copper dissolution in ammonia solutions: identification of the mechanism at low overpotentials

Journal of The Electrochemical Society, 156 �7� C222-C229 �2009�C222

Copper Dissolution in Ammonia Solutions: Identificationof the Mechanism at Low OverpotentialsDušan Strmčnik,a Miran Gaberšček,a,*,z Boris Pihlar,b Drago Kočar,b andJanko Jamnika

aNational Institute of Chemistry, SI-1000 Ljubljana, SloveniabFaculty of Chemistry and Chemical Technology, University of Ljubljana, SI-1000, Ljubljana, Slovenia

Corrosion of copper in ammonia solutions is significantly affected by a large number of parameters such as the concentration ofammonia, pH, temperature, concentration of Cu2+, the presence/absence of dissolved oxygen, the chemical nature, and theconcentration of the anion but also by selected corrosion products, in particular, Cu+, various adsorbed intermediates, and finallypassive films. In the present work we try to elucidate the corrosion of copper in a wide potential window �from �1.4 to 0 vsmercury/mercurous sulfate electrode �MSE�� and in a broad range of concentrations of various species �0.2–3.5 mol/L NH3, 0–0.1mol/L Cu2+, pH 10–12.5�. Then, we focus on the first peak occurring within �1.0 to �0.6 V vs MSE with the aim to explain theunderlying mechanism. We show that the reaction order of the dissolution reaction with respect to ammonia is 2. We further showthat using conventional electrochemical methods in combination with an optical method �scanning electron microscopy�, atwo-step �electrochemical-chemical� reaction yielding Cu2O is identified as the most likely passivation mechanism, consistent withprevious assumptions by other authors. Finally, we confirm this mechanism by performing impedance analysis at various experi-mental conditions.© 2009 The Electrochemical Society. �DOI: 10.1149/1.3123289� All rights reserved.

0013-4651/2009/156�7�/C222/8/$25.00 © The Electrochemical Society

Manuscript submitted November 9, 2008; revised manuscript received April 2, 2009. Published May 5, 2009.

The electrochemical behavior of copper in ammonia-containingsolutions is important in various industrial processes, such as etch-ing of printed circuit boards, cleaning of copper surfaces, and elec-trodeposition of copper. It is also important for understanding cor-rosion processes in copper alloys, e.g., brass.

The thermodynamics of the Cu–NH3–H2O system has been in-vestigated by several authors.1-6 The calculated potential-pH dia-grams for this system have been used to interpret the occurrence ofcorrosion products on copper and brass. There has been some con-troversy regarding the stability regions of copper�I� and copper�II�oxides. The results have been summarized and commented on byTromans,7 who pointed out that ammonia had an activity greaterthan 1 in concentrated solutions, which led to slightly modified sta-bility domains of copper species in the potential-pH diagrams.Halpern8 investigated the corrosion rate in aerated ammonia solu-tions of different concentrations. He proposed the following corro-sion reaction

Cu + 4NH3�aq� + 1/2 O2 + H2O → Cu�NH3�42+ + 2 OH− �1�

which, presumably, proceeded through the formation of a very thinoxide film, followed by the formation of an activation complex�NH3–Cu2+–O2−�. Sedzimir and Bujanska9 investigated the influ-ence of ammonia concentration and temperature on corrosion veloc-ity using a rotating disk method. The proposed net corrosion reac-tion was

Cu + Cu�NH3�42+ → 2Cu�NH3�2

+ �2�They concluded that this reaction was under mixed control. They

also claimed that ammonia concentration did not influence the rateof surface reaction. Extensive work has been done by Khobotova etal.,10-13 who investigated products of the positive-going and chemi-cal dissolution of copper in a Cu�NH3�4Cl2 medium. They observeddifferent corrosion products, including CuCl, Cu2O, Cu�OH�2, andCuO. Darchen and Drissi-Daoudi14 also reported selected electro-chemical investigations of copper in ammonia/chloride media.

Despite the quite extensive work performed on this system, nei-ther the detailed corrosion mechanism nor the mechanism of disso-lution processes, at potentials different from the corrosion potential,has been explained. One of the reasons could be that the positive-going part of the corrosion reaction is very fast. It is therefore very

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important to use a very concentrated supporting electrolyte; other-wise the solution resistance completely prevails, thus blurring theinformation about the reaction mechanism.

