A review about the surface resistance technique in electrochemistry

Surface Science Reports 56 (2004) 85–157 www.elsevier.com/locate/surfrep

A review about the surface resistance technique in electrochemistry R. Tucceri* Instituto de Investigaciones Fisicoquı´micas Teo´ricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina Received 12 August 2004 Available online 13 October 2004

Abstract The use of the surface resistance changes as an alternative method to study the electrochemical interface is reviewed considering both experimental and theoretical aspects. Particular emphasis is laid on the effect of the adsorption on the resistance of thin film electrodes, including adsorption processes of ions, organic compounds, oxygen, hydrogen and underpotential deposition. Relevant and recent experiments, where the technique was used to detect small quantities of cations in solution and redox sites distributions at the metal–polymer interface are also considered. Morphology changes and roughening and corrosion processes of electrode surfaces studied by resistance measurements are also reviewed. Results obtained by coupling surface resistance with both optical methods and Hall effect in electrochemistry, and the important problem of the electrode emersion are also described. Scattering models to explain surface resistance changes are outlined on the basis of their phenomenological parameters, which can be determined by electrochemical measurements. # 2004 Elsevier B.V. All rights reserved. Keywords: Surface resistance; Thin film electrodes; Adsorption processes; Scattering models

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

2. Resistive changes in thin film electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

* Tel.: +54 221 425 7291/7430; fax: +54 221 425 4642. E-mail address: [email protected]. 0167-5729/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfrep.2004.09.001

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2.1. The field effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. The size effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Surface adsorption on thin film electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Ionic adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Molecular adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3. Hydrogen adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4. Oxygen electrosorption and oxide formation processes . . . . . . . . . . . . . . . . . . . . 2.3.5. The resistance change during the underpotential deposition (upd) process. Its use as an analytical tool to detection of trace concentrations of cations in solution. Diffusion of metal adatoms from the surface film to the bulk film . . . . . . . . . . . . 2.3.6. Detection of surface structural changes, roughening and corrosion effects on thin film electrodes by resistance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7. Surface conductance and reflectance measurements on thin film electrodes. Electrode emersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.8. Surface resistivity and Hall effect in thin film electrodes . . . . . . . . . . . . . . . . . . 2.3.9. Surface resistance measurements on a thin metal film coated with an electroactive polymer film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

93 98 102 104 111 114 115

.

119

.

128

. .

132 134

.

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3. Phenomenological parameters of scattering models determined from surface resistance measurements in electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4. The measurement of the surface resistance in electrochemistry. Instrumentation. Designs and preparation of electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Conductivity or electrical resistance of a metal is affected by processes occurring at its surface. However, when working with bulk metals, it is practically impossible to detect variations of the conductivity caused by processes on their surfaces. Quite different conditions take place in the case of thin metal films (thickness, 10 nm < d < 30 nm), where electronic transport is strongly affected by interfacial phenomena. As these thin metal films have a large ratio of surface to volume, they have been regarded as ‘‘all surface’’ [1]. In this sense, the ‘‘surface resistance’’ of these materials can be measured. Then, surface resistance refers to the changes of resistivity (or conductivity) brought about by defects, impurities and carriers concentration in the interfacial region of the exposed face of the material sample assuming all the bulk defects and other conditions remain unaltered. Surface resistance has been used for many years to study adsorption of gases on different thin metal films and also to verify the physics laws, which describe the resistance change with metal film thickness and surface coverage [2–8]. The technique was extended to study adsorption of different foreign metal

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87

Nomenclature a0 aH A ˚ A AH AHo b0 c cv C Cdl d dR/dE dr/di d(DR)/dE dk drJL DdRi De D0 e E EFermi Epzc Eupl E1 , E2 F G G0 (¼ l=w) DG DG/G i Im Ip j

constant in the surface Linde’s rule (see Eqs. (26) and (27)) relative change of the Hall coefficient considering changes of the specularity parameter p1 during adsorption (see Eq. (30)) ampere (unit of electric current) angstrom (unit of length) Hall coefficient of a thin metal film (see Eq. (29)) Hall coefficient of the bulk metal (see Eq. (29)) constant in the surface Linde’s rule (see Eqs. (26) and (27)) redox sites concentration of the electroactive polymer poly-o-aminophenol concentration in volume of the surface scattering centres (see Eq. (15)) coulomb (unit of charge) double layer capacitance (see for instance Eq. (9)) film (or sample) thickness derivative of the dc film resistance versus electrode potential E (see [35,37]) expression used to represent derivative resistance voltammetric spectra (see [18]), i is the voltammetric current density expression used to represent derived resistance curves in [36] change of the film thickness to mean free path of conduction electrons ratio (see Eq. (29)) change of the resistivity of the metal film for the Juretschke–Lucas modification of the FS resistivity (Eq. (29)) method used in [50] to measure surface resistance in electrochemical processes electron diffusion coefficient of poly-o-aminophenol (Section 2.3.9) representative crystallite dimension for a thin metal film (see Eq. (5)) electron charge electrode potential (also USCE as in [18]) Fermi energy potential of zero charge upper positive potential value during a potential sweep values of potential at the two ends, respectively, of a rectangular resistive electrode (see Eq. (46)) Faraday constant (96,487 C mol
1) conductance of a resistive electrode geometrical constant representing the (length/width) ratio for a rectangular metal film, l is the length and w is the width electrical conductance change of a film electrode relative conductance change current density in voltammetric measurements (also j) measuring current applied along a thin film electrode (see Eq. (45)) polarisation current applied to a thin film electrode (see Eq. (45)) current density in voltammetric experiments (see [36])

88

k k0 kq

kp k1 k3 (=l0rbsa) k1 k0

K K0 K3 KI K0 l0 lB L M m n0 napp Dn0 Na Ne Ns p p1 p2 Dp qe

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proportionality constant between the relative resistivity change and the degree of coverage of thiourea on a platinum film electrode (see Eq. (24)) proportionality constant between the resistance change and the degree of oxidation of a polymeric material deposited on a metal film (see Eq. (34)) proportionality constant between the conductivity change and the surface concentration of adsorbed ions (see [96]). This constant indicates the degree of charge transfer of the adsorbed ion wave vector component parallel to the surface (see Eq. (38)) proportionality constant between the specularity change and the surface concentration of an adsorbed entity (see Eq. (12)) proportionality constant given in Eq. (17) velocity constant given in Eq. (21) proportionality constant between the relative change of the total resistance and the surface charge density for bisulphate adsorption on a thin gold film electrode (see Eqs. (19) and (44)) proportionality constant between the relative resistance change and surface concentration of an adsorbed entity (Eq. (22)) proportionality constant between the resistivity change and the surface concentration of an adsorbed entity (see Eq. (13)) proportionality constant between the resistivity change and the number of adsorbed molecules per unit of geometrical surface (see Eq. (16)) proportionality constant between the relative conductance change and the surface charge density for I
adsorption on a gold thin film electrode (see Eq. (18)) parameter containing the probability of an electron being scattered at a grain boundary (see Eq. (5)) mean free path (mfp) of the conduction electrons (see Eqs. (3) and (4)) thickness of a surface layer lower than the film thickness, d (see Eq. (37)) liter (unit of capacity) adsorbate mass (see Eq. (36)) effective electron mass (see Eq. (1)) number electron density (see Eq. (1)) apparent number of exchanged electrons during the stripping reaction of mercury on a gold film electrode (see Eq. (28)) electron density change (see Eq. (37)) surface density of adsorbed species (see Eq. (36)) surface density of induced free electrons (see Eq. (41)) surface density of a given type, s, of scattering centre (see Eq. (5)) specularity parameter of a thin film electrode (see Eqs. (3) and (4)) specularity parameter of the surface film in contact with adsorbed species (upper metal film surface) (see Eq. (30)) specularity parameter of the surface film contacting the substrate (lower metal film surface) (see Eq. (30)) change of the specularity parameter (see Eq. (6)) free electron charge used to charge the electrode–solution interface (see [46,47])

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qH Dqe Dqe/qe DqH/qH Qa Qc QHg QRed Qupd DQa/Qa DQc/Qc DQupd r rAu rCu rJL

R R0 (¼ Rw=l) DR DR/R (DR/R)T D(DR)/DQa D(DR)/DQc D(DR/R)/DQa D(DR/R)/DQc S Si t

89

surface charge involved in the hydrogen adsorption process on a metal film electrode (see Eq. (25)) free electron charge change relative free electron charge change relative surface charge change during the hydrogen adsorption process (see Eq. (25)) exchanged surface charge during the oxygen adsorption process on a thin metal film electrode (see [76]) exchanged surface charge during the oxygen desorption process on a thin metal film electrode (see [76]) surface charge involved in the desorption process of Hg adatoms from a metal film electrode (see Eq. (28)) surface charge involved in the voltammetric reduction of poly-o-aminophenol. It is considered as representative of the polymer film thickness surface charge involved in the adatom deposition process during upd relative surface charge change during the oxygen adsorption process relative surface charge change during the oxygen desorption process surface charge change during the adatom deposition process (upd processes) site interaction parameter of poly-o-aminophenol (ra between oxidised sites and rc between reduced sites) atomic radii of gold atomic radii of copper relative change of the rJL resistivity, considering changes of the specularity parameter p1 during adsorption (see Eq. (31)). JL refers to the Juretschke–Lucas modification of the FS resistivity electrode electrical resistance square resistance for a rectangular film electrode (see [109]), w/l is the width/ length ratio electrical resistance change of the film electrode (see Eq. (6)) relative resistance change relative change of the total film resistance resistance change respect to the surface charge change during the oxygen adsorption process (see [76]) resistance change respect to the surface charge change during the oxygen desorption process (see [76]) relative resistance change respect to the surface charge change during the oxygen adsorption process (see [76]) relative resistance change respect to the surface charge change during the oxygen desorption process (see [76]) surface charge density corresponding to a complete monolayer of anions (see Eq. (20)) the limit of the (aH/rJL) ratio at zero coverage (see Eq. (32)) time

90

th u vf DV x0 z Z (=Zads Zads Zsubs

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time period during which a given potential is held at a constant value during a voltammetric potential scan cosine of the incident angle of the conduction electrons to the surface (see Eq. (40)) mean velocity of the electron at the surface of the Fermi distribution voltage drop along the thin film electrode (see Eq. (46)) proportionality constant which rationalises the effect of the adsorbed species to the conduction electrons (see Eq. (10)) number of exchanged electrons during an electrosorption process
Zsubs) difference between the number of valence electrons of the adsorbate and the substrate (see Eqs. (26) and (27)) number of valence electrons of the adsorbate (see Eq. (27)) number of valence electrons of he substrate (Eq. (27))

adl aHy aS aupd de d(DG/dE) D Drf Drf/rf Dsf Dsf/sf DsX Dt fp F gX Gadat Gads h k (=d/l0) lF m

Greek letters proportionality constant between the conductance change and the electrode charge in the double-layer region proportionality constant between the relative conductance change and the relative charge density change during the hydrogen electrosorption process (see Eq. (25)) resistance sensitivity coefficient defined in Eq. (8) proportionality constant between the relative conductance change and the relative charge change during upd processes the average number of localised conduction electrons per adsorbate (see Eq. (37)) relative conductance change respect to the electrode potential (see Eq. (9)) (see [81]) in general, refers to changes surface resistivity change of a thin film electrode relative surface resistivity change of a thin film electrode (see Eq. (2)) surface conductivity change of a thin film electrode relative surface conductivity change of a thin film electrode (see Eq. (2)) surface charge density change due to different specifically adsorbed anions (superscript X indicates anions, X = I
, HSO4
, etc.) change of the relaxation time (see Eq. (36)) thickness of a poly-o-aminophenol film width of the resonance states induced by the adsorbate (Eq. (38)) electrosorption valence (superscript X indicates different adsorbates, X = Br
, I
, etc.) surface concentration of atoms deposited during upd processes (in mol cm
2) (see Eq. (11)) surface concentration of specifically adsorbed ionic species (in mol cm
2) (see Eq. (11)) friction coefficient (see Eq. (38)) film thickness to mean free path of conduction electrons ratio (see Eqs. (3) and (4)) Fermi wavelength of the conduction electrons in a metal ionic strength of a solution

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mfe n uox ured uX ra(EF) rb rf rJL sa sb sf ss sm sX P

s

t V

91

field effect mobility (see Eq. (9)) potential sweep rate degree of oxidation of poly-o-aminophenol (see Eq. (34)) degree of reduction of poly-o-aminophenol degree of surface coverage (superscript X represents different adsorbed or deposited species, X = HSO4
, thiourea, adatoms, etc.) adsorbate-induced density of states at the Fermi level (see Eq. (38)) resistivity of the massive metal metal film resistivity resistivity of the metal film for the Juretschke–Lucas modification of the FS resistivity (see Eq. (31)) scattering cross section of different adsorbed species (subscript a represents different species, a = I
, Br
, etc.) (see Eqs. (8) and (20)) bulk metal conductivity (see Eq. (1)) metal film conductivity scattering cross-section of different, s, types of scattering centres (see Eq. (5)) metal surface charge density considering the field effect at the electrode–solution interface (see Eq. (2)) charge density due to different specifically adsorbed anions (superscript X denotes X = I
, SO42
, etc.) (see, for instance, Eqs. (18) and (19)) summation on the different types, s, of scattering centres (see Eq. (5)) relaxation time (see Eqs. (1) and (35)) ohm (unit of electric resistance)

atoms on thin gold films [9–13]. Additional evidence gained from the vacuum system indicated that resistivity is sensitive not only to the number of adsorbed species but also to their adsorption state [13,14]. The impact of gas adsorption on the resistivity of thin metal films was first reported by Fuchs in 1938 [15]. While several methods exist to explain gas adsorption-induced resistance, the surface scattering model was the most widely accepted during years [15–17]. Surface resistance measurements were also employed to examine the electrode–solution interface. In electrochemistry thin film resistivity offers experimental conditions far superior to those available in the gas phase. In addition to an almost unlimited variety of adsorbing species to choose from, the electrode– electrolyte system allows adsorption of ionic and molecular species to be precisely controlled and monitored through the electrode potential and charge. There are some interesting and worthy publications which cover the literature on surface resistance in electrochemistry up to 1994 [18–20]. However, after read these reviews one can realise that despite the high sensitivity of the thin film resistance to study surface and growth processes in electrochemistry, there was during years a lack of investigations of high quality due to the utilisation of both not well-characterised metal film surfaces, which affect the sensitivity of the technique, and refinements to improve the Fuchs–Sondheimer theory which offer little real advantage in the interpretation of experimental results. In the last decade, there has been a revival of interest in surface resistivity for several reasons. Experimental surface science provides methods of modifying the surface in controlled and well-characterised ways, and improved surface optical and spectroscopic probes make it possible to probe the effects of those modifications

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in unprecedented detail. Also, technological developments on the nano-scale have made an understanding of surface effects on electrical transport a matter of urgent importance: for instance, adsorbate effects on the electrical resistance of metallic nanowires [21] and carbon nanotubes [22] have recently been reported. Adsorbate-induced resistance and reflectance changes can also be used as a real-time, non-invasive probe of adsorption kinetics [23,24]. Finally, only recently theoretical understanding about resistance measurements advanced beyond the purely phenomenological aspect allowing the connection between surface resistance and diverse phenomena such as, atomic scale-friction [25], electromigration [26] and vibrational spectroscopy [27,28]. In this sense, Persson and co-workers [29,30] developed a model for diffuse scattering of carriers at surfaces, which invokes the electronic structure of the adsorbate and metal in a natural way. Despite of these recent theoretical and experimental developments in the study of surface effects on electrical transport, they have not been completely profited in the field of the surface resistance in electrochemistry. I hope that this review were useful to convince the colleagues that even more experimental and theoretical correlation should be established between surface resistance in electrochemistry and in UHV. In this sense, old resistometric experiments in electrochemistry should be considered in terms of both the modern surface physics and the modern theory of Persson. In the present review paper, I have attempted to identify and document the most significant advances that have been reported about both experimental and theoretical aspects of the surface resistance applied to the electrochemical research until 2003. In this sense, the review covers the literature from Shimizu’s works [31–33], where for the first time resistance changes of a thin metal film were used to study the adsorption process of hydrogen electrochemically formed on platinum surfaces, up to one of the more recent application of the technique related to the determination of heavy metal concentrations in aqueous solutions [34,35], where the high stability of epitaxial thin film electrodes has proved to offer a superior sensitivity to the technique and for longer time periods under electrochemical conditions [36–38]. Subject areas covered by the review include new trends directed to the utilisation of the film resistivity changes to study different surface processes such as, chemisorption of alkanethiolates at the metal liquid interface [39], distributions of redox sites at the metal–polymer interface [40–42] and morphology and roughening of electrodes [43]. This paper is organised as follows. In Section 2, the different contributions to resistivity changes in electrochemistry, that is, the field effect, the size effect and surface adsorption, are discussed in the light of experimental methods used to detect them and also in terms of fundamentals and mechanisms employed to explain them. The last subject area, surface adsorption, includes: ionic and molecular adsorption, hydrogen adsorption, oxygen electrosorption and oxide formation processes, and also the underpotential (upd) process and the formation of bulk alloys in metal film electrodes. Concerning the upd process, the effect of the metal cations adsorption on thin film electrodes resistance is discussed and updated on the basis of its recent use as an analytical tool to detection of trace concentrations of cations in solution. In this connection a recent study of irreversibly adsorbed copper cations on gold film electrodes detected by surface resistance is also reported. Another aspect of this section concerns to structural changes, roughening and corrosion effects detected by surface resistance when thin film electrodes are subjected to drastic electrochemical treatments (presence of chloride anion, extensive positive polarisation, etc.). Correlation established between surface resistance measurements and reflectance and Hall coefficient measurements in electrochemistry, respectively, are discussed in terms of their relative sensitivity to changes on the film surface during adsorption and simple electrode charging. In this connection, the important problem of the emersed double-layer studied by surface resistance and electroreflectance is considered. At the end of this section a recent application of the surface resistance

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technique to study the redox process of an electroactive polymer film deposited on a gold film is described. In Section 3, a brief compilation of the different theoretical developments based on the scattering model and the phenomenological parameters contained in them and used to explain resistance changes on thin metal film, is given. Also, in this section is demonstrated how some of these parameters were experimentally determined in electrochemistry by using surface resistance measurements. In Section 4, the measurement of the surface resistance is discussed from the experimental point of view, considering the problem of current and potential distribution along a resistive electrode, the different methods employed to measure the film resistance and the different electrode designs and circuitry used. Finally, Section 5 contains the concluding remarks.

