response of a rotating ring-disk electrode: application to 2-d and 3-d film formation in anodic...

8/12/2019 RESPONSE OF A ROTATING RING-DISK ELECTRODE: APPLICATION TO 2-D AND 3-D FILM FORMATION IN ANODIC PRO

1/8

UC RESPONSE OF A ROTATING RING DISK ELECTROD E:APPLICATION TO 2 D AND 3 D FILM FORMATION IN

ANODIC PROCESSES

biCd/dEdQ/d-W)El,

fioi,Ko. iNd(w)Nd(m)NW)NW)NSNWNWN'(w)N(O)N,0RIQr112r3z=,I-YAe

5:w;1;

N.BENZEKRI,M.KEDDAM and H. TAKENOUTILP 15 du CNR S Physique des Liquides et Electrochimie, Universitk P. M. Curie, tour 22, 4 placeJussieu, 75252 Paris Cedex 05, France

(Received 9 Januar y 1989)Abstract-The reaction m echanism for the metal dissolution often implicates the surface coverage by 2-Dadsorbed layer and for the passivation by 3-D film developing beyond th e monom olecular layer. The surfacerelaxatiop of which is revealed by a capacitive or by an inductive feature in the electrode impedan ce, bu t theamoun t of these layers is hardly to be evaluated. The rotating ring-disk electrode (rrde) under a smallperturbation of the disk current describes quantitatively the kinetics of charge storing during the formationof these films at the electrode surface. In this paper, first we exam ine theoretically this possibility, thenillustrate how to extract the available data from the rrde technique on the basis of reaction models, andfinally we apply it to the active dissolution and the passivation of iron in a molar sulfuric acid solution.

NOMENCLATURETafels constant for K,, V-lDouble layer capacitance, FDiffusion coefficient, cm* s- Differential disk capacitance, F cm-*Low frequency limit of dQ/dE, F crnm2Disk electrode p otential, VFaraday constant, 96 500 CFrequency of ac signal, HzDisk current, ARing current, AReaction rate of the i step, mol s-l cm-Reaction rate constant at E=OV, mols-cm-*Kinetic emission efficiency, C - 1High frequency limit of Nd(w ), C-Low frequency limit of Nd(o), C 1Kinetic efficiency of the ring processSteadpstate collection efficiencyHydrodynam ic collection efficiencyExperim ental collection efficiency under ac signalN(w) corrected for CdLow frequency limit of N w)Steady-state collection efficiency relative to fluxesNumber of electrons involved in the disk reactionNumber of electrons involved in the ring reactionCharge, C cm - Disk radius, cmInternal ring radius, cmExternal ring radius, cmOverall impedance including Cd, ohmFaradaic impedance of the disk, ohmDifferential disk capacitance calculated from Z,,F cm-Maximum concentration of the adsorbed inter-mediate, mol cm - *Indicates a signal of small amplitudeFractional surface coverageKinematic viscosity, cm2 s- Flux of species leaving the disk, mol s- 1Flux of species reaching the ring, mol s- Angular frequency 2xf). rad s- Dimensionless frequencyRotation freqneyc, Hz

INTRODUCTIONThe impedance techniques are nowadays largely usedin the electrode kinetics studies. The time constantsobserved when not ascribed to bulk processes areoften interpreted by the relaxation of reaction inter-mediate species covering the electrode surface in 2-Dor in 3-D layers. However the existence of suchintermediate species remains largely hypothetical andtheir quantitative estimation is quite a hard task.Albery and coworkers investigated extensively[ 11in the late 60s the rotating ring-disk electrode (m-de).In their final papers on this subject, they showed thatthe rrde under an ac signal m ay give informationabout the charge included by the adsorption of reac-tion intermediates. If a certain numb er of experimentswere carried out on the basis of the steady-state rrdetechniques, one remarks only a few examples of use ofthis technique in the transient regime[2,3]. These twostudies concern merely selection of reaction mechan-isms and remained qualitative. The present paper i saimed a t evaluating the possibilities of the rrde tech-niques in the quantitative investigation of electrodeprocesses. To achieve new information about theelectrode kinetics, the rrde data were coupled with theresults of impedance measuremen ts on the disk elec-trode.

