Journal of Electroanalytical Chemistry 448 (1998) 139–142

Short communication

Impedance of rough capacitive electrodes: the role of surface disorder

Zsolt Kerner, Tamas Pajkossy *

KFKI Atomic Energy Research Institute, POB 49, H-1525 Budapest 114, Hungary

Received 22 October 1997; received in revised form 12 December 1997; accepted 23 December 1997

Abstract

The interfacial impedance of solid electrodes in the absence of Faradaic reactions usually deviates from purely capacitivebehaviour; this effect is enhanced on rough electrodes. We present a qualitative experiment showing that capacitance dispersionon solid electrodes is due to surface disorder (i.e. heterogeneities on the atomic scale) rather than roughness (i.e. geometricirregularities much larger than those on the atomic scale). © 1998 Elsevier Science S.A. All rights reserved.

Keywords: Interfacial impedance; Solid electrodes; Capacitance dispersion; Heterogeneity; Atomic scale

1. Introduction: the problem

According to the well-established principles of elec-trochemistry, the electrode�electrolyte interface is ex-pected to behave as a capacitor from the electrical pointof view, provided that Faradaic reactions are absent.Such an ideal behaviour can indeed be observed withliquid mercury electrodes or single crystalline metalelectrodes; however, on polycrystalline solid electrodesthe impedance often has a functional form as if thedouble-layer capacitance were frequency dependent. Inother words, ‘frequency dispersion of capacitance’ orsimply ‘capacitance dispersion’ is observed. This meansthat any attempt to determine exact double-layer capac-itances and to extract quantities of thermodynamicsignificance from them cannot be successful. To charac-terize dispersion, the interfacial capacitance is oftenapproximated by a constant phase element1 (CPE); in

other words, C(v)8 (iv)a−1, where i is the imaginaryunit. Such behaviour with exponent a between 0.7 and0.9 is often obtained with solid electrodes in the audioand sub-audio frequency range.

Polycrystalline solid surfaces are never perfectly flat:they are neither planar on the atomic scale due to steps,kinks, dislocations; nor on a much larger scale due tocorrugations, scratches, pits, grooves, etc. This is espe-cially true for electrodes with a mechanical finish, e.g.polished electrodes. We shall distinguish the two typesof irregularities by denoting the atomic scale imperfec-tions as ‘surface disorder’ (which refers to the presenceof both the geometric and energetic inhomogeneities),whereas the term ‘rough’ will be used exclusively forgeometric imperfections of characteristic size largerthan, say, 10 nm. Surface disorder and roughness arefrequently interrelated: e.g. a mechanically coarsenedsurface carries a great number of dislocations.

The connection between capacitance dispersion andsurface roughness was recognized about half a centuryago [1]; for a review of the early observations andtheories see Ref. [2]. Until now the simplest—andalmost exclusively followed—way of theoretically treat-ing this phenomenon has been to disregard atomic scaleheterogeneities and to assume that the capacitance of

* Corresponding author. Hungarian Academy of Sciences, CentralResearch Institute of Physics, P.O. Box 49, 1525 Budapest 114,Hungary. Fax: +36 1 3959042; e-mail: pajkossy@sunserv.kfki.hu

1 We apply the usual definition of constant phase elements, viz.admittance is Y(v)=s*(iv)a. For ideal capacitances a=1.

0022-0728/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.PII S0022-0728(98)00025-4