2. Resistive changes in thin film electrodes The most important contributions to resistivity changes in electrochemistry are (i) the field effect, by which application of an electric field modifies the sample conductivity, (ii) the size effect, which refers to conductivity changes brought about by changes of the film thickness and (iii) adsorption effects. 2.1. The field effect Electric fields externally imposed affect the resistance of a thin metal film [1]. This effect refers to the variation of conductance with surface charge density induced by the electric field applied. Since the screening distance of the electric field is the order of atomic dimensions, the field effect becomes a significant contribution to the conductivity only when the thickness of the sample is comparable to the mean free path of conduction electrons [44]. Modulation of the conductivity of metal films in vacuum by addition of surface charges was studied by Bonfiglioli et al. [45]. For gold films it was demonstrated that conductance varies linearly with the induced charge [45]. For electrochemists, the field effect is particularly important since relatively large fields can be applied at the electrode–solution interface by the imposed electrode potential. In terms of the simple free electron model and the kinetic method [44], the metal conductivity sb, can be written as: n0 e2 t (1) m where n0 is the number electron density, e is the electron charge, t is the relaxation time and m is the effective electron mass. Considering a sample of thickness, d, the effect of the surface charge density, sm, assuming it to be uniformly distributed over the whole thickness of the sample, would simply be to change n0 by an amount (sm/ed), that is, the total number of carriers in the sample. Consequently, the relative surface conductivity change of the sample of thickness d (Dsf/sf), would be: sb ¼

Ds f Dr sm ¼
f ¼
sf rf n0 ed

(2)

where rf and sf are the resistivity and the conductivity, respectively. If Eq. (2) were true, a plot Drf/rf versus sm should give a straight line of slope (n0ed)
1. As was above indicated, a such linearity has been clearly confirmed for metal films in vacuum [45].

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Several attempts have been made to explain satisfactorily the effect of an electric field on conductance or conductivity of a metal film electrode [46–55]. The metal–solution interface, in the absence of specific adsorption, should be suitable for the study of the effect of the surface charge on the surface conductance. However, dependencies such as that predicted by Eq. (2) are difficult to analyse in electrochemistry because often they are masked by ionic adsorption effects [51,52]. Anderson and Hansen [46,47] employing thin gold films as working electrodes in 0.1 M Na2SO4 solution measured the relative change of conductance as a function of voltammetric charge corresponding to the double-layer region, where faradaic reactions should be absent. In this work surface charge values were extracted from integration of the corresponding potentiodynamic curves. They observed a good agreement between experimental results and those calculated from Eq. (2). Tucceri and co-workers [48,49] also studied the surface conductance of thin gold films in 0.5 M H2SO4 solutions within the potential range corresponding to the double-layer region. Experimental relative resistance change versus surface charge density (DR/R
sm) dependence gives a slope value 4.64  10
5 cm2 mC
1. This value coincides acceptably with that predicted by Eq. (2), which is (n0ed)
1 = 4.22  10
5 cm2 mC
1 for a film thickness, d = 25 nm. Rath and Hansen [50] observed a linear region for the relative resistance change versus potential dependence for gold films in 0.01 M NaF solutions at pH 5.1. Constant and symmetric currents on voltammetric curves were considered as indicative of only simple charging of the electrode–electrolyte double layer. Calculation of field effects in this region leads to a value 2.4 times greater than for a bulk phenomenon [50]. Tucceri and Posadas examined the validity of the field effect on gold [51] and silver [52] films contacting different surface inactive or weakly active electrolytes (KF and KPF6). In these works [51,52] also the DR/R
sm dependence was analysed. However, in this case the charge on the metal was calculated by integration of the capacitance versus potential (Cdl versus E) curves, following the procedure already applied by others workers [56] for pure salts in order to obtain firstly the sm versus E dependence. DR/R versus sm dependencies for Ag contacting both KF and KPF6 solutions of different concentration, are shown in [52]. DR/R versus sm dependencies for Ag contacting KF solutions of different concentration are shown in Fig. 1 of this work. The main features of these dependencies are the absence of a clear linear region at negative charges and also a slope at positive sm values which does not agree with that predicted by Eq. (2). By comparing (DR/R)/sm slopes in the linear portion at positive sm values for Ag contacting both KF and KPF6 electrolytes, a higher value results for KF (1.75  10
4 cm2 mC
1) (Fig. 1) as compared with KPF6 (1.3  10
4 cm2 mC
1) [52]. Also, a small dip at sm = 0 is observed in the DR/R versus sm dependencies showed in Fig. 1, which becomes more pronounced with decreasing the ionic strength of the solution. Also, in the case of Ag/KPF6 a small dip at sm = 0 is observed which becomes more marked as the ionic strength decreases. Thus, experimental DR/ R versus sm dependencies for Ag, suggest that at low ionic strength the screening conditions at the solution side have some influence on the DR/R change. If it is the case, this screening effect could be altered by replacing the water molecules in the immediate vicinity of the electrode by molecules of an organic compound. This might alter the dielectric constant in the inner part of the double-layer and the position of the outer Helmholtz plane. This effect was verified for gold films contacting pentan-1-ol solutions of different concentration, where a broad dip dependent on the alcohol concentration is observed on the DR/R versus E dependence [55]. On the other hand, gold films in contact with K2SO4 solutions show an almost constant DR/R versus sm slope at negative charges (Fig. 2) [51]. Also, in this case sm was calculated from the capacitance curves. The observed slope value is close to the theoretical one predicted by Eq. (2) for the field effect. However, by comparing with the results obtained for the

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Fig. 1. DR/R vs. surface charge density sm for a thin silver film electrode in the presence of different KF concentrations. Film thickness 25 nm. Charge values were extracted from capacitance vs. E curves. Concentration values: (&) 0.5 M; (*) 0.2 M; (~) 0.1 M; (5) 0.04 M; (+) 0.02 M; (*) 0.01 M; () 0.005 M. From [52].

alkali halide salts (see above), specially concerning to the lower adsorbabilty of KF as compared with sulphate, one could say that in the presence of sulphate anions there is not a true field effect as previously suggested [46–48], but it is a special feature of K2SO4. In this connection, also, at positive charges a slope increase is observed in the gold/sulphate system (Fig. 2). This increase in the slope at higher charges would indicate the specific adsorption of the anion whether HSO4
, SO42
or both. It is well-known that in acid media HSO4
exhibits a slow adsorption rate on gold [57]. This is experimentally confirmed by the dependence of the surface conductivity of gold films contacting sulphate anions, on the potential scan rate (n) [51]. As the scan rate increases both gold film capacity (Cdl) and DR/R change decrease [51]. This is opposite to the behaviour of KF, and in our opinion it might indicate that in the case of sulphate the anion adsorption is sweep rate dependent [51]. In general, two qualitative explanations have been given to rationalise the asymmetry between the positive and negative branches of the DR/R versus sm dependence in the absence of specific adsorption (KF and KPF6) and then, where the field effect should be more evident. One of them is the reorientation process of water dipoles in the presence of an electric field [51]. The reorientation process of water dipoles becomes evident from the capacitance–potential curves of both gold and silver films contacting

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Fig. 2. DR/R vs. surface charge density sm for a thin gold film electrode in the presence of a 0.02 M K2SO4 solution: (&) experimental data; (—) Dependence predicted by Eq. (2). Film thickness: 25 nm. Charge values were extracted from capacitance vs. E curves. From [51].

alkali halides, where two capacitive peaks are observed [51,52]. The peak occurring at the more negative potential values has been assigned to water reorientation. As the strength of the adsorption increases the capacity peak at the more positive potential values increases, and moves toward more negative potentials and then, there is a narrower potential or charge range for the occurrence of solvent reorientation. It is within this range that, at least in principle, the field effect should appear. The effect of dipole reorientation should make the water molecules present the positive end of the dipole (down position) to the metal at high negative charges and the negatives ones (up position) at positive charges to the point of equal orientation. One can further rationalise this phenomenon by arguing that the effect of water should be to increase the resistance in the down position and to decrease it in the up position, as in fact was found by measurements of the resistance change during water adsorption from the gas phase on polycrystalline gold [58]. Also, the asymmetry in the DR/R versus sm dependence can be explained qualitatively as follows: for sm > 0 the surface charge on the metal is due to the uncompensated positive background at the surface. The positive cores can be efficiently screened [44] by the conduction electrons, leading to localizated scattering centres at the metal surface. On the other hand when sm < 0, the surface charge is due to an excess of electrons in the surface region. Electron–electron interaction would make a very small

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contribution to the scattering probability, even if the negative charge were localised in space. Then, as pointed out by Ziman [44], screening will be less concentrated, because it would be necessary to create a deficit of charge around the impurity and thus the scattering probability would be smaller. Then, the conductivity change would be very small at sm < 0, as observed experimentally. The influence of the ionic strength (m) on DR/R near sm = 0, can be explained as follows. At low m values the Debye screening distance at the solution side increases with m and decreases with sm. This suggests the possibility that the charge induced on the metal by ions present at the outer Helmholtz plane tends to increase the resistance. This view is confirmed by the experiments with amyl alcohol [55]. There, the replacement of the water layer immediately adjacent to the electrode by a layer of amyl alcohol molecules weakens the coulombic interaction between the ions and the electron plasma by increasing their separation distance. This leads to an increase of conductivity. As the charge increases in absolute value, the amyl alcohol molecules become desorbed and the conductivity decreases, reaching the values corresponding to the base electrolyte. Similar behaviour has been observed for thin gold films contacting other organic compounds [59]. It is interesting to note that the magnitude of the field effect (Eq. (2)) has been estimated from a model of a free electron gas where it is further assumed that all the thermodynamic charge on the electrode contributes to change the density of free electrons in the film and thus to the resistance change. The model of the metal as a perfect conductor at the metal–solution interface is an oversimplification. Calculations on the contributions of the electrons to the differential electrode capacity based on improved Jellium models [60] show that there is a direct but no linear relation between the interfacial electron density and the charge on the metal. Further, if the electrons are assumed to reflect at the Jellium edge, most probably the predicted field effect based on a Jellium model would be smaller. Fujihira and Kuwana [53] found a linear relationship between the relative change in conductivity and the electrode charge in the double-layer region for Pt films contacting 1 M H2SO4 and 0.2 M HClO4 ˚ , the proportionality constant between solutions. For Pt films of thickness ranging between 200 and 300 A these relative changes was about of adl = 1.5  0.6. However, for the thickness range employed in this work, the relative conductance change (DG/G) was less than 0.01 and therefore is difficult to measure with high degree of accuracy. To rationalise a proportionality constant higher than 1, the authors considered that DG must be due not only to changes in the total free electronic charge or total number of conducting electrons, but also it should be influenced by the changing of the electric field. Fujihira and Kuwana invoke similar results obtained for Au and Ag films in vacuum where the change of conductivity as a function of the temperature suggests that the Jerertschke’s theory [61] might account for adl > 1. Thus, the field affects the mobility of the surface charge carriers. Bluvstein et al. [54] found that for bismuth films contacting non-adsorbing electrolytes (NaF, LiClO4 and Na2SO4), the conductance versus potential (DG versus E) curve exhibits a minimum within the potential range corresponding to a positive charge of the surface. Taking into account the semi-metallic nature of bismuth film this result can be explained in terms of a transition from predominantly electron (at negative charge of the surface) to predominantly hole (at positive charge) surface conductance. Intersection of the DG versus E curves corresponding to different electrolyte concentrations near the zero charge potential, suggests that DG is determined by the electrode free charge sm and the surface scattering effect of the carriers can be neglected. By using a set of DG versus E curves for different electrolytes concentrations, the authors were able to verify the linearity of the DG versus sm dependence. In conclusion, one can say that the surface conductance measurements of gold and silver films in different electrolytes show that in the double-layer charge region where ionic adsorption is expected to be

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absent, the contribution of the field effect to the relative resistance change is either smaller than predicted by the free electron gas model or it is balanced by the solvent dipole reorientation. Thus both, a more profound analysis about the influence of the water reorientation effect on the metal–electrolyte interface and the use of a more realistic model for the electrons in the metal would be necessary to explain the absence of a noticeable field effect on metal film electrodes in the presence of inactive electrolytes. In this connection besides change of carriers concentration, there may be other effects to consider. Juretschke [61] predicted that the effective mobility of added charge carriers is greater than that of the carrier population already present, thus the charge being added by the induced field. Then, mechanistic conclusions about field effects to conductivity changes in electrochemistry, remain still inconclusive. 2.2. The size effect When a metal sample has a thickness comparable to the mean-free-path (mfp) of the conduction electrons, surfaces impose a restraint on the electron motion. In this sense, the dispersion of conduction electrons at planar interfaces defined by the top and bottom surfaces of a metal sample, can contribute significantly to its resistivity. Using the Boltzmann equation to describe a free electron gas distribution in an ideal solid, Fuchs [15] and Sondheimer [62] developed a theory for the so called ‘‘size effect’’ on the electron transport properties. Considering a thin metal film of thickness d, comparable to the mfp, l0 of the conduction electrons, its the electrical resistivity rf is higher than the bulk resistivity rb of the massive metal of the same structure as the metal film and the rf/rb ratio decreases with increasing the film thickness, d. The exact expression for the dependence of the film resistivity as a function of the film thickness is complicated. However, it can be reduced to two limiting forms: rf 3ð1
pÞ ¼1þ ; 8k rb

k>1

(3)

and    
1 rf 4 1
p 1 ¼ ; k log k rb 3 1 þ p

k<1

(4)

where k = d/l0 is the ratio of the film thickness to the mfp and p is the specularity parameter. Eq. (4) is only valid for small p values and when k < 0.1. Calculated values of the rf/rb ratio from Eq. (3) are apparently in good agreement with those calculated by using the exact expression [15,62], and disagree by a maximum of ca. 7% for values of k lower than 0.1. Consequently, Eq. (3) has been used when the thickness film is approximately equal to or greater than the mfp. The specularity parameter represents the probability of an electron being reflected specularly or diffusely at the film surface. The p value ranges from 0 for complete diffuse scattering to 1 for complete specular scattering. Theoretical advances in modelling surface phenomena have shown that this parameter is intrinsically dependent on the electron incident angle [63]. Other theories suggest the influence of the film structure on this parameter [64]. At first, it should be considered that thin metal films can be prepared satisfying the Fuch’s model in a sufficient way to exhibit a specularity parameter near 1 (a surface with a smooth mirrorlike finish which is free of defects). However, this parameter, which is also interpreted as the fraction of the surface which specularly reflects electrons, depends on the quality of the metal film surface, that is, on the method of preparation of the metal film electrode [17]. In this sense, an appreciable fraction of the conduction

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electrons can scatter diffusely and give rise to an additional resistance which correlates with roughness of surface topography, the presence of surface defects and imperfections, which should lead to experimental p values lower than 1. Modifications of the Fuchs theory to account for some of its deficiencies have been made for the presence of grain boundaries [65], atomic scale surface roughness [66,67], large scale surface roughness [68,69] and for a separate scattering parameter to describe the film–substrate interface [61,70]. An alternative formulation to describe a non-ideal film was presented by Wedler and Wissmann (WW) [71]. In this treatment, the presence of surface defects, such as adsorbed species, dislocations and steps are described through scattering centres, since these defects will be accompanied by localised charges in the film similar in effect to scattering centres produced by lattice vacancies in the bulk. Assuming an additive law, similar to the Mathiessen’s rule [72], the total resistivity rf is expressed as the sum of the different contributions due to the scattering centres on the surface and to those present within (interior) the film: " # K 0 l 0 X Ns s s (5) þ rf ¼ rb 1 þ D0 k s in Eq. (5), the parameter K0 contains the probability of an electron being scattered at a grain boundary with D0 as a representative crystallite dimension and Ns is the surface density of a type of scattering centre with ss as its scattering cross section. Here, rb is the measurable bulk resistivity, since the thickness dependence on internal P structure has been included as a separate entity, and l0 and k were previously defined for Eq. (3). s represents a summation on different types of scattering centre. Experimental verifications of the size effect theory are difficult because, as was above indicated, film properties depend on the method of film preparation. Best agreement between theory and experimental results has been obtained for films prepared by fast rates of evaporation [73] or sputtering, or by evaporation on freshly cleaved mica surface [74]. In this connection, the initial value of the specularity parameter p corresponding to a sample freshly prepared was considered as representative of the quality of the new surface. In gas phase experiments, Chauvineau and Pariset [9,11–13] have shown that Eq. (3) can be only verified if the density of defects remains constant for the different film thickness. Small p values (0.3 < p < 0.6) are indicative of a relatively large amount of surface defects in an atomic scale but when these films are thermally heated the reduction of atomic defects increases the p value (0.8 < p < 0.9) due to formation of steps. The size effects in electrochemistry have been considered in a few number of papers. Fujihira and Kuwana [53] studied size effects at potentials corresponding to the double layer region by using thin platinum films as working electrodes in 1 M H2SO4 solutions. The authors obtained the experimental (rfd) versus d dependence, where d is the film thickness. By using Eq. (3) to fit experimental data (Fig. 3), an interception value (rf d), at d = 0, about four times larger than that predicted by Eq. (3), was obtained. Unless p assumes negative values, Eq. (3) does not represent adequately experimental data. Also, if the mfp is calculated from experimental intercept value using p = 0 and the value of the bulk resistivity of platinum, an unreasonable l0 value results. These disagreements have been assigned to film imperfections [75]. As was above indicated the concentration of surface defects should depend on the film thickness. Ganon et al. [76] analysed the thickness effect on the resistivity of thin gold films contacting NaF solutions. Assuming that the specularity, p, is the principal parameter affected during the electrochemical

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Fig. 3. Representation of (rfd) vs. film thickness d for Pt films. Open circles are experimental data with rf values taken at ˚ and E = 0.4 V (vs. NHE). Straight-line (b) is the fitting of experimental data by using Eq. (3) with p = 0; l0 = 105 A ˚ and rb = 13  10
6 V cm. From [53]. rb = 10.4  10
6 V cm. Straight-line (c) fitting using Eq. (3) with p = 0, l0 = 105 A

process occurring at the electrode–solution interface, the resistance change DR was obtained by differentiation of Eq. (3) in terms of p: DRd2 3 ¼
l0 rb Dp 8 G0