In this paper, we show that in solutions with low ionic strengththe rate-determining step of the dissolution reaction is the migrationof ions in the electrolyte. The second reason for the unclear pictureconcerning the corrosion mechanism in this system is that, despitethe relatively simple composition of the solution, the corrosion issignificantly affected by a surprisingly large number of parameterssuch as the concentration of ammonia, pH, temperature, concentra-tion of Cu2+, the presence/absence of dissolved oxygen, and eventhe chemical nature and the concentration of the anion. The corro-sion is markedly influenced by selected corrosion products, in par-ticular, Cu+, various adsorbed intermediates, and finally passivefilms. The third reason for the poor understanding of corrosionmechanism in this system is probably the relatively narrow concen-tration window explored by various authors. For example, using anammonia concentration window of 4–6.5 mol/L, Sedzimir andBujanska9 came to a conclusion that the surface reaction was inde-pendent of the ammonia concentration. As shown in the presentwork, in which a much wider ammonia concentration window isused, the concentration of ammonia plays a very important role inthe rate of surface reaction.

The main aim of the present work is thus to get a clearer generalpicture about the corrosion behavior of copper in ammonia solu-tions. We investigate the electrochemical behavior of copper in awide potential window �from �1.4 to 0 vs mercury/mercurous sul-fate electrode �MSE�� and in a broad range of concentrations ofvarious species �0.2–3.5 mol/L NH3, 0–0.1 mol/L Cu2+, pH 10–12.5�. After that we focus on the first peak occurring within �1.0 to�0.6 V vs MSE with the aim to elucidate the underlying mecha-nism. In pursuing this goal, potentiodynamic measurements, an op-tical method �scanning electron microscopy�, and finally a detailedelectrochemical impedance study are used.

Experimental

For all electrochemical measurements, a standard three-electrodesetup was used. The working electrode was a copper disk electrodewith a diameter of 1 mm embedded into a propylene stick and prop-erly sealed at contacts. The electrode was polished with a 1200 SiCemery paper and with 5 and 0.5 �m alumina, then sonicated inacetone and Milli-Q water. The counter electrode was a platinumwire. The reference electrode was a Radiometer Analytical MSEwith the measured potential of 0.70 V vs standard hydrogen elec-trode. All measurements were performed on a PAR 283 potentiostat/galvanostat coupled with a Solartron SI-1260 impedance/gain-phase

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C223Journal of The Electrochemical Society, 156 �7� C222-C229 �2009� C223

analyzer. Before each experiment, the electrode was conditioned at�1.4 V vs MSE to reduce any oxide present on the surface. Imped-ance spectra were recorded in the frequency range from 65,000 to0.01 Hz.

The solutions were prepared using Mill-Q water, Na2SO4 �Fluka,purified agent, p.a.�, 25% ammonia �Merck p.a.�, �NH4�2SO4�Merck p.a.�, and CuSO4 · 5H2O �Merck p.a.�. 1.25 M Na2SO4 wasused as a supporting electrolyte. In experiments at low ionicstrength, the concentration of Na2SO4 was 0.0125 M. The ammoniaconcentration was between 0 and 3.5 M. The Cu2+ concentrationwas between 0 and 0.1 M. The pH values were adjusted with theaddition of �NH4�2SO4 to NH3 solution and were between 12.5 and11. pH was measured with a Metrohm 744 pH meter. If not explic-itly stated otherwise, in each experiment only one parameter waschanged while keeping all the others constant. In particular, forvariation in NH3 concentration, the pH and the supporting electro-lyte concentration, as well as all the other experimental parameters,were held constant.

Results and Discussion

A typical polarization curve, measured with a scan rate of 0.1mV/s in the potential window from �1.4 to 0 vs MSE, is shown inFig. 1. According to the Pourbaix diagrams for theCu–NH3–H2O–SO4

2− system found in Ref. 7, one would expect thesteady-state curve to essentially contain a single peak correspondingto a competition of two processes, i.e., oxidation of Cu to Cu�NH3�2

+

and oxidation of Cu�NH3�2+ to CuO. From the polarization curve,

however, we observe four peaks, suggesting that the nature of theunderlying process�es� is more complex than expected from theknown Pourbaix diagrams. A reason for this can be that the disso-lution of copper involves additional, kinetically stable, surface struc-tures that cannot be predicted from the thermodynamic data. An-other possibility is that the thermodynamic data are inaccurate orincomplete. In the present work we wish to identify as accurately aspossible at least some of the passivation processes.