PRINCIPLELet us consider that the species S transforms elec-trochemically into B at the disk:

S A B+nue-. (1)The species B leaves the disk, is transported byconvective diffusion up to the ring, where it is trans-formed into P:

1159


2/8

1160 N BENZEKRI eta1

B A P+n,e-. (2)The product R may be identical to S, the initialspecies, as in the case of a redox system, or different, asit is actually the case in this paper. The number ofelectrons concerned in the Reaction (1) or (2), ie n, ornR, is positive for an anodic and neg ative for a cathodic

process. It can be seen that the rrde operates in threedistinct processes: electrochemical reaction at the disk,coupling between the disk and the ring through theconvective diffusion and collection at the ring.What one measures experimentally in the rrdeexperiments is the disk and the ring current respect-ively in and i,. At the steady-state, the correspondingcollection efficiency (Ns) can be defined as:Ns=. in (3)

In a similar way, the collection efficiency under an acsignal at the angular frequency w is to be defined by:N(w) ~2Al, (4)

where A indicates a signal of small amplitude. In thelow frequency limit, one has the general relationbetween the real quantities:AN, AiR i, Ai,AE, ------.i,AE, i:, AE D

One obtains, if ANs/AE,=O:i, Ai,_=__.i, Ai, ie Ns = N(0).

rt is worth emphasizing that the steady-state collec-tion efficiency Ns is identical to the zero frequencylimit of the dynam ic collection efficiency N(w) only ifNs is independent of En. In other words, if the diskprocess changes with potential, for instance the val-ency of the disk dissolution varies w ith the potential,then Equation (6) is no longer valid and deviationswith respect to this equation are given b y Equation (5).As stated above, the disk and the ring currents arelinked through three distinct steps. N(w) can hence besplit in the following fashion:

= Nd w) .Nt(w)/Nr(w), (7)Nr(w), ie A&/Aik, is the kinetic efficiency of the ringprocess (2). If this process is fast enough that itskinetics is entirely controlled by the convective diffu-sion, then Nr(w)= l/n,F, where F is the Farada yconstant. The applicability of the rrde is, in fact, closelydependent on the possibility of finding a suitable ringmaterial and electrochemical system for which Nr(w)is to be considered constant.

Nt(w), ie A4J A4, , is determined completely bymass transport. This term was actually the main objectof the extensive work carried out by Albery[l]. The

steady-state collection efficiency N, in terms of fluxescan be expressed by:

N,= 1-F +/123(1 -F(a))0-_ I +a+@ I{ -F(i)(l+a+p)},

where:

F(@=~ln(~)+~tgg(~)+~.(8)

From this equation, it can be seen that N, dependsonly on the geometry of the ring-disk electrode,namely rJr, and r,/r,: rl, r2 and r3 stand for the diskradius, the inner and outer radii of the ring, respect-ively.In the transient regime, Nt(w) exhibits a compli-cated frequency dependence and no analytical ex-pression is available. However, on a very general basis,Nt(o) can be reduced by the dimensionless frequencyW:

I%=157 1/J f-,Rwhere v is the kinematic viscosity, D the diffusivity, fthe frequency of perturbing signal at the disk and fithe rotation speed of the rrde. The last two term s areexpressed in Hz. Albery[l] proposed an approachedexpression of Nt(w) for a thin ring valid for W rangingbetween 1 and 16.

Nd(w), ie A&/A&,, is the kinetic emission efficiencydepending only up on the kinetics at the disk electrode,and contains the information we are interested in. Atthe steady-state provided that the overall valence beindependent of electrode potential the Farada y lawwill be respected, hence:lim Nd(w) = & (10)0-o D

In the transient regime, a fraction of the disk currentAir, may be stored at the disk surface as the charge AQ,implied in the faradaic process through the formationof adsorbed intermediate species (2-D) or of films (3-D). From the conservation of electrical charge, onecan derive[4]:

11)Under a sine-wave perturbing signal, dAQ/d t =jwAQ,then Equation (11) becomes:

n,F 3 +jw = n,F Nd(w) +jw = 1.D D n 12)It can be seen easily that at the steady-state (w=O),Equation (12) reduces to Equation (lo), based merely


3/8

ac Response of a rotating rrde 1161on the Farada y law. Provided that AQ/Ai, be deter-mined, one can calculate dQ/dE, the faradaic capaci-tance of the disk electrode:

dQ dQ din AQ 1_=-.__=_._dE din dE, Ai, Z, (13)where Z, is the faradaic impedance of the disk process.dQ/dE is an important kinetic param eter, which al-lows us to evaluate the frequency dependence of theamount of charge stored at the electrode surface.Furthermore, the integration of its low frequency limitdB/dE(O) allows us to evaluate the charge stored at theelectrode surface between E, and E,:

As shown by Equation (13), to obtain this informationexperimentally, the disk impedance must be measuredtogether with the ac collection efficiency N(w).