(6)

where G0 is a geometrical constant given by the ratio (length/width) for a rectangular film of thickness d. Then, at constant surface coverage (Dp constant) and different film thickness, Eq. (7) should be valid: DRd2 ¼ const G0

(7)

In other words, the relationship (7) results independent of the size effects. In [76], experimental DR values corresponding to different film thickness (25 nm < d < 85 nm) are shown. DR values were calculated as the difference between measured values in air and those obtained in a NaF 2  10
2 M solution at
0.75 V (versus SCE) (double layer region of gold). Also, in [76], the corresponding DRd2/G0 values calculated using Eq. (6), are presented. The mean resulting value of this constant is DRd2/ G0 = 1.12  104 V A2. Considering typical values of rb (=2.84  10
6 V cm) and l0 (=2.94  10
6 cm) for thin gold films, a Dp value about 0.40 results. Nevertheless, the authors conclude that the difficulty to

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obtain real values of p is caused by the strong dispersion of experimental data. In this sense, different values of p in electrochemical experiments were attributed to differences in the film electrode preparation and different crystal sizes of the prepared film electrodes [77–79]. Rath and Hansen by using the DdRi method [50] calculated the resistance sensitivity coefficient as for the adsorption process of I
on gold films of different thickness contacting NaI solutions. as was defined in terms of the electrosorption valence g [80] and by a factor that contains the size dependent sensitivity of the resistance on the surface phenomena:  "  
1 # 1 sa K0 1þ (8) as ¼
gF k k The last factor in Eq. (8) was expressed in the framework of the scattering hypothesis of Wedler– Wissmann (WW) [71] (see Eq. (5)). Concerning Eq. (5), it is interesting to note that as in electrochemical experiments the resistivity is sensitive to the induced electrode charge (field effect) and P the amount of specifically adsorbed species (see below), the last term in Eq. (5) may include the sum sNsss/k = Nese/ k + Nasa/k, where Ne and Na are the surface densities of the induced free electrons and adsorbed species of cross sections se and sa, respectively. Thus, in Eq. (8), F is the Faraday constant and sa is the scattering cross section of I
anion. As a first order approximation as should be inversely proportional to the film thickness, provided that the scattering cross section sa is indeed a constant. The coefficient as for iodide adsorption on several gold films was determined in [50]. The as versus k
1 representation for iodide is given in [50]. With the intercept at the origin, as required by all size effects theories, a linear relation is well defined for the three thicker films (d = 43, 127, and 184 nm). However, a large deviation was observed for 15 nm thick films. Bluvstein et al. [81] studied how structure and thickness of a bismuth film contacting different electrolytes, affect its surface conductance. They demonstrate that Bi films 20–150 nm thick are optimal for surface conductance studies. The authors show curves of conductance versus thickness (DG versus d) of Bi films contacting a 0.5 M Na2SO4 + 10
3 M KI solution and relative surface conductance changes versus thickness (dDG/dE versus d) in a 0.2 M Na2SO4 solution. The relative dDG/dE change was written as: dDG ¼ mfe Cdl dE

(9)

where mfe is the field effect mobility and Cdl is the capacitance of the film–electrolyte interface. From Eq. (9) authors indicate that size effects may be caused by a change in either mfe, Cdl or both of them. However, from experimental dDG/dE versus d and DG versus d dependencies the authors conclude that size effect is mainly caused by the double-layer capacitance change. Sverdlova et al. [82] used the dependence of the conductivity of iridium films on their thickness to study the oxide layer formation. Ir films that are thinner than 10 nm exhibit an island structure, and thus the values of their conductivity became unstable and poorly reproducible. However, as the Ir film thickness increases from 15 to 45 nm, the specific conductivity of the film is linear with thickness. Size effects have also been invoked to interpret conductivity changes of Rh and Pd films during dissolution under potentiodynamic conditions [83], oxidation of iron thin films in alkaline solutions [84] and roughening of thin silver films [43]. In [83], Rh and Pd films contacting a 0.5 M H2SO4 solution were subjected to oxidation and anodic dissolution, which cause a conductance decrease. After cycling the

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potential within the range 0.05 V < E < 1.4 V (versus RHE) for long time periods, etching on the Rh and Pd films was observed, which proceeds probably along the intergrain area. Then, the bond between individuals microcrystals weakens and the film transforms from continuous crystalline state into the islet state. This effect causes a resistance increase. In [43], surface roughening was considered as due to distortions in the smooth surface potential which gives rise to diffuse surface scattering and therefore to enhanced resistivity in a similar way to size effects. 2.3. Surface adsorption on thin film electrodes Several mechanisms have been proposed to explain the influence of surface adsorption on thin films resistivity: (a) adsorption affects the number of free electrons of the metal film [85–87], (b) adsorbates form new scattering centres on the metal surface for the conduction electrons [71] and (c) the adsorbate reacts with the surface metal atoms and removes a layer of conducting film [5]. All these mechanisms were analysed in the light of the Fuchs–Sondheimer theory [15,62] (see Eq. (3)). For instance, mechanism (a) was considered by Toya [88] by assuming that surface adsorption only affects the value of the number of free electrons (contained in rb in Eq. (3)) while others parameters, p, l0 and d remain constant. A similar relationship between the conductance change DG and the total number of free electrons in the film, Ne, was also suggested by Wissmann [87]:   DG 0 Na ¼x (10)
G Ne where Na is the number of adsorbed molecules on the surface of the film and x0 is a proportionality constant, which rationalises the effect of the adsorbed molecules to the conduction electrons. The value of x0 has been considered to correspond to the fraction of electron donated from the adsorbate to the metal and to be correlated to the electron affinity of the adsorbate with respect to the metal. If the electron affinity of adsorbate is high compared to the metal, then adsorption is expected to decrease the conductance and vice-versa in the reverse case. The second mechanism (b) can be justified on the basis of Fuchs–Sondheimer theory by assuming that the specularity p is the principal parameter influenced by the surface concentration of adsorbate, Gads. Differentiation of Eq. (3) in terms of p leads to the relationship:   3 l0 rb (11) DpðG ads Þ Drf ðG ads Þ ¼
8 d where it has been assumed that the specularity parameter p is proportional to the surface concentration of adsorbed species: Dp ¼
k1 G ads

(12)

Thus, the presence of adsorbed entities on the metal surface increases the diffuse scattering of conduction electrons and provokes a reduction of p (p ! 0). Consequently, according to Eq. (11), it should result an increase of resistivity during adsorption: Drf ¼ K0 G ads

(13)

The other possible effect of surface adsorption (mechanism (c)) on metal films is to change the film thickness, d, without variations in p, l0 and the number of free electrons of the metal film. This is the case

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when the adsorbate reacts with the metal surface. This reaction thus, removes a Dd thickness of conducting film. The resistivity change is then dependent on Dd, and it can be written as (see Eq. (3)): Dd (14) d The theoretical approach derived by Wissmann [87,89] has also been used to explain the resistivity changes of thin films caused by the interaction of conduction electrons with adsorbed molecules. According to Wissmann [87], the resistivity change can be expressed as (see Eq. (5)):   mvf Drf ¼ s a cv (15) n0 e2 Drf ¼
ðrf
rb Þ

where cv is the concentration in volume of the surface scattering centres, sa is the apparent scattering cross-section of adsorbed entities, vf is the mean velocity of the electron at the surface of the Fermi distribution, e is the electron charge, m is its effective mass and n0 is the electron density. cv can be associated to (Na/d) ratio in Eq. (5) for a given type of scattering centre. This interpretation assumes that both surface and volumetric resistivities are additives (Mathiessen rule) and that the scattering cross section is independent of cv . Considering in Eq. (15) the number of adsorbed molecules per unit of geometrical surface, Na, the corresponding resistivity is: K3 Na (16) d where K3 (=samvf/n0e2) is a constant and d is the film thickness. Then, the resistance change DR during adsorption can be expressed as: Drf ¼

DRd 2 ¼ k3 Na G0

(17)

where k3 (=l0rbsa) is a new constant and G0 is a geometrical constant given by the ratio (length/width) for a rectangular film. Eq. (17) is equivalent to Eq. (6) used to analyse size effects. The mechanisms given above to explain resistance changes during adsorption on thin metal films were extended to the electrochemical interface. Concerning mechanism (b) (Eq. (13)), in electrochemical processes the surface concentration Gads can be referred to several interfacial phenomena: ionic and organic molecules adsorption, coverage by surface oxides, interaction of metal surface with foreign adatoms during the underpotential deposition (upd) process, etc. In the case of ionic adsorption in the double-layer potential region, the value of Gads can be expressed in terms of the corresponding value of the charge density of specifically adsorbed ions, which can be calculated by integration of the capacitance–potential curves [51]. In organic compounds adsorption studies, resistance changes have been expressed in terms of the degree of surface coverage of adsorbate [90]. In studies of oxygen electrosorption processes the surface concentration of species corresponding to a given surface oxide structure has been expressed as a function of the exchanged charge Q during the formation of oxide layer as Gads = Q/zF, where z is the number of exchanged electrons during the corresponding electrosorption process [76]. The value of Q can be obtained by integration of the voltammetric curve. In the following sections we shall describe as these last considerations have been employed to interpret the different types of interaction at the thin film electrode–solution interface, detected by surface resistivity changes. However, several points should be take into account here. Unless the scattering effect

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by adsorbed entities were much higher than that corresponding to the field effect, the coverage should be analysed at constant electrode charge in order to keep the latter constant. Secondly, adsorption effects should be considered at very low coverages where the effect of the lateral interactions adsorbates or effects arising from the surface structure of the adsorbate phase, can be disregarded. In electrochemistry, when considering adsorption of organic molecules and ions, the corresponding surface excess of the adsorbed species should be calculated. Furthermore, in the case of ionic adsorption only the charge specifically adsorbed is the relevant quantity to be considered. However, it is necessary to indicate that in most of experimental works related to surface conductance measurements in electrochemistry, the electrode charge or the amount of adsorbed species, have been determined by using approximated methods. 2.3.1. Ionic adsorption Several papers deal with resistivity changes of thin film electrodes caused by ionic adsorption [90–98]. In general, electrical conductivity decreases with increasing the degree of adsorption. Bockris et al. [91] examined the influence of the electrolyte concentration (HClO4–H3PO4) on the electrical conduction of thin films of Pt sputtered onto glass. They also analysed the effect of the temperature on the resistivity changes. The Russian school studied the effects of many types of adsorbing species on the resistance of platinum, rhodium, gold and palladium thin film electrodes [90,92–98]. In [93], it was suggested that for relatively weak adsorption (adsorption of SO42
, Cl
, Zn2+) the change of resistance of platinum and rhodium films is mainly determined by the change of the free surface charge while in the case of strong adsorption (I
and Tl+) the increase of resistance is due to the fixation and scattering of conduction electrons, the change of the thickness of the conduction layer and other effects. Mu¨ ller et al. [90] applied the resistometric method to study the adsorption process of SO42
, Cl
, I
, Tl+ and Zn2+ on Pt and Rh thin film electrodes. Mansurov et al. [95] analysed the influence of concentration and pH of 5  10
4 M H2SO4+ x M Na2SO4 (10
2 < x < 0.5) solutions on the resistance of Au and Pt thin films. On Pt film electrodes is observed that the film resistance is proportional to the Na2SO4 concentration over the whole potential range (0.0 < E < 0.85 V versus RHE). An increase of the film resistance within the double layer region is in qualitative agreement with the expression DR/R = const  Dqe, where Dqe is the change of the free surface charge [95]. However, no quantitative agreement with this expression was observed. It was attributed to the specific adsorption of sulphate anions. The nature of the resistance change with increasing the pH is in accordance with the fact that as pH increases the strength of the bonds between the Pt surface and hydrogen and oxygen increases. The resistance of gold films passes through a minimum and over the whole potential range (0.0 < E < 1.5 V versus RHE) it increases with solution concentration. The existence of a minimum cannot be explained in terms of the expression DR/R = const Dqe and it was attributed to water adsorption on the gold surface. The kinetics of adsorption of Cl
and Br
anions on gold thin film electrodes was studied by Bluvshtein et al. [96] and also adsorption isotherms were constructed from surface conductivity data. A direct proportionality between the conductivity change and time (Dsf–t1/2) was observed in 5  10
5 M of KCl and KBr solutions, which was indicative of rates adsorption limited by diffusion. Considering the validity of the expression (Dsf = kqGads, where Gads is the surface concentration of adsorbed ions, the increase of kq with increasing the positive potential was associated to the increase of the degree of charge transfer of the anion. A higher kq value for Br
as compared with Cl
allowed the authors to conclude that for the same values of Gads and potential, bromide adsorption occurs with a larger degree of charge transfer as compared with chloride adsorption.

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The electrosorption process of In3+ ions on gold thin film electrodes was studied by Bluvshtein and Mansurov [98]. Also, Mansurov et al. [99] studied the adsorption of In3+ cations on Pt thin films from 10
3 M In2(SO4)3 + 0.5 M H2SO4 solutions. The resistance of Pt films decreases during adsorption of In3+ cations. This decrease was attributed to field effects. The results show that indium adsorption reduces the amount of adsorbed hydrogen on Pt but practically no influence on the oxygen adsorption process was observed. The indium adsorption at moderate coverage values obeys the Temkin isotherm. Indium adsorption on Pt films seems not to occur with a In3+ ! In0 conversion. Instead, authors postulate an associated adsorption of In3+ and SO42
anions. Vasina et al. [97] investigated by resistance measurements the effect of thallium deposition onto Pt and Rh thin film electrodes. One of the more complete analysis about the potentiality of the resistometric technique to study ionic adsorption is represented by the Anderson and Hansen’s works [46,47,100]. These authors studied the adsorption of I
anion on thin gold film electrodes. From the difference between voltammetric curves in the presence and the absence of I
anion in solution, the charge density (sI) caused by I
specifically adsorbed on the electrode surface was calculated. In a similar way, the corresponding relative conductance change DG/G due to the specific adsorption of I
anion, was obtained. For low sI values (up to 15 mC cm
2) a linear DG/G versus sI dependence was observed. However, the proportionality constant is more than a factor of two larger, than the value predicted by the relationship: DG ¼ K IsI G

(18)

The DG/G versus sI dependence is no longer linear as the anion surface coverage increases. In this last case, the adsorbed ionic layer is considered to be more like a charged plane than a few randomly space point charges and thus, the electron charging contribution to the conductance change is also affected. In another paper, Hansen [101] discuss the application of the resistometric technique to the study of halides adsorption on polycrystalline gold film electrodes. From the linearity of the relative resistance change versus surface concentration of bromide, the author determines the electrosorption valency of
Br
anion (g Br =
0.83). Rath and Hansen [50] studied the specific adsorption of Br
and I
ions on polycrystalline gold film electrodes by applying the so called dRi method. It is shown that the resistance of the gold film varies linearly with the coverage of these species as determined from integration of the voltammetric currents. The graph of the normalised current versus the derivative resistance permits to obtain the as coefficient (see Eq. (8)), which describes the sensitivity of the resistance to ionic adsorption. The ratio of the resistance sensitivities to these halides, with a given electrode, is a constant. This coefficient as was used to calculate the apparent scattering cross section sa of adsorbing ions. The value for bromide was determined to be 0.66 times the value corresponding to iodide. These experimental evaluations require that the electrosorption valency of ad-ions and the roughness factor of the film surface, be known. In the Rath’s review [18], many of the features of in situ resistance monitoring are exemplified by the chloride adsorption. In this sense, Rath [18] compares simultaneously the cyclic voltammogram, the resistance spectrum and the derivativeresistance voltammetric spectrum for the chloride adsorption on an epitaxial (1 1 1) gold film electrode. This is shown in Fig. 4. Since the resistance is an integral measurement (curve (b) in Fig. 4), the voltammetric current (curve (a) in Fig. 4) was directly correlated to the derivative of the resistance. Fig. 4(c) shows the derivative-resistance spectrum (dr/di versus potential) obtained by differentiating the resistance measurement. The close resemblance of the last curve to the voltammo-

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Fig. 4. (a) Cyclic voltammogram, (b) resistance and (c) derivative resistance voltammetric spectra for chloride adsorption with 150 nm (1 1 1) gold film at scan rate of 50 mV s
1. Electrolyte is 50 mM NaCl in 10 mM HClO4. From [18].

gram in the chloride adsorption region lends additional credence for the concept of linearity between resistance and charge. Also, from the derivative-resistance spectrum, changes in the nature of the adlayer due to either an oxidation reaction or coadsorption of an oxide species can be detected. Then, the derivative technique enhances the deviation process from the ideal adsorption system. Furthermore, Rath [18] shows with the linearity of the resistance to specific adsorbed ions, which is found in the case of chloride, the resistance measurement tracks the coverage of the adsorbed chloride with simple charging effects discriminated against. Also, it is shown that the resistance is insensitive to the hydrogen evolution (compares curves (a) and (b) in Fig. 4), which gives definite proof that the process is a ‘‘true’’ faradaic reaction in the sense that the interfacial region essentially remains unchanged. Rath also compares values of apparent scattering cross sections of halides experimentally determined in a previous work [50], with those values obtained from the Fuchs–Sondheimer theory modified by the approximations of Green and O’ Donnell [63] and Watanabe [102]. The theoretical model correlates well with experimental results (see Section 2.3). Dickinson and Sutton [103] in their investigation analysed the dc method of resistance measurements by monitoring the adsorption process of several anions and cations on platinum films. An apparent scattering cross section value for the bisulphate anion was estimated by Tucceri et al. [48] by employing cyclic voltammetry (CV) and surface resistance measurements to study gold film electrodes in contact with a 0.5 M H2SO4 solution. The total surface resistance change (DR/R)T within the potential region corresponding to the double-layer region was attributed to two main effects: the field effect, where the change of the surface charge density on the metal, sm is given by Eq. (2) and the electron

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dispersion effect brought about by the presence of adsorbed entities on the metal surface, that is,  T DR ¼ s m ðn0 edÞ
1
k0 s HSO4 (19) R In Eq. (19), s HSO4 is the surface charge density corresponding to specifically adsorbed sulphate ions and k0 is related to its scattering cross section. A very small k0 value was obtained from the treatment used in [48]. However, considering the adsorption reaction of bisulphate on gold is a displacement reaction, according to: AuðH2 OÞads þ HSO
4 , AuðHSO4 Þads þ H2 O

