 h, which characterize the time it takes for ions to diffusethrough the surface layer (but not for the measurement after10 h, where the W element better describes diffusion).

For measurement after 100 h of immersion, the goodness of thefit using the RX(Qf(Rf(Cdl(RctW)))) model is in the same range as forRX(RctQdl)(RfWQf). The former model describes the porous surfacelayer, as depicted in Fig. 5b [35]. In this case, Rf is the electrolyteresistance in the pore, where the composition is different than thatin the bulk solution. Moreover, the electrochemical reactions occuronly on the exposed surface at the end of the pore. The insulatingpart – MBIH-coated Cu – is considered to be a capacitor(represented as Qf). The fitting procedure according to this modelcompared to RX(RctQdl)(RfWQf) gave an order of magnitude lowervalues for Rct and Rf and an order of magnitude higher values forCdl, whereas W remains within the same order of magnitude andQf is very close for the two models used in the fitting procedure(Fig. 5). It has to be pointed out that fitting using theRX(Qf(Rf(Cdl (RctW)))) model for the measurements at 10 and 50 hof immersion gave much higher v2 compared to the v2 when usingRX(RctQdl)(RfWQf) and RX(RctQdl)(RfOQf). On that basis, it is less likelythat the surface layer would rearrange from that in Fig. 5a to that inFig. 5b after prolonging the immersion time from 50 h to 100 h.

It has to be pointed out that some v2 values in Table 1 are closewhen employing O and W elements. Therefore, no exact descrip-tion of the diffusion process and EEC model exists, leaving both op-tions probable.

One could determine the thickness of the MBIH surface layerafter, for example, 50 or 100 h immersion, using different tech-niques (e.g. ellipsometry, IR spectroscopy [64], and detailed analy-sis of the background in the XPS spectra by the Tougaard method[28]). Using this information, a diffusion coefficient can be calcu-lated by employing Eq. (7) and the B values reported in Table 1for diffusion through the finite thickness layer (not for 10 h ofimmersion, where semi-infinite diffusion better describes the cor-rosion process, see above). Moreover, by assuming that this surfacelayer behaves like a parallel plate condenser, it is possible to calcu-late e – the dielectric constant of the MBIH surface layer – by usingEq. (12). This approach has been used before by Metikoš-Hukovicet al. [48,49], Babic et al. [50,51], and Hayon et al. [52]. However,for MBIH this will remain an open subject for subsequent studies.

3.2.2. Potentiodynamic curve measurementsPotentiodynamic curves for Cu in 3 wt.% NaCl solution were

measured in the absence and presence of 1 mM MBIH after 100 hof immersion and are presented in Fig. 6. The purpose of the quitelong immersion time before conducting a potentiodynamic scan isso that the corrosion process can achieve a steady-state [65]. Ascan rate of 0.1 mV/s was employed in order to avoid the effectsof capacitance and so that the current/voltage relationship onlyreflects the interfacial corrosion process at every potential of thepolarization scan [65,66].

Dissolved oxygen and hydrogen ions are the only reducible spe-cies in the solutions. At the potentials where the measurements ofthe potentiodynamic curves were initiated (around �250 mV vs.

Fig. 6. Potentiodynamic curves measured after 100 h of immersion in 3 wt.% NaClwith or without 1 mM MBIH, m = 0.1 mV/s.

88 M. Finšgar / Corrosion Science 72 (2013) 82–89

Eoc), hydrogen evolution primarily determines the cathodic polari-zation behaviour. At more positive potentials, closer to Ecorr, thebehaviour is determined by the mass-transport controlled reduc-tion of dissolved oxygen. Above Ecorr, it was proposed that anodicdissolution of the Cu electrode in chloride media occurs at activepotentials in the absence of copper oxide formation [67]. In theactive region the anodic dissolution of copper is under mixed con-trol by the electrodissolution and chemical reactions (Eqs. (13) and(14), respectively) and the diffusion of soluble CuCl�2 from the outerHelmholz plane into the bulk solution [68,69]. The linear relation-ship between the potential and log (i) (i is the current density) inthe active region ceases when CuCl�2 activity exceeds its solubilityequilibrium and the formation of CuCl film starts to predominate[69]. Accordingly, at a potential of �51 mV the current peak inFigs. 6 for pure 3 wt.% NaCl is observed.

Cuþ Cl�¢ CuClads þ e� ð13Þ

CuClads þ Cl�¢ CuCl�2 ð14Þ

When 1 mM MBIH was added to the 3 wt.% NaCl solution asignificant reduction in the cathodic current density is observed,together with a shift of Ecorr in the anodic direction of about+20 mV (Fig. 6). In the anodic part of the polarization curves asignificant reduction in the anodic current density is also observed.This behaviour shows that MBIH acts as a very effective mixed-type inhibitor.

4. Conclusions

Corrosion inhibition of Cu in 3 wt.% aqueous NaCl solution by2-mercaptobenzimidazole (MBIH) was studied using immersiontests, 3D-profilometer, and electrochemical techniques. The mainfindings are as follows:

1. MBIH inhibition effectiveness calculated on the basis of a 180-day immersion test was 87.5%. After the immersion test theCu surface was significantly rougher compared to an inhibitedsolution, as shown by the 3D-profilometric measurements.

2. The impedance spectra at various immersion times were ana-lysed according to two time constants, the first one relating tothe charge transfer process and double layer capacitance, whilethe second includes mass transport of copper ions through thepartly resistive and capacitive MBIH surface layer. Therefore, Cucorrosion in 3 wt.% NaCl solution containing MBIH followskinetic-controlled and diffusion-controlled processes.

3. After 10 h of immersion the diffusion process was bestdescribed by semi-infinite diffusion. After 50 h and 100 h thestructure of the surface layer rearranged – the ion conductingpaths closed and aggravated movement – and the diffusionprocess is best described by diffusion through the finite lengththickness MBIH surface layer. Moreover, it was shown that thebuild-up of the protective surface layer and its inhibitioneffectiveness is time dependent.

4. Potentiodynamic curve measurements after 100 h of immersionshow that MBIH is an effective mixed-type inhibitor.

5. This study unambiguously shows the high inhibition ability ofMBIH in 3 wt.% NaCl. In Part II of this study, MBIH molecularbinding and models of adsorption on Cu from 3 wt.% NaCl solu-tion will be presented.

Acknowledgements

The author would like to thank Dr. Peter Panjan and Dr. DarinkaKek-Merl for their valuable discussions.

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