Potentiodynamic measurements.— A typical cyclic voltammo-gram for the Cu–NH3–H2O–SO4

2− system recorded at a sweep rateof 50 mV/s is shown in Fig. 2. The features observed in the slowpotentiodynamic scan �Fig. 1� are now much more pronounced. Letus designate the peaks obtained in the positive-going direction withthe letter “A” and those obtained in the negative-going directionwith the letter “C.” The first shoulder �A1� which appears at �0.85V is followed by the peak itself at �0.77 V �A2�. Peak A3 appearsat �0.5 V with a subsequent shoulder at �0.3 V �A4�. An interest-

Figure 1. A typical slow potential scan of the Cu–NH3–H2O–SO42− system

from �1.4 to 0 V vs MSE. Concentration of NH3 = 1 M, concentration ofNa2SO4 = 1.25 M, and pH 11.4. Scan rate: 0.1 mV/s starting at �1.4 V.


ing feature of this cyclic voltammogram are the positive-currentpeaks obtained in the negative-going direction, such as Ac5 at �0.5V and a smaller one �Ac6� at �0.75 V. These are then followed byseveral “true” negative-going peaks: C1 at �0.85 V, C2 at �0.98 V,and sometimes �depending on the pH� C3 at �1.1 V. For compari-son, a cyclic voltammogram measured in a solution with a lowsupporting electrolyte concentration �0.0125 mol/L� is also pre-sented in Fig. 2 �dotted line�. The linear curve observed above ca.�1.1 V �vs MSE� clearly reflects the presence of an ohmic resis-tance which, as found in separate measurements using impedancespectroscopy �not shown�, exactly coincides with the bulk solutionresistance. This result suggests that if the concentration of the sup-porting electrolyte is not high enough �e.g., below ca. 1 M�, therate-determining step for the corrosion is the migration of ionsacross the electrolyte �causing a rather big ohmic drop� rather thanthe rate of corrosion reaction itself. To some extent, this probablyexplains the significant variation in previous kinetic results wheredifferent �including quite low� concentrations were used.9-14

We focus on the first peak �A2� and its shoulder �A1�. First,while A2 was clearly detected at all experimental conditions of in-terest, the occurrence of A1 depended significantly on the experi-mental conditions, such as scan rate, pH, ionic strength, etc. Figure3 shows the positive-going part of cyclic voltammograms between�1.4 and �0.6 V vs MSE. The effect of ammonia concentrationfrom 0.25 to 3.5 mol/L is shown in the graphs Fig. 3a and b whilethe effect of pH variation from 11.4 to 12.5 is displayed in thegraphs in Fig. 3c and d. Contrary to the results of Sedzimir andBujanska,9 who found that changing the ammonia concentrationfrom 4 to 6.5 mol/L had no effect on the surface reaction, we findthat ammonia has a significant effect on the rate of positive-goingreaction. Here, we must stress that Sedzimir and Bujanska measuredthe net corrosion reaction where the rate-determining step was mostlikely diffusion of Cu2+ to the electrode surface rather than the elec-trochemical reaction itself. In a separate set of experiments �notshown�, we found no dependence of the positive-going electro-chemical reaction on the concentration of Cu2+. Conversely, asshown in Fig. 3d, pH has a pronounced effect on the peak height andposition. Combining these data, we propose that peak A2 with itsshoulder A1 corresponds to the following reactions

Cu + 2NH3 → Cu�NH3�2+ + e− �3�

Figure 2. Two cyclic voltammograms for the Cu–NH3–H2O–SO42− system

recorded at a sweep rate of 50 mV/s. Solid line: High ionic strength �1.25 MNa2SO4�; dotted line: Low ionic strength �0.0125 M Na2SO4�. Other condi-tions are the same as in Fig. 1. A, positive-going peaks; Ac, positive-goingpeaks appearing in the negative-going direction; and C, negative-goingpeaks.




C224 Journal of The Electrochemical Society, 156 �7� C222-C229 �2009�C224

2Cu + H2O → Cu2O + 2H+ + 2e− �4�both simultaneously proceeding on the electrode surface.

