Characterisation of Au(111) and Au(210) ∣ aqueous solution interfaces by electrochemical immittance spectroscopy1

Journal of Electroanalytical Chemistry 455 (1998) 107 – 119

Characterisation of Au(111) and Au(210) aqueous solution interfaces by electrochemical immittance spectroscopy1 A. Sadkowski a,*, A.J. Motheo b, R.S. Neves b a b

Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44 /52, 01 -224 Warsaw, Poland Instituto de Quimica de Sa˜o Carlos, Uni6ersidade de Sa˜o Paulo, Cx.P. 780, Sa˜o Carlos, SP 13560 -970, Brazil Received 10 December 1997; received in revised form 22 May 1998; accepted 9 June 1998

Abstract Gold single crystals oriented to expose the (111) and (210) faces were investigated using electrochemical immittance spectroscopy (EIS) in aqueous solutions of HClO4 and KF in the double layer region with the aim of identifying and explaining the frequency dispersion of interfacial capacitance known as constant phase angle (CPA) dispersion. Au(111) and Au(210) were chosen as representing the whole range of variance of electrochemical properties of Au(hkl) electrodes. Au(111) as the most uniform, microscopically smooth surface behaved with almost ideal capacitance in HClO4 solutions in the whole potential range and also in KF solutions, in that case with the exception of potentials well positive to the potential of zero charge (pzc). Au(210) being microscopically the most corrugated surface displayed significant CPA dispersion in both electrolytes. In HClO4, dispersion on Au(210) occurred mostly in the potential region slightly positive to the potential of zero charge where the capacitance hump of the Helmholtz layer appeared. Analogous dispersion occurred on Au(210) in KF solutions only at high concentrations. The behaviour closest to ideal, dispersionless behaviour was always observed at sufficiently negative potentials. In KF solutions at positive potentials dispersion on both electrodes may be attributed to the adsorption (OH − , HF). In the intermediate potential range, close to the Helmholtz capacitance hump it can be attributed to solvent-metal interactions. Dispersion was lower in well conducting (concentrated) electrolytes and this suggests its geometrical nature is related possibly to the fractal pattern of the structured solvent. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Gold single crystals; Double layer; Electrochemical immittance; Capacitance dispersion; Constant phase element; Fractal electrodes

1. Introduction The interface between a liquid mercury electrode and a liquid electrolyte constituted for many years a paradigm of the electrochemical science due to its almost perfect agreement with the laws of thermodynamics [1]. The determination of the double layer capacitance–potential relation (C – E plots), the most important thermodynamic experiment in electrochem-

* Corresponding author. Fax: +48 22 6325276; e-mail: [email protected] 1 Paper presented at the 1997 Fischer Symposium, 15–19 June 1997, Karlsruhe, Germany.

istry [2], was carried out routinely on mercury in a broad frequency range giving consistent data [3]. When integrated once with respect to the electrode potential these capacitance data give the charge of the electrode and, integrated twice, they give the interfacial tension of the electrode, which can be verified in a direct experiment proving the consistency of the whole procedure. All these data laid the basis for theories of the double layer [4,5] and its influence on the electrode kinetics [2,6] on metals in general, including solid electrodes. This elegant thermodynamic approach unfortunately often fails for solid electrodes for which the very meaning of interfacial energy is still involved in uncertainty

0022-0728/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0022-0728(98)00237-X

108

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

[1,7] and that of the interfacial immittance, including double layer capacitance, is obscured by the puzzling dependence on frequency often referred to as frequency dispersion of the interfacial capacitance [8]. Electrodes which are ordinarily considered as ideally polarizable (Au, Ag, Pt), at least in a certain range of electrolyte compositions and electrode potentials, display a capacitance dispersion characterised by a constant phase angle (CPA) in a remarkably broad range of frequencies and their interfacial admittance is described by: Y = Y0(iv)n

(1)

and including electrolyte resistance Rs, assumed to be uniform along the electrode surface. The interfacial impedance Z=1/Y then becomes: Z =Rs + (1/Y0)(iv) − n

(2)

where i= − 1 (imaginary unit); Y0-called here the pre-exponential coefficient [9,10] is an analogue of the double layer capacitance (Cdl); n is the CPA exponent, usually 0.5 BnB1; when n =1, Y0 reduces to Cdl; v= 2pf is angular frequency, (rad s − 1), f, frequency (Hz). We have to note in passing that throughout this paper we use the term immittance in place of impedance which is still more popular in the electrochemical literature. This is because immittance is the more general term denoting various small signal inputoutput relations in frequency domains while impedence is merely the voltage-to-current ratio. The general term immittance covers both impedance and its reciprocaladmittance, as particular cases. A distributed electrical element with an admittance function given by Eq. (1) is called a constant phase element-CPE [11,12] and it cannot be represented by any finite number of lumped elements such as R, C, and L. The kind of the fractional exponent (power) dependence on frequency as in Eq. (1) is equivalent to the fractional power time dependence [13,14] (fractional power laws [15]) in relaxation experiments. Mathematically it represents the inadequacy of the system’s description in terms of ordinary differential equations with constant coefficients as is done for systems with lumped parameters [16]. The mathematical description in this case is done in terms of the partial differential equations as for the systems with distributed parameters [16]. It is interesting that the kind of fractional frequency dependence shown in Eq. (1) and the corresponding fractional power dependence in the time domain is quite common in dynamics of some heterogeneous, non-uniform or mesoscopic systems from diverse areas of science and engineering [15] such as dielectric physics [17] and mechanics [18] and it was labelled as a ‘new universality’ by Jonscher [19].

