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Differential Capacity of Bromide Anions Adsorption onto Ag(100) in the Absence,and onto Ag(poly) inthe Presenceof NaClO4

V. D. Jovi

Institute for Multidisciplinary Research,11030 Belgrade, P. O. Box 33, Serbiae-mail: [email protected]

In this work, the adsorption of bromide anions onto Ag(100) and Ag(poly) in theabsence and presence of NaClO4 was investigated. The cyclic voltammetry, EIS and Cdiffvs. Emeasurement results were analyzed. For the determination of the adsorption param-eters, the equivalent circuit containing constant phase element (CPE) instead of the dou-

ble layer capacity (Cdl) and new equations for the analysis of the anion adsorption, basedon a different definition of the CPE, have been developed and used. It was shown thatthe proposed equivalent circuit and corresponding equations for the differential capacity(C

diff

) as a function of frequency (w) can successfully be applied in the investigated sys-tems. Excellent agreement between the cyclic voltammograms (CVs) and the Cdiff vs. Ecurves recorded at frequencies lower than 10 Hz has been detected. The homogeneity ofthe charge distribution over the real single crystal surfaces, as well as other parameters ofthe adsorption process were found to change with the potential. In the presence of thesupporting (non-adsorbing) electrolyte (0.1 M NaClO4) diffusion-like phenomenonwas detected and ascribed to the slow step in exchanging anions adsorbed in the innerHelmholtz plane.

Key words:

Bromide anions adsorption, differential capacity, CPE, surface homogeneity

IntroductionThe determination of the double layer capaci-

ties in the available literature is, so far, mainly basedon either differential capacity measurements (Cdiffvs. E curves) performed at a single frequency,16 oron impedance measurements performed in a broadrange of frequencies and the analysis of impedancediagrams using the adsorption impedance theorydeveloped by M. Sluyters-Rehbach et al.7 Usingequations for the impedance and capacitance de-fined by this theory7,8 the equation for the differen-tial capacity is defined as

C Ydiff lmcorr= =-w 1

(1)

= ++

+ + + -C

C C

C C Rdl

ad ad

ad ad ad

( )

( ) (

/

/ /

1

1

1 2

1 2 2 2 2 1 2

w s

w s w w s)2

where YImcorr represents imaginary component of ad-mittance corrected for Rs, w is the angular fre-quency (w = 2pf, fbeing the frequency), Rs repre-sents resistance of the solution, Cdl the double layercapacity, while Cad, Rad and scorrespond to the ca-pacity, resistance and the Warburg coefficient of theanion adsorption, respectively. It should be notedthat in order to obtain the real value for the Cdl, so-lution resistance (Rs) must be subtracted from thetotal electrode impedance (YIm

corr in the eq. (1)).

Taking into account that the Warburg coefficient ofthe anion adsorption (s) depends on the concentra-tion (c) and the diffusion coefficient (D) of adsorb-ing anions, it could be concluded from the eq. (1)that at high frequencies and low concentrations ofadsorbing anions, the contribution of the secondterm in this equation becomes insignificant and theCdiff vs. fcorresponds to the double layer capacityonly. Using the values for Cdl = 60 mF cm2, Cad =200 mF cm2, Rad = 50 W cm2, D = 1 105 cm2 s1

and varying the value of c from 100 mM to0.01 mM in eq. (1), Cdiff vs. fdiagrams presented in

Fig. 1 were obtained. As can be seen, for higherconcentrations of anions (1, 10 and 100 mM) theirdiffusion has no influence on the shape of the Cdiffvs. fcurves. The total capacitance is independent offrequency and equal to Cdl at f> 102 Hz (point A),while at f< 100 Hz, the total capacitance is alsoindependent of frequency and equal to the sumCdl + Cad (point B). At lower concentrations (0.1and 0.01 mM), the differential capacity is again inde-pendent of frequency and equal to Cdl at f> 102 Hz(point A), while Cdiff depends on frequency at fre-quencies lower than 102 Hz, as a consequence ofthe anion diffusion, and does not represent thesum Cdl + Cad (its value cannot reach the sum ofCdl + Cad even at f= 104 Hz). This indicates thatthe real value of the Cad (independent of frequency)

V. D. JOVI, Differential Capacity of Bromide Anions Adsorption onto Ag(100) , Chem. Biochem. Eng. Q. 23 (1) 1122 (2009) 11

Original scientific paperReceived: June 9, 2008

Accepted: October 5, 2008

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cannot be determined from the Cdiff vs. fcurves forthese concentrations of anions. It is important tonote that most of the experiments concerning Cdiffvs. E curves were performed in the solutions of in-vestigated anion concentrations lower than 100mM, usually of the order of 1 mM in the frequencyrange between 10 and 20 Hz,5,6 exactly in the re-gion of frequencies where Cdiff increases sharplywith decreasing the frequency (frequency regionbetween A and B). In order to decrease the solutionresistance in almost all cases a supporting (non-ad-sorbing mostly perchlorate) electrolyte wasadded to the solution.

All the above mentioned consideration is validfor the systems where the double layer capacity be-haves as an ideal double layer, i.e. assuming ho-mogeneous electrode surfaces (homogeneouscharge distribution over the surface) and the doublelayer capacity being represented by a parallel platecondenser.18 The introduction of the constant phaseelement (CPE) instead of the double layer capacityis also discussed in the literature.924 Several phe-nomena, such as distributed surface reactivity, sur-face heterogeneity, roughness or fractal geometry,electrode porosity and current and potential distri-bution associated with electrode geometry were at-tributed to the CPE behavior in the literature.924

The different expressions given for the CPE indi-cates that its physical meaning is not yet clear.