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the double layer is uniform along the rough surface,and the only role of geometry is that the effectivesolution resistance is greater at the bottom of thehollows than at the top of the protrusions of theelectrode. With this point of departure in mind—andassuming some specific electrode geometry—one canset up an equivalent circuit or, more generally, cancalculate the potential distribution within the solution,and hence the Z(v) function. Although this tends to berather difficult, the electrode geometries of certain sym-metries lead to relatively simple Z(v) functions. Forexample, the geometry of a spongy electrode can bemodelled by a parallel set of infinitely long narrowpores with perpendicular cross-links; the theory [3]predicts that the impedance of such a system—havingtranslational symmetry—is of CPE form with a=1/2.Rough electrodes have been modelled by surfaces offractal geometry which possesses dilatational symmetry;this class of theories yields CPE behaviour with afractional exponent depending on the fractal dimension[4]. Unfortunately, the oversimplification in models tak-ing into account the geometry only, leads to unrealisticresults: the frequency range in which these modelspredict that the capacitance dispersion is much higher(kHz to GHz) than that at which the dispersion isusually observed. Therefore, the models taking intoaccount geometry only are not suitable for interpretingthe de facto link between roughness and capacitancedispersion. Instead, considering additional points aswell, it has been suggested [5] that the degree of devia-tion from ideal capacitive behaviour depends on thesurface heterogeneity, ‘disorder’ of the electrode sur-face, and on whether or not the anions of the elec-trolyte are specifically adsorbed on the electrode.

The latter effect, i.e. the role of specific anion adsorp-tion and its consequences, has recently been analysedusing electrodes of uniform surface by the case study ofmeasuring the voltammetry and impedance spectra ofsingle crystalline gold electrodes in bromide-containingperchlorate solutions [6]. Capacitance dispersion fromthree sources was found:

(1) ‘classical’ adsorption impedance due to slow dif-fusion to and/or slow adsorption on the surface [7];

(2) dispersion due to phase transitions of the upper-most gold layer (lifting of the reconstruction of the goldsurface [8]) and of the bromide adlayer [9];

(3) compression of the adlayer.It is worth mentioning that, in the absence of specific

anion adsorption on homogeneous surfaces, capaci-tance dispersion vanishes: on single crystalline goldelectrodes, in pure perchlorate solutions, at potentialsclose to the negative end of the ideally polarizableregion, (almost) ideal capacitive impedances can bemeasured. The extent of the dispersion can be charac-terized by approximating these impedances by CPEs:the exponents differ from unity by as little as about

0.01 in the frequency range between 0.1 Hz and 1 kHz[6].

In this paper we disregard specific anion adsorptionand focus our attention on the role of the nature of thesurface. We show a set of impedance experimentsdemonstrating that the capacitance dispersion on roughelectrodes is due to atomic scale non-uniformities (sur-face disorder) rather than to roughness.

2. Experimental

In this section we show a very simple—qualitative—experiment carried out with noble metal electrodes(polycrystalline gold) in inert electrolyte (deaeratedaqueous 0.1 M HClO4 solutions) at potentials wherethe Faradaic reactions can be safely disregarded. Themethod (impedance measurements) and the experimen-tal details are very similar to those described in Refs.[5,6]; the purity of our electrochemical system was justas high as that described in Ref. [6]. The measuredimpedance spectra were transformed by calculating theC(v)=1/([(Z(v)−Z(v��)]× iv×Ag) ‘complexcapacitance’ function, where Ag stands for macroscopicarea. Being a complex quantity, C(v) can be plotted inBode representation. The extent of the capacitancedispersion is nil if the log(Cabs) vs. log( f ) curve is ahorizontal line and the phase angle, u, is 0 everywhere.Increasing capacitance dispersion means more andmore tilted log(Cabs) vs. log( f ) curves and increasing u

values. An ideal CPE appears as a straight line of slopea−1 on the log(Cabs) vs. log( f ) plot, and the phaseangle is constant, u=90(1−a).