EXPERIMENTALSThe disk was made of Fe (Johnson Matthey), theradius of which was 1 .4 mm. The platinum ring (Lyon-Alemand ) was mounted on a stainless-steel holder.The inner and the outer radii of the ring was respect-ively 1.5 and 2.1 mm. The collection efficiency N, wascalculated to be equal to 0.48 according to Equation(8). The latera l surface of these electrodes was coveredwith a cataphoretic paint providing an excellent pro-tection against infiltration of electrolyte between m e-tal and insulator. One obtains thus a stable andreproducible passive current. The gap between the

disk and the ring was filled u p with a wax. The outerpart of the ring was surrounded by a large epoxy resincylinder, the radius of which w as 9.5 mm.The counter electrode was a large platinum net (ca200 cm*) and the reference electrode was Hg/Hg,SO,in sat. K,SO,. The d isk potential is given as measuredwithout any correction. The cylindrical electrolyticcell contained about 300 ml of a molar sulfuric acid.Experiments were carried out at 25C under Aratmosphere.The electrode interfaces (disk and ring) were polar-ized by a home-mad e bi-potentiostat including acorrection circuit for the ohmic coupling between thedisk and the ring[4]. The collection efficiency and thedisk impedance were measured sim ultaneously by the4-Channel Frequency Response Analyzer (SolartronFRA-125 4). These measuremen ts were controlled by apersonal com puter (SORD M68), also used toperform numerical simulations of models and post-processing of results to calculate, for instance Nd(w)and dQ/dE.

MODELSIt will be shown below how Nd(w) and dQ/dE canbe calculated from a reaction model. For this sake,models for active dissolution and passivation weredealt with, both of them concern 2-D film formation:

Active dissolutionIt is now gen erally admitted that iron dissolvesthrough two consecutive and irreversible steps inacidic m edia. Fe(I) species adsorbed at the electrodesurface, is considered to be the reaction inter-mediate[5-77:

Fe -% Fe(I),, + e - ,

Fe(I) x2J Fe(H),,, + e -. 13The reaction rates Ki are assumed to obey the Tafellaw, ie Ki=Komi exp(biE). K,,i is the reaction rateconstant at E =O V for an arbitrary potential scale.The cha rge an d mass balances of this reaction can bewritten by:

i,=F{K,(l--B)+K,B}, (16)

where y stands for the maximu m concentration of theadsorbed intermediate and 0 its fractional surfacecoverage. The calculation of the electrode impedancefor this model was given elsewhere[5-7]. The peculiarequation to the rrde is the flux of final species leavingthe disk which can be expressed by:

& =K,8. (18)The Taylor expansion of Equation (18) gives:

d&=(blK,8)dE+K,d0,hence:

W,dE=b2K2e+K2 ;.

Then the Faraday law allows us to calculate directlydQ/dE:d de~=v@~ 20)

On the other hand, the following relationship caneasily be derived:

> ZF, (21)where Z, stands for the faradaic impedance. From thisequation it can be seen that the time constant involvedin Nd(o) is the same a s in the electrode impedance.

In the literature, sometimes the iron dissolutionmechanism through a catalytic reaction is proposedC8,91. In this case, the first step is reversible and thesecond step does not consume Fe(I),,:x1Fe - Fe(I), +e-,x-1

Fe + Fe(I)., z Fe(I),, + Fe(II),, + 2e -. (22)Then, the charge and mass balance can be written by:

i,=F{K,(l-e)-K_,e+2K,e), (23)y +K,(l--8)--X_,e. (24)


4/8

1162 N. BENZEKRI et ~1.The p articularity of this reaction lays on the fact thatthe mass balance [Equation (24)] does not containK,0 giving the dissolution rate of iron. The flux ofFe(II),,, is expressed by Equation (18). Formally,Equations (20) and (21) remain valid though dB/dEand ZF are different from the consecutive mechanism.