(I)

it is possible that the scattering cross section experimentally determined, corresponds to the difference between that of the bisulphate anion and that of the water molecule (see Section 2.3). In another work, Tucceri and Posadas [49] studied the adsorption of HSO4
on thin gold film electrodes from 0.5 M H2SO4 solutions by applying simultaneously surface conductance and multipulse potentiodynamic techniques. The ensemble of these techniques allowed us to obtain the experimental dependence between the relative resistance change DR/R and the corresponding degree of surface coverage of anions, uHSO4
[57,104]. According to Wissmann approach [87,89], the DðDR=RÞ=DuHSO4 slope was written in terms of the apparent scattering cross section s HSO4 of the adsorbing ion, as DðDR=RÞ s HSO4 (20) ¼ ðl0 SÞ
HSO 4 d du where l0 is the effective mfp of the conduction electrons, S is the value of the surface charge corresponding to a complete monolayer of anions (considered as 222 mC cm
2) and d is the film thickness. The experimental s HSO4 value determined in this work results 0.2 A2 per ion. This value is lower than those obtained by Rath and Hansen [50] for I
(1.1 A2) and Br
(0.71 A2) ions. In this same work, we verified the first order kinetics proposed for bisulphate adsorption on gold films [57]. Under these conditions the surface coverage of bisulphate as a function of time was expressed as:


4 uHSO4 ðtÞ ¼ uHSO max ½1
expð
k1 tÞ

(21)

where k1 is the velocity constant which depends on potential and concentration of ion in solution and HSO4 =uHSO4 Þ 4 uHSO max is the maximum degree of coverage of anions. Eq. (21) predicts a linear ln½1
ðu max versus t dependence, where the slope is k1. We also obtained the corresponding resistance change as ln[1
(DR/R)/(DR/Rmax)] versus t. Tucceri and Posadas [51] applied surface conductance and capacitance measurements to study the adsorption processes of several anions on gold thin film electrodes. Resistance and capacitance curves as a function of the electrode potential were recorded for gold films contacting 0.04 M KF, KBr, KI and 0.01 M K2SO4 solutions, respectively. In some cases, effects of concentration and pH changes of the solution and sweep rate change, on the corresponding resistance and capacitive curves were also explored. At low coverages, the relative resistance change DR/R as a function of the surface concentration of the adsorbed entity Gads was analysed on the basis of Eq. (22): DR ¼ KG ads (22) R Gads was expressed in terms of the specifically adsorbed charge, which was calculated from integration of

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capacitance versus potential curves [56]. For the different anions studied in this work it is found that as the potential is increased in the positive direction, the resistance change reaches a limiting value, which follows the same order of anion adsorbability on gold (F
< HSO4
< Cl
< Br
< I
). On the basis of Eq. (22) it was accepted, as more likely explanation, that the reason for the limiting DR/R value is the existence of a limiting coverage Gads,lim of the adsorbed species on the film surface. Besides, for Br
it was observed that the limiting DR/R value depends on the anion concentration. The dependence of the limiting DR/R value on anion concentration in the case of the Br
was attributed to a Gads,lim dependence on the anion concentration in solution. This last effect was explained by assuming that before the saturation coverage were reached, a partial charge transfer process occurs [56,105]. This was also suggested by a change detected in the in-phase component of the impedance response of gold contacting a 0.4 M KBr solution [51]. Since a net DR/R change with increasing the potential in the positive direction was also observed for gold films contacting a 0.04 M KF solution and this effect could be related to the formation of an ‘‘incipient oxide’’ on the gold surface [106], the solution pH in the presence of F
anions was changed. It was found that the limiting DR/R value depends on HO
concentration. This is agreement with previous observations [107] in which the formation of an ‘‘incipient oxide’’ was postulated in order to explain the difference between the capacitive curves and the voltammograms for Au(1 1 0) contacting a 0.02 M NaF solution. However, the fact that DR/R changes by about of 15% for a pH change from 5.4 to 8.4 surely indicates that the ‘‘incipient oxide’’ contribution would not account [107] for the total observed DR/R change with pH. Although these results can only be considered as indicatives, they suggest that the F
anion adsorbs on polycrystalline gold in appreciable amounts. Whether this is due to floride anion or to impurities it is difficult to decide since the capacitive–potential curves depend on the sweep rate. Results concerning to HSO4
anion adsorption were associated to field effects (see Section 2.1). Silver films [52] in the presence of halide solutions, whose anions exhibit specific adsorption, give DR/ R versus sX curves (sX represents the specifically adsorbed charge for the corresponding halide) similar to those obtained for gold films [51] contacting the same electrolytic media. However, for silver films there is a steeper rise of DR/R change and higher DR/R values are reached at the extreme positive sX values, as compared with gold films. These dependencies are compared in Fig. 5. In both metals, the final slope at high positive charge values reaches a value of 4  10
5 cm2 mC
1 independently of the nature of the salt and of the metal. Surprisingly, this value compares well with that predicted by Eq. (2) for the field effect ((n0ed)
1 = 4.63  10
5 cm2 mC
1, where d = 25 nm). From Fig. 5, it is clear that D(DR/R)/DsX slope values in the region of nearly linear variation of DR/R versus sX dependence, increases in the order Cl
< Br
< I
. Although the DR/R change is much larger than in the case of weakly adsorbed ions, such as F
and PF6
, the slope is smaller. Ko¨ rwer et al. [108] studied resistivity changes of silver thin film electrodes due to adsorption of Cl
and ClO4
anions. It was found that the relative resistivity change induced by Cl
is about twice that induced by ClO4
. Moreover, by comparing resistometric curves for Cl
and ClO4
the authors remark two interesting facts. Firstly, at potentials negative of the point of zero charge (about
0.9 V versus SCE) no resistance change could be observed. This was assigned to a negligible influence of negative potentials on the dispersion of surface plasmon polaritons on silver electrodes. Secondly, the Cl
curve shows a hysteresis while that of ClO4
doesn’t. Concerning Cl
adsorption (see Fig. 4 in [108]) starting at
1.4 V (versus SCE) the resistivity firstly increases because of Cl
adsorption. Then, a monolayer of AgCl is formed in between
0.3 Vand 0.0 V (versus SCE). The onset of AgCl formation leads to a sharp increase in resistivity because of the smaller conducting cross section of the film together with an increase in the number of scattering centres at the surface. On the backscan, resistivity decreases again with reduction of

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Fig. 5. DR/R vs. surface charge density sX for (—) gold and (- - -) silver film electrodes contacting different potassium halides. The same concentration for the different halides: 0.04 M. sX values were extracted from capacitance vs. E curves for the different halides. Film thickness: 25 nm. From [52].

the AgCl adlayer and furthermore with desorption of Cl
. However, morphology changes and corrosion of the silver film also occurs in the presence of Cl
anion. In order to improve surface resistance measurements of thin film electrodes Winkes et al. [36] developed epitaxially grown silver electrodes of about 20 nm in thickness to study different adsorption processes. With these single-crystal electrodes the authors studied adsorption of halides (Cl
, Br
and I
) on Ag(1 0 0) and Ag(1 1 1) and adsorption of SCN
anion on Ag(1 0 0). For both, Ag(1 0 0) and Ag(1 1 1) epitaxial silver films in the presence of the different halides, the increase of surface resistance reached at the more positive end of the potential range follows the same order as the strength of specific adsorption of halides (Cl
< Br
< I
) on polycrystalline silver and gold film electrodes. Also, phase transitions in these adsorbed layers were detected by surface resistance measurements. In the case of Ag(1 0 0)/Cl
system a small structure at about
0.45 V (versus SCE) on the DR/R versus E curve was considered to be indicative of a such phase transition. In the case of Ag(1 1 1)/Cl
system a resistance decrease at about 0.0 V (versus SCE) was assigned to the formation of an ordered (31/2  31/2)R308 adlayer. It was considered that an ordered layer can scatter electrons only with momentum transfer according to the reciprocal vectors of the ordered adsorbate mesh, whereas for unordered adsorption all scattering channels are open. Thus, an ordered layer will lead to a decrease on the adsorbate-induced

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resistivity, but not to its total disappearance. The authors do not detect phase transitions during adsorption of Br
and I
on Ag(1 1 1). Voltammetric, capacitive and surface resistance measurements were also employed in [36] to study SCN
adsorption on Ag(1 0 0) thin film electrodes. The DR/R versus E curve allows to distinguish an adsorption range, a saturation range and a range of phase transition in the thiocyanate adlayer within the whole potential region comprised between
1.4 V < E < 0.0 V (versus SCE). In order to check in detail the phase transition process at potential greater than
0.5 V (versus SCE), ex situ XPS measurements were performed. It was found that the phase transition in the SCN
adlayer is accompanied by an increase in packing density of about 50%, where the increase of surface resistance is proportional to the increase in SCN
coverage. XPS measurements seems to indicate two different orientations of SCN
on the Ag(1 0 0) surface. The authors conclude that the stability of the epitaxial films prepared by them allows a systematic study of the resistance change as a function of the concentration and the electrochemical potential, from which one can approximately infer the change of the partial charge transfer to the adsorbed molecules as a function of the electrochemical potential, provided that the other changes of the double layer, for example, due to water dipoles, do not influence the resistance. In this way, resistivity data should allow to discriminate between the different contributions to the thermodynamically defined electrosorption valency, as a function of the electrochemical potential. Hanewinkel et al. [109] analysed dc-resistance changes of epitaxial Ag(1 0 0) films contacting 0.04 M KClO4 + 0.01 M KBr solutions. The square resistance R0 (¼ Rw=l, where R is the measured resistance and w and l are the width and the length, respectively, of the rectangular sample) as a function of potential was compared with both bromide coverage in four-fold hollow sites determined from the analysis of Xray diffraction signal during potential scans and bromide coverage obtained from chronocoulometry. It was found that R’ scales approximately linearly with the former parameter. No changes in the slope was observed during the transition, previously reported for this system [110], from a lattice gas of bromide randomly adsorbed at four-fold hollow sites to a commensurate c(2  2) structure of bromide in four-fold hollow sites. These observations were explained considering that there is bromide in the double layer (Helmholtz layer) which has little or no electron exchange with the metal. As it is difficult to explain the contribution of non-specifically adsorbed ions to the electrode resistance, the authors discuss experimental results on the basis of the covalent bond model of surface resistance in which the electron exchange between the metal and the specifically adsorbed moieties is treated in the sense of the Newns– Anderson model [27]. The approximately linear correlation between the resistance and the coverage of the four-fold hollow sites indicates a cross-section of diffuse scattering of electrons at EFermi independent of coverage, which implies further a negligible overlap of the Br 4p orbitals at neighbouring four-fold hollow sites. In a recent work, Hanewinkel et al. [38] analysed perchlorate adsorption on thin (1 1 1) oriented silver films by resistance measurements. Linear potential scan and potential step experiments were used to study the hysteresis observed on the resistance response during the adsorption and desorption processes of perchlorate. Bluvshtein et al. [111] studied the features of surface conductance exhibited by Bi film electrodes as a function of several variables: halide ion X
, solution concentration, adsorption time and electrode potential. Conductance versus potential (DG versus E) dependencies of these electrodes contacting the different halides Cl
, Br
and I
, show similar forms. Conductance exhibits a minimum value at a given potential value Emin for each halide anion. At constant halide ion concentration, the shift of the minimum along the potential axis, relative to the base curve, increases following the order Cl
< Br
< I
.

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However, two different conductance behaviours were observed respect to the Emin value. At E < Emin, DG depends on two factors. On one hand, the halide adsorption results in an increase in the differential capacitance. On the other hand, considering the band structure of Bi as a semimetal and on account for the image forces, X
adsorption should lead to an increase in hole concentration in the space charge region, which will give rise to higher conductivity and hence to a lower slope in the DG versus E dependence. These two effects act oppositely on the conductance, hence they more or less compensate one another leading to the experimentally observed DG versus E dependence. At potential values E > Emin, a sharp increase in conductance was observed. Within this potential region it is postulated that a charge transfer process from the halide anion X
to the positive charged electrode and a decrease of capacitance Cdl occur. In the opinion of the authors, this effect can be explained assuming that the acceptor-type surface states developing upon X atom adsorption can capture valence-band electrons of the Bi film, which leads to hole injection into the space-charge region and thus to an increase in conductance. Moreover, at these potentials bismuth oxyhalides may form on the electrode surface. The oxyhalides can also be regarded as adsorptive surface states influencing the carrier concentration in the charge-space region. These authors also examined the magnitude of the cathodic shift of the ascending branches in the DG versus E curves with increasing the halide concentration in the electrolyte. At these potential values a strong charge transfer process should occur during halide adsorption. The degree of charge transfer for the different halides was calculated. By stepping the potential from E =
1.0 V to Eads in the region where Eads > Emin, the kinetics of halide ion adsorption was also studied. The corresponding DG versus t dependencies are reported in this work. It was observed that within this potential region the adsorption kinetics of halide anions can be described by the Roginskii–Zel’dovich equation. The potential dependence of the adsorption rate constants for the different halides was also determined. 2.3.2. Molecular adsorption There is a few number of papers concerning the effect of organic compounds adsorption on the resistance of thin film electrodes. Niki and Shirato [59] analysed resistivity changes as a function of potential for gold film electrodes contacting benzoic acid and n-amyl alcohol, respectively. They found that maximum resistivity changes occur at the potential of zero charge (pzc). Opposite to benzoic acid, n-amyl alcohol yields a decrease in the surface conductance, respect to that of the base electrolyte. Muller et al. [90] studied adsorption of thiourea (TU), sulfide and urea on Pt film electrodes in the presence of 0.5 M H2SO4, as supporting electrolyte solution. Addition of TU to the 0.5 M H2SO4, solution during a linear potential sweep between 0.05 and 0.8 V (versus RHE) leads to a sudden increase of the Pt film resistance. After this, there is a slow further increase in film resistance during cyclic polarisation. However, resistance changes of Pt films covered with TU is effectively potential independent within the range 0.05–1.0 V and the weak potential dependence after adsorption seems to be due to a bond strengthening process with time. The authors conclude that the increase in resistance during TU adsorption is mainly due to adsorbed S after the rupture of C–S bond. This was verified by studying SH2 adsorption on Pt films. It was found that resistance changes of Pt films in the presence of TU and SH2 are quite similar. The decrease of the quantity of adsorbed hydrogen in the presence of thiourea was used by to determinate the quantity of adsorbed thiourea on Pt by means of the relationship: uH ¼ 1
uTU

(23)

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where uH is the degree of coverage due to hydrogen adsorption and uTU the corresponding degree of coverage due to thiourea. The authors show that the equation: Drf ¼ kuTU rf

(24)

is fulfilled for a wide interval of uTU values (0.2 < uTU < 0.8). Taking into account the decomposition of TU by chemisorption on Pt and the fact that the rates of removal of the products of decomposition from the Pt surface are different, this result was interpreted by assuming that the adsorbed sulphur is the responsible for the observed change of the film resistance. Also, a linear Drf/rf versus u relationship was obtained for adsorption of sulphide on Pt film electrodes from a 0.5 M H2SO4 solution. As compared with TU and sulphide, a small resistance change was observed after to add urea to a 0.5 M H2SO4 solution The group of Bohn studied adsorption of different organic compounds at the Au–liquid interface by using in plane-resistivity measurements performed in a four-point probe configuration [39,112,113]. Resistance response of gold films to full monolayers formed from alkanethiols in the homologous series CnH2n+1SH where 2 < n < 16, result independent of the length of the alkyl chain but it is dependent on the molecular character of the adsorbate [112]. The results suggest that for alkanethiols the increase in resistivity Drf/rf is based on the S-headgroup interactions with the Au and is less sensitive to nonbonded portions of the adsorbate molecule. This conclusion is also supported by observations of different adsorbates, which were separated in three groups according to the magnitude of the Drf/rf change: alkanethiols produced the highest resistometric effect, followed by parasubstituted benzenethiols and a last group, consisting of pyridine, phenoxide ion and dodecanesulfonate, which produced no observable resistance change. These differences were assigned to the impact of surface dipoles on the diffuse scattering of charge carriers at the solid–liquid interface [29,30]. This explanation is consistent with the less polar Au–S bond for the aromatics compounds, the independence of the Drf/rf change within the alkanethiolate series, and the absence of an effect for physisorbed, e.g., pyridine and phenoxide, and non adsorbed, e.g., dodecanesulfonate, species. In another work [113] resistivity changes during alkanethiolate self-assembly on gold films were correlated to evolution of the dielectric response obtained by simultaneous surface plasmon resonance (SPR) measurements. Resistivity changes at saturation coverage were independent of n for the series of even-n alkanethiolate adsorbates CnH2n+1SH where 2 < n < 16, in contradiction to the dielectric response, which was linearly dependent on n. Further, the observed non-linear regions of the Drf versus Gads dependence was interpreted in terms of heightened mobility, at low coverage, and structural rearrangement, at saturation coverage. Also, in this work, it was demonstrated that the change in resistivity proved to be a remarkably reproducible indicator for the surface chemistry, allowing the authors to follow the state of the Au surface through a complex series of chemical redox manipulations. In a further work, Bohn and co-workers [39] used the adsorption of hexadecanethiol (C16H33SH) on Au films to study how morphology and surface electronic states interact to produce the changes of in electron wavepacket scattering responsible for the observed changes in resistivity. In this work, alkanethiol monolayer assembly-stripping cycles were used to detect resistivity changes during surface roughness. With regard to alkanethiol films formed on Au surfaces, the metal– alkanethiol–metal configuration was recently thought of as being a model of molecular wire, which is important to the research field of molecular electronics. In this connection in a recent paper [114] a quantitative analysis about the transport properties to the metal–alkanethiols–metal junction was carried out. It was determined how conduction channels arise from molecular orbitals inside the scattering region. Also, it was found that the resistance of alkanethiol chains involving 4–8 carbons is in the range of