Some of the possible reaction pathways for these two reactionsare as follows

Cu → Cu+ + e−

Cu+ + NH3 → Cu�NH3�+

Cu�NH3�+ + NH3 → Cu�NH3�2+ �5�

Cu + NH3 → Cu�NH3�+ + e−

Cu�NH3�+ + NH3 → Cu�NH3�2+ �6�

Cu + 2NH3 → Cu�NH3�2+ + e− �7�

Cu → Cu+ + e−

2Cu+ + 2OH− → Cu2O + H2O �8�

Cu − H2Oads → Cu − OH + H+ + e−

2Cu − OH → Cu2O + H2O �9�

2Cu − H2Oads → Cu2O + 2H+ + 2e− �10�First, we consider in some detail the dissolution Reaction 3. The

measured steady-state potentiodynamic curves �measured at 0.1mV/s� for copper in solutions of different ammonia concentrationsare shown in Fig. 4a. Assuming that the steady-state current re-sponse is mainly due to Reaction 3, and using the Tafel equation forthe positive-going branch, we find for the transfer coefficient for thepositive-going branch, �, a value of 0.68 � 0.02. The slope of thelog I0 vs log�cNH3

� plot �Fig. 4b� gives the order of reaction withrespect to ammonia according to15

� log I0

� log cNH3

= ZNH3+ ��NH3

z

n�11�

where I0 is the exchange current density, cNH3is the concentration of

NH3, ZNH3is the reaction order with respect to NH3, � is the stoi-

chiometric factor for ammonia in Reaction 3, z is the number ofelectrons transferred in the rate-determining step, and n is the num-

Figure 3. Positive-going parts of cyclic voltammograms between �1.4 and�0.6 V vs MSE taken ��a� and �b�� for large concentration variations inammonia �0.25–3.5 mol/L� and ��c� and �d�� for different pH values �11.4–12.5�. In graphs �b� and �d� the values of current peaks as functions of therespective variables are presented. In graph �d� the peak position as a func-tion of pH is displayed �open circles, right y-axis�.


ber of electrons transferred in the overall reaction. Inserting thevalue of � obtained from the Tafel slope into Eq. 11, the value ofZNH3

is 2.1 � 0.1. It is reasonable to assume that the reaction orderwith respect to ammonia is 2, which means that the most likelyreaction pathway for the dissolution reaction is Eq. 7.

Reaction 4 is the formation of copper�I� oxide on the electrodesurface which partly blocks Reaction 3, as naturally deduced fromthe occurrence of peak A2. Formation of such a passive film on theelectrode surface is well documented in the literature dealing withthe electrochemical behavior of copper in neutral and basicsolutions.16-20 A common agreement is that the oxide formation oncopper proceeds via Reaction 9. However, as mentioned before, ac-cording to the corresponding Pourbaix diagram,7 the occurrence ofan oxide in the present system is unexpected. Nevertheless, that thepeak must be oxide related, and, in particular, independent of thepresence of ammonia, can be further extracted from measurementsof cyclic voltammograms in the absence of ammonia, covering a pHrange of 11–12, as shown in Fig. 5. Indeed, both the position of thepeaks and their shift with changing pH coincide with analogousgraphs recorded in the presence of ammonia �cf. Fig. 3�. Anothersimilarity between the curves recorded in the presence and absenceof ammonia is that the peak �A2� is always preceded by a shoulder�A1�. The shoulder is well expressed at pH 11 but almost disappearsat pH 12 as the peak is shifted to more negative potentials. Except inthe experiments published by Castro Luna de Medina et al.20 wherethe observed cyclic voltammogram in 0.01 M NaOH+ 0.1 NaClO also exhibited a shoulderlike response before the ox-

Figure 4. �a� Steady-state potentiodynamic curves for copper in solutions ofdifferent ammonia concentrations. �b� A log I0 vs log�cNH3

� plot �point� anda linear fit �solid line� �see also Eq. 11�.

4





ide peak, to our knowledge no other authors have observed a similareffect. Again, it is necessary to stress that the appearance of shoulderA1 greatly varied with the conditions, and even at the same condi-tions, it did not necessarily appear at exactly the same potential.From the results shown above, it is not possible to conclude whetherthe shoulder is oxide related or should be ascribed to an effect of thesupporting electrolyte. In either case, its observable irreproducibilitycould be ascribed to the significant surface roughness developed as aconsequence of quite high dissolution current density and to othersurface nonuniformities. We hoped that a deeper insight into thepassivation mechanism could be gained using impedance spectros-copy measured at various electrode potentials.

Impedance spectroscopy measurements.— The values of elec-trode potential at which the impedance spectra were recorded areindicated in Fig. 6a as circles. The corresponding impedance spectraare displayed in Fig. 6b. Both the shape and the magnitude of im-pedance spectra vary significantly with the electrode potential. Itwas nicely shown by Keddam et al.21,22 on the example of ironcorrosion/passivation that such large variations in impedance behav-ior could be effectively used for discrimination between differentpossible reaction mechanisms. In the present case we adopt a similarapproach.