The constant phase angle behaviour was for many years associated with the roughness of solid surfaces and this association survived in titles of reviews devoted to the subject as: ‘impedance of rough... electrodes...’ [8,20], also in cases not really related to rough surfaces. It was claimed that the geometry of the interface was responsible for fractional power effects by inseparable coupling of the local electrolyte resistance with the local interfacial capacities in pores of rough or, on otherwise non-uniform surfaces. The non-uniformity postulated was of a fractal nature, which assumed self-similarity on scaling [21,22]. This kind of non-uniformity does not allow a clear distinction between its micro- and macroscale effects as long as the range delimited by lower cut-off and higher cut-off limits spans from micro- to macro-scale dimensions. These effects may be also referred to as meso-scale effects which are macro- with relation to the molecular dimensions and micro- with relation to the size of the electrode. Numerous theoretical models were put forward ([23–28] and references there), some of them relating the CPA behaviour to the fractal geometry of the interface and, in quantitative terms, relating the fractional exponent n to the fractal dimension D. Many of these models dealt with the fractality of voluminous phases of considerable roughness such as those obtained by diffusion limited electroor chemical deposition [29–31] and therefore they have only an indirect reference to our case of extremely smooth electrodes and should not be expected to provide an adequate explanation for the CPA capacitance dispersion. Only recently it was admitted that aside from (or instead of!) the geometry of the interface, the physicochemical factors such as adsorption of electrolyte components [8] or effects of the solvent [9,10] are significant. It is therefore important to separate the geometrical from the chemical factors by a proper design of the experiment. To achieve this, one should eliminate as far as possible the geometrical factors by using smooth and uniform monocrystalline surfaces and by careful configuration of electrodes to assure a uniform distribution of the electrical field and the proper sensing of the electrode potential which should be uniform along the electrode surface. In this context it has to be noted that it was found often that the smoother and cleaner the interface, the higher (closer to 1.0) is the exponent in Eq. (1), i.e. the closer the electrode to the ideal capacitive behaviour [8]. Hence, sceptical views were expressed sometimes that the CPA behaviour is not a real, intrinsic property of the solid electrodes but is rather an artefact that is very difficult to eliminate. There are reports suggesting this point of view especially for well defined surfaces of platinum [32] but also for polycrystalline electrodes [33]. In recent studies of capacitance dispersion on Au(111) and (Au(100) [34,35] it was concluded that

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

CPA dispersion can be simply the effect of adsorption and that without adsorption these electrodes present purely capacitive immittance. Another interesting point [36,37] of relevance to the present discussion is the dependence of the roughness factor Rf of solid electrodes as determined, e.g. from Parsons–Zobel plots [38], on purely physicochemical factors such as electrolyte composition, concentration, electrode potential etc. this being in disagreement with the simple, intuitive understanding of roughness as Rf = Ar/Aapp (Ar, Aapp-real and apparent surface area, respectively). Considering the postulated relation between roughness and CPA behaviour, it is highly probable that similar factors (but not necessarily real, ‘geometrical’ roughness itself) play a significant role in CPA capacitance dispersion and the deviation of capacitance from the ideal Parsons – Zobel relation on solid electrodes. The aim of the present work is to verify the relevance of the CPA immittance as defined by Eq. (2) on well defined surfaces close to what is considered as ‘ideally smooth’ and polarizable electrodes. There are at least two reasons to strive to solve the dilemma of the CPA behaviour as being either physical reality or a phantom result of experimental imperfection. 1. Electrodes exhibiting CPA immittance do not satisfy the premises of ideal polarizability and the thermodynamic approach is not applicable to them. They are intrinsically irreversible and the mere process of (non-Faradaic) charging/discharging of the interface takes place dissipatively. Consequently, determination of charges, surface concentrations and other thermodynamic variables is not well founded [34]. This is important in view of the fact that all theories of electrified interfaces operate mainly in terms of capacitance-charge relations [4,5] and charge itself is taken from integration of capacitance with respect to the electrode potential. For this integration to be reliable, the capacitance has to be dispersionless. In this context one has to invoke Lipkowski’s reservation against ac immittance data used to investigate thermodynamics of organic adsorption on Ag(hkl) and Au(hkl) electrodes as unreliable and his insistence on using instead the chronocoulommetry technique [39]. 2. On electrodes exhibiting CPA immittance the nonuniform distribution of local capacities (charge densities) results in even stronger non-uniformity of kinetic activities as caused by e.g. exponential distribution of the activation energy of interfacial charge transfer reactions [8]. This can (and probably does) obscure the determination of kinetic parameters such as the rate constant and the transfer coefficient. In the present work the results of the study on two

109

representative gold monocrystalline surfaces: Au(111) and Au(210) are reported as being opposites in the entire range of Au(hkl) properties and situated at the extrema of the whole set of Au(hkl) surfaces [40–43]. Au(111) is densely packed, smooth on the microscopic scale, has a low concentration of broken bonds (dbb) per unit cell of the surface (a 2): dbb/a 2 = 6.92, [41], the highest potential of the zero charge and work function. Au(210) has an open structure, is rough on the microscopic scale, has the highest concentration of broken bonds: dbb/a 2 = 8.94, [41] and the lowest potential of the zero charge and work function and hence the range of adsorption activity shifted to negative potentials. Another rationale for this selection was the prevalence of these crystallographic orientations in the research of electrochemical adsorption [44] in which profound differences of their activity were found. It is believed that any attempt to elucidate the differences observed for these two electrodes will shed light on the whole problem of the origin of CPA dispersion on solid electrodes in general and their electrocatalytic activity in particular.

2. Experimental The experimental procedure was detailed elsewhere [9,10]. Here we will presented only two points important for the reliability of the immittance data. 1. Au(hkl) electrodes cleaned by flame-annealing and protected by drop of ultra-pure Milli-Q water were put in contact with the electrolyte solution at open circuit potential which, as a rule, was close to the pzc. The electrode characterisation was done by CV plots with step-by-step potential window-opening. The potential window was opened first with a scan in the negative direction, then in the positive one. Lack of hysteresis and the almost ideal overlap of plots [10] was considered as a proof of cleanliness according to Hamelin and Martins [42,43]. 2. It was tried to vary the mutual configuration of the electrodes, especially the reference and the counter electrode, with respect to the hanging meniscus of the working electrode. Except for some evidently incorrect arrangements such as counter electrode located between the meniscus and reference electrode, no effects of this variation on the immittance spectra were found in the frequency range of interest for this study. The high frequency part of the immittance spectrum was sometimes distorted for some configurations especially at low electrolyte concentrations and so, these configurations were avoided in the experiments. The present data were obtained under conditions where no influence of mutual arrangement of electrodes was observed, so they represent purely interfacial effects.