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0.2 V to 200 MV, respectively, and also that the resistance roughly scales as R = R0 exp(bn), where n is the number of carbon atoms. Tucceri and Posadas studied adsorption of pentan-1-ol on thin gold film electrodes by capacitance and surface conductance measurements [55]. The coverage and electrode charge were obtained from a complete thermodynamic analysis based on the Gibbs adsorption isotherm. In this way, it was possible to obtain the coverage of the organic compound at constant electrode charge. The adsorption behaviour of this alcohol is quite similar to that of di-ethyl ether on single crystal gold electrodes [115]. Also, from the resistometric viewpoint the results obtained are in agreement with those obtained by Niki and Shirato [59], that is, as the potential increases in the positive direction, DR/R decreases, firstly almost linearly with potential, and then more rapidly until it reaches a minimum value. The observed resistometric behaviour was interpreted in terms of field and adsorption effects together with a two states model for the solvent at the compact layer (see also discussion about organic adsoption on the field effect given in Section 2.1). It is known that this alcohol adsorbs on mercury with the hydrocarbon chain facing to the metal surface. Then, it should be expected that this orientation remains the same on polycrystalline gold [115]. Since the free energy of adsorption on polycrystalline gold is smaller than on mercury, it follows that the chemical interaction between gold and the alcohol should be very small [116]. Under these conditions, the dispersion coefficient of pentan-1-ol for the conduction electrons of gold was considered to be small. Thus, the main effect of the alcohol adsorption would be to displace solvent molecules and to change the surface charge. This consideration was used to explain qualitatively the sign and the slope of the resistance change with potential. Bluvshtein et al. [117] studied the adsorption of different organic compounds, such as, camphor, adamantanol, cyclohexanol, thiourea and benzoic acid, on bismuth thin film electrodes. Together with potentiodynamic sweeps, conductance changes were recorded during the different adsorption processes. Adsorption of all these compounds on bismuth films causes a decrease in conductance, G, also giving rise to the existence of a minimum value on the DG versus E dependence at nearly the same potential value at which the corresponding capacitance versus potential curve exhibits a minimum value. However, these compounds were separated in three different classes according to its influence on the surface conductance versus potential dependence. DG versus E dependencies for cyclohexanol, camphor and adamantol are similar in character. The descending branches of DG versus E traces become less steep when these substances are adsorbed on Bi. Also, increase of the concentration of these compounds yields a shift of the minimum value on the DG versus E curves towards the positive potential direction. The thiourea adsorption causes a shift of the minimum in the DG versus E towards the negative potential direction. This compound exhibits a rather strong interaction with the Bi surface via its sulphur atom. This effect of the thiourea on the DG versus E curves is analogous to that of halides ions [111]. The adsorption of aromatic compounds is attended by p-electron interaction between the adsorbate and the surface. The most typical features of conductance curves recorded in the presence of benzoic acid are the strong shift of the minimum in the curve DG versus E curves towards the positive potential direction and a considerable conductance rise. The benzoic acid adsorption strongly inhibits oxygen adsorption, which probably is the main reason for the positive potential shift in the conductance minimum. The influence of the adsorption of an organic molecule such as uracil on the resistance of Ag(1 0 0) thin film electrodes was studied by Winkes et al. [36]. Resistance changes of a 22 nm thick Ag(1 0 0) film electrode in the presence of a 0.05 M KClO4 solution and in the presence of the same solution after adding 20 mM uracil were compared. While in the only presence of ClO4
anions a resistance increase is observed at potential values more positive than E =
0.6 V (versus SCE) during the potential scan

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Fig. 6. (a) Relative resistance change of a Ag(1 0 0) thin film electrode (22 nm thick) in pure 0.05 M KClO4 and after adding 20 mM uracil. The resistance minimum of the electrode was 9.5 V. The scan rate was 50 mV s
1. (b) Voltammogram of the 22 nm Ag(1 0 0) electrode in pure KClO4, and after adding 20 mM uracil. The scan rate was 50 mV s
1. From [36].

towards the positive direction, in the presence of uracil the resistance starts to increase at potential values more negative, that is, at E =
0.8 V (versus SCE) (Fig. 6). This effect was attributed to the strong bonding of the chemisorbed uracil adlayer, resulting in a stronger influence on the conducting electrons reflected at the Ag(1 0 0) thin film surface. Comparison of both resistometric and voltammetric responses allowed to establish that a phase transition occurs in the uracil adlayer at potential values more positive than
0.8 V (versus SCE). 2.3.3. Hydrogen adsorption Shimizu studied resistance changes of platinum film electrodes during both negative and positive polarisation, in the presence of 10
3N sulphuric acid solutions. This author investigated the mechanism hydrogen adsorption on Pt by employing galvanostatic methods [31–33]. Fujihira and Kuwana [53] found that for Pt film electrodes contacting 1 M H2SO4 solutions, the relative conductance change DG/G increases as the potential is scanned towards the negative potential

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direction from 0.35 to 0.20 V (versus NHE). This potential region corresponds to the first wave of the hydrogen adsorption region on Pt surfaces (related to Hads at (1 0 0) crystallographic sites). However, conductance changes very little as the potential scan is continued at values E < 0.2 V (NHE), where adsorbed H atoms are present on the Pt surface associated to (1 1 1) crystallographic sites. By discounting for the contribution of the relative charge density change Dqe/qe of the double-layer capacitance, the authors were able to calculate the amount of DG/G corresponding to the DqH/qH due to adsorbed hydrogen at sites of (1 0 0) nearest neighbours co-ordination of the Pt surface. On the assumption that Eq. (25) (see Eq. (2) for the field effect) is valid: DG DqH ¼ aHy G qH

(25)

an average value of aHy around 0.65  0.06 was obtained for the hydrogen adsorption region corresponding to the more positive wave. For the potential region corresponding to the less positive wave the value of aHy is considerably lower than 0.65. Little aHy values were attributed to a little change of the specularity parameter, p. 2.3.4. Oxygen electrosorption and oxide formation processes Several authors studied the electrosorption process of oxygen on thin metal film electrodes by employing surface resistance measurements. Fujihira and Kuwana [53] studied the oxygen electrosorption process on Pt thin film electrodes. Relative conductance change versus potential (DG/G
E) and charge versus potential (DQa/Qa
E) dependencies were recorded for potential values more positive than E = 0.8 V (versus NHE), where Pt oxidation occurs. The relative conductance change decreases as the potential is scanned within the potential region corresponding to oxygen electrosorption process on Pt. DG/G versus DQa/Qa curves were obtained for Pt films of different thickness. It is found that the initial portion of the DG/G versus DQa/Qa dependence exhibits a slope value near 1. This slope value within this first potential region was attributed to a monovalent adsorbed species, such as PtOH. For the different Pt film thickness used in this work, DG/G versus DQa/Qa curves deviate from the slope value 1 at ca. 1.0 V (NEH) and finally the slope becomes equal to 0.46  0.02 beyond 1.1 V (versus NEH), which is about half of the value corresponding to the initial portion. The change of the slope was associated to a change in valence of adsorbed oxygen species. It seems to be in agreement with the existence of bivalent adsorbed species, such as PtO, beyond 1.1 V (versus NHE) on Pt surfaces [118]. Ganon et al. [76] studied the oxygen electrosorption process on gold film electrodes of preferential orientation (1 1 1) in the presence of 0.02 M NaF solutions. Resistance changes versus charge (DR–Qa,c) dependencies obtained for both adsorption and desorption processes of oxygen exhibit five linear portions, where breaks always appear at the same values of charge or potential, independently of the film thickness. In Fig. 7 is shown the resistance change versus charge (DR–Qa) dependence for the oxygen adsorption process. These results were interpreted by assuming the existence of different structures and valence states of the oxide monolayer formed on gold. Experimental values of the surface concentration of oxygen atoms on gold, Gexp,a (=Qexp,a/zF), were calculated from experimental Qexp,a charge values corresponding to the different slope changes on the DR–Qa dependency (Fig. 7). Qexp,a was obtained from integration of voltammetric curves and z is the number of exchanged electrons during the corresponding electrosorption process represented by the reaction (II): Oz
, Oads þ ze


(II)

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Fig. 7. Resistance change DR vs. surface charge Qa during the oxygen adsorption process on a 50 nm thick gold film electrode. Electrolyte: a 0.02 M NaF solution. From [76].

Experimental Gexp,a and calculated Gcalc,a values are compared in [76]. Gcalc,a values were obtained considering the formation of surface compounds such as Au(HO) and AuO, where z = 1 or 2 values, respectively, were assumed for a Au(1 1 1) film electrode of roughness coefficient equal to 1. By employing the Wissmann’s theory [87] to interpret the D(DR)/DQexp,a slope values during the oxidation process of gold film electrodes, the authors conclude that this slope is proportional to the ratio between the scattering cross section of adsorbed species and the number of exchanged electrons during its formation. Taking into account the proposed structures, a mechanism for the adsorption process of oxygen on gold is proposed in [76]. This mechanism implies oxidation steps consecutively involving each one of the different structures presented in Table 5 in [76]. It is interesting to note that in this mechanism, the simultaneous coexistence of different adsorbates being disregarded. On the other hand, a constant value of the surface scattering cross section, was assumed for the different oxidation states of gold surface corresponding to each proposed structure. Tucceri et al. [48] studied the oxygen electrosorption process on thin gold film electrodes from 1N H2SO4 solutions by using both, cyclic voltammetry and the surface resistance technique. The process was analysed within the potential region comprised between 1.3 and 1.8 V (versus NHE). DR versus Qa,c

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117

dependence for both, oxygen adsorption and desorption processes becomes linear within the whole charge range. Also, it was found that the D(DR)/DQa,c slope for both oxidation and reduction processes increases with increasing the potential sweep rate, n. Furthermore, the D(DR)/DQc slope for the reduction process depends on the upper positive potential limit reached during the formation of the gold surface oxide. In this last sense, while for different positive potential limits up to Ea = 1.6 V (versus NHE), a constant slope results for the reduction process of oxygen, this slope increases for positive potential limits E > 1.6 V (versus NHE). At the same time, an inflection point at E = 1.6 V is observed on the Qa–E dependence for the oxidation process. In agreement with other authors [119,120] these findings were considered in terms of the occurrence of a AuO monolayer on the electrode surface at E = 1.6 V (versus NHE). Experimental slopes reported in [48] were corrected by a roughness factor of 1.3. This factor was calculated by comparing experimental values for the oxidation charge obtained up to E = 1.6 V (Qexp,a = 560 mC cm
2) with the theoretical value corresponding to a monolayer of O2
species on a Au(1 1 1) surface assuming a ratio 1:1 between O2
species and Au atoms (Qtheor,a = 444 mC cm
2). The absence of breaks on the DR versus Qa dependence in the presence of H2SO4 [48] and also K2SO4 [76] solutions, as compared with F
anions [76], was attributed to the stronger adsorption of HSO4
anions, which should avoid the interaction of HO
species with the gold surface to form Au(HO)ads species. The dependence of the D(DR)/DQa,c slope on n was explained by assuming that gold surface coverage by species of low oxidation state (low z values) increases with increasing n. In [48], scattering cross sections were estimated from experimental D(DR)/DQa,c slopes and they were compared with those reported by Ganon et al. [76] for the different oxide surface structures formed in the presence of floride anions. In another work, Tucceri et al. [121] studied in more detail the effect of HSO4
anions adsorption on the surface oxide formation process on gold thin film electrodes. A multipulse potential program followed by a linear potential sweep was employed in these experiments [49,57]. The effect of HSO4
adsorption on the gold surface oxide formation was studied by holding the electrode potential at different values within potential regions corresponding both, the double-layer and the proper oxygen electrosorption process. The corresponding inhibition of the pseudo-capacitive voltammetric response for the oxygen adatoms formation (oxide charge diminution DQa) during HSO4
anions adsorption [104] was employed to assess the gold surface blocking by bisulphate anions. Resistance changes (DR/R) as a function of potential during both continuos potentiodynamic cycling and also during subsequent potential scans after holding the electrode potential at different values, were recorded. Also, DR/R changes as a function of time were recorded at different holding potential values within the potential region corresponding to the oxygen adsorption process (1.5 < E < 1.68 V versus NHE). At a given holding potential value, an increase of DR/R with time was observed, which follows a first order kinetics. D(DR/R)/DQa,c slopes as a function of
the surface coverage uHSO4 for both, adsorption and desorption processes of oxygen were calculated in [121] from experimental data. Also, at constant anion coverage, the D(DR/R)/DQc slope for the reduction process was analysed as a function of the upper positive potential limit reached during the surface oxide formation. These slopes were used to discern between different possible species present on the gold surface at the different positive potential limits reached. It was observed that even when the slope for the reduction process becomes independent of the positive potential limit between 1.35 V < E < 1.5 V
(NHE), it drastically decreases with increasing uHSO4 . For E > 1.55 V (NHE), the slope value increases for all anionic coverages. Resistometric data seem to indicate that surface species formed on gold during different holding times exhibit larger scattering cross sections than those formed during continuous potential cycling. On the basis of both, voltammetric and resistometric results, a mechanism for the oxidation process of gold film electrodes in the presence of bisulphate anions was proposed in [121].

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Within the potential region comprised between 1.3 V < E < 1.55 V versus NHE, the discharge of water on the metal surface should produce an adsorbed species, probably AuO, according to the reaction: Au þ H2 O , ðAuOÞads þ Hþ þ e


(III)

followed of a rapid conversion, ðAuOÞads , ðAuOÞads

(IV) HSO
4

. For more positive potential where the scattering cross section of ðAuOÞads species depends on u values, it is assumed the occurrence of a slow ‘‘re-accommodation’’ reaction that produces species with higher scattering sections. Assuming that a complete monolayer of AuO species is formed up to E = 1.50 V versus NHE, the posterior re-accommodation reaction was interpreted as a reaction in volume where a bulk oxide is formed within the metal lattice [119,120]. Bluvshtein et al. [122] studied the oxygen adsorption process on bismuth film electrodes by conductivity measurements. Typical voltammetric and DG versus E curves for Bi films contacting a 0.2 M Na2SO4 (pH 6.2) solution are shown in [122]. Also, DG versus total charge Qa calculated from graphical integration of voltammetric curves are reported. The relation between DG and Qa, at positive values of the surface charge is complex. In this connection at potential values E >
0.6 V versus SCE, at least two processes seem to be involved, a field effect and the proper oxygen adsorption process. The contribution of each one of these processes to DG was inferred from the time dependence of DG following a potential step applied to the electrode from the pzc to various values of E in the region of the positive side of the minimum in DG versus E curve. Contrary to gold and platinum film electrodes, bismuth films exhibit an increase in conductivity upon oxygen adsorption. This effect was explained considering the band structure of Bi as a semimetal. Surface states generated during the oxygen adsorption process capture valence band electrons, thus leading to the injection of holes into the space charge region of the Bi film, and this yields an increase in conductivity. The positive ends of the Bi-OH surface dipoles being able to localise a valence band electron which could function as acceptor-type surface states of this kind. The authors also studied the oxygen adsorption kinetics. Adsorption rate constants as a function of the electrode potential were determined by stepping the potential from E =
0.7 V versus SCE to different Eads values. For a quantitative interpretation of the adsorption kinetics according to surface conductivity data the authors used a relation based on the Riginskii– Zel’dovich equation. Also, the oxygen adsorption process on Bi was analysed at different pH values. Resistance of thin Iridium film electrodes in 0.05 M H2SO4 solution, decreases at the potential corresponding to the transition from Ir2O3 to IrO2. This effect was attributed to the semiconducting nature of the latter oxide [123]. Electrical and corrosion properties of iridium thin film electrodes at different stages of oxidation in 0.5 M H2SO4 solutions were also studied by Sverdlova et al. [82] by using resistometric and potentiodynamic techniques and also different spectroscopies. When the electrode is cycled within the potential range 0.05 V < E < 1.35 V (versus RHE) the potential dependence of its resistance was similar to that exhibited by other metal of the platinum group. However, within this potential region the total resistance of the Ir film increases during cycling. This was explained considering that despite the same oxide structures are present of the film at different stages of the cycling, the amount of these oxides increases with the number of cycles. Dependencies of conductivity change versus anodic charge (Dsf–Qa) were calculated at different states of the cycling. A bend on these dependencies were attributed to changes of the oxide’s electrical properties which correspond to a transition Ir(III) ! Ir(IV). For potential values E > 1.45 V (versus RHE) a layer of a nonstoichiometric

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hydrated oxide is formed on the film surface, which leads to a significant change of the electrical properties of the electrode. An analysis of IR spectra shows that the ratio of the content of the nonstoichiometric oxide to the content of the iridium(IV) oxide with the structure of rutile becomes 5:1. Experimental results were quantitatively discussed in terms of an oxidation model, which presumes that the oxide gradually ‘‘intergrows’’ into the bulk of the film at separate active centres. Oxide formation was invoked to explain the resistometric behaviour observed during corrosion and passivation processes occurring on chromium film electrodes [124]. In this sense, Mansurov and Boguslavskaya [124] studied passivation and transpassivation processes of chromium thin film electrodes in acid media by resistance measurements recorded under both potentiodynamic and potentiostatic conditions. The authors explained the minimum on the potentiodynamic resistance curve by the increase of the relative concentration of carriers as a result of the formation of chromium oxides of higher valence and the subsequent increase as due to the electrochemical dissolution of these oxides in the form of dichromate ions. Also, Safonov et al. [125] studied oxidation and reduction processes of iron thin film electrodes in alkaline solutions. The measurements were carried out galvanostatically. The initial increase in DR versus t curve was ascribed to the oxidation of iron to Fe(II). This oxidation was considered equivalent to a thinning of the original metallic film, since the oxide has much lower conductivity than metallic iron. No resistance change was detected during further anodic oxidation. This last effect was attributed to formation of Fe(III), which does not occur directly from metalic iron. A functional relationship between the conductance change and the charge consumed during the oxidation process of the iron film was derived in this work. The authors also studied the effect to S2
ions on the anodic oxidation of Fe films in alkaline solutions. It was found that in this case the metal is oxidised in greater depth, which is evidenced by the larger change in 1/R. Oxygen adsorption on Pt, Pd and Rh thin film electrodes under positive polarisation was studied by Sverdlova et al. [83]. From potentiodynamic and resistometric curves the derivative of the conductance with respect to the total quantity of adsorbed oxygen was determined. A transition from sharp to weak changes of conductance was observed at potential values where a transformation of the Me-OH monolayer occurs. This transformation takes place as a result of the ‘‘aging’’ of the adsorbed oxygen layer. As conclusion it should be indicated that the physical sense of D(DR/R)/DQa,c slopes employed in some works is unclear when the mechanism of oxidation considers consecutive and simultaneous occurrence of several surface structures corresponding to different oxidation states of the metal. On the other hand, these slopes should not be very sensitive to the microscopical surface structure changes as the voltammetric current because DR and Qa,c are integral values. However, the surface conductance provides an alternative technique to study qualitatively the oxidation processes of thin film electrodes. 2.3.5. The resistance change during the underpotential deposition (upd) process. Its use as an analytical tool to detection of trace concentrations of cations in solution. Diffusion of metal adatoms from the surface film to the bulk film Fujihira and Kuwana [53] studied the copper adatoms deposition on platinum film electrodes. By comparing resistance–potential curves in the presence of copper (1 M CuSO4 + 1 M H2SO4) with those obtained in the only presence of the supporting electrolyte (1 M H2SO4), the authors found that deposition of a Cu monolayer on Pt films decreases the resistance of the substrate. This was ascribed to a contribution of the electron structure of the Cu adatom to the conduction electrons of Pt substrate. The proportionality constant aupd between the relative conductance change and the corresponding charge