A recent experimental study of Kerner et al.25

showed that capacitance dispersion on solid elec-trodes was due to surface disorder (i.e. hetero-geneities on the atomic scale) rather than roughness(i.e. geometric irregularities much larger than thoseon the atomic scale). Kim et al.26 also showed thatthe contribution of surface heterogeneity can bemuch higher than the contribution of the surface ir-

regularity to the capacitance dispersion.Most recently M. Orazem et al.27 discussed dif-

ferent procedures for the treatment of the distribu-

tion of time constants and pointed out that the im-pedance of an equivalent circuit for parallel connec-tion ofCPE and resistance (R) can be expressed bytwo different equations

ZR

j CR( )

( )w

w a=

+1(2)

and

ZR

j CR( )

( )w

w a=

+1(3)

It is important to note that eq. (3) was used inall commercially available software for fitting im-pedance spectra, as well as in our previous paper.28

In such a case CPEwas considered as an independ-ent element of the equivalent circuit and its imped-ance29,30 was defined as ZCPE = 1/[Y0(jw)a], whilethe values ofY0 and a were obtained by fitting pro-cedure, with the constant Y0 having dimensionW1cm2sa. Accordingly, its value should be cor-rected by the procedure defined in the paper of Hsuet al.31 in order to obtain correct dimension for thecapacity, by following equation

C Y= -01( )maxw alm (4)

with wImmaxbeing the frequency of the maximum on

ZIm vs. log w dependence, independent of thevalue ofa. Eq. (4) is a result of the application ofeq. (2) in the case of the analysis of the equivalentcircuit with the parallel connection between CPEand R. If the value ofwIm

max cannot be determined(in the case where the maximum on ZIm vs. log wdependence, i.e. the maximum on the semi-circle ofthe complex plane ZIm vs. ZRe does not exist, whichis almost always the case on these diagrams ob-tained for anion adsorption, the real (dimensionallycorrect) value of the capacity cannot also be deter-mined. In such a case the following equation should

be used.C Y R= -[ ( ) ] /0

1 1a a (5)

Eqs. (2), (4) and (5) assume that both parame-ters, Cand R depend on a in the same way. The fre-quency dispersion of the capacity as a consequenceof the surface heterogeneity (expressed as a) isclosely related to the charge distribution over thesame surface and these two parameters are mutuallydependent. Such a statement is also pointed out byVan Meirhaege32 in the analysis of the capacity ofsemiconductors.33 According to these two refer-ences, the frequency dependence of the capacitymust be accompanied by a frequency-dependentparallel resistance.

12 V. D. JOVI, Differential Capacity of Bromide Anions Adsorption onto Ag(100) , Chem. Biochem. Eng. Q. 23 (1) 1122 (2009)

F i g . 1 Calculated Cdiff vs. f curves for the adsorption of anions defined by eq. (1) for the following parameter values:

Rad = 50 W cm2; Cdl = 60 mF cm

2; Cad = 200 mF cm2;

D = 1 105 cm2 s1. The concentrations of anions (c) aremarked in the figure.

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The model and the equivalent circuit foranion adsorption onto real single crystals

After the in situ STM technique is introducedin the processes of the double layer and anion ad-sorption investigation onto single crystal surfaces,34

it was obvious that even single crystal surfaces arenot perfectly flat, but to the contrary, it is shownthat they consist preferentially of a significant num-ber of atomically flat terraces separated by mono-atomic steps (for the best surface).3445 A typical ex-ample is demonstrated in Fig. 1 of Ref. 35, showingnot only monoatomic steps, but also the presence ofmuch more pronounced irregularities on the realsingle crystal surfaces of Ag(111) and Ag(100). It isalso shown that during the process of anion adsorp-tion, the first step is adsorption of anions at the

monoatomic steps accompanied by the dynamicchange of the STM image and movement of themonoatomic steps and terraces along the electrodesurface,3742 indicating the presence of heteroge-neous charge distribution over the single crystalsurface. Simultaneously with the adsorption of an-ions at the monoatomic steps, adsorption of anionsalso takes place at the flat terraces with a formationof 2D islands of (most probably ordered) adsorbedstructures (homogeneous charge transfer distribu-tion over the terrace), while the movement ofmonoatomic steps and terraces along the electrode

surface still occurs.3742

After reaching the poten-tials of the sharp peaks on the CVs, in all cases or-dered adsorbed structures were detected all over theelectrode surface and the movement of monoatomicsteps and terraces was not so pronounced.3445

Hence, in such a case it would be reasonable to as-sume that these two processes, the adsorption onthe heterogeneous and the homogeneous part of theelectrode surface, occur simultaneously during theanion adsorption in a certain potential region.

In our previous papers, it was shown for theAg(111) in 0.01 M NaCl28 and Cu single crystals in

0.1 M NaOH46

that Cdiff vs. Ecurves are very sensi-tive to the frequency although the process of anionadsorption is not controlled by anion diffusion, in-dicating that even single crystal surfaces cannot betreated as being homogeneous and that, instead ofCdl, a CPE should be introduced in the analysis ofCdiff vs. w curves.