110

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

3. Results The characterisation of the cleanliness of the electrochemical cell and the reliability of the preparation of the Au(hkl) electrodes was done according to the recommendations by Hamelin and Martins [40,42,43] and presented in our previous reports [9,10]. Since the CPA-type capacitance dispersion has been related recently to processes of adsorption [8,34,35] and perchlorate and fluoride anions are considered as nonadsorbing on gold surfaces, the experiments were carried out in HClO4 and KF aqueous solutions. Before fitting the parameters of an appropriate model using CNLLS (Complex Non-Linear Least Squares) programs [45,46] it was helpful to inspect the immittance data in different coordinates to identify the equivalent circuit whose parameters are to be fitted subsequently. The importance of the equivalent circuits should not be overemphasised and they are used here merely as a pictorial representation of the immittance function F(iv) with various forms of F derived from the complex impedance or admittance [11,12,45,46] such as the complex capacitance C(iv) = Y(iv)/v or modulus = Z(iv)*v. In Fig. 1 the immittance plots ‘as measured’ for Au(210) in 10 − 2 M HClO4 in two coordinates’ systems are presented. The coordinates were chosen which make easier the distinction between the ideal, dispersionless capacitive behaviour and the CPA dispersive behaviour governed by Eqs. (1) and (2). The plots in polar impedance coordinates in Fig. 1(a) (Z1 =Re(Z), Z2 =Im(Z)) display slopes indicative of the deviation from the ideal capacitive behaviour. The effect is purposely exaggerated by using unequal axes but nonetheless the deviation of low frequency parts of the plots from vertical is beyond any doubt. These coordinates (Z1, − Z2) emphasise the low frequencies on the immittance spectrum with its high frequency part shrunk to the point of intersection with the Z1 axis at Z1 = Rs. Quite informative and useful especially for displaying low frequency capacitance dispersion are polar capacitance plots (Y1/v, Y2/v) (Fig. 1(b)) which, analogously to (Z1, −Z2) coordinates but in another way, emphasise the low frequency part of the spectrum. The high frequency ends of the plots shrink to the origin of the axis (0, 0) (negligible ‘geometric capacitance’) but at low frequency, slight but distinct kinks are visible on almost all plots. These kinks are also manifestations of the deviation of the interfacial immittance from purely capacitive behaviour and its compliance with the CPA immittance (Eq. (2)). From the mere inspection of the immittance plots in two different coordinates in Fig. 1, it can be concluded that Au(210) in 10 − 2 M HClO4 solution displays a

distinct CPA dispersion in the double layer region and, at least qualitatively, its immittance complies with Eq. (2). Fig. 2 presents similar data for Au(111) in 10 − 2 M HClO4. The shapes of plots are similar to those in Fig. 1; however, the effect of dispersion is less for Au(111) than for Au(210). Analogous effects were observed on the plots for Au(210) and Au(111) in various concentrations of HClO4 [10] and also, for other non-adsorbing electrolytes including aqueous solutions of KF and also of KOH. It has to be noted that the general tendency

Fig. 1. Electrochemical immittance data for Au(210) in 10 − 2 M HClO4 solutions at different potentials (reversible hydrogen electrode (RHE) scale). Data ‘as measured’ shown in two coordinates’ systems emphasizing low frequency dispersion of interfacial capacitance; (a) polar impedance: (Z% , −Z¦); (b) polar complex capacitance: (Y%/ v, Y¦/ v).

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

Fig. 2. Electrochemical immittance data for Au(111) in 10 − 2 M HClO4 solutions at different potentials (reversible hydrogen electrode (RHE) scale). Data ‘as measured’ presented analogously to those on Fig. 1.

observed was that the higher the solution concentration and consequently, the higher the conductivity, the lower was the capacitance dispersion, i.e. the behaviour was closer to ideal capacitive. However, in all cases investigated the dispersion on Au(210) was distinctly higher than on Au(111). For the quantitative analysis the CNLLS fitting of the parameters of Eq. (2) to the experimental data was carried out. In a few cases, to satisfy the convergence condition (x 2 B10 − 4 [10]) it was necessary to add an equivalent resistance or a Warburg impedance related to the Faradaic processes: (i) at the most negative potentials close to hydrogen evolution; (ii) at the most positive potentials, on the brink of oxygen adsorption;

111

(iii) in the intermediate potential region if traces of oxygen were present in the solution. In such a case the equivalent circuit used was R(QR) or R(QW) according to Boukamp’s Circuit Description Code [45] (R, resistance, Q, CPA element). Most of our fits were carried out using the EQUIVCRT program [45] owing to its ‘user-friendliness’; however, the same results were obtained with Macdonalds’ LEVM [46] used for comparison. Fig. 3 shows the potential dependence of parameters Y0 and n for Au(210) in 10 − 2 M HClO4. The horizontal line marks the value n=0.98 that we accepted as the limit above which (n\ 0.98) the deviation from the ideal, capacitive behaviour, is immaterial [10] for most practical purposes. As one can see in Fig. 3, over a considerable potential range this deviation for the Au(210) electrode is much more pronounced than that. The largest deviation of n is at ERHE = 470 mV (:110 mV per SCE) which almost coincides with the maximum of the parameter Y0. Fig. 4 shows the same relations for the Au(111) electrode and it is easy to note that the capacitance dispersion in this case is small and in most of the potential range it can be considered immaterial according to our criterion of n= 0.98 marked by a horizontal line. The dependence of (Y0, n) on E for Au(210) for different concentrations of KF is presented in Figs. 5–7. On Au(111) the CPA dispersion was less and in Fig. 8 typical plots for Au(111) in 10 − 2 M KF are presented. It can be observed that at negative potentials (electrode charges) the immittance of Au(210) in dilute KF solutions also becomes close to ideal capacitive in contrast to that observed in HClO4. At ESCE B −400 mV there is almost no difference in the n–E relations for Au(210) and Au(111) as one can seen from comparing Figs. 6 and 8. At positive charges, on passing the maximum of Y0, the dispersion for Au(210) in KF solution grows strongly (nB 0.92) and this is true, but to a lower extent, also for Au(111). This is in contrast to the behaviour observed in HClO4 (Figs. 3 and 4) where at positive potentials, up to the brink of oxygen adsorption, the dispersion was negligible for Au(111) and it was moderate for Au(210). There is a distinct similarity of n–E and Y0 – E plots for Au(210) at 10 − 1 M KF (the highest concentration used in the present work) and the plots recorded for Au(210) at much lower concentrations of HClO4. There were maxima on the Y0 –E plots at slightly positive charges and corresponding minima on the n–E plots indicating noticeable CPE dispersion in that potential region. The plots for Au(210) electrodes acquired this characteristic shape in KF solutions only at the highest concentrations while in HClO4 this shape was observed for all concentrations [10]. The maxima on Y0 – E plots represent the exposition of the inner Helmholtz layer with specific metal-solvent interactions attributed usu-