PassivationThe mechanism for the passivation of iron wasstudied by Keddam et aI.[6]. and is rather compli-cated. For the sake of simplicity, we will consider inthis paper an approximated model which includes twoadsorbates: Fe(H),, as a dissolution intermediate andFe(III),, as a passivating species:K,Fe - Fe(II),,, +2e-,

Fe - Fe(II),, + 2e-, 25)

WW,, 2 Fe(II),,, (non-catalytic),or:

K.Fe(II),, + Fe _+ Fe(II),, + Fe(II),,,+ 2e-(catalytic process),

K4Fe(II),, - Fe(III),, + e -,K-4KSFWW,, - WIW,,,(chemical dissolution of passive film).

The equations for charge and mass balances in thecase of non-catalytic process are given b elow:i,=F(2(K, +K,)~+K,e,--K_-482}, (26)

Y~=~,Z-(K,+K,)H,+K~,B,, (27)

f-f=K,e,-(K_,+K,)e,, (28)where 0, and O2 are the fractional surface coverage ofFe(II),, and Fe(III),, respectively, and E = 1 - o1 - e2.As for the specific equations for the rrde, the flux ofFe(II),,, and Fe(III),,, should be distinguished:

4, = K,C+ K,B, f l ux of FeQU, , ,) , (29)& = K,B, (flux of Fe(III),,). (30)

From Equation (26H28), the steady-state charac-teristics and electrode impedance can be derived alongthe same usual procedure. For the charge stored at theelectrode surface, Fe(II),, and Fe(III)., cannot bedistinguished hence, dQ/dE becomes:(31)

By contrast, the flux of ferrous and ferric species m aybe distinguished according to the ring reaction selec-

ted then:W, dENd(w& ,,= -p* -=dE din b,K,C+b,K,O,)

--(K, -K,) K, fI2, (32)

WzNd(w),.u,,, = di = b,K,H,+K,~ ZP (33)D >

In the case of the catalytic process, Equations (26) and(27) may be modified in the similar way to the activedissolution.This paragraph illustrates the close similarity be-tween the modelling for the rrde, in particular for thecalculation of kinetic emission efficiency Nd(w) andthat of the electrode impedance. No additional hypo-thesis is necessary to calculate the parameters specificto the rrde technique compared with the well-estab-lished electrode impedances derivation.

RESULTS AND DISCUSSIONSimulation calculations

Active dissolution. Figure 1 displays the results ofsimulation calculation for the consecutive two-stepdissolution given above, for three polarization pointsmarked by A to C on the steady-state polarizationcurve. In the impedance diagrams (upper row ), thecontribution of the double layer capacitance Cd to theoverall impedance 2 was included by the followingrelation:i = + jwCd.F (34)

As was stated in[5], the faradaic impedance is induc-tive in low potentials where K, -z K,, and capacitivefor high anodic overvo ltage (cf diagram C). Thediagram for Nd(w) (lower row) is a semi-circle in theupper half plane (negative imaginary part). It can beremarked that its shape and size is independent of thepolarization potential. The low frequency limit of Nd,2FNd(O), is equal to unity in agreement with Equa-tion (12). Its high frequency limit, 2FNd(oo), is equalto 0.22, value determined solely by b, and b,. Only thecharacteristic frequency, defined by that at the maxi-mum of the imaginary part, changes with the poten-tial. This frequency is close to that observed in thefaradaic impedance.Figure 2 shows the results of simulations for thecatalytic model. Since the metal is likely to dissolveaccording to the consecutive step mechanism, thevalues of kinetic param eters are arbitrary. At moreanodic potentials than those given here, the faradaicimpedance exhibits a capacitive feature. Nd w ) is asemi-circle. 2FNd(O) is unity as in the case of theformer model. On the contrary, 2 FNd(m) depends onthe potential, and approaches to unity with the in-creasing anodic voltage. Thus the diameter of Nd w )becomes vanishingly small with increasing anodicpotential. Though this was not shown here, the lowfrequency limit of dQ/dE fairly sm aller in this catalyticmechanism than in the case of consecutive step one, ascan be expected by the very na ture of the reaction.