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change (DG/G = aupd DQupd/Qupd), from zero to full surface coverage was found to be about 0.65. Resistance decrease in Pt thin film electrodes during copper atom adsorption was also observed by Safonov et al. [94]. This was explained considering that for adatoms or strongly adsorbed ions, the number of free electrons, Ne, in the film substrate can depend on both potential E and the degree of coverage uadat of deposited particles. Then, again it was considered that for copper adsorption on Pt a transfer of the valence electron from the copper atom to the conduction band of Pt occurs and then a positive (DNe/Duadat)E change results, which should lead to a resistance decrease of the Pt substrate. In [93], adsorption of a weakly adsorbed cation, such as, Tl+ on Pt films was investigated. The resistance increase of Pt during Tl+ adsorption was also explained in terms of a partial charge transfer process and a pzc shift in the negative potential direction. Lapa et al. [126] studied copper adsorption on smooth rhodium film electrodes by a potentiodynamic pulse technique and resistance measurements. In a similar way as for Cu adsorption on Pt films, copper adatoms causes a significant decrease of the Rh films resistance. Again, this was explained considering that valence electrons of the copper adatoms pass into the conduction band of Rh, increasing in this way the number of free electrons in the film, which causes a resistance decrease. It is interesting to remark that the resistance change versus coverage (DR–uadat) for copper deposition on Rh films is linear over a broad range of uadat values and for uadat  1, the Rh film resistance remains practically unchanged. Adsorption of Sn(IV) on Pt films was studied using both a pulse potentiodynamic technique and resistance measurements [127]. At a potential value about 0.05 V (versus a hydrogen electrode in a 5 M H2SO4 solution) the layer of adsorbed Sn causes an increase of the Pt film resistance, in contrast to the layer of copper adatoms on Pt films. A very interesting peculiarity of the Pt/Sn(IV) system is the fact that an increase in resistance is also observed after the tin coverage reaches the monolayer level. This was ascribed to the formation of a surface alloy of tin with Pt, which takes place slowly with time. Hansen in [101] discuss the application of resistance measurements to study the upd processes of lead ˚ thick polycrystalline gold film electrodes. In Fig. 8, the results of the upd of lead are and copper on 300 A shown. Besides the voltammogram (plot (a) in Fig. 8) the resistance is displayed in two ways, versus potential (plot (b) in Fig. 8) and versus charge passed to the electrode (plot (c) in Fig. 8). The amount of lead deposited is indicated by the surface charge after to be corrected by the double layer component. As can be seen by comparing plots (b) and (c) in Fig. 8, while the resistance change is irreversible versus electrode potential, it is nearly a single valued function of the surface charge. However, this is no so evident when the potential scan is extended to high enough positive values. An enormous increase of the gold film resistance is observed during the first half of the lead coverage (uadat 1/2). The sensitivity of resistance to charge is higher than simple charging would predict and in the opposite direction. That is, as the electron population of the electrode is increasing the resistance is also increasing rapidly. The situation is eventually reversed, however, and after passing through a maximum, the resistance is roughly linear again with the surface charge. The slope at high coverage now corresponds well with the slope for simple charging. This fits the model that the added electrons (those which causes the surface charge to become more negative) now behave like electrons added by simple charging, in spite of the presence of added lead atom cores. This rapid increase of the gold film resistance at less than half coverage was attributed to the increased surface scattering of gold free electrons with lead deposition. Eventually, this effect saturates or perhaps at higher coverages the lead layer becomes submerged in the Fermi Sea of gold. In this way, some electrons from each added lead atom should contribute to the gold conductance. On the contrary, gold film resistance decreases with copper upd from the beginning and shows a monotonic variation as a function of the surface charge. This was explained assuming that copper atoms

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Fig. 8. The upd of lead on polycrystalline gold. (a) Cyclic voltammogram for maximum upd with no bulk deposition. (b) Simultaneous resistance curve. (c) Simultaneous resistance plotted against electrode charge. Electrolyte is aqueous 10
3 M Pb(NO3)2, 10
2 M HClO4. Scan rate is 75 mV s
1. From [101].

can be accommodated at the gold surface in much the same way, as extra gold atoms would be. This effect seems to be confirmed by the fact that free electron contribution of Cu to the Fermi Sea is approximately the same than that of gold. The initial observed behaviour for Cu continues during all stages of the upd process. As the Fermi surfaces of Cu and Au are similar, one might expect this behaviour. The evolution of the resistance response of a gold film contacting a solution containing Pb2+ during potentiodynamic cycling within the potential range
0.6 V < E < 1.3 V (versus SCE) is described in detail by Rath [18]. On the basis of results showed in Fig. 9, Rath [18] examined both the proper lead upd process and the effect of cations lead in solution on the gold surface oxide region. With regard to the lead upd process, the resistance curve (curve (b) in Fig. 9) shows a marked hysteresis with scan direction at low coverages of lead. However, the traces nearly coincide as the monolayer is completed (E <
0.4 V versus SCE). Concerning the surface oxide region, while the presence of lead only provokes slight changes on the voltammetric response (curve (a) in Fig. 9), drastic changes are observed on the resistance spectrum (curve (b) in Fig. 9). In the presence of Pb2+ a pronounced dip is observed on the resistometric curve at potential values corresponding to oxygen adsorption process, which is not present in a solution

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Fig. 9. (a) Cyclic voltammogram and (b) resistance voltammetric spectrum for lead upd with 200 nm gold film at scan rate of 10 mV s
1. Electrolyte is 1 mM Pb(ClO4)2 in 10 mM HClO4. From [18].

free of lead cation. Also, at intermediate potential values (0.0 V < E < 0.4 V versus SCE) a minimum resistance value is observed, which depends on the potential scan direction. In addition, comparison of resistance spectra in the presence and absence of lead cation, in the last case the resistance increases much more rapidly during the positive potential scan direction than in the presence of lead cation. During the initial deposition of lead (monolayer peak on the voltammetric response, see curve (a) in Fig. 9), the resistance varies linearly with the lead coverage. As more lead is deposited, the relative sensitivity of the resistance decreases until a potential lying in the valley of the voltammetric doublet peaks, when the total resistance reaches a maximum value, and then it decreases. The clarity on the resistance maximal depends strongly on the scan rate. In the region of the doublet peaks, the added lead may displace those adatoms already present to less preferential sites, so that the net result on the adlayer–electrode interaction may either increase or decrease, which is reflected in the diametrically opposite effects seen in the resistance. With the formation of the close-packed layer, the resistance decreases slightly until the Nernst potential is reached. At this point the bulk deposition of lead has little effect on the measurement. This suggests that the first layer remains the same with bulk lead deposited because the effective sampling distance of the conduction electrons lies within the first layer. During the stripping scan, the resistance essentially retraces itself until reaching the more positive side of the doublet, at which it does not fall off near as rapidly. This hysteresis was attributed to irreversibly deposited lead at

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intercrystalline boundary sites of gold film electrodes, which is stripped during the voltammetric peak at 40 mV (see curve (a) in Fig. 9). The sensitivity of the resistance to this irreversibly deposited lead is the same as was found for the monolayer of lead, both in depositing and stripping. Considering that at low coverage lead is mostly ionic in character, Rath [18] also compares the sensitivity of the resistance response to the initial lead deposition on gold with sensitivities obtained by studding other adsorbing systems (halide ions). Experimental apparent scattering cross sections, sa, for several species deposited under upd conditions were determined by employing the approach developed by Rath and Hansen in [50]. Ganon and Clavilier [78] studied the electrochemical adsorption of lead and bismuth on thin gold films with a (1 1 1) preferential orientation of their surfaces. The aim of this work was to compare the electrochemical adsorption of Pb and Bi on such a substrate with the adsorption process of the same elements from their vapour phase. The electrochemical growth of the ad-layers for each species at vecinal (1 1 1) surfaces was interpreted employing a steric model proposed by the same authors in [128]. Different DR/Qupd slopes were obtained within the whole charge range corresponding to electrochemical adsorption of these species on gold. These different slopes were associated to the occurrence of successive surface structures. Particularly, initial slopes conform the Linde’ law in the form: Drf ð%adsÞ ¼ a0 þ b0 Z 2

(26)

where Drf is the electrical resistivity change due to the scattering process of the conduction electrons of the film substrate by the adsorbed atoms, (%ads) is the adatoms percentage relative to the number of atoms of the substrate, a0 and b0 are constants for a given substrate and Z is the excess of valence between the adsorbate and the substrate [129,130]. In this connection, Z = Zads
Zsubst if the adsorbate acts a substitutional impurity and Z = Zads if it acts an interstitial one. This rule was verified by Chauvineau and Pariset for adsorbed species from gas phase [9,11–13]. In electrochemical experiments an a0 value near zero was observed, suggesting that the initial adsorption occurs at steps with a propagation of the deposition process along the step. Different DR/Qupd slopes were observed within the whole charge range corresponding to electrochemical adsorption of these species on gold. With regard to lead deposition, the DR versus Qupd dependence exhibits the same shape as that recorded when lead is adsorbed on gold films from the vapour phase at low temperature (
40 8C) [9]. The initial increase in resistance shows that adsorbing species are populating one family of identical sites. This in agreement with the idea that the adsorption begins at steps [131,132]. A subsequent linear portion on the DR–Qupd dependence was attributed to a transitional structure in the neighbourhood of the steps and it was associated to a total number of seven atoms adsorbed on the elementary gold surface cell. A posterior increment of the slope was ascribed to an increase in the distance between adatoms resulting from their displacement when the transitional structure is changed to the stable p(H3  H3)R308 structure [133], which grows on (1 1 1) terraces by an island mechanism. The maximum on the DR–Qupd dependence observed at high charges values was attributed to the formation of a more compact lead layer according to the model developed by Geus in [8]. Structures such as 2(2  2) and 3(2  2) have been assumed at high charge values. Finally, a minimum on the DR–Qupd curve appears at the end of the formation of the lead monolayer. A 3(2  2) structure was considered for the monolayer of lead, which again is in agreement with the model proposed in [128]. The initial deposition of Bi on gold also conforms the Linde’s rule. The very first atoms are adsorbed at steps, giving rise to the existence and displacement of only one kink. The first break in the DR–Qupd dependence for Bi was adjudicated to the transformation of a transitional structure to a more stable (2  2) structure. The appearance of a 2(2  2) structure with a lower distance between adatoms

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leads to a more specular reflection of the conduction electrons of gold. Thus, at charge values enough high, the resistance decreases but much more slowly than in the case of Pb. This decreasing was attributed to the formation of the monolayer (uadat = 1). At higher charge values (uadat  1) a 6(1 1 1)  (1 0 0) surface structure appears, which corresponds to a charge value of 465 mC cm
2. This value is lower than the charge value corresponding to an hexagonal compact layer (480 mC cm
2) for a surface without steps. Romeo et al. [79] analysed surface conductivity changes during upd and ups processes of Tl, Cd, Pb, Bi, Cu and Ag on gold and Tl, Cd, Pb and Bi on silver. In the range of very low and low coverages, where the distance between adatoms is much greater than the Fermi wavelength of the conduction electrons in the metal lF [8] and also adsorption sites might be considered as equivalent, a linear resistance versus coverage dependence was observed for most of these systems. More precisely, except for Cu and Ag on gold, it was verified that at very low coverages resistance versus coverage dependence conforms the Linde rule [131] in the form: 2 ðDR=RÞG
1 adat ¼ a0 þ b0 ðZads
Zsubs Þ

(27)

where Gadat is the surface concentration of the impurity, DR/R is the corresponding relative resistance change and the other parameters are the same as in Eq. (26). Experimental DR/RGadat slopes for the upd processes of Tl, Cd, Pb and Bi on both gold and silver films as substrates, obey Eq. (27) with values of a0 and b0 depending of the metal film substrate. The difference between silver and gold as substrates was explained in terms of the size correction proposed by Geus [8] for a bulk impurity. In this connection, for a surface impurity the constant a0 includes a term proportional to the difference between atomic radius of adatom and substrate, respectively. Also, for the different systems studied in [79] it was found that DR/R values corresponding to monolayer coverages, follow the sequence of atomic radius of adsorbates. This behaviour was explained assuming that it is not possible to accommodate exactly a monolayer of foreign atoms in register with the substrate structure and even more, when the atomic volume of the foreign atom is much greater than that corresponding to the substrate atom, more imperfect should be the misfit between the adsorbed monolayer and the surface atomic layer of the substrate. In this sense, the foreign adlayer on the substrate will be less compact as larger is the difference of sizes between the adatom and the substrate atom. In consequence, the conduction electrons of the base metal will be more diffusely scattered when the adlayer is less densely packed. In this connection, Smoluchowski [134] suggested that the anisotropy of the work function of metals is connected with the surface atom density. Thus, a higher work function is expected on smooth densely packed planes [135]. Peculiar behaviours were observed in [79] for depositions of Ag and Cu on gold, respectively. In agreement with the surface Linde’s rule no detectable DR change was observed during the upd process of Ag on gold (compare atomic dimensions and Z values). However, this may also suggest that silver adsorption on gold occurs at kinks and steps, leading to a displacement of them with no variation of resistance [78]. The system Cu2+/gold shows a continuous DR/R decrease within the whole copper coverage range. Three different linear portions on the resistance-coverage dependence for this system were detected. Since (Zads
Zsubst) is zero in this case, the DR decrease in the first linear portion was attributed to differences in atomic radius. That is, copper adlayer could be more densely packed than gold surface atoms themselves and then, a more specular reflection of the conduction electrons at the gold surface covered by copper should be expected, which in turn leads to a resistance decrease. Also, in the same way as for other substrates such as Pt, it could be considered that for copper adsorption on gold a

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transfer of the valence electron from the copper adatom to the conduction band of gold occurs and then a decrease of the gold film resistance should be observed due to the increase in the number of free electrons of the gold film. Resistance values reached at coverages corresponding to a monolayer of adsorbate can also be treated on the basis of the specularity parameter p of the Fuchs–Sondheimer’s theory (see Eq. (6)). If the product rbl0 in Eq. (6) is considered independent of the presence of bulk and surface defects, then it is expected that changes in p were only related to effects of adatoms. Values of (
Dp) in Eq. (6) were assembled for the different adsorbates studied in [79]. This sequence of values seems to be correlated with the atomic volume of the adatom. In this connection, a more diffuse scattering is observed for adsorbates whose atomic radius is higher than that corresponding to the gold atom. This also could be in agreement with the observed behaviour in the case of Cu2+/gold system, where conversely an increase of the specularity parameter seems to occur due to the lower dimension of copper atom as compared with gold atom (rAu = 0.144 nm and rCu = 0.128 nm). In this sense, the gold surface completely covered with copper should reflect conduction electrons better than the substrate itself, suggesting in this case that the Cu surface phase is more compact than the gold surface itself. A similar interpretation was proposed at intermediate coverages (lower than that corresponding to the monolayer) where a maximum DR/R value is observed for the different adsorbates [79]. With the exception of Tl on silver this maximum DR/R value is related to the atomic volume of the adsorbate. Recently, electrochemical deposition and stripping processes of Ni2+ at a polycrystalline gold film electrode were studied by SC and cyclic voltammetry [136]. At low adatom coverages nickel deposition on gold fulfils the surface Linde’rule for a substitutional impurity. On the basis of Eq. (27), a DR/RGadat slope value about 0.27  107 (g at)
1 cm2 was obtained for this system. This value fits reasonably well with previous ones reported in [79] for other metals. A decrease of the gold film resistance during bulk nickel deposition was observed. In agreement wit the size effect theory [15,62], this decrease was attributed to an increase of the gold film thickness. The influence of copper adatoms on the Zn upd on polycrystalline gold film electrodes was also recently studied by surface conductance measurements [137]. In this last work firstly the upd of Zn and the effect of Cu irreversibly adsorbed on the conductivity of gold film electrodes were separately studied. Zn upd on gold does not conform the Linde’s rule. Cu irreversibly adsorbed on gold shows a gold film resistance decrease with increasing the degree of coverage. Secondly, the upd of Zn in the presence of previously adsorbed copper on the gold film, was studied in [137]. Cu blocks the upd of Zn on gold. Zn stars depositing as soon as the coverage of Cu decreases. Experimental results show that Cu and Zn reduced species do not interact with each other. Also, experiments seem to indicate that the final product of zinc upd is not Zn(0). The high sensitivity of the surface resistance signal to deposition processes of different cations in solution seems to indicate in the last years the existence of some optimism to employ this technique in the detection of very small concentration of metal cations [34–37]. With the aim to demonstrate that the resistance technique can be used as a new method to determine the quantity of adsorbed species on solid electrodes Hanewinkel et al. [37] investigated the lead upd process on well-defined epitaxial Ag(1 1 1) thin film electrodes by dc-resistance measurements. Analysing the Pb upd process from a 1 mM Pb2+ solution, the detection limit of lead was estimated to be 1% of a monolayer of adsorbed Pb. In these experiments, the derivative of the dc-resistance (dR/dE) during the adsorption process of lead, was compared with the corresponding electrochemical current density after to discount the double-layer charging current density. When these parameters are represented as a function of potential, broad