Accordingly, considering all above mentioned,it could be concluded that the equivalent circuit forthe anion adsorption onto real single crystal sur-faces should be represented by the one shown inFig. 2, with Radhe and CPEdlhe corresponding to theadsorption resistance and constant phase element onthe heterogeneous part of the surface respectively(practically the inner Helmholtz layer, including theouter Helmholtz layer on the whole surface) and

Radho and Cad corresponding to the adsorption resis-

tance and capacity on the homogeneous part of thesurface respectively. By analysis of the equivalentcircuit presented in Fig. 2, the following equationwas obtained for the Cdiff (after subtraction of thesolution resistance, Rs, as in eq. (1)):

Y C C Rlm diff dl adhew w

apa a- - =

+1 1

2( ) ( ) sin

++

CC R

ad

ad adho1 2 2 2w ( ) ( )

(6)

Using the values for Cdl = 60 mF cm2, Cad =200 mF cm2, Rad

ho = 50 W cm2 and Radhe = 5000 W cm2

and varying the value ofa from 1.00 to 0.80, thediagrams presented in Fig. 3a were obtained. Ascan be seen, this dependence is very sensitive to thevalue ofa (as well as to the other parameters) in awhole range of frequencies, being characterized bytwo inflection points (marked in the figure as A andB, as in the case of Fig. 1). In the range of high fre-

quencies (f> 102

Hz for given equivalent circuit pa-rameters) Cdiff slightly changes with fdown to theinflection point A for all values a < 1. Between theinflection points A and B sharp, a non-linear in-crease of Cdiff with foccurs, while with further de-crease of frequency Cdiff exponentially increases,with this increase being more pronounced at lowervalues ofa. The values of Cdiff at inflection pointsare defined by the values of Cdl (A) and Cad + Cdl(B). The position of the inflection points on the fre-quency axis (not shown in this work) is also sensi-tive to the values of the resistances Radho and Radhe.It should be noted here that eq. (6) is dimensionallycorrect, i.e. its dimension is capacitance per unitarea. Hence, it could be concluded that if Cdiff vs. ffunction is dependent on frequency in the whole


F i g . 2 Equivalent circuit for the anion adsorption onto realsingle crystal surfaces: Rs solution resistance; Rad

he chargetransfer resistance corresponding to the adsorption of anions onthe heterogeneous part of the surface; CPEdl

he constant phaseelement corresponding to the adsorption of anions on the hetero-

geneous part of the surface; Radho charge transfer resistance

corresponding to the adsorption of anions on the homogeneouspart of the surface; Cad capacitance corresponding to the ad-sorption of anions onto homogeneous part of the surface.

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range of applied frequencies, a is lower than 1 and,accordingly, Cdl should be replaced with CPEin theequivalent circuit.

For the results presented in Fig. 3a it was as-

sumed that the adsorption process was under activa-tion control (higher concentration of anions than 1mM). If the diffusion, represented by the Warburgimpedance, was introduced in the equivalent circuit(in series with Cad and Radho), the following equa-tion for the Cdiff vs. w was obtained.

C C Rdiff dl adhe=

+-( ) ( ) sina aw

ap12

++

+ + + -C C

C C R

ad ad

ad ad adho

( )

( ) ( )

/

/ /

1

1

1 2

1 2 2 2 2 1 2

w s

w s w w s 2

(7)

Using the same parameter values as in Fig. 3afor the concentration (c) of 0.1 mM, the Cdiff vs. fdependences shown in Fig. 3b were obtained. Ascan be seen, inflection points A and B are definedonly fora = 1, while for all other values ofa prac-tically exponential dependence is obtained in thewhole range of frequencies. Hence, if the diffusionphenomena are involved and the charge distributionis not homogeneous, it is practically impossibleto determine the values of the adsorption parame-ters by plotting Cdiff vs. E curve for a single fre-quency.

In this paper, the dependences of the Cdiffvs. w,as well as Cdiff vs. E for the systems Ag(100)/0.01M NaBr and Ag(poly)/0.01 M NaBr + 0.1 MNaClO4, using the above-mentioned approach, wereanalyzed and discussed.

Experimental

All experiments were carried out in a two-com-partment electrochemical cell at the temperature of25 1 oC. The single crystal and polycrystallineelectrodes (Monocrystals Company, d = 0.9 cm)were sealed in an epoxy resin (resin EPON 828 +hardener TETA) in such a way that only the discsurfaces were exposed to the solution (0.636 cm2).

The counter electrode was a Pt sheet and wasplaced parallel to the working electrode surface.The reference electrode was a saturated calomelelectrode (SCE) placed in a separate compartmentand connected to the working compartment bymeans of a Luggin capillary. Solutions were madefrom pure NaBr (99.999 % Aldrich) and NaClO4(99.98 % Aldrich) chemicals and extra pure UVwater (Smart2PureUV, TKA). All potentials aregiven vs. SCE.

The single and polycrystalline surfaces wereprepared by a mechanical polishing procedure fol-lowed by chemical polishing in the solution con-taining NaCN and H2O2 as explained in detailin previous papers.28,46,47,6265 Before each experi-ment, the electrolyte was purged with high puritynitrogen (99.999 %) for 45 min, while a nitrogen at-mosphere was maintained over the solution duringthe experiment to prevent contamination with oxy-gen.

The cyclic voltammetry experiments were per-formed using a universal programmer PAR M-175,a potentiostat PAR M-173 and an X-Y recorder(Houston Instrument 2000R). A potentiostat Refer-ence 600 and a software EIS300 version 5.0(Gamry Instruments) were used to perform EIS anddifferential capacity measurements with an ampli-tude of 10 mV.