A closer inspection of the measured impedance spectra in Fig. 6reveals the presence of three distinctly different relaxation times.For example, graphs 4, 5, and 6 consist of a high frequency arc,followed by a medium frequency “inductive” loop which continuesinto a third, again “capacitive,” arc at lowest frequencies. The ca-pacitance associated with the high frequency arc is on the order of10–50 �F cm−2 and is thus ascribed to the double-layercapacitance.21,22 The corresponding high frequency resistance is dueto a dissolution reaction, e.g., Eq. 7. According to the mechanismproposed above, one of the other two relaxation times �medium andlow frequency loops/arcs� is supposed to be due to Reaction 9.There remains a third process that has not been clearly identified inthe potentiodynamic measurements, although we have detected apositive-going shoulder of unknown origin �see the discussionabove�. Based on the fact that the impedance spectra contain theso-called inductive feature, we propose the introduction of an arbi-trary adsorbed species Aads with the desired properties. This speciesneed not enter the corrosion/passivation reaction as such; it can beviewed as an independent “spectator” originating from the electro-lyte and covering part of the active surface. Simultaneously, we

Figure 5. �Color online� Cyclic voltammograms for the Cu–H2O–SO42− sys-

tem recorded in the absence of ammonia at three pH values. Scan rate: 50mV/s.


propose that the second step in Reaction 9 is much faster than thefirst step. This way, the model to be considered for impedance analy-sis consists of the following reactions

Figure 6. �Color online� �a� Quasi-steady-state current–potential curve forthe Cu–NH3–SO4

2− system recorded at a potential scan rate of 0.1 mV/s.Circles denote conditions at which the impedance spectra shown were re-corded. �b� Impedance spectra recorded at selected points on the steady-statecurve. The legend shows potentials of these points in V vs SCE. For easieridentification, the graphs are labeled with numbers from 1 to 9. Frequencyrange: 65,000–0.01 Hz. Amplitude: 10 mV. Electrode surface area:0.00785 cm2. Solution pH: 12. Concentration of NH3: 1 M. For clarity,selected spectra from graph �b� are magnified in graph �c�.





Cu + 2NH3�k−1

k1

Cu�NH3�2+ + e− �12�

Cu + H2O�k−2

k2

Cu − OHads + H+ + e− �13�

Figure 7. �Color online� Comparison of calculated �dashed curves� and mea-sured �solid curves� impedance spectra for the Cu–NH3–H2O–SO4

2− system.The legend shows the steady-state potentials in V vs SCE. For clarity, theeight pairs of impedance spectra are displayed in three separate graphs, �a�–�c�. The values of calculated rate constants �in cm2 s−1� are as follows:k0,1 = 7.0 � 10−7, k0,−1 = 1.1 � 10−8, k0,2 = 2.4 � 10−10, k0,−2 = 6.4� 10−10, k0,4 = 2.6 � 10−8, and k0,−4 = 2.6 � 10−9. The results are given forthe actual surface area of the measured Cu electrode: 0.00785 cm2.


Aads�k−4

k4

A+�sol� + e− �14�

All the reactions are written as equilibrium reactions although someof them could be treated as proceeding preferentially in the forwarddirection �“irreversible” type of reactions�. We did not wish to re-strict the mechanism unnecessarily. As shown later on, even withoutsuch restrictions, the proposed system is simple enough that aunique determination of all its unknowns is possible by comparing�fitting� the calculated spectra merely to spectra measured at twodifferent conditions �voltage bias, concentration, pH, etc.�.

Derivation of impedance response of the proposed scheme.— Thecurrent due to each elementary electrochemical step i is described bythe Butler–Volmer type of equation where individual reaction ratehas the form of ki = k0,i exp��z�iF/RT�E� � k0,i exp�biE�. Here,k0,i is the rate at E = 0 determined with respect to a selected refer-ence potential, z is the number of electrons exchanged in the step, �iis the transfer coefficient, F is Faraday’s constant, R is the gas con-stant, and T is the temperature.