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structures for the Pb dissolution process, as compared with the deposition one, were observed. This was attributed to the dissolution of Pb upd in the first layer and of dissolution of Pb in the second layer. This implies that even before the upd of Pb monolayer was complete, lead may also grow on the top of the first layer patches. This is supported by the dc-resistance curve, where only the first monolayer causes a measurable effect. Also, current and resistance versus time dependencies were used to demonstrate that the observed resistance increase was only due to the formation of the lead upd on the surface and that there was not change in the Ag(1 1 1) thin film itself after the stripping of lead. By using the Persson’s theory [29,30] to interpret the resistance curves at very small coverages, the cross-section of lead on Ag(1 1 1) was estimated. The influence of deposition and dissolution of lead on the surface resistance of gold thin film electrodes during potentiodynamic potential scans was used to demonstrate the ability of the ‘‘Voltohmmetry’’ as a new method to trace determination of heavy metals in solution [34]. Significant resistance changes were observed even at low Pb2+ concentration in solution. In general, cyclic voltohmmetry seems to be suitable for lead determinations down to 20 mg L
1 with a sensitivity of 3.2 mV/mg L
1. It is interesting to remark that the detection principle of voltohmmetry is not restricted to the investigation of analytes, which undergo heterogeneous faradaic reactions at film electrodes. That is, it is not necessary to deposit species of interest by electrolysis at the metal film electrode if there is a sufficient interaction between the adsorbed analyte and the metal film surface. This is due to the fact that resistance changes are not the direct result of the electron transfer between the adsorbate and the metal film surface but they rather originate from the effect of foreign surface particles on the conduction electrons of the metal film electrode. Surface resistance measurements on thin gold film electrodes were employed by Glu¨ ck et al. [35] to trace determinations of different heavy metal cations (Cd2+, Ni2+, Pb2+, Tl+ and Zn2+) in aqueous solutions. Surface resistance versus potential curves obtained during the adsortion processes of these different cations, were firstly employed for a qualitative analysis. On these curves two parameters were examined: the amplitude of the resistance decrease DR caused by the dissolution, of the previously deposited species, during the positive sweep and the potential that corresponds to the inflection point of the decreasing part the measured curve. The inflection point was determined by plotting the derivative dR/dE of the film resistance versus the electrode potential. Deposition processes of Cd and Ni were studied in detail. For Cd, measured values of the resistance drop DR versus deposition potential dependence were fitted with a sigmoid function which resulted a Boltzmann distribution for the probability of the Cd atoms to occupy the reduced (dissolved) or oxidised (deposited) state at a given deposition potential. For Ni the possibility of formation of AuNi alloy was reported. For quantitative analysis cyclic measurements were performed by using solutions containing different concentrations of Cd+2 cations. It was demonstrated that with a proper choose of the deposition time a linear relationship between the observed resistance change and the cadmium cation concentration in solution can be obtained over a wide concentration range from 4 to 1 ppm. Deviations of the resistance change from the linear fit towards lower values were associated to an increase of the specularity parameter for large amounts of deposited cadmium cations, i.e., high surface coverages. Also, speciation analysis was proved to be possible by using the surface resistance technique. In this sense, the authors [35] were able to distinguish Cd-EDTA complexes from hydrated cadmium cations. Winkes et al. [36] reported a surface resistance study on Ag(1 0 0) and Ag(1 1 1) thin film electrodes during the upd process of thallium cations. These two different electrode surfaces were employed to analyse the effect of the surface orientation on their resistometric behaviours. The derived resistance curves d(DR)/dE show a difference about 100 mV between the upd potentials of thallium on Ag(1 0 0) and Ag(1 1 1) single crystals, respectively.

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Recently, Hanewinkel et al. [38] studied the resistance change of thin (1 1 1) oriented silver films by upd of lead, for the detection of trace concentrations of Pb2+. Linear potential scans and potential step experiments were carried out to study both perchlorate adsorption and lead upd processes. In this work is demonstrated that by choosing a given potential–time program one can obtain a calibration curve to measure unknown aqueous concentrations of Pb2+ down 10
6 M. For potential step experiments the concentration dependence of the thin film resistance as well as of the accumulated charge of lead (converted to surface coverage) after 10 s at an electrode potential of
0.45 V (versus SCE) were obtained. For linear potential scan experiments, voltammetric and resistance–potential curves were recorded for different concentrations of lead cation in solution. By integrating the current peak due to the lead dissolution, the maximum formal lead coverage as a function of the lead concentration in solution was obtained. Also, from resistometric curves the overall resistance change DR0max as a function of lead concentration in solution was recorded. The DR0max value was considered as the difference between the minimum value of resistance at
0.3 V (versus SCE) during the negative potential scan direction and the maximum resistance value at
0.46 V (versus SCE) in the positive potential scan direction on the corresponding resistance–potential curve. Differences between magnitudes obtained from linear potential scan and from step potential experiments are discussed. It is demonstrated that within given concentration, potential and coverage ranges, the resistance change only depends on the transferred charge due to lead adsorption, but it does not depend on the deposition conditions. With regard to applications of thin film electrodes to electroanalysis, electrically conducting diamond thin-film electrodes should be mentioned [138]. However, electrochemical measurements in this case only involve electrical signals, such as, potential, current or charge. Romeo et al. [139] studied the deposition process of mercury on gold by surface resistance measurements. In this work diffusion of adatoms from the surface phase to the bulk film substrate was detected. DR/R versus E curves for a gold film in the presence of a 0.1 M HClO4 solution and in the presence of a 0.1 M HClO4 + 2  10
5 M Hg(II) were compared (see Fig. 10). Starting at a given positive potential limit about E = 1.4 V (versus SCE) towards the negative potential direction both responses coincide until the potential corresponding to the gold surface oxide reduction is reached (E = 0.95 V versus SCE). From there on, in the solution containing Hg(II), DR/R increases, showing that some species are progressively adsorbing on the electrode surface. Within this potential region, DR/R depends on the scan direction. This is due to the fact that during the negative scan Hg upd can only be formed on the surface sites free from surface oxide. Once all the surface oxide was reduced (E  0.7 V), DR/R becomes independent of the potential scan direction, thus showing that the surface process is reversible. In Fig. 11, DR/R as a function of the anodic stripping charge, QHg for the Hg upd process is shown. In order to calculate uHg the mercury surface concentration GHg was used in the form: G Hg ¼

QHg napp F

(28)

where napp is the apparent number of exchanged electrons during the stripping reaction. This last value was taken as napp = 1.7 [140]. Fig. 11 shows three liner portions. The second portion goes up to uHg = 0.7. Considering that napp is a constant within the potential range 0.4 < E < 0.9 V (versus SCE) [140,141], this behaviour suggests an island type growth with a constant surface structure up to this surface coverage value. Since the atomic radii of the adsorbate is bigger than that of the substrate, a change from a commensurate to an incommensurate surface structure should occur for a coverage value uHg = 0.7 [142]. Application of the Linde’s rule at low mercury surface coverages leads to Z = 2 (see Eq. (27)) which

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Fig. 10. DR/R vs. E response for a 25 nm thick gold film electrode contacting respectively, a 0.1 M HClO4 + 2  10
5 M Hg(II) solution (–––) and a 0.1 M HClO4 (- - -) solution. Scan rate n = 2  10
2 V s
1. Potentials are referred to the SCE. From [139].

would mean that either the effective valence of mercury is Zads = 3 or the adsorbed mercury is behaving as an interstitial impurity. Since it is difficult to interpret a value of Zads = 3, this would mean the adsorbed mercury acts as an interstitial surface impurity. If the lower potential limit Elow is extended to values lower than 0.4 V (versus SCE) and the potential is held at different values lower than 0.4 V for a given th time period, the voltammetric profile during the stripping process exhibits a broad anodic peak characteristic of the stripping process of Hg from a Hg–Au alloy [139]. The DR/R response for the stripping of Hg–Au alloy shows a small shift respect to its initial value during the th time period. This shift was related to the change of the bulk conductivity of the gold film as the alloy is formed. The potential dependence of DR/R during the anodic scan is independent of th. This shows that the surface conductance is detecting only (or mostly) the surface concentration of adatoms and that it does not change significantly during the stripping of the alloy. 2.3.6. Detection of surface structural changes, roughening and corrosion effects on thin film electrodes by resistance measurements It is well-known that the surface of metal electrodes undergoes drastic changes when subjected to different electrochemical treatments (potential cycling, oxidation–reduction reactions, adsorption– desorption of anions, upd process, etc.) [143–149]. Surface structural changes of silver in certain

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Fig. 11. DR/R vs. QHg (and degree of coverage, uHg) response for a 25 nm thick gold film electrode contacting a 0.1 M HClO4 + 2  10
5 M Hg(II) solution. QHg is the anodic stripping charge. The different symbols represent different negative potential limits. From [139].

electrolytes, particularly chloride, have received much attention because of their connection with the appearance of the SERS effect [144–146,150–152]. Surface structural changes of silver film electrodes during adsorption of Cl
anions were detected by capacitance and surface resistance measurements [153]. In this connection, by cycling the electrode potential within the range
1.3 V < E < 0.3 V (versus SCE) no changes are observed on the capacitance–potential curves of silver films contacting a 0.04 M KCl solution. The capacitive response of silver film electrodes used in [153] was similar to that exhibited by Ag(1 1 0) single crystal electrodes. However, as the upper positive potential limit is increased up to E = 0.0 V (versus SCE), without reaching the region of massive AgCl formation, profound changes in the capacitive curves with the number of potential cycles were observed. In this connection, the shape of the capacitive curve of these thin film electrodes becomes progressively similar to that of polycrystalline silver in contact with electrolyte media containing chloride anions [154,155]. Also, the evolution of the electrode resistance, R, at the lower potential limit E =
1.4 V (versus SCE) was monitored as a function of the number of potential cycles. A small increase in R was observed until a stationary value is reached. The total resistance change

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was around DR = 0.012 V. This small change was attributed to a very small number of atomic defects created during the reduction of the adsorbed AgCl, in a similar way to the effect observed by Chauvineau and Pariset [9] during the deposition of gold on gold at room temperature in gas phase. It was concluded that the observed changes are due to a surface reconstruction effect involving displacement of silver surface atoms, which occurs during formation and reduction of the AgCl monolayer. The resistance increase observed when a 20 nm silver film electrode in contact with a 0.1 M KCl solution is subjected to oxidation–reduction cycles within the range
1.4 V < E < 0.2 V (versus SCE) was used by Ko¨ rwer et al. [108] to demonstrate that resistance measurements can be used to detect surface roughness. These authors observed that after Cl
adsorption, a monolayer of AgCl is formed between
0.3 and 0.0 V (versus SCE). The onset of AgCl formation leads to a sharp increase in resistivity because of the smaller conducting cross-section of the film together with an increase in the number of scattering centres at the surface. On the backscan, resistivity decreases again with reduction of the AgCl adlayer and furthermore with desorption of Cl
. After this treatment, the silver film resistance has a much higher value than before to subject the film to oxidation–reduction cycles. The resulting resistivity change was purely attributed to the modified structure of the silver film. Also, in this work the creation of surface roughness by silver deposition was monitored with the help of surface resistance. In this sense, the sharp increase in the SERsignal observed when a silver film electrode contacts a 0.5 mM AgNO3 solution was accompanied by a resistance increase. Ko¨ rwer et al. [108] also examined resistance changes of silver film electrodes caused by corrosion processes in the presence of chloride anion. Authors monitored resistance changes of silver film in contact with a 0.1 M KClO4 solution after adding Cl
and pyridine to the electrolyte under open circuit conditions. The rate of the resistance increase caused by corrosion due to Cl
anion was diminished by the co-adsorption of pyridine (Fig. 12). Resistivity and transmittance changes of thin silver film electrodes during adsorption of water, pyridine and Cl
anion were used by Bilmes [43] to study corrosion and roughening processes of silver surfaces. A resistance increase with time was observed when silver films contact water at open circuit. Addition of Cl
anion to the Ag–H2O stabilised interface causes a more pronounced increase in the film resistance. However, the addition of pyridine inhibits the Cl
anion effect. Under potential control the relative resistance change of a silver film in contact with chloride anion increases for potential values more positive than the potential of zero charge (Epzc = 0.9 V versus SCE). This effect was attributed to Cl
adsorption, which induces a resistivity increase of about 10%, as the surface becomes positively charged. To explain the observed resistivity and transmittance changes it was considered that upon contact with adsorbates, the initially quasi-flat surface of the annealed silver film becomes progressively rougher. The roughening was considered as a consequence of nucleation and growth of silver atoms at sites on the surface with high reduction potential. In this sense, a rough surface was envisioned as an ensemble of spheroids with a given dimension. These spheres have a scattering cross-section and an absorption cross-section both depending on their radius. Thus, resistivity has enough sensitivity to detect changes on the atomic scale due to adtoms, clusters and nuclei formed during electrodeposition processes. Structural changes and corrosion effects on Pt, Pd and Rh thin film electrodes under positive polarisation were studied by Sverdlova et al. [83]. Potentiostatic treatment of Rh films in a 0.5 M H2SO4 solution at enough positive potential values such as 0.9 and 1.4 V (versus RHE in the same solution) led to a decrease of the film conductance with time. Inflection points in the conductance-time dependencies were attributed to changes in the quantity of adsorbed oxygen and also to film dissolution. A sharp decrease in the film conductance after a 4 h electrode treatment in the solution was accompanied

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Fig. 12. Relative resistance change of a 20 nm silver film in 0.1 M NaClO4 under open circuit conditions caused by the addition of: (a) NaCl and pyridine, (b) pyridine and NaCl and (c) pyridine and NaCl with the potential of the electrode held at
0.6 V (vs. SCE). From [108].

by simultaneous decrease on the film dissolution rate. These processes seem to depend on both the base substrate on which the film was deposited and the film thickness. Similar resistometric behaviour was observed for Pd films. Analogous studies on Pt films show that their conductance does not change during the potentiostatic treatment and no Pt dissolution was detected. These results were explained on the basis of a lower rate of Pt dissolution in its passive state, respect to Rh and Pd films. Cyclic experiments were also performed on these film electrodes. After to subject the films to potential cycling during a certain time, the potential scanning was stopped and the electrode resistivity was measured at a potential value E = 0.05 V (versus RHE) and then the potential sweep was again continued. Inflection points were

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observed on conductivity versus ln t dependence. It was observed that after continuous potential cycling surface transformations, such as, etching, microcraks and also thickness variations occur. After long cycling time the film transforms from a continuos crystalline state into a islet state. However, diffraction patterns showed that metal-to-oxide phase ratio remained invariant during the different stages of film dissolution. Conductance versus mass dependence during dissolution of Rh films under potentiostatic conditions revealed the existence of size effects. After cycling the potential during 5 h Rh films showed a surface loosening. The roughness factor changed from 1.35 to 1.88. The reduction of the potential cycling interval by either decreasing the upper positive potential limit (E = 0.9 V versus RHE) or increasing the lower potential limit value up to E = 0.25 V (versus RHE) led to a decrease in the change of the film conductivity caused by the film dissolution. These results seem to indicate that the mechanism of Rh dissolution involves partial transition of oxygen-containing species into solution during the negative potential sweep. When the lower potential limit value is restricted, the oxide film has not time to be completely reduced, thus hindering the dissolution process. For Pd films similar results were found. In contrast, resistance of Pt films remained unchanged during potential cycling and also continuous potential cycling of Pt films only led to the removal of impurities and a slight levelling of the film surface. Resistometric behaviour during corrosion and passivation processes occurring on chromium film electrodes was described by Mansurov and Boguslavskaya [124]. As was reported in [108] when a silver film electrode being subjected to oxidation–reduction cycles within the potential region
1.4 V < E < 0.2 V (versus SCE) in a 0.1 M KCl solution, a resistance increase is observed due to creation of surface roughness [16]. However, a smoothing of this surface, with the consequent resistance decrease, was achieved by using the so-called quench pulses [156]. The effect was explained as due to chloride desorption allowing surface diffusion of Ag atoms at the surface and incorporation of the atoms into the lattice. In this connection, the group of Bohn [39] reported the ability of I
self-assembles to reduce the surface roughness of gold films. Experiments clearly demonstrate than an intermediate degree of surface roughness, as obtained from sequential CN
and I
etches, produces surface with the optimal response to molecular adsorption. To explain the results the authors propose a two-site model, in which two types of surface sites are potentially available for adsorption. 2.3.7. Surface conductance and reflectance measurements on thin film electrodes. Electrode emersion It is well-known that while resistivity of thin metal films is sensitive to both surface scattering and electron density changes caused by adsorbates, optical reflectance, in a first approximation, is only affected by surface scattering [66,157]. In gas phase experiments, where adsorbates do not change the electron density but merely act as scattering centres, a linear relationship between the resistivity and the infrared reflectance for well-characterised film surfaces, was observed [158]. Anderson and Hansen [46,47] demonstrated that reflectance and conductance measurements used together provide a sensitive method for observing the electrode interface. In their first work [46], they compare surface conductance with reflectance measurements of gold films when no faradaic currents or significant adsorption exist and also in the presence of ionic adsorption. It is demonstrated that the reflectance response is sensible to the ionic adsorption but in a different way from the change in conductance, thus giving an independent sets of data of the changes at the electrode surface. For the cases where the relative conductance change DG/G is proportional to the relative free electron charge change Dqe/qe (all of the charge flowing into the electrode is used to charge the electrode–solution interface), the electroreflectance was also proportional to Dqe/qe. Electroreflectance deviated only slightly from being proportional to Dqe/qe when large hydrogen-evolution faradaic current was present. It was observed that