F i g . 3 (a) Cdiff vs. f curves calculated using eq. (6): Radho

= 50 W cm2; Radhe = 5000 W cm2; Cdl = 60 mF cm

2; Cad =

200 mF cm2. The values of a are marked in the figure. (b) Cdiffvs. f curves calculated using eq. (7): Rad

ho = 50 W cm2; Radhe =

5000 W cm2; Cdl = 60 mF cm2; Cad = 200 mF cm

2; c =0.1 mM. The values of a are marked in the figure.

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The differential capacity vs. potential curvesfor the system Ag(100)/0.01 M NaBr were obtainedby the following procedure: Potential of the elec-trode was changed in steps of 50 mV starting from1.2 V and finishing at 0.1 V; at each applied po-tential the values of the real and imaginary compo-nents of the impedance were recorded at differentfrequencies (1000, 700, 400, 200, 100, 70, 40, 20,10, 7, 4, 2, 1, 0.7, 0.4, 0.2 and 0.1 Hz); these valueswere corrected for the solution resistance Rs (deter-mined from the high frequency intercept on the ZReaxis ofZIm vs. ZRe diagrams, see Figs. 5 and 9) andconverted into Cdiff. For each potential the Cdiff vs.w curves were plotted. The EIS measurements atthree different potentials were performed in the fre-quency range from 0.01 Hz to 10 kHz with 10points per decade and the same amplitude. Fittingof Cdiff vs. w curves was performed using the com-mercially available Origin 6.1 program. One of themost powerful and complex components of the Ori-gin program is its nonlinear least squares fitting(NLSF) capability. Its nonlinear regression methodis based on the Levenberg-Marquardt (LM) algo-rithm and is the most widely used algorithm in non-linear least squares fitting. The NLSF always repor-ted the reduced chi2 value, varying from 1.02 1012

to 6.07 1015, as well as the coefficient of determi-nation (R2), varying from 0.99748 to 0.99987 withno weighting function. The curves connecting ex-

perimental points presented in Figs. 4a, 5, 7, 8b, 9and 11 were obtained by using B-spline function(smoothing the curve) defined in the Origin pro-gram.

In the case of the system Ag(poly)/0.01 MNaBr + 0.1 M NaClO4, CV and EIS were recordedusing the Gamry Reference 600 potentiostat. In-stead of using the previously described procedure,the EIS measurements were performed at differentpotentials (in steps of 50 mV) from 1.0 V to 0.05 V(in the frequency range from 0.1 Hz to 10 kHz withthe amplitude of 10 mV). For each potential, theCdiff vs. w curves were plotted and analyzed by thesame procedure as for the Ag(100)/0.01 M NaBrsystem (using Origin program). In order to plot Cdiffvs. E curves, the Cdiff values at certain frequencies(0.1, 1, 10 and 100 Hz) were used. It should be em-phasized that the value of the differential capacitywas calculated in all cases using the equation

CY

Z

Z R Zdiff

lmcorr

lm

Re s lm= =

- +

w w

( ) ( )2 2(8)

Each experiment was repeated three times andthe average values presented in this paper. The vari-ation of the results was 5 %.

Results

System Ag(100)/0.01M NaBr

The CV recorded for the Ag(100) in 0.01 MNaBr solution at a sweep rate of 100 mV s1 isshown in Fig. 4a. As can be seen, the voltammo-gram is in good agreement with the results of otherauthors,48,49 being characterized by almost revers-ible pairs of broad and sharp peaks.

Fig. 5 shows the results of the EIS measure-ments performed for the same system at three con-stant potentials (frequencies are in Hz). The highfrequency ends of the ZIm vs. ZRe diagrams are pre-sented in the inset of the figure. The solution resis-tance was determined by linear extrapolation to the


F i g . 4 (a) CV of Ag(100) in 0.01 M NaBr recorded at asweep rate of 100 mV s1. (b) Corresponding Cdiffvs. E curvesrecorded at different frequencies (marked in the figure in Hz).

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ZRe axis, whereby the value Rs = 102 W cm2

was ob-tained for all potentials. As can be seen, none of theimpedance diagrams is even close to the shape typi-cal for ideal double layer behavior.

Some of the obtained Cdiff vs. E curves areshown in Fig. 4b. The dispersion of points on theCdiff vs. E curves at the frequencies f> 400 Hz wassignificant and these results were not used for fur-ther analysis (at high frequencies the difference be-tween the values ofZRe and Rs is very small and, ac-cordingly, the value of ZRe-Rs becomes very sensi-tive to the measured ZRe and extrapolated Rs, pro-

ducing dissipation of points on the Cdiff vs. Ecurves). As can be seen, Cdiff was found to dependon frequency in the whole range of investigated fre-quencies, as it was the case with Ag(111) in 0.01 MNaCl (Ref. 28, Fig. 5).

Using the values ofCdiff at a constant potential(from the Cdiff vs. E curves), Cdiff vs. w curves wereplotted, some of which have been presented in Fig.6. In order to obtain the values for Cdl, Cad, Radho,Rad

he and a, fitting of the Cdiff vs. w curves was per-formed using eq. (6), as explained in the experi-mental section. The experimental points are pre-sented by squares, circles, triangles, etc., while the

lines represent the fitting curves. Potentials aremarked in the figure for each curve. As can be seen,good fits were obtained with very high values ofthe coefficient of determination (R2) (see experi-mental). Identical results were obtained for the restof the Cdiff vs. w curves, not presented in Fig. 6.