112

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

Fig. 3. Electrode potential dependence of CPE components Y0 (open circles) and n (solid circles) representing interfacial immittance of Au(210) in 10 − 2 M HClO4 according to Eq. (1). Y0 dimensioned as capacitance irrespective of the CPA exponent value. Error bars show limits of fitting error; RHE and SCE potential scales shown.

ally to the reorientation of the solvent molecules on the metal surface. Finally it has to be noted that the Y0 – E plots for Au(111) in KF and HClO4 solutions, up to potentials slightly positive to the pzc, were almost coincident with the cyclic voltammograms in ‘capacitive’ coordinates: j/(dE/dt)−E. This is in agreement with the ideal capacitive, dispersionless immittance, so Y0 $Cdl for Au(111) in these conditions. For Au(210) the deviations between the Y0 –E and the CV plots were discernible concurrently with some hystereses on CV plots. This also confirms the more pronounced CPA dispersion on Au(210) electrodes according to the calculated time-domain responses of CPA dispersive electrodes [13].

4. Discussion

4.1. The scope and reality of the CPA-type capacitance dispersion It is necessary first to detail the scope of the capacitance dispersion of the CPA type we deal with here. This covers all the cases when charging/discharging of the electrochemical interface cannot be modelled by a simple equivalent circuit made up with R, C and Zw elements (Zw, Warburg type diffusion impedance) or, in mathematical terms, it is not governed by any ordinary differential equations and/or partial differential equation related to Fickian diffusion (infinite, limited or

bounded diffusion etc.). This excludes from consideration the trivial cases when the interpretation of the complex capacitance dispersion C(iv) Y(iv)/(iv) [8], invokes the standard concepts of adsorption kinetics [47–49] such as those discussed by Pajkossy et al. (1996) [35]. In this reference it was concluded that interfaces of Au(111) and Au(100) in HClO4 are ideally capacitive and the process of mere charging/discharging of the double layer can be represented by an ideal capacitance Cdl. In the presence of adsorbates, the response to the harmonic perturbation, in addition to Cdl, involves also a contribution from the adsorption kinetics represented by two lumped elements: adsorption capacitance (equilibrium), and adsorption resistance (interfacial kinetics) and one distributed element, Warburg type impedance (diffusion of the adsorbate to and from the electrode surface), such as shown in Fig. 6 of Ref. [35]. As pointed out above, such cases, interpretable in terms of the classical model of electrochemical adsorption, do not represent the CPA capacitance dispersion we deal with here and our attention is focused on anomalies with respect to the classical description in the absence of any effects of the electrode reactions or kinetically hindered adsorption. This was our motivation to choose HClO4 and KF as non-adsorbing electrolytes so it can be expected that the process of charging/discharging of the interface will not introduce Faradaic elements. Rs-CPE with the impedance function of Eq. (2) is the simplest model applied which takes into account the

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

113

Fig. 4. Electrode potential dependence of CPE components Y0 (open symbols) and n (solid symbols) representing interfacial immittance of Au(111) in 10 − 2 M HClO4 according to Eq. (1). Presentation analogous to this in Fig. 3.

CPA dispersion. As the rather non-restrictive criterion of significance of the dispersion we suggested [10] nB 0.98, that is we considered CPA dispersion with 0.98B n5 1 as insubstantial for most practical purposes. This limit is marked by horizontal lines in Figs. 3 – 8. One can see that Au(111) in 10 − 2 M HClO4 and in 10 − 2 M KF at negative charges does respond reversibly according to this criterion, whereas at positive charges and for Au(210) close to the pzc the substantial CPA dispersion appears with a CPA exponent declining down to 0.9. However, it should be stressed that even for these cases when the interfacial capacitance was almost nondispersive according to our criterion, i.e. for CPA exponent 0.98 B nB 1.0, the value of this exponent could still be determined with sufficient accuracy and the fact of its deviation from unity could be checked by the CNLLS procedure and also by a mere inspection of the immittance plots in properly selected co-ordinates. At this point it is suitable to warn against the underestimation of the consequences of the CPA capacitance dispersion with the fractional CPA exponent close to one. A deviation of CPA exponent from unity is the measure of the charging/discharging irreversibility of the double layer. Even for an apparently minor dispersion the degree of irreversibility may still be significant. As the quantitative measurement of the irreversibility one can take the ratio of the dissipated power in one harmonic cycle to the whole power transferred in one cycle. The complex power is: S= Eac j *ac = P + iQ. where Eac, j *ac are the harmonic potential and the cur-

rent density (conjugated) in complex number notation; P is the dissipated power; Q is the reversibly exchanged power. The irreversibility or dissipated power ratio may be expressed as: DissCPE = P/ S = cos(np/2)

(3)

Table 1 presents this ratio for several selected values of the CPA exponent. The ratio of dissipated power for n= 0.95 equal to 7.85% may already be important if one is to consider the irreversibility of the charging/discharging process and the resultant heat evolution at the interface [50]. There is still the problem of discrimination of the CPA-type dispersion of interfacial capacitance from any other, including the trivial case of classical adsorption kinetics and transport phenomena mentioned above which we strove to eliminate. We tried to minimise the role of adsorption in our experiments by selection of perchlorate and fluoride ions i.e. apparently non-adsorbing electrolytes although their adsorbability cannot be wholly excluded [51–53]. Our attempts to Table 1 The percentage ratio of the dissipated power in one harmonic cycle to the whole power transferred in one cycle for various values of the CPA exponent n Dissipated powerCPE (%)

1 0

0.99 1.57

0.98 3.14

0.97 4.72

0.96 6.28

0.95 7.85

114

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

Fig. 5. Electrode potential dependences of CPE paramers: Y0 (open symbols) and n (solid symbols) for Au(210) in 10 − 3 M KF.