The total current due to mechanism Reactions 12-14 is then

I = F��k1 − k−1 + k2 − k−4��1 − �1 − �2� − k−2�1 + k4�2� �15�

Mass balance relationships involving the adsorbed species are givenby

�1d�1

dt= k2�1 − �1 − �2� − k−2�1 �16�

�2d�2

dt= − k4�2 + k−4�1 − �1 − �2� �17�

At steady-state conditions, the derivatives on the left are equal tozero, and the surface concentrations become

�1 =k2k4

k4�k2 + k−2� + k−2k−4�18�

�2 =k−2k−4

k4�k2 + k−2� + k−2k−4�19�

The steady-state current then reads

I =F�k1 − k−1�k−2k3

k4�k2 + k−2� + k−2k−4�20�

The interfacial admittance is obtained by differentiation of Eq. 15

1

F

� I

� E= �b1k1 + b−1k−1 + b2k2 + b−4k−4��1 − �1 − �2� + b−2k−2�1

+ b4k4�2 + �− k1 + k−1 − k2 − k−2 + k−4�� 1

� E

+ �− k1 + k−1 − k2 + k4 + k−4�� 2

� E�21�

The partial derivatives �qi/�E are obtained based on the generalexpressions A-4 derived in the Appendix where for functions f andg, one takes the Fourier-transformed Eq. 16 and 17, respectively.The obtained admittance was empirically supplemented by a paralleldouble-layer capacitance �20 �F cm−2�.

Comparing/“fitting” the derived impedance response 21 to the mea-sured impedance spectra.— First, we checked if the derived imped-ance response 21 was able to reproduce the main features of mea-sured spectra. Equation 21, as a whole, contains 14 free parameters�6 standard rate constants k0,i, 6 exponential factors bi, and 2 valuesfor �i�. An impedance spectrum containing three semicircles isuniquely determined with merely six parameters: for example, threeresistors and three capacitances �or with an equivalent set of six





parameters�. As one of the capacitances has to be Cdl �ca.20 �F cm−2�, we can actually extract only five unknowns from asingle measurement.

Obviously, Eq. 21 is considerably overparametrized, so it is veryconvenient if the number of model unknowns is reduced. Followingthe suggestion by Keddam et al.,21-24 we select �i= 10−8 mol cm−2. Furthermore, because all electron transfers in-volve one electron, we propose for all bi a value of 19.5 V−1. Here,we implicitly assume that for all transfer coefficients �i = 0.5which, of course, is a very rough approximation. The benefit of thisrough approximation is that now there only remain six unknowns inthe model �the six standard rate constants k0,i�. These six unknownscan be uniquely determined by comparing/fitting the model to twoimpedance spectra measured at different potentials. Of course, thiscan only be done accurately if the measured spectra are true semi-


circles and not arcs. Unfortunately, in our case, the shape of thespectra deviates significantly from the ideal semicircles. The mecha-nistic reason for this deviation is generally not known, so thesedeviations in shape could not be included into the model. For thisreason, we modified the non-linear least-square fitting �NLSF� pro-cedure whereby we only took into account the sizes of individualarcs and the peak frequencies. This way, we could still efficientlyachieve our main goal: to get rid of all unknowns and to get adeterministic model without any free parameters. For example, us-ing an NLSF method we fitted Eq. 21 to the arc sizes and peakfrequencies of the particular spectra taken at �0.40 and �0.31 V vssaturated calomel electrode �SCE� �spectra 1 and 4 in Fig. 6�. Thisway, we obtained values for all six rate constants. Using these val-ues, we could predict the model spectra for all other potentials ofchoice �in particular, for potentials corresponding to other measured

Figure 8. Comparison of real and imagi-nary parts of measured and fitted/simulated spectra as functions of log�fre-quency� for the Cu–NH3–H2O–SO4

2−

system. These data complete the informa-tion given in Fig. 7. Open and solidpoints: Real and imaginary parts of themeasured impedance spectra, respectively.Lines: Corresponding real and imaginaryparts of fitted/predicted impedance spec-tra.




eter.


spectra �2, 3, and 5–8 in Fig. 6��. We are aware that our model isrough and simplified in many aspects. However, in dynamic corro-sion problems with fast corrosion rates and only partial corrosioninhibition, one is frequently satisfied with a model that can at leastqualitatively predict the system’s behavior.