The dependences of the parameters Cdl, Cad,(Cdl + Cad), Radho, Radhe and a on potential are shownin Fig. 7. As can be seen in Fig. 7a, only Cad vs. Ecurve coincide well with the corresponding CV,whereas the value of a sharply decreases at themaximum on the Cad vs. E (r) curve, indicatingsignificant heterogeneity of the charge distributionover the electrode surface at potentials more posi-tive than the potential of the sharp peak on the CV(Fig. 4a). Resulting Radho vs. E and Radhe vs. Edependences are also different, as shown in Fig. 7b.


F i g . 5 ZIm vs. ZRe diagrams recorded at potentials of 1.10 V (), 0.50 V () and 0.30 V (r) in the frequencyrange from 0.01 to 10000 Hz for the system Ag(100)/0.01 M

NaBr. The high frequency ends of ZIm vs. ZRe diagrams, used fordetermination of Rs, are presented in the inset. Frequencies aremarked in Hz.

F i g . 6 Cdiffvs. w curves for different potentials (marked in

the figure) obtained from the Cdiff vs. E curves for the systemAg(100)/0.01 M NaBr. The squares, circles, triangles, etc. rep-resent the experimental points, while the full lines represent the

fitted curves obtained by using eq. (6).

F i g . 7 Results obtained by fitting the Cdiffvs. w curves for

different potentials with eq. (6) for the system Ag(100)/0.01 MNaBr; (a) Cad vs. E (r), Cdl vs. E (), (Cdl + Cad) vs. E () anda vs. E (q) curves. (b) Cad vs. E (r), Rad

ho vs. E () and Radhe

vs. E () curves.

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The charge recorded under the anodic part ofthe voltammogram shown in Fig. 4a, as well as thecharges obtained by the integration ofCdl vs. E, Cadvs. E and (Cdl + Cad) vs. E curves presented in Fig.7a are given in Table 1.

System Ag(poly)/0.01 M NaBr + 0.1 M NaClO4

The CV recorded at the Ag(poly) in 0.01 MNaBr + 0.1 M NaClO4 solution at a sweep rate of100 mV s1 is shown in Fig. 8a, while Cdiff vs. Ecurves are shown in Fig. 8b (frequencies are in Hz).As can be seen, the CV is in good agreement withthe Cdiff vs. E curves recorded for low frequencies(< 10 Hz), particularly with the curve recorded forf= 0.1 Hz. The CV (as well as Cdiff vs. E curves) ischaracterized with three different regions, doublelayer region (A) and adsorption regions (B) and(C). At the potentials close to zero, a nucleationloop reflecting formation of 3D layer of AgBr isdetected.

Fig. 9 shows the EIS measurements performedfor this system at four constant potentials. The highfrequency ends of the ZIm vs. ZRe diagrams are pre-sented in the inset of the figure. The solution resis-tance was determined by linear extrapolation to theZ

Reaxis, whereby the value R

s= 8.16 W cm2 was

obtained for all potentials. As in a previous case,none of the impedance diagrams is even close to theshape typical for ideal double layer behavior.

Some of the Cdiff vs. w curves were plotted inFig. 10. As can be seen, the shape of these curvesdepends on the potential regions, being sensitive tothe potential in the regions (A) and (B), and practi-cally insensitive to the potential in the region (C).In order to obtain values for Cdl, Cad, Radho, Radhe, sand a, fitting of the Cdiff vs. w curves was per-formed using eq. (7) since the use of eq. (6) couldnot give good results (see discussion). The experi-mental points are presented by squares, circles, tri-angles, etc., while the lines represent the fittingcurves. Potentials are marked in the figure for each


T a b l e 1 Charge recorded under corresponding curves forthe system Ag(100)/0.01 M NaBr. Theoreticalcharge for c(2x2) = 96mC cm2(assuming com-

plete charge transfer).

Curve Charge

Anodic part of the CV 105 mC cm2

Cad vs. E 31 mC cm2

Cdl vs. E 32 mC cm2

(Cdl + Cad) vs. E 63 mC cm2

F i g . 8 (a) CV of Ag(poly) in 0.01 M NaBr + 0.1 MNaClO4 recorded at a sweep rate of 100 mV s

1. (b) Corre-sponding Cdiff vs. E curves recorded at different frequencies(marked in the figure in Hz).

F i g . 9 ZIm vs. ZRe diagrams recorded at different poten-

tials (marked in the figure) in the frequency range from 0.01 to10000 Hz for the system Ag(poly)/0.01 M NaBr + 0.1 M

NaClO4. The high frequency ends of ZIm vs. ZRe diagrams, usedfor determination of Rs, are presented in the inset.

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curve. Identical results were obtained for the rest ofthe Cdiff vs. w curves, not presented in Fig. 10.

The dependences of the parameters Cdl, Cad,(Cdl + Cad), Rad

ho, Radhe, sand a as a function of po-

tential are shown in Fig. 11. From Fig. 11a it can beseen that the value of Cdl is practically negligible,and that (Cdl + Cad) vs. E and Cad vs. E curves areidentical, coinciding well with the correspondingCV, whereas the value ofa is much smaller in com-parison with the one detected for the Ag(100) (seeFig. 7a, before the sharp peak on the CV), decreas-

ing at the maximum on the Cad vs. E (r) curve.Such behavior ofa indicates significant heteroge-neity of the charge distribution over the electrodesurface in the entire investigated potential range, asshould be expected for the polycrystalline surface.Hence, in the presence of the supporting, non-ad-sorbing electrolyte, Cdl is practically independentof potential. The Rad

ho vs. E and Cad vs. Edependences, shown in Fig. 11b, possess the shapesexpected for a serial connection of Rad

ho and Cad.Although the process of bromide anions adsorptioncannot be diffusion controlled, the high value of theWarburg constant s, shown in Fig. 11c, indicatesthat some diffusion-like phenomenon is involved inthe process of anion adsorption.