5/8

ac Response of a rotating rrde 1163-8,0 . . I 1 I I -I,2 , , , , , , ( , -0;l III. IA B C

REAL PART; 2F b d w) ; dimensionlessFig. 1. Simulation results: active dissolution of Fe Model III). Constan ts correspon ding to 1 M H,SO,.y=lO-sm~lcn-~, Cd=100~Fcm-2, K,=4x105 exp 38.4 E), K, = 8 x lo- exp 7 E). Upper row :impedance, lower row: ZFNd(w); (A)-(C) correspond to the points marked on the I-E curve.

1

o.otf. I 1 I,100Hz A1 o.ot, 0 100H-rf, I I1 .r .I o.ot o-L1 I I.1 II-I0 100 70.2lkHz 11 08 105 098REAL PART;2F Nd (w) ; dimQnsiontess I,01

Fig. 2. Sim ulation results: active dissolution of Fe Model 22). K, = 1Oex p 19.2E), K _ 1.5 x 10-lexp( - 19.2 E), others cf Fig. 1.

Thus, it can be concluded that the rrde techniquemay con stitute a useful tool to check the reactionmechanism as suggested by other authors[2, 31. It isalso noteworthy that Nd(w) diagram is located in theupper plane, that is dQ/din >O [cf: Equation (12)]. Inother words, the increase of current is accompan iedwith tha t of the charge at the electrode interface. Thisis also an important feature directly accessible to acrrde techniques.

Passivation. Figure 3 displays the results of simu-lations for the passivation process 25 with non-catalytic reaction. The set of kinetic parameterschosen here is rather roug h since the model givenabove was found to be oversimplified to describeaccurately the experiments. The impedance diagramsshown here (upper row) do not contain the contribu-

tion of the double layer capacitance, since introducingit makes the high frequency loop of faradaic impe-dance difficult to visualize in certain cases. The im pe-dance diagrams show then two capacitive loops corre-sponding to the surface relaxation of the two inter-mediates. F urthermore, the low frequency limit of theimpedance is negative in agreement with the slope ofthe polarization curve. As expected Nd(o) shows alsotwo loops. The high frequency behaviour can berelated to the dissolution intermediate Fe(II),,. On thecontrary, that showing up at low frequencies is to beattributed to the passivation process. In relation withEquation (12), it can be concluded that if the increaseof the surface coverage makes decrease the current,then Nd(w) should be displayed in the lower part of theplane (positive imaginary part). In other words, thereis a straight forward relationship between the feature


6/8

1164 N. BFNZEKRIet al.

REAL PART 1 2F Nd O IFccnj , dimensionlessFig. 3. Simulation results: passivation or iron [Model 25). K 1 = lo- exp 12 E), K, = 5 x lo- exp 6 E), K,=2x IO-, K,=3 x 1O-9 ~~~ 19.2 E), K_,= 10-l exp ~ 19.2 E), K,= 10-r. Double layer capacitancewas neglected. Others cf Fig. 1.

of Nd(w) and the kinetic role of the adsorbed species.This contrasts definitively with the electrode impe-dance w here the adsorption of a same species may giverise to either an inductive or a capacitive loop accord-ing to the kinetic param eters. 2FNd(O ) is unity even inthe fully passive range, w hereas the main process isessentially the passive dissolution, forming Fe(III),,,.In the potential range examined here, the dissolutionvalence changes from two to three, hence Ns is nolonger equa l to N(0). Furthermore when the potentialincreases, 8, tends to unity, and the modulation ofpotential modifies neither 8, value nor the dissolutionrate of the passive film. Only a small change of 0, andFe(I1) dissolution are made. However this argumentmay be no longer valid if the passivation process isdescribed by the formatuion of a 3-D film.Experimental results

Active dissolution. Figure 4 is relative to the exper-imental results obtained during the anodic dissolutionor iron in 1 M H,SO,. The impedan ce diagram A andB are in a good agreement with that of simulationshowing one inductive loop in low frequency range.On the contrary, on the diagram C two indu ctiveloops can be clearly seen, as reported in[6]. On thesecond row of this figure, the results of N(w) aredisplayed. These curves have a half-cardioidal shape ieNt(w) is predominant in the frequency dependence ofN(w). From these uncorrected results, it is difficult toforesee Nd(w). The calcuiation of Nd(w) is performedfirst by correcting for the contribution of the charge ofthe double layer in the overall current: experimen talN(w) is replaced by N(o):