Figures 7 and 8 show a comparison between the predicted andthe measured impedance spectra �we use the complex plane repre-sentation in conjunction with the “log�frequency�” representation togive full impedance information�. Obviously, the inductive loops arefully reproduced. However, we can see that the shape of individualcalculated spectra somewhat deviates from the measured shapes.This deviation has at least two possible sources: �i� the approxi-mated bi values �fixed at 19.5 V−1� and �ii� the fact that the mea-surements contain the so-called distribution of relaxation times�transforming semicircles into arcs�, while this feature is neglectedin our modeling. Disregarding these secondary effects, the develop-ment of shape with potential is basically reproduced. For example,beside the inductive loops �Fig. 7b�, the transition from first to sec-ond quadrant at low frequencies �appearance of a negative differen-tial resistance, see Fig. 7c� is also observed. Besides the shape, themagnitudes of calculated spectra at given potentials also match quitewell with those of the corresponding measured spectra. As a whole,we estimate that the proposed mechanism represents a reasonablygood description of the present system which is rather surprisinggiven the limited number of mechanistic steps and a small numberof free model parameters.

Further model predictions: Steady-state current–potentialcurves.— Once all the model parameters have been uniquely deter-mined, it becomes possible to make further model predictions andthus additionally check for their relevance. For example, one canpredict the steady-state current-voltage curve using Eq. 20. It isdesirable that such predictions are made for different experimentalconditions, for example, for different concentrations of species in-volved in the model. In the present model, such parameters areammonia concentration and pH �see Fig. 3�. If the model parametersdetermined by impedance analysis are correct, they should be ableto correctly predict the variation in current at different conditions.To take account of these variations, we simply make the followingsubstitutions for selected rate constants in Eq. 18-20

k1 = k1�c2�NH3� �22�

k2 = k2�c�OH−� �23�These replacements do not introduce new free parameters; theymerely explicitly separate the known values of concentrations ofselected species from the rate constants. Now it becomes possible topredict uniquely the steady-state current–voltage curves from theknown rate constants obtained by impedance analysis and known�experimentally controlled� variation in concentrations with respectto the concentrations used in impedance experiments �c�NH3�= 0.5 M, pH 11.5�. Figure 9 shows the predicted and the measuredsteady-state I-E curves for different concentrations of ammonia. Thechange in peak height is well reproduced. Only at the highest con-centration �2 M� is there a slight deviation in the predicted peakmagnitude. This is attributed to the concentration polarizationwhich, at high concentrations, may affect the overall transportmechanism. The position of the calculated peaks is independent ofpotential, in rough agreement with the measurements. The shape ofthe predicted curves, however, deviates somewhat from the shape ofthe measured curves. As in impedance measurements, the shapecould be better reproduced if we released the exponential parameterto acquire values other than exactly 19.5 V−1. However, as we areonly interested in identification of the main mechanistic steps in thepresent corrosion mechanism, we are satisfied with a description thatshows the correct trends.

In the last set of experiments, we varied the pH of the solution.Cyclic voltammograms in Fig. 10a show the main trends when pH isincreased from 11.4 to 12.5. The corresponding predicted steady-


Figure 10. �a� Measured cyclic voltammograms for the Cu–NH3–SO42− sys-

tem at different pH values �the values are denoted on the graph�. Concentra-tion of NH3: 1 M. �b� Simulated steady-state curves for the same system atdifferent pH values. The simulated curves were calculated based on the rateconstants determined from the impedance analysis �see Fig. 7� without anyfurther assumption or any new free parameter.

Figure 9. �Color online� Measured and simulated steady-state current-potential curves for different concentrations of NH3 in theCu–NH3–H2O–SO4

2− system. pH of solution was 12. The simulated curveswere calculated based on the rate constants determined from the impedanceanalysis �see Fig. 7� without any further assumption or any new free param-





state current–voltage curves are displayed in Fig. 10b. The steady-state curves are somewhat steeper, especially at potentials lowerthan the peak potential. Likewise, the peak currents are somewhatlower. However, the decrease in peak height as well as the decreasein peak potential with increasing pH are well reproduced.

In summary, the impedance analysis and the comparison ofmodel predictions with the actual measurements at various condi-tions �Fig. 7-10� confirm the proposed corrosion/passivation mecha-nism �Reactions 12 and 13�. The adsorbed species �Eq. 14�, has arole of spectator, covering part of the active surface, and is notinvolved directly into the mechanism. Most likely, this is a speciesrelated to the sulfate anion. For example, there are indications thatbisulfate may electroadsorb onto the Cu�111� surface close to thepotential of the present peak.25 Although the exact nature of theadsorbed species cannot be determined from the present analysis, itsmain role in the overall mechanism is quite clear. In particular, Eq.14 takes care of the correct mass balance at intermediate frequencieswhile its contribution to current generation is very small comparedto the other two reactions.