Discussion

The bromide anions are known as strongly ad-sorbing species characterized by the formation ofordered adsorbate structures on all investigated sin-gle crystal faces.4860 It is important to note that, ex-cept in our recent papers28,46 and papers of Kerneret al.13 and Pajkossy,12,14,15 in all previous18 andlater4856 investigations it was assumed that the dou-ble layer behaves as an ideal double layer, ne-glecting the possibility of heterogeneity of the elec-trode surface. Different techniques were employedin these investigations: LEED-Auger,51 in situSTM,43,45 in situ XAFS,52 in situ X-ray,53,54 EIS,5557differential capacity measurements,4850 thermody-namic analysis chronocoulometric curves4850 and


F i g . 1 0 Cdiff vs. w curves for different potentials (marked in the figure) obtained from the EIS measurements for the systemAg(poly)/0.01 M NaBr + 0.1 M NaClO4. The squares, circles, triangles, etc. represent the experimental points, whilethe full lines represent the fitted curves obtained by using eq. (7).

F i g . 1 1 Results obtained by fitting the Cdiff vs. w curves

for different potentials with eq. (7) for the system Ag(poly)/0.01M NaBr + 0.1 M NaClO4; (a) Cad vs. E (r), Cdl vs. E (),(Cdl + Cad) vs. E () anda vs. E (q) curves. (b) Cad vs. E (r)and Rad

ho vs. E (). (c) Cad vs. E (r) andsvs. E () curves.

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cyclic voltammetry in all papers.567 Most of the ex-periments were performed in the presence of thenon-adsorbing supporting electrolyte (mainlyKClO4 or HClO4) with the addition of a low con-centration of bromide anions (up to 10 mM), whilein a few of them one component (KBr, NaBr, HBr)electrolytes were used43,51,53 respectively, and ad-sorption of bromide anion was investigated in theabsence of the supporting electrolyte. A commonfeature of the experiments performed in the pres-ence of non-adsorbing supporting electrolyte isthe appearance of peaks on CVs for pure supportingelectrolyte, corresponding to the specific adsorptionof ClO4 anions to some extent.4850,5557 Also, in allpapers with differential capacity measurements, theCdiff vs. E curves were recorded only at one con-stant frequency (1 Hz or 18 Hz) at the sweep rate of

10 mV s1 and 10 mV peak-to-peak amplitude. T.Wandlowski et al.48 clearly stated that differentialcapacity vs. potential curves do not provide equilib-rium data for Br adsorption onto Ag(100) surfacein the low and medium concentration regions, withthis comment being relevant to the curves recordedat one frequency only. It should also be stated herethat the differential capacity dispersion, recordedeven in a pure supporting electrolyte (0.1 M HClO4),as well as in the presence of adsorbing anions in avery narrow frequency range (12 Hz < f< 80 Hz),has been observed by Hamelin and coworkers on

perfect single crystals.5

All authors employingthermodynamic analysis4850 assumed that the ad-sorption of anions from the supporting electrolyte isnegligible. It is characteristic that, in all these cases,the values of the electrosorption valence (-g) weresmaller than 1, indicating partial charge transfer duringbromide anions adsorption. On the other hand, inonly one paper53 was the value of g = -1 0.2for bromide anions adsorption onto Au(111) ob-tained by the analysis ofG vs. E curves at differentanion concentrations. It is characteristic that insome papers employing EIS,68,56,57 ZIm vs. ZRe dia-grams were used for fitting experimental resultswith corresponding equivalent circuit for the diffu-sion control of anion adsorption. It is importantto note here a statement of D. Eberhardt et al.55

concerning the fitting procedure for such a case:Although the resulting equivalent circuit repre-sents very well the surface processes occurring atthe interface, it should be pointed out that the em-ployment of such a complicated combination of ele-ments conduces to rather high correlation factor be-tween the fitted values, so that the individual ele-ments can be determined only with a fairly largeuncertainty.

Hence, the generally accepted explanation forthe frequency dependence of the interfacial differ-ential capacity (capacity dispersion) could be

given as: this phenomenon is a consequence of ei-ther adsorption of organic or certain inorganic spe-cies58,59 or molecules,60,61 or surface roughness andheterogeneity,915,28,46 or specific adsorption of an-ions.28,4650,62,63 It should be emphasized here that,except in our previous papers,28,46 the capacity dis-persion as a consequence of both anion adsorptionand surface heterogeneity, has not been consideredin the literature.

This work considers both cases: adsorption ofonly one anion (solution of pure NaBr salt) in theabsence of supporting electrolyte, and adsorption ofthe same anion of the same concentration in thepresence of non-adsorbing supporting electrolyte(0.1 M NaClO4 possible competitive adsorption).At the same time, the possibility for diffusion-con-trolled adsorption of anions is avoided by using

concentrations at which the adsorption process isunder activation control.