account for adsorption in CNLLS fitting by invoking its electrical parameters (e.g. adsorption capacitance and resistance in series) while fixing the CPA exponent at n= 1.0, resulted in a spectacular decline of the fit quality with confidence limits of adsorption capacitance DCads/ Cads in some cases exceeding 100%. The fitting quality evaluated as the x 2 criterion and the examination of the correlation matrix of fitted parameters [45,46] helps in the selection of the model or equivalent circuit properly representing the physical reality [11]. It is known [54,55] that any correct impedance function, i.e. the one satisfying Kramers– Kroenig relations [11,45] can be modelled by at least one (R, C) equivalent circuit such as Foster- or Cauer-type circuits [55], i.e. it can be approximated by the rational function of complex frequency (iv), provided that the modelling circuit is of sufficient complexity (length) or, in mathematical terms, that the order of the rational immittance function is sufficiently high with respect to complex frequency (iv). Such an arbitrary or ‘par force’ modelling, referred to as a measurement modelling [54], is abstracted of any physical significance of the individual elements despite the high quality of the fit obtained for sufficiently extended modelling circuits. To accept the model as properly representing the physical reality one has to resort to additional information from the outside of the domain of sheer modelling. In our case this additional information is the assumed simplicity of the system in the absence of any Faradaic reactions. This requires the model to be as simple as possible, starting from only two parameters of an Rs – Cdl equivalent circuit. For most of our data this simplest Rs – Cdl model was inadequate and additional parameters had to be included. The criterion of their selection was the im-

provement of the fitting quality by the minimisation of the standard deviations while keeping low values of the correlation parameters. For a typical number of data points in the impedance spectra used (25–40 points) a satisfying procedure should give a fit quality of x 2 B10 − 4 [45] and the confidence limits of the parameters less than 1%. The use of a three-parameter Rs-CPE model in most cases was sufficient to get very good fit quality as proved by the x 2 criterion and in some cases, especially for Au(111) in 10 − 2 M HClO4, it was x 2 B 10 − 5 with the relative error of the CPA exponent: Dn/n B 0.001. These facts were considered as adequate to recognise the Rs –CPE circuit and its impedance function (Eq. (2)) as suitable to model the behaviour of the electrodes under study, i.e. to represent properly the physical reality in the process of physical modelling. Some problems related to this assertion still have to be noted. First, as we already mentioned, close to the negative and positive ends of the potential range investigated, i.e. close to hydrogen evolution and oxide deposition, it was suitable to complement the simple Rs –CPE model by adding the resistance of the Faradaic process Rf and/or Warburg impedance Zw. This resulted in a considerable improvement in the fit quality as proved by decrease of x 2. The values of Rf and/or Zw added represented reasonably the contribution of the secondary Faradaic processes. Secondly, the parameters Y0 and n were often strongly correlated one with another as correlation matrices created by CNLLS fitting procedure showed. Such correlation is also seen directly on the (Y0, n)–E plots (Figs. 3 and 7) on which the variations of Y0 and n look as if synchronised one with another with the minimum of n–E plot almost coincident with the maximum of Y0 –E plot. This correlation may raise

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

115

Fig. 6. Electrode potential dependences of CPE paramers: Y0 (open symbols) and n (solid symbols) for Au(210) in 10 − 2 M KF.

doubts as to the validity of the model and its immittance expressed by Eq. (1) or Eq. (2) and may suggest its replacement by another one with non-correlated parameters. However, the analysis of intrinsically uncorrelated ‘synthetic data’ obtained directly from Eqs. (1) and (2) with added random noise showed that the Y0 and n parameters obtained from CNLLS fitting displayed also high correlation due apparently to the noisy signal and the process of fitting. Evidently, the high correlation of parameters resulting from fitting was the intrinsic mathematical property of CNLLS procedures even when immittance Eqs. (1) and (2) were perturbed by random (uncorrelated) noise. Regarding the correlation seen in Figs. 3 and 7 as a ‘mirror inversion’ of Y0 – E and n–E plots we have to presume this to represent the physical reality. That is, the same phenomena which underlie the variations of Y0 seen on the Y0 – E plots are effective also in increasing the CPA dispersion seen as minima on the n–E plots. No simple model with only few adjustable parameters from among those we tested could represent the immittance spectra of the electrodes under study with such an accuracy as the RS – CPE circuit and without a considerable correlation between parameters. Therefore, this model (equivalent circuit) we accepted as the proper representation of the behaviour of the Au(hkl) electrodes in the presence of non-adsorbing electrolytes without having any alternative based on the reasonable physical basis. One can speculate, somewhat philosophically, about a relation between the physical entity and its mathematical model [56] but this finally leads us to the problem of selecting the best model from several possible i.e. the one which most closely or most usefully represents the physical reality.

4.2. Inferences on the origin of CPA dispersion Our main point of interest is now the physical nature of the CPA-type frequency dispersion of interfacial capacitance. Although only electrochemical data have been reported here and in our previous reports [9,10], they form a sufficient basis for inferences to be made about the nature of this dispersion by comparing the dependence of (Y0, n) parameters on crystallographic orientation, composition and concentration of electrolytes and on electrode potential. Despite the remarkable successes of in-situ methods of surface physics applied to electrochemical interfaces [57] the electrochemical methods are still the easiest, the most sensitive and reliable in testing the correctness of electrochemical experiments with single crystals, in particular the cleanliness and stability of crystal structure of gold electrodes [40,42,43]. The construction of the electrochemical cell and the configuration of electrodes suitable for methods of surface physics are usually not best suited for reliable EIS experiments. This makes difficult a direct comparison of EIS and surface structure data. Regarding the structures of Au(hkl) surfaces and structure and composition of adjacent electrolyte (solvent) we rely on recent reports both experimental [53,58–61] and theoretical [62–69] on analogous systems. First to note are distinct differences of immittance spectra for Au(111) and Au(210) especially in HClO4 solutions. Considering the same procedure of preparation applied to these electrodes and similar roughness estimated from pzc minima of Y0 in dilute solutions (usually at pzc 0.98 BnB 1.0, hence Y0,min : Cdl,min), we conclude that differences of immittance spectra and especially differences of capacitance dispersion are re-

116

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

Fig. 7. Electrode potential dependences of CPE paramers: Y0 (open symbols) and n (solid symbols) for Au(210) in 10 − 1 M KF.