Conclusion

The steady-state current–potential curve for theCu–NH3–H2O–SO4

2− system recorded from �1.4 to 0 V contains atleast four peaks. A typical cyclic voltammogram consists of twopositive-going peaks with two shoulders and, interestingly, twopositive-going peaks in the negative-going direction, followed bytwo or three negative-going peaks. The first positive-going peak andits shoulder correspond to a combination of a dissolution reaction ofthe order of 2 with respect to ammonia and a two-step passivationreaction yielding Cu2O. A more detailed mechanism �Eq. 12-14�was identified by analyzing a set of nine impedance spectra recordedat different electrode potentials. Its relevance was additionally con-firmed by showing a good agreement between the predicted and themeasured steady-state current-potential curves at variable NH3 con-centration and variable pH of solution. The role of an adsorbedspectator from the solution was also briefly discussed.

Acknowledgment

Financial support from the Research Agency of the Republic ofSlovenia is gratefully acknowledged.

National Institute of Chemistry assisted in meeting the publication costsof this article.

Appendix

General interfacial admittance for two adsorbed intermediates.— Derivation ofgeneral interfacial impedance involving adsorbed electrochemically active species fol-lows the well-established procedures extensively used by Keddam et al. on active–passive transition of iron.21-23 A similar approach was then used and extended to nickel,copper, and zinc26-29 and used by other authors in theoretical studies30 or in variousapplications such as fuel cells,31,32 alloys,33 etc.

For easier discussion of the present corrosion mechanism �see the Results andDiscussion section�, we appropriately adjust the main steps in impedance derivation thatare otherwise well known from the aforementioned papers.21-23,26-33 In particular, wefocus on the case where the interfacial current I is a function of potential across theinterface E and of coverage by exactly two types of electrochemically active species, S1and S2, with respective fractions of coverages �1 and �2. Differentiating the current weobtain

I = � � I

� E�

�1,�2

E + � � I

� �1�

E,�2

�1 + � � I

� �2�

E,�1

�2 �A-1�

Faradaic admittance of the interface is then defined as

YF �� I

� E= � � I

� E�

�1,�2

+ � � I

� �1�

E,�2� � �1

� E� + � � I

� �2�

E,�1� � �2

� E� �A-2�

Evidently, to calculate YF explicitly, we need to know how �1 and �2 depend on E.These relations are usually found from the corresponding mass balance equations.21,22

For the case of two species adsorbed in the form of a monolayer, these can be generallywritten as

�1d�1 = f�E,�1,�2� �A-3a�
dt

�2d�2

dt= g�E,�1,�2� �A-3b�

where �1 and �2 are the complete monolayer surface concentrations of species S1 andS2, respectively, while t is the time.

Functional dependencies f and g in Eq. A-3a and A-3b crucially determine theactual surface model. The present form already implicitly assumes that both coveragesare correlated because both f and g contain dependence on both surface coverages, �1and �2. This interdependence of both surface species somewhat complicates the furthertreatment. For example, we are not aware of any equivalent circuit that has been devel-oped for such a model. Nevertheless, a closed-form solution for the admittance given byEq. A-2 is still possible. Thus, after Fourier transformingc and differentiating Eq. A-3aand A-3b, one can get the explicit forms for the two unknown derivatives in Eq. A-2

� � �1

� E� =

df

dE

dg

d�2−

df

d�2

dg

dE− j�2

df

dE

df

d�2

dg

d�1−

df

d�1

dg

d�2+ 2�1�2 + j��2

df

d�1+ �1

dg

d�2� �A-4a�

� � �2

� E� =

dg

dE

df

d�1−

df

dE

dg

d�1− j�1

dg

dE

df

d�2

dg

d�1−

df

d�1

dg

d�2+ 2�1�2 + j��2

df

d�1+ �1

dg

d�2� �A-4b�

where j = �−1. Inserting Eq. A–4a and A-4b into Eq. A-2 one readily calculates thefaradaic admittance �the inverse of Faradaic impedance� of the system. Usually, the finalinterfacial impedance takes into account the double-layer capacitance, Cdl, which isempirically added in parallel to the faradaic impedance.

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c To avoid unnecessary complication, we do not introduce special notation for
Fourier-transformed quantities.



copper dissolution in ammonia solutions: identification of the mechanism at low overpotentials

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