System Ag(100)/0.01 M NaBr

As can be seen, the CV shown in Fig. 4a is ingood agreement with the results of other au-thors.4850

The shape of the impedance diagrams shown inFig. 5 indicates deviation from the ideal doublelayer behavior.915 Impedance diagram recorded at0.3 V vs. SCE (r) is very similar to the one that

might correspond to diffusion-controlled adsorp-tion,7but an attempt to fit this diagram with the cor-responding equation for diffusion-controlled im-pedance was not possible, and this is one more ar-gument for the statement that such a shape of theimpedance diagram could be a consequence of sur-face heterogeneity, as well as specific anion adsorp-tion.

The importance of the solution resistance sub-traction should be emphasized here. As can be seenin the inset of Fig. 5, values of ZRe at frequencieslower than 1 kHz are very close to the value of Rsand if R

sis not subtracted, lower values for C

diffwould be obtained (see eq. (8)).The Cdiff vs. E curves as a function of fre-

quency are presented in Fig. 4b. The shape of theCdiff vs. Ecurves is practically identical to the shapeof CV at low frequencies (lower than 10 Hz). Theinfluence of the frequency on the shape of this de-pendence is also evidence of the deviation from theideal double layer behavior, while the similaritybetween the shape ofCdiff vs. fcurves simulated andpresented in Fig. 3a and the experimentally ob-tained ones (Cdiff vs. w presented in Fig. 6) couldonly be ascribed to the presence of both specific ad-sorption of anions and the surface heterogeneity.

Comparing (Cdl + Cad) vs. E curve (Fig. 7a)with Cdiff vs. E curves (Fig. 4b), it could be con-


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cluded that Cdiffvs. Ecurves show higher values forthe capacity than the one presented in Fig. 7a.Hence, it seems that neither of the curves presentedin Fig. 4b could be considered relevant for the sys-tem Ag(100)/0.01 M NaBr. Only after fitting C

diffvs. w curves recorded at different potentials wasthe correct differential capacity vs. potential curve,(Cdl + Cad) vs. E obtained.

Considering the results presented in Fig. 7a, itcould be concluded that the shape of the Cad vs. Ecurve is much more similar to the shape of CV thanthe other two curves. Fig. 7a illustrates that Cdl in-creases with potential up to 0.75 V and thensharply decreases to the very small values of about35 mF cm2. At the position of a maximum on theCad vs. E curve, Cdl is practically negligible and atpotentials more positive than 0.60 V a total capac-ity (Cdl + Cad) is practically determined by the valueofCad. The value ofa sharply decreases from about0.95 at 0.70 V to about 0.45 at 0.10 V. This sys-tem has already been analyzed by Wandlowski etal.48 and it was shown by SXS analysis that with in-creasing electrode potential, bromide undergoes aphase transition from a lattice gas to an orderedc(2x2) structure, and that this structure is formed atthe potential of the sharp peak on both the CV andCdiff vs. E curves. Taking into account that, in thecase of bromide adsorption, incommensurate ad-sorbed structures, compressing uniformly with in-

creasing potential, have been detected5355 after thecommensurate ordered structures were formed(sharp peak on the CV), such a change of the sur-face homogeneity, i.e. the change ofa, could be ex-pected. At the same time, it is important to note thatat potentials close to 0.0 V vs. SCE a nucleationloop can be detected (not shown in this figure), in-dicating the formation of 3D layer (see Fig. 8a) ofAgBr (similar to behavior of Ag(111) in 0.1 MNaCl64). It is quite reasonable to assume that thetransformation of ordered c(2x2) adsorbed structureinto 3D layer should be accompanied by the change

of the charge distribution, i.e. the homogeneity ofthe electrode surface.Concerning the Radho vs. E and Radhe vs. E

curves it is seen that the values of Radho and Radhe areof the same order of magnitude, varying between0.1 and 4.5 kW cm2 (Fig. 7b). At the beginning ofthe adsorption process, the Radho is high, whereasRad

he is low, indicating faster adsorption of bromideanions at the monoatomic steps. In the region ofsharp peaks on Cad vs. E curve, Radho sharply de-creases, while Radhe sharply increases, as it could beexpected. It is important to note that in this case theshapes of C

advs. E and R

ad

ho vs. E curves are farfrom being a mirror-image of one another.28 Such abehavior is most likely the consequence of the for-mation of incommensurate adsorbed structures at

potentials more positive than the potential of sharppeak on the CV,5355 i.e. a sharp decrease of surfacehomogeneity (decrease ofa).

Finally, considering charges presented in Table

1, it could be concluded that the charge under theanodic part of the CV is higher than that obtainedby integration of (Cdl + Cad) vs. E curve. At thesame time, charges corresponding to the Cad vs. Eand Cdl vs. E curves are almost identical. Takinginto account that for a formation of ordered c(2x2)structure the theoretical charge needed (assumingcomplete charge transfer) amounts to 96 mC cm2, itappears that for the formation of this structure g =0.32 (31 mC cm2 over 96 mC cm2). Hence, thisanalysis clearly indicates that neither the charge un-der the CV, nor that underCdiff vs. Ecurve recordedat a single frequency and C

advs. E and C

dlvs. E

curves, can be considered relevant for determiningeither the structure of adsorbed anions or the valueof g. At the same time, in order to define correctcharges corresponding to the adsorption on the het-erogeneous and the homogeneous part of the sur-face (as well as correct values of Cdl and Cad) it isnecessary to know exactly the corresponding sur-face area (on the atomic level), which is practicallyimpossible using present techniques for the surfacecharacterization.