lated to microscopic (atomic scale) differences of the surface structure. On Au(111) it is a densely packed, uniform and ‘isotropic’ structure in the sense that among the main symmetry axes on the surface none is favoured; there are only few broken bonds [41,42] and these factors are manifested by the highest potential of the zero charge and the highest work function for this orientation. This is in contrast to the surface of Au(210) electrodes which are microscopically non-uniform, i.e. containing the highest density of mono-atomic steps with the shortest terraces in between. This is displayed as two equivalent TLK (terrace-ledge-kink) [41,43,70] notations for this orientation: (210)= 2(110) − (100) or (210)= 2(100)−(110). This structure is also anisotropic in the sense that its properties in the direction of steps are different from those at different orientations, e.g. perpendicular to steps and similar anisotropy may be expected for adsorbed layers on this surface. The consequences of the microscopic surface heterogeneity of Au(210) are the most negative potential of pzc and consequently the lowest work function. The high density of broken bonds on Au(210) accounts for the high activity for adsorption of organic species such as pyridine [44,71]. This adsorption activity may be attributed alternatively to the most negative potential of the pzc resulting in relatively low charges at potentials of relevance for adsorption of organic species. Whichever factor is considered more important, one should recognise that ultimately it is the structure of the surface, corrugated and microscopically non-uniform on Au(210) and smooth and uniform on Au(111) which is the primary origin of both factors (broken bonds and charge density) determining the adsorption activity.

The microscopically heterogeneous surface of Au(210) is remarkably stable and does not reconstruct under the conditions of our study [43,58]. This is not true for Au(111) which when freshly prepared by flameannealing is reconstructed and the reconstruction is lifted during potential scanning into the region of positive charges [35,59]. However, on the basis of the literature data referenced, we consider this reconstruction of Au(111) as being of minor importance for the electrochemical response averaged over the whole electrode surface since it involves single kinks separated by broad terraces of 23 atomic units. In our experiments we never observed any electrochemical manifestation of reconstruction/lifting for Au(111) or Au(210) electrodes such as the sharp reconstruction peaks observed usually on cyclic voltammograms of Au(110) or Au(poly) electrodes. Notable is the difference of dispersion on Au(210) electrodes in various solutions. Plots of Y0 –E and n–E for Au(210) in HClO4 are correlated, being almost mirror images of one another. Corresponding plots for Au(210) in KF solutions are free of this intriguing correlation except possibly at the highest concentration (Fig. 7). This shows that the correlation in question is related to the kind and concentration of electrolyte in a similar way as is the capacitance dispersion itself, being different in HClO4 and in KF solution. Effects of HClO4 concentration on Au(210) were presented in Motheo et al. (1997) [10] leading to the conclusion that the higher the concentration, the lower is the dispersion and the weaker the correlation of n and Y0. It was also concluded that the capacitance dispersion has to be related to the inner (Helmholtz) layer of the metal electrolyte interface.

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

117

Fig. 8. Electrode potential dependences of CPE paramers: Y0 (open symbols) and n (solid symbols) for Au(111) in 10 − 2 M KF.

The capacitance dispersion was generally higher on Au(210) than on Au(111) in both electrolytes investigated. Au(111) behaves almost ideally both in HClO4 (Fig. 4) and KF solutions except at potentials highly positive to the pzc where a remarkably strong dispersion is noted (Fig. 8). This dispersion at positive charges was also more pronounced in dilute electrolytes and was smaller in concentrated electrolytes analogously to the hump-related dispersion on Au(210) in HClO4. Incidentally, the n – E plot in Fig. 4, with n \0.99 in most of the potential range, is an example of an almost completely dispersion-free system and in this way, indirectly, it is the ‘proof of authenticity’ of discernible dispersion recorded in analogous experiments on other electrodes. Interesting are variations of dispersion with potential (charge). In general, the dispersion was lowest at negative charges in the potential range which is known as the easiest to interpret and the closest to theoretical models of the metal electrolyte interface [5,62]. Negative charge repels anions and organic molecules, forces water orientation with oxygen atoms away from the surface and in the absence of de-solvated cations the interface approximates the ideal case of a metal in contact with non-interacting solvent. It was postulated that the properties of the interface in the region of negative charge are determined mostly by the solution side and only to a lesser extent by the nature of the metal [5,72,66]. On Au(210) in HClO4 the pronounced variations of Y0 at negative charges (0BERHE (mV) B250) were accompanied by only slight variations of n: 0.98Bn : 1.0,

hence Y0 $ Cdl. In this region, dominated by the electrolyte side of the interface, the behaviour of the interface is almost ideally capacitive, i.e. dispersionless. The minor deviations of n from unity at the most negative limit indicate merely the onset of cathodic hydrogen evolution. As soon as the hump on the Y0 –E plot emerged, n fell considerably to 0.92 to regain subsequently its level close to 1.0 on passing over the Y0 hump (800B ERHE (mV)B 1200). For Au(210) in KF solutions the hump on Y0 –E plots and concomitant increased dispersion were observed only at higher concentrations (Fig. 7). It is known that on polycrystalline Au and Ag electrodes such a hump appears in almost all ‘non-adsorbing’ electrolytes so it does not seem to be anion-specific. The coincidence of the potential of the greatest capacitance dispersion on Au(210) with the potential of the Y0 (‘capacitance’) hump is intriguing. The hump situated slightly positive with respect to the zero charge potential (pzc) ([40,42,43]) displays the properties of the inner (Helmholtz) layer [10]. The vicinity of the pzc is also the region of increased structuring of the solvent and increased adsorption of neutral (organic) molecules [73,44] owing to the relatively weak electric field. Each of these factors can contribute to the increased capacity dispersion by: 1. solvent structuring due to its non-uniform quasicrystalline aggregation 2. non-uniform adsorption due to the strong kinetic heterogeneity as proposed by Pajkossy [8]. Processes of adsorption from aqueous solution, especially the adsorption of large oxyanions such as ClO4− , apart from purely electrostatic forces, result from re-