N(w) = N(w)1 -jwCdZ (35)where Z is the overall disk impedance. Nd(o) is thencalculated acco rding to Equation (7).Preliminary work performed in various conditionsindicated that the best manner to achieve Nd(w) is to

determine Nt(w)/Nr(w) together in the same solutionas that used for performing the rrde experiments. Inthe particular case given here, 1 M H,SO,+10 mM Fe,(SO,), solution wa s prepared. The Fe(II),,,is produced at the disk then reoxidized at the ring.The results of calculation were given in the lowerrow of Fig. 4. The results diverge significantly for thefrequencies higher than several Hz. This phenomenoncan be attributed to Nt(w): in fact, Nt(w) behaves as alow-pass filter, and a vanishingly small UC signal wasobserved in raw N(w) data for frequencies higher thanseveral Hz.Nd(oo), though depending somehow on potentials,

remains small which is in the favour of the two-stepconsecutive mechanism. Howe ver ZFNd(0) is signifi-cantly small than unity. It was also found that thehigher is the rotation speed, the smaller is Nd(O), andalso when the solution pH increases, Nd(0) decreases.This unexpected feature was interpreted by the pres-ence of at least two reaction paths to produce Fe(II),,,in agreement with our previous work[6]. The reactionpath, major a t low anodic potentials, produces adivalent species Fe(II),,, easily oxidizable at the ring,whereas the other, through a catalytic process, forms aspecies unable to be collected at the ring. The latterspecies transforms into usual Fe(II),,, by an homo-geneous chemical step taking place meanw hile thetransport from the disk to the ring. The relative weightof two pa ths depends both on the potential and thesolution pH, as was suggested in[6].The high frequency cut-off behaviour of Nt(o) andthe complication observed for the collection ofFe(II),,, at the ring make further quantitative analysishazardous. At the present time no derivation of Nt(w)taking into account this homogeneous step is avail-able.

Passiuation. Figure 5 exhibits the results obtainedin the passivation range of iron in sulfuric acid. Theelectrode impedance is quite similar to those predictedby numerical simulations. N(o) displays, at highercurrent (diagram C), a very depressed feature. The


7/8

(IC Response of a rotating rrde

d o), 0hm.ct-n

REAL PART, 2F Nd w), dimensionlessFig. 4. Experim ental results. Active dissolution in 1 M H,S04, 900 rpm. Disk: Fe, polarized a t points(AHC) marked on the I-E curve, E,= 2 mV, Ring (Pt): Fe(II)-rFe(III), E,=0.8V. Upper row:impedance, middle: N(o) and lower: ZFNd(w).

1. k *C2E El-5VO +5q-75 0E ,,mVufS.S.E ~~~~~~~~~~I 1,2 /-0,3 1, Z- 0, 6

REAL PART, 2F Nd W) , dlmenslonlessO/9

Fig. 5. Experimental results. Passivation in 1 M H,SO,, 620 rpm. Disk: Fe, AS,== k 10 mV, Ring:Fe(II)dFe(III), E=0.8 V. Upper, middle and lower rows, see Fig. 4.

correction for double layer effects according toEquation (35) has a little effect du e to the low frequen-cies while correction for Nt(w) restitutes the Nd(o)data shown in the lower row. In agreement withsimulated data, the diagrams are located in the lowerhalf-plane exhibiting directly the passivating role ofthe surface process involved in the charge storing. Thefrequency corresponding to the maxim um imaginary

part is equal to that shown by the low frequen cyimpedance at the same polarization point.The less anodic the potential, the more visible is thederivation with respect to the model prediction.2FN40 ) becomes significantly lower than unity and itwas verified that correlatively 3FNd (w) correspondingto the flux of Fe(III),, increases. At the same time thereal part of N d o) becomes negative in the high