System Ag(poly)/0.01 M NaBr + 0.1 M NaClO4

In the case of polycrystalline surface, sharppeaks for ordered adsorbed structures cannot be ex-pected, as can be seen on the CV shown in Fig. 8a.Comparing CVs recorded for single crystal sur-faces4860,65 one can conclude that in the region (B)adsorption on the heterogeneous part of the surfacetakes place, while, most probably, ordered struc-tures are formed in the region (C). The nucleationloop at potential close to 0.0 V vs. SCE is a conse-quence of the formation of 3D layer of AgBr.64 Asimilar conclusion can be drawn from the shape ofthe C

diff

vs. E curves, shown in Fig. 8b.The EIS results (Fig. 9) clearly show deviation

from the ideal double layer behavior at all inves-tigated potentials, as well as much lower value of Rsin the presence of the supporting electrolyte (insetof Fig. 9) in comparison with the one recorded forthe system Ag(100)/0.01 M NaBr. Although the so-lution resistance is much smaller in the presence of0.1 M NaClO4, the importance of its subtraction isas significant as in the system Ag(100)/0.01 MNaBr, since at high frequencies ZRe values are alsovery close to the value ofRs and the precision of theRs determination is very important.

A very good fit of the experimentally recordedCdiff vs. w curves (Fig. 10) clearly indicates that forthis system eq. (7) must be used. Resulting values


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of adsorption parameters, presented in Fig. 11 as afunction of potential, confirm that in the presenceof 0.1 M NaClO4 different dependences were ob-tained in comparison with those recorded in a pureNaBr salt. The (C

dl

+ Cad

) vs. E curve is practicallyidentical to the Cad vs. E curve, while the value ofCdl is almost independent of potential and muchsmaller than expected for the ideal double layercapacity (Cdl = 20 F cm2, Fig. 11a). At the sametime, as it might be expected, charge distributionover the polycrystalline surface is heterogeneous,reaching maximum value of a = 0.8 (Fig. 11a).Considering the shapes of Cad vs. E and Radho vs. Ecurves, one can conclude that they are more or lessa mirror-image of one another28 (Fig. 11b). Themost interesting is svs. E dependence. Taking intoaccount that the constant s represents the presence

of Warburg-like impedance and that the diffusion ofanions from the bulk of solution is excluded at suchanion concentration, it seems most likely that thediffusion phenomenon is connected with the re-placement and exchange of anions in the innerHelmholtz plane. Actually, ClO4 anions are alreadyadsorbed on the electrode surface when Br anionsstart to adsorb. Since the adsorption of Br anions ismuch stronger, ClO4 anions must be desorbed andreplaced with bromides. This process is obviouslyslow step in the overall reaction, being expressed asthe diffusion-like phenomenon, and accordingly eq.

(7) must be used to fit experimentally recorded Cdiffvs. w curves (Fig. 10). According to the results pre-sented in Fig. 11c, this effect is more pronounced inthe region of ordered (more dense) adsorbed struc-ture formation (potential region C), where all ClO4

anions must be removed and replaced with bro-mides. It is most likely that removed ClO4 anionsagain adsorb on the bromide layer, as it was thecase in UPD of Cd onto Cu(111)66 and Cd ontoAg(111) in the presence of chloride anions.67 A sim-ilar effect has recently been recognized by T.Pajkossy and D. M. Kolb68 in the double layer re-gion of Pt(111) and Ir(111) in the presence of onlyone anion (much simpler case) and they attributedthe frequency dependence of the interfacial capaci-tance to the relatively slow exchange of anions be-tween the outer and inner Helmholtz planes. At thismoment a convincing explanation for the observedphenomenon is missing and it will be the subject offurther investigations.

Conclusion

For the determination of the adsorption param-eters, a new equivalent circuit and correspondingequation for analyzing anion adsorption, based on adifferent definition of the constant phase element,

has been developed and used in this work. It isshown that such analysis can successfully be ap-plied in the case of bromide anions adsorption intwo systems: Ag(100)/0.01 M NaBr andAg(poly)/0.01 M NaBr + 0.1 M NaClO

4

. Homoge-neity of the charge distribution over the electrodesurface was found to change as a consequence ofthe adsorption of bromide anions in both cases. Itwas shown that in the presence of the supportingelectrolyte (0.1 M NaClO4) Warburg impedancemust be introduced in the equivalent circuit (andcorresponding equation for Cdiff) in order to fit ex-perimentally recorded Cdiff vs. w curves. This phe-nomenon was explained by the slow step of re-placement of already adsorbed perchlorate anionswith bromide anions.

S y m b o l s

C capacitance, F cm2

c concentration of adsorbing anions, M

Cad adsorption capacitance, F cm2

Cdiff differential capacitance, F cm2

Cdl double layer capacitance, F cm2

CPE constant phase element

CPEdlhe constant phase element of the heterogeneous

part of the surface

D diffusion coefficient of adsorbing anions, cm2 s1

f frequency, HzR resistance, W cm2

Rad adsorption resistance, W cm2

Radhe adsorption resistance on the heterogeneous part

of the surface, W cm2

Radho adsorption resistance on the homogeneous part of

the surface, W cm2

Rs solution resistance, W cm2

YIm imaginary component of admittance, W1 cm2

Y0 constant, W1 cm2 sa

ZRe real component of impedance, W cm2

ZIm imaginary component of impedance, W cm2

ZCPE impedance of the CPE

a factor of the charge distribution homogeneity

s Warburg coefficient, W cm2 s1/2

w angular frequency, s1

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