118

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119

structuring of the solvent near the interface with hydrogen bond breaking and freeing of ions from collapsing clathrate cages [72] of the solvent. Hence, both solvent restructuring and anion adsorption may be looked at as two manifestations of the same charge (electric field) induced phenomenon which evidently is also the origin of the increased capacitance dispersion observed in the vicinity of the hump. On Au(111) we observed no hump and no hump-related enhanced dispersion in HClO4 and KF solutions. In KF solutions, apart from the hump-related dispersion on Au(210) electrodes, especially at higher concentration (Fig. 7), the considerable dispersion both on Au(111) and on Au(210) was observed at positive potentials. This can be attributed to effects of adsorption of OH − ions and the start of oxide layer formation [51,52] which begins in neutral electrolytes at potentials less positive than in acids and results in local acidifying of the unstirred electrolyte. Some interference (adsorption?) of HF molecules present in KF solutions, especially after the local drop of pH, also cannot be ruled out. Two arguments may be invoked however against the direct role played by anion adsorption in capacitance dispersion: 1. On Au(210) in HClO4 solutions dispersion was lower (CPA exponent closer to 1) in more concentrated solutions [10]. If it was the anion adsorption directly responsible for the dispersion, the higher electrolyte concentrations would result rather in an enhanced dispersion. 2. Potential dependence of CPA exponent. On passing the maximum dispersion region close to the Y0 hump (Figs. 3 and 7) the capacitance dispersion decreased or gradually disappeared when potential was more positive. The direct effect of anions adsorption should be opposite. These arguments suggest that an important role in CPA-type dispersion has to be attributed to the geometric factors which were almost entirely (but possibly prematurely) dismissed by Pajkossy [8]. These we understand as geometric non-uniformity of the surface leading to the unseparable coupling of local electrolyte resistances and regularly (structured) or randomly distributed (meso- or macro-scale) capacitances. The role of electrolyte concentration consists in its resistance effective in local R – C coupling. The distribution of local capacitances evidently is more pronounced on non-uniform Au(210) than on Au(111). Finally we have to comment on conclusions reported in Ref. [35] that no frequency dispersion of double layer capacitance was detected in pure ClO4− electrolyte. In view of our findings this conclusion can be explained by confining the investigation reported in Refs. [34,35] to the most uniform and densely packed orientations of Au(111) and Au(100) which indeed dis-

play only minor dispersion [10] especially at negative potentials. Polycrystalline and rough electrodes Au(poly) have many features in common with Au(110) and high-index orientations such as Au(210) [40,42,43]. Our results for Au(110) and Au(210) [10] suggest that for Au(poly) one should not expect dispersionless characteristics (such as those for Au(111)) even on very careful surface preparation.

5. Conclusions The two single crystals investigated, Au(111) and Au(210), present significantly different immittance characteristics as far as the capacitance dispersion is concerned. The microscopically smooth and uniform Au(111) in non-adsorbing electrolytes behaves almost ideally presenting in the whole double layer range capacitive characteristics with the constant phase (CPA) exponent in between 0.98 and 1.0. Au(210) having the most non-uniform and microscopically corrugated surface, displays a significant capacitance dispersion at potentials slightly positive with respect to the pzc, i.e. close to the characteristic hump on inner layer (Helmholtz) capacitance. The dispersion disappears at both higher and lower potentials and in KF solutions it appears in a similar shape only for high electrolyte concentrations. We attribute the hump-related dispersion to the metal-solvent interaction often referred to as solvent structuring and well known from in-situ surface physical studies. The concentration dependence suggests the geometrical nature of CPA dispersion involving inseparable coupling of the local electrolyte resistances with capacity nonuniformly distributed along the surface. At potentials considerably higher than the pzc in KF solutions the processes of adsorption contribute additionally to the increased capacitance dispersion.

Acknowledgements This research was supported by the Fundac¸ao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP), Brazil, Process No 96/ 3504-2. A.S. acknowledges the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil (Process No 452119/ 96-0) for an individual research grant.

References [1] R. Parsons, in: J.O’M. Bockris, B.E. Conway, E. Yeager (Eds.), Comprehensive Treatise of Electrochemistry, Chapter 1, vol. 1, Plenum, New York, 1980.

A. Sadkowski et al. / Journal of Electroanalytical Chemistry 455 (1998) 107–119 [2] P. Delahay, Double Layer and Electrode Kinetics, part I, Interscience, New York, 1965. [3] D.C. Graham, J. Am. Chem. Soc. 76 (1954) 4819. [4] L. Blum, Adv. Chem. Phys. 78 (1990) 171. [5] S. Amokrane, J.P. Badialli, in: J.O’M. Bockris, B.E. Conway, R.E. White (Eds.), Modern Aspects of Electrochemistry, no. 22, Plenum Press, New York, 1992. [6] A.N. Frumkin, Potencyaly Nulyevogo Zaryada (Potentials of Zero Charge), Chapter 9, Nauka, Moscow, 1979. [7] G. Lang, K.E. Heusler, J. Electroanal. Chem. 377 (1994) 1. [8] T. Pajkossy, J. Electroanal. Chem. 364 (1994) 111. [9] A.J. Motheo, J.R. Santos Jr., A. Sadkowski, A. Hamelin, J. Electroanal. Chem. 397 (1995) 331. [10] A.J. Motheo, A. Sadkowski, R.S. Neves, J. Electroanal. Chem. 430 (1997) 253. [11] J.R. Macdonald (Ed.), Impedance Spectroscopy, Wiley, New York, 1987. [12] M. Sluyters-Rehbach, Pure Appl. Chem. 66 (1994) 1831. [13] A. Sadkowski, Electrochim. Acta 38 (1993) 2051. [14] J.R. Macdonald, J. Appl. Phys. 62 (1987) 51. [15] O. Malcai, D.A. Lidar, O. Biham, D. Avnir, Phys. Rev. E 56 (1997) 2817. [16] L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits, McGraw Hill, New York, 1987. [17] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983. [18] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York, 1972. [19] A.K. Jonscher, Nature 267 (1977) 673. [20] R. de Levie, J. Electroanal. Chem. 281 (1990) 1. [21] B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982. [22] A. Le Mehaute, G. Crepy, Solid State Ionics 9–10 (1983) 17. [23] S.H. Liu, Phys. Rev. Lett. 55 (1985) 529. [24] L. Nyikos, T. Pajkossy, Electrochim. Acta 30 (1985) 1533. [25] W.H. Mulder, J.H. Sluyters, Electrochim. Acta 33 (1988) 303. [26] W.H. Mulder, J.H. Sluyters, J. Electroanal. Chem. 282 (1990) 27. [27] T. Pajkossy, L. Nyikos, J. Electroanal. Chem. 332 (1992) 55. [28] E.D. Bidoia, L.O. Bulhoes, R.C. Rocha-Filho, Electrochim. Acta 39 (1994) 763. [29] A.E. Larsen, D.G. Grier, T.C. Halsey, Phys. Rev. E 52 (1995) 2161. [30] T. Vicsek, Fractal Growth Phenomena, World Scientific, Singapore, 1989. [31] A. Kuhn, F. Argoul, J. Electroanal. Chem. 397 (1995) 93. [32] S. Morin, H. Dumond, B.E. Conway, J. Electroanal. Chem. 412 (1996) 39. [33] B. Piela, P. Wrona, J. Electroanal. Chem. 388 (1995) 69. [34] T. Pajkossy, Solid State Ionics 94 (1997) 123. [35] T. Pajkossy, T. Wandlowski, D.M. Kolb, J. Electroanal. Chem. 414 (1996) 209. [36] G. Jarzabek, Z. Borkowska, Electrochim. Acta 42 (1997) 2915. [37] M.L. Foresti, R. Guidelli, A. Hamelin, J. Electroanal. Chem. 346 (1993) 73. [38] R. Parsons, F.G.R. Zobel, J. Electroanal. Chem. 9 (1996) 333. [39] J. Richer, J. Lipkowski, J. Electrochem. Soc. 133 (1986) 121. [40] A. Hamelin, in: B.E. Conway, R.E. White, J.O’M. Bockris (Eds.), Modern Aspects of Electrochemistry, Chapter 1, vol. 16, Plenum Press, New York, 1985. [41] R. de Levie, J. Electroanal. Chem. 280 (1990) 179.