Rough gold electrodes were prepared by meltingpieces of gold on a quartz plate with a hydrogen flameto yield hemispherically shaped samples; their flat sidewas roughened with emery paper of grit 120. (This flatside was in contact with the electrolyte during themeasurements via a ‘hanging meniscus’.) The electrodewas then cleaned chemically by alternately soaking infreshly made caroic acid (conc. H2SO4 containingH2O2) and in 10% KOH solution; it was then thor-oughly rinsed by ultrapure water. Cleaning in such away means that the electrode can safely be regarded asclean. The capacitance of this electrode, measured in0.1 M HClO4 solution at −0.2 V, showed a definitedispersion (Fig. 1, squares). Were the interfacialimpedance approximated by a CPE, the exponent awould be around 0.9 (note that the capacitance disper-sion with single-crystal gold electrodes, but otherwiseidentical conditions was much less, a:0.99). After thismeasurement the electrode was annealed in a bunsenburner flame for a short time (5 s), during which the redglow was barely visible (during the annealing the sur-face temperature remains much lower than the meltingpoint of the gold, so the surface geometry does not

Z. Kerner, T. Pajkossy / Journal of Electroanalytical Chemistry 448 (1998) 139–142 141

change). After annealing the electrode was quenched inultrapure water and transferred to the cell and theimpedance was again measured. The capacitance dis-persion was found to be markedly decreased (triangles)and, with a longer annealing (1 min), the dispersionfurther decreased (diamonds). We were not able toachieve any further, significant decrease of the disper-sion by simple flame annealing. However, the disper-sion could be further decreased by anodically etchingthe electrode in concentrated CaCl2 solution, therebyremoving the scratched upper layer. The etching gave abright surface with a number of crystal faces; thecapacitance spectrum of these electrodes approachedideal behaviour (circles).

We interpret this result in such a way that theannealing cannot change the surface geometry, it canonly affect the defects of the surface: it tempers themand thus reduces the surface energetic heterogeneities.By etching, we can remove the thick surface layer whichwas affected by the roughening; the remaining polycrys-talline surface is much more homogeneous.

A remark on reproducibility is due here: we repeatedthe very same experiment five times, and further exper-iments were carried out at other electrode potentials.The individual spectra are not reproducible mainlybecause the procedure—roughening with emery paperand flame annealing—is not a standardized one. How-ever, the tendency towards decreasing dispersion isclearly reproducible, for each potential (the seriesshown in Fig. 1 are typical spectra).

3. Conclusions

Electrode preparation is a key issue in electrodekinetics. There are many electrode substances andpreparation methods, and one cannot suggest ‘the best’preparation technique. For studies with single-crystalnoble metals the electrode preparation technology in-volves flame annealing, which yields clean, high qualitysurfaces (thereby yielding low capacitance dispersion).Most electrochemical tests, however, are carried out onimperfect surfaces where there is no possibility forthermal treatment. In these cases one should not besurprised to observe ‘ill-behaved’ impedances.

It is generally accepted that the capacitance of roughsolid electrodes depends upon frequency; our views onthe extent of the dependence are influenced markedlyby the results of five sets of measurements which gaverather large dispersions [10–14]. By approximating theresults of these measurements by CPEs, we get valuesranging from 0.8 to 0.96 for a. These low a values havebeen obtained with unannealed electrodes (there is nomention of annealing among the experimental proce-dures). On the other hand, whenever polycrystallineelectrodes are thermally annealed or ‘electrochemicallyannealed’ by potential cycling, we get exponents muchcloser to unity, between 0.95 and 1 (in the case of gold,see, for example, Ref. [15]).

The conclusion to be drawn from our measurementresults is very simple: a significant portion of capaci-tance dispersion observed when studying polycrystallinesolid electrodes is due to the atomic scale heterogeneity.The extent of capacitance dispersion of electrodes ofrough surfaces is larger than on smooth ones becausethe former are much more heterogeneous on the atomicscale than the latter.

Acknowledgements

The financial support of the Hungarian Science Re-search Fund OTKA (No. T016374) is acknowledged.

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Fig. 1. Capacitance spectra of a polycrystalline gold electrode in 0.1M HClO4 solution at −0.2 V vs SCE. Squares, original, roughenedelectrode; triangles, after short annealing; diamonds, after long an-nealing; circles, after etching. Full and open symbols refer to log(Cabs)and to u values, respectively.

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