8/8

1166 N. BENZEKRI et ul.

frequency range. In perchloric medium this high fre-quency feature is even more apparent and the Nd w)diagram turns around the origin, Nd(oo) being posi-tive. The m odel given above is clearly unable toexplain in details the Nd(w) data, and particularly thefastest processes of passivation, whilst the impedanceis correctly restituted. T his illustrates the highestselectivity of the rrde under ac polarization. Nd(w) wasprocessed further according to Equation I I to yieldthe complex ratio AQ/AE (w) describing the frequencyresponse of the surface charge. The low frequency limitis of particular interest and is shown as a function of Ein Fig. 6.In the range investigated dQ/dE decreases w ithincreasing E and tends towards a value of about6 mFcm_ at about 0 V, then increases again. Ac-cording to the model based on a 2-D passivating layerthis quantity should vanish as the coverage is com-pleting to unity. This discrepancy is obviously due tothe 3-D character of the passive film developingbeyond the active-passive transition. The value ob-tained is in reasonable agreement with calculation onthe basis of normally assumed thickness voltage de-pendence.On the same figure, the capacitance r determinedfrom impedance data at low frequencies[lO] is alsodisplayed. This value increases monotonously withpotential and reaches ca 20 mF cm - at 0.6 V. A closeexamination of the faradaic impedance expression fora film forming process show ed actually that the chargestored a t the surface cannot be determined withaccuracy by impedance technique. The rrde techniqueapplied in this field shows aga in a definite advanta gecompared with the impedance method.

CONCLUSIONThe n-de technique under a small ac perturbation ofthe disk current was applied in the study of the anodicprocesses lead ing to the formation of 2-D or 3-Dlayers. The theoretical examination of the operatingparameters allowed us to distinguish three factors: thekinetic emission at the disk, the mass transport coup-ling between the disk and the ring and the collection atthe ring. The relevant quantity is the kinetic em issionefficiency of the disk, since it gives directly the amountof charge involved at the disk interface, in the course ofa faradaic process a parameter of outstanding import-ance for the electrode kinetics investigation.By applying the technique to the active dissolution

of iron, it was found that the time constant exhibitedby this system is too short to get the whole informa-tion with the present performance of the rrde. Thedecrease of Nd(0) with respect to the increasing poten-tial and solution pH was interpreted consistently withthe reaction paths previously introduced in the impe-dance modelling.The passivation process will be a promising field tobe investigated by the rrde. The time constants in-volved are large enough and Nd(w) can be calculated

30 I I I I+

20 _l-4kLLE )I

fc0 *

o,%p - _t(f_+ /L . P

00

0 I I I I j100 -50 0 50 100

E D / mV5sEFig. 6. Differential capacitance for the formation of passivefilm Fe/lM H,SO,, c/ Fig. 5. dQ/dB deduced from the rrdeand disk impedance measurements. r calculated from lowfrequency data of the disk impedance, *, 0: 620rpm; f, 0:

900 rpm.with a good accuracy. Then the formation of anodicfilm leading to passivity was evaluated more satis-factorily than by the impedance method. It is worth toemphasize that the coupling of N(w) measuremen tswith the disk impedance is absolutely necessary toachieve quantitative analysis of the results.Acknowledgement-This work was performed in the frame-work of the thesis of one of the authors N. B.). She is gratefulto the Ministry of the Education of Morocco for providinga scholarship.

5.6.7.8.9.

10.

REFERENCESW. J. Albery and M. L. Hitchman, Ring-Disk Electrodes,Oxford University Press 1971).T. Tsuru, N. Nishimura and S. Haruyama, Mater. Sci.Forum, 8, 429 1986).W. J. Albery, A. H. Davis and A. J. Mason, Faraday Disc.them. Sot. 56, 317 1974).N. Benzekri. M. Keddam and H. Takenouti, in Surfaces,I nhibi tion and Pussivativn (Edited by E. McCafferty andR. J. Brodd), 86-7, p. 524, Electrochemical Society,Pennington, NJ 1986).I. Epelboin and M. Keddam, J. electrochem. Sot. 117,1052 1970).M. Keddam, 0. R. Mattes and H. Takenouti, J. electro-them. Sot. 128, 257, 266 1981).H. Schweikert, W. J. Lorenz and H. Friedburg, J. electro-them. Sot. 128, 1294 1981).K. E. Heusler, Ber. Bunsenyes. phys. Chem. 72. 11971968).

P. Lorbeer and W. J. Lorenz, Electrochim. Actn 25, 3751980).M. Keddam, J. F. Lizee, C. Pallotta and H. Takenouti,J. electrochem. Sot. 131, 2016 (1984).

response of a rotating ring-disk electrode: application to 2-d and 3-d film formation in anodic...

Documents