.

119

[42] A. Hamelin, J. Electroanal. Chem. 407 (1996) 1. [43] A. Hamelin, A.M. Martins, J. Electroanal. Chem. 407 (1996) 13. [44] J. Lipkowski, L. Stolberg, in: J. Lipkowski, P.N. Ross (Eds.), Adsorption of Molecules at Metal Electrodes, VCH, 1992. [45] B.A.. Boukamp, EQUIVCRT Equivalent Circuit, VER. 4.51, University of Twente, with KRAMKRON program for testing Kramers-Kroenig relations, April 1993. [46] J.R. Macdonald, Complex Nonlinear Least Squares Immitance Fitting Program, University of North Carolina, NC, 1986. [47] A.N. Frumkin, V.I. Melik-Gaykasyan, Dokl. Akad. Nauka 5 (1951) 855. [48] W. Lorenz, F. Moeckel, Z. Elektrochem. 60 (1956) 507. [49] R.D. Armstrong, P. Rice, H.R. Thirsk, J. Electroanal. Chem. 16 (1981) 177. [50] D. Bedeaux, S. K. Ratkije, J. Electrochem. Soc. 143 (1996) 767. [51] H.A. Kozlowska, B.E. Conway, A. Hamelin, L. Stoicoviciu, J. Electroanal. Chem. 228 (1987) 429. [52] H.A. Kozlowska, B.E. Conway, K. Tellefsen, B. Barnett, Electrochim. Acta 34 (1989) 1045. [53] K. Ataka, T. Yotsuyanagi, M. Osawa, J. Phys. Chem. 100 (25) (1996) 10664. [54] P. Agarwal, M.E. Orazem, L.H. Garcia-Rubio, J, Electrochem. Soc. 139 (1992) 1917. [55] L. Weinberg, Network Analysis and Synthesis, McGraw-Hill, New York, 1962. [56] R.Z. Morawski, IEEE Trans. Instrument. and Meas. 43 (1994) 226. [57] Surf. Sci., 335 (1995) 10, 23. [58] X. Gao, G.J. Edens, F.-C. Liu, A. Hamelin, M.J. Weaver, Surf. Sci 218 (1994) 1. [59] D.M. Kolb, in: J. Lipkowski, P.N. Ross (Eds.), Structure of Electrified Interfaces, Frontiers in Electrochemistry Series, Chapter 8, VCH, 1993, p. 65. [60] M.F. Toney, J.N. Howard, J. Richer, G.L. Borges, J.G. Gordon, O.R. Melroy, D.G. Wiesler, D. Yee, L.B. Sorensen, Nature 368 (1994) 444. [61] M.F. Toney, J.N. Howard, J. Richer, G.L. Borges, J.G. Gordon, O.R. Melroy, D.G. Wiesler, D. Yee, L.B. Sorensen, Surf. Sci. 335 (1995) 32. [62] W. Schmickler, in: J. Lipkowski, P.N. Ross (Eds.), Structure of Electrified Interfaces, Frontiers in Electrochemistry Series, Chapter 6, VCH, 1993, p. 201. [63] B. Damaskin, A.N. Frumkin, Electrochim. Acta 19 (1974) 173. [64] R. Parsons, J. Electroanal. Chem. 59 (1975) 229. [65] W.R. Fawcett, S. Levine, R.M. deNobriaga, C.M. McDonald, J. Electroanal. Chem. 111 (1980) 163. [66] S. Amokrane, J.P. Badiali, J. Electroanal. Chem. 266 (1989) 21. [67] E. Spohr, K. Heinzinger, Ber. Bunsenges. Phys. Chem. 92 (1988) 1358. [68] X. Xia, L. Perera, U. Essmann, M.L. Berkowitz, Surf. Sci. 335 (1995) 401. [69] M.R. Philpot, J.N. Ghosli, J. Electrochem. Soc. 142 (1995) 25. [70] B. Lang, R.W. Joyner, G.A. Samorjai, Surf. Sci. 30 (1973) 454. [71] D.F. Yang, L. Stolberg, J. Lipkowski, D.E. Irish, J. Electroanal. Chem. 329 (1992) 259. [72] Z. Borkowska, U. Stimming, in: J. Lipkowski, P.N. Ross (Eds.), Structure of Electrified Interfaces, Frontiers in Electrochemistry Series, Chap. 8, VCH, 1993, p. 277. [73] B.B. Damaskin, O.A. Petrii, V.V. Batrakov, Adsavbtsya Organicheskikh Soedinenii na Elektrodakh (Adsorption of Ogranic Componds on the Electrodes), Nauka, Moscow, 1968, p. 30.