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as the conductivity change increased during ionic adsorption, the reflectance change also increased. This was verified for a 6 nm thick gold film electrode contacting a 0.1 M Na2SO4 + 10 mM IK (pH 7) solution. However, for this system, a reflectance change five times larger than any electroreflectance previously reported was observed. When reflectance changes as a function of the wavelength in the absence and presence of iodide anion were compared, a change one order of magnitude larger was observed in the presence of I
. The reflectance change is also enhanced during adsorption of hydroxide ion. While an abrupt change in the conductance curve was observed as the pH value was increased above 4, the electroreflectance still changed almost linearly with potential. In another work, Anderson and Hansen [47] compare conductance and reflectance measurements of optically transparent electrodes. Reflectance measurements were made by using internal reflection. Detailed theoretical developments are given in [47] to interpret the observed surface conductance and electroreflectance changes at the electrode–solution interface. Calculations on the basis of the free electron theory to interpret conductance changes and by means of the theory proposed by the authors to explain reflectance changes, were made and compared with experimental results. It was demonstrated that while the electroreflectance effect is caused primarily by interband transitions and the surface free electrons concentration, the conductance effect is due to the average free electron density and the scattering of conduction electrons by adsorbed species. Measured and calculated conductance and reflectance curves as a function of the electrode charge density were obtained for a 6.1 nm thick gold film electrode contacting a 0.1 M Na2SO4 + 0.1 M NaI (pH 4) solution. Considering the I
desorption, it was observed that while the conductance increases much more rapidly than predicted by the free electron theory the reflectance increases at a slightly higher rate than predicted by the electroreflectance theory proposed by the authors. The electroreflectance was also calculated as a function of the wavelength. Experimental and theoretical curves agree very closely in the infrared region but the agreement becomes poor towards the UV region. Discrepancies between experimental and calculated dependencies were explained on the basis of different contributions to the electroreflectance such as, possible refractive index changes of the double layer, the surface roughness effect and surface free electron scattering. Similar comparisons were made in the presence of Cs+ cation, where conductance and reflectance changes as a function of charge for cesium desorption were obtained. When the Cs+ is adsorbed, there is an increase in the surface scattering, thus decreasing the conductance drastically. Also, during Cs+ adsorption the reflectance increases but with a smaller slope than that predicted by the theory and again the discrepancy was explained invoking the same effects which were postulated for iodide adsorption. Also, in this work voltammetric and conductance curves for a gold film electrode contacting 0.1 M Na2SO4 solutions of different pHs were compared. It was suggested that current peaks and conductance changes at high pH values could be assigned to slight Na+ adsorption or changes in the electrode hydration sheath. The magnitude of the conductance changes caused by I
and Cs+ ions was compared with that yielded by Na+, K+ and Li+ cations. While conductance changes for I
and Cs+ species are of the order of 10%, the corresponding changes for Na+, K+ and Li+ cations were about 1%. This seems to be in agreement with the different adsorption strength reported for these species. Experiments using surface resistance, reflection spectroscopy, XPS and work function measurements were used by Hansen et al. [101,159–161] to investigate the important problem of the emersed double layer. By monitoring electrode current density and electrode resistance it was demonstrated that the electrochemical double layer is retained intact on an electrode surface as the electrode is emersed from the electrolytic solution [101,159]. To the extent that the resistance remains constant, the free electron charge on the electrode also should remain. Since any area of the electrode plus double layer must be

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neutral overall, the ionic charge density of the double layer also should remain constant. The emersed double layer was also investigated by other means. XPS results indicate that some surface ions are rigorously conserved in vacuum and the XPS environment, while others do not remains long enough to be measured. In [101], XPS spectra of a gold electrode emersed from aqueous NaClO4 at a large positive potential is shown. Two peaks are observed which correspond respectively to Cl in perchlorate and Cl as adsorbed chloride ions. The amount of chloride increases with time relative to the amount of perchlorate. Evidently the perchlorate gradually decomposes to give chloride in the presence of X-rays, secondary electrons and high vacuum. Also other measurements indicate that part of the chlorine was gradually lost from the surface. Kolb and Hansen confirmed previous results about double layer emersion by electroreflectance [160] and work function [161] measurements. The emersion does not change whatever causes the electroreflectance spectra. The work function is sensitive to potential rather than charge. It is therefore sensitive to collapse of the double layer or other rearrangement as well as to discharge. Also, authors confirmed that the work function of emersed electrodes, in its double layer stable range, is independent of electrode material and supporting electrolyte. 2.3.8. Surface resistivity and Hall effect in thin film electrodes The effect of the gaseous adsorption on the Hall coefficient of thin metal films was demonstrated for several metal–gas systems [162,163]. Also, dependence of the Hall coefficient on film thickness was observed for the group IB metals [164,165]. Sondheimer [62] extended the Fuchs Size Effect theory of the electrical conductivity to include galvanomagnetic phenomena. However, despite the Fuchs– Sondheimer (FS) theory was developed for a quasi-free electron film having an isotropic electron relaxation time and a spherical Fermi surface, the Hall coefficient of metals depends on the shape of the Fermi surface and the anisotropy of the electron relaxation time [166]. In this sense, the group IB metals have a Fermi surface which is multiply connected to the (1 1 1) directions. Thus, it is not apparent that this theory can be applied to describe the behaviour of the Hall coefficient for these metals [167]. However, as the group IB metals have isotropic relaxation times at room temperature [168], it is expected that these systems should better approximate the free-electron gas model of FS theory. Rath has discussed in detail the measurements of the Hall effect in electrochemical applications [169]. He examined the influence of the simple charge and the electrochemical adsorption of bromide and iodide on the Hall coefficient by using the Juretschke–Lucas [61,70] modification of the FS theory, which establishes a connection between the Hall coefficient of the film and its resistivity thought the equation: AH ¼ AHo

     rJL k drJL 1þ rJL dk rb

(29)

In Eq. (29), AH is the Hall coefficient of thin metal film, AHo is the corresponding value of bulk metal, rb is the resistivity of bulk metal, rJL is the resistivity of thin metal film for Juretschke–Lucas modification of the FS theory and k is the ratio of film thickness to bulk mean-free-path. The probability of electron scattering from an adsorbed species at the film surface is described with the specularity parameter p1, implicitly contained in the resistivity rJL. The size effects dependence, such as electron scattering at surface defects and roughness, is incorporated in the scattering parameter for the lower metal film surface, p2, which may include internal defects and upper surface deformations. In this interpretation, the specularity parameter p1 is the unity in the absence of species adsorbed on the surface. The

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relative changes in the Hall coefficient and resistivity are written, respectively, as: aH ¼

½AH ðp2 ; p1 ; kÞ
AH ðp2 ; 1:0; kÞ AH ðp2 ; 1:0; kÞ

(30)

rJL ¼

½rJL ðp2 ; p1 ; kÞ
rJL ðp2 ; 1:0; kÞ rJL ðp2 ; 1:0; kÞ

(31)

and

The application of this theory to experiment should be straightforward as these quantities are measurable and they can be correlated. In [169] relations of the relative changes in the Hall coefficient aH with the relative change in the resistivity rJL, for film thickness corresponding to k values of 0.4 and 1.0, were obtained. The different dependencies were evaluated with the specularity parameter p1 changing within the range 0 < p1 < 1.0. The quantities AH(p2,1.0, k)/AHo and rJL(p2,1.0, k)/rb are listed in [169] for given values of the film thickness and values of the parameter p2. For p2 values different from the unity, it was observed that initial adsorption causes a larger effect on the Hall coefficient than on the resistivity. Since the resistivity is a monotonic function of the specularity parameter p1, the Hall coefficient could even change sign for increased adsorption coverage. However, for the film thickness used by Rath in [169], changes in the Hall coefficient should be linear and of the same sign as the change in the film resistance. Thus, Rath characterised metal films through the comparison of the adsorption effects on the Hall coefficient and the electrode resistance. With the Hall coefficient treated as a function of resistance, the zero coverage slope of this dependence was expressed as:   aH (32) Si ¼ lim r ! 0 rJL The experimental dependence of the initial slope, Si, on the parameter p2, for different values of k is shown in [169]. Then, when the film thickness is known the parameter p2 can by readily determinate from the experimental evaluation of Si. The method chosen by Rath in [169] to study these processes utilises the immersion–emersion technique where the electrode is removed from the solution while the electrode potential is hold constant. As was indicated in Section 2.3.7, Hansen [101] demonstrated that in the absence of faradaic reactions the compact double layer remains intact on the electrode during the emersion process. Hansen and coworkers [159,170] have also demonstrated this phenomenon for the case of specific adsorption through ESCA. With this indisputable empirical evidence, the Hall effect of an electrode used in this manner must reflect the in situ phenomena. Effects of the simple charging on the Hall effect were studied by Rath [169] with 15 nm thick gold film electrodes. It was observed that the Hall coefficient is in general less sensitive than the resistance to changes in the film surface. With electrode emersions, the Hall measurements were repeatedly taken with no discernible change in the Hall coefficient. There is an upper limit of 0.3% for the relative change in the Hall coefficient for the effects of simple charging. The maximum relative change of resistance in this process was 0.2%. The possibility of simple charging resulting in changes in the free-electron surface density also cannot be ruled out, since a change of about 15 mC cm
2 on the electrode charge should correspond to a 0.1% change of the total electron population. Thus, the observation of a non-detectable change in the Hall coefficient is consistent with the FS theory. With bromide adsorption studied on 15 nm thick gold films, the changes of the Hall coefficient were readily detectable [169]. For this experiment the

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dependence of the Hall coefficient with the electrode resistance was linear. A Si (Eq. (32)) value of 0.80 was obtained. Under the same electrochemical conditions the bromide adsorption effects were studied with a 43 nm thick gold film. In this case adsorption effects on the Hall coefficient were smaller than anticipated and could barely be resolved. The slope, Si of this process was determinated to be at most 0.09. Iodide adsorption effects on the Hall coefficient were also studied with the 15 nm thick gold film. The relative change of the Hall coefficient as a function of the electrode resistance was again linear. A slope value Si = 0.64 was obtained. However, the FS theory predicts that the Hall coefficient will be a single valued function of the electrode resistance independent of the origin of the changes in the surface scattering. The observation of Rath [169] about the differing influences of iodide and bromide adsorption on this relation conflicts with this theory. Rath concludes that the discrepancy in the experimental slopes, Si, cannot be attributed to statistical errors or to electrode effects, since the same 15 nm gold film was used in both experiments. Also, the interaction of the halides with the electrode is believed to have the same nature and this cannot account for the observed discrepancy. Thus, Rath concludes that the FS theory is inadequate to describe the adsorption effects on the galvanomagnetic properties of gold. The relative changes in the Hall coefficient of the 15 nm gold film may be further examined through the known resistance response of bromide and iodide adsorption. The relative cross-section of bromide on gold was found to be 0.65. With this parameter the sensitivity of the Hall coefficient to bromide adsorption coverage is smaller than that of iodide by a factor of 0.8. This result is not surprising, since the strengths of the halide adlayer–electrode bond are different. Hansen [101] and Hansen and Kolb [161] devised a technique for the accurate measurement of the Hall effect in situ, with a sensitivity better than one per 1000. They studied the simple charging, the bromide adsorption and the deposition of copper and lead on 30 nm thick gold films. The electrode resistance and the Hall coefficient were obtained as functions of the electrode potential. The effect of the simple charging on the Hall coefficient was not observable to 1 part in 1000 for an electron population change of 0.1%. The similar slope of the Hall coefficient and electrode resistance as function of potential with bromide adsorption implied a linearity between these responses to this ionic adsorption. The response of the Hall coefficient with the underpotential deposition of copper on gold could not be attributed to a simple mechanism such as electron surface scattering or free electron population. Lead deposition on gold provided evidence of the inadequacy of the FS theory, since the most of the Hall voltage change occurs in the region of the ‘‘heads’’ of the resistance versus potential curves. This could imply that the effective resultant Fermi surface of the lead upd on gold changes rapidly in this region, while little change occurs in other regions because the Hall effect is relatively insensitive to surface scattering. It is evident that the theory of the Hall effect is presently in a rudimentary state by relation to surface effects. 2.3.9. Surface resistance measurements on a thin metal film coated with an electroactive polymer film In recent works [40–42], it was demonstrated that the oxidation-reduction process of an electroactive polymer, such as poly(o-aminophenol) (POAP), deposited on a thin gold film electrode has a significant effect on the electronic transport of the base metal film. The experimental arrangement in these investigations was one in which a POAP film is supported on a thin gold film of thickness (d  30 nm). While cyclic voltammetry (CV) was used to characterise quantitatively the redox species transformation on the gold film surface contacting the polymer film, surface resistance (SR) was employed to investigate changes in the electronic properties at the gold–POAP interface during the redox

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Fig. 13. DR/R vs. E response for poly(o-aminophenol) (POAP) coated gold film electrodes. Polymer thickness, fp: (—) 0 mm; (- - -) 5 nm; (– – –) 10 nm; (–––) 60 nm. Scan rate: n = 5  10
3 V s
1; d = 30 nm. Electrolyte: 0.1 M HClO4 + 0.4 M NaClO4. From [40].

conversion of the polymer. The effect of different variables on the resistometric response of the POAP coated gold film electrodes were analysed: the degree of oxidation of the polymer film [40,41], the polymer film thickness, fp [40], the composition of the external electrolyte contacting the polymer film [41], the thickness of the metal film, d [41] and the degree of degradation of the polymer [42]. The resistometric behaviours of a gold film free and coated with a POAP film, both of them contacting a 0.1 M HClO4 + 0.4 M NaClO4 solution, were compared within the potential range
0.2 V < E < 0.5 V (versus SCE) where POAP exhibits its maximal electroactivity (Fig. 13) [40]. As POAP becomes conductive at positive potentials (oxidised state) the DR/R versus E changes were referred to the potential value E =
0.2 V where POAP is its reduced state [171,172]. The increase of the resistance of the naked gold film electrode (free of polymer) going from
0.2 to 0.5 V was ascribed to ClO4
adsorption (Fig. 13) [52]. Also, within the same potential region a resistance increase is observed for the gold film modified with POAP. However, the observed DR/R change appears attenuated respect to the gold film free of POAP and this attenuation becomes more pronounced as thicker is the polymer film. However, for high polymer thickness (fp > 60 nm) the DR/R change becomes independent of fp. Furthermore, for fp > 60 nm (or in terms of the voltammetric reduction charge Qred > 2.8 mC cm
2) the resistometric behaviour of the base gold film is independent not only of the polymer thickness but also of the external electrolyte composition (Fig. 14) [41]. Under these conditions, the DR/R increase going from

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Fig. 14. DR/R vs. E response for a gold film electrode (d = 30 nm) coated with (a) a 0.12 mC cm
2 thick POAP film and (b) a 2.8 mC cm
2 thick POAP film, in the presence of different electrolytes: (—) 0.1 M HClO4 + 0.4 M NaClO4; (- - -); 0.4 M Na2SO4 + 0.1 M H2SO4 and (– – –) 0.4 M sodium benzenesulphonate + 0.1 M benzenesulphonic acid. Scan rate: n = 10
2 V s
1. From [41].

the reduced to the oxidised state of POAP (curves (b) in Fig. 14) was ascribed to the proper redox conversion of the POAP film. That is, starting at the reduced state of POAP (E =
0.2 V), during polymer oxidation generation of charged electronic entities at the polymer chains near the gold surface occurs by electron transfer across the polymer
metal interface. In this sense, the redox switching of POAP was interpreted in terms of the oxidation of the amino groups to imine [173]. Thus, it is not unreasonable to expect that imine sites act themselves as different scattering centres compared with amine sites, increasing in this way the diffuse reflection (increase of DR) of conduction electrons on the gold film surface during POAP oxidation. In this connection, it was established that by means of resistance measurements on a gold film surface blocked with an enough thick POAP film (Qred = 2.8 mC cm
2) the attention is paid to only one process: the redox transformation of the polymer film due to its interfacial exchange with the metal surface. In this connection, the same resistance measurements applied to gold films coated with thinner POAP films (Qred = 0.2 mC cm
2) (curves (a) in Fig. 14), which could not be sufficiently compact at the gold–POAP interface to prevent the interaction of species proceeding from the external electrolyte with the gold film surface, indicate some anion adsorption effects on the gold surface. As it can be seen in Fig. 14, for a very thin POAP film more distinguishable resistometric responses (curves (a)) are obtained in the presence of different electrolytes, as compared with the resistometric

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responses (curves (b)) corresponding to a thick POAP film coating the gold film. Then, even when these resistometric responses (curves (a) in Fig. 14) are attenuated respect to that corresponding to a gold film free of polymer, they follow the same tendency for the anion adsorption on gold, that is ClO4
< SO42
< BS (see Section 2.3.1). This should be indicative of some anion interaction with the gold surface. Also, similar effects of the external electrolyte on the resistometric response of gold films coated with very thin POAP films were observed in the presence of cations able to be deposited on gold under upd conditions [41]. Then, for thin POAP films resistometric changes could reflect interfacial effects (metal–polymer interface) due to a competition between the adsorption of different species proceeding from the supporting electrolyte and the own redox transformation at the metal–polymer interface. It is possible that at very low POAP thickness (<0.15 mC cm
2) either polymer islands (a continuous film is formed by fusion of these islands) or polymer layers with imperfections exist on the gold surface. In this sense, high permeability values of some polymer films [174] to transport of species from the solution in contact with the polymer to the metal substrate have been attributed to dispersed polymer structures with imperfections (e.g. pinholes and large channels) with dimensions large compared to those of species present in solution. Also, it was found that reflecting properties of the gold-POAP interface are affected by the presence of some redox active species in solution, such as hydroquinone/benzoquinone, able to permeate though the polymer and reach the metal–polymer interface at high degree of oxidation. In this case, together the redox reaction of the polymer, adsorption of these species at the gold surface is conceivable [40]. At this point, it should be pointed out that despite the creation of chemical bonds between the polymer and the metal film, the absolute value of the gold film resistance at a given thickness (for instance, R  20 V for d = 30 nm) does not change with POAP deposition, only the relative DR/R value, referred to either the reduced (E =
0.2 V) or the oxidised (E = 0.5 V) state of the polymer, varies with the potential scanning (
0.2 V < E < 0.5 V). This should be indicative of a resistometric change only related to an interfacial (metal–polymer) electron dispersion process which occurs during oxidation–reduction of the polymer. On the contrary, generation of a nonconducting dead layer (subsurface impurity) during POAP deposition leading to a reduction of the metallic thickness (size effects), should yield an increase of the absolute value of the gold film resistance. As was indicated, the resistometric response of a gold film electrode coated with a thick POAP film becomes unique and independent of the type of external electrolyte contacting the polymer. Under these conditions, a linear increase of DR as a function of the degree of oxidation uox of the POAP film was also observed [41]. This was explained in terms of an interfacial distribution of scatterers (imine sites) in the oxidised state with a spacing among them constant and larger than that corresponding to amine sites in the reduced state [8]. In this connection, during POAP oxidation only one in every four or five amine sites are converted to the corresponding imine sites [173]. This gives rise to gaps which eventually would yield a distribution of oxidised sites less compact than the corresponding distribution of reduced ones. Another confirmation about the different reflecting properties of the oxidised and reduced state of POAP can be found in the different values of the site interaction parameters (r) obtained from the cathodic and anodic voltammetric responses of POAP [175]. Non-ideal behaviour of POAP, which is actually expected considering the rather high concentration of active sites on the film (i.e. c = 4.7 M [176]), leads to the following values of anodic and cathodic site interaction parameters: ra =
0.55 M
1 and rc =
0.18 M
1, respectively. Both are negative, thus involving a repulsive energy of interaction [177–180]. As a higher repulsion is observed between oxidised sites than reduced ones at POAP films, then a more extended configuration of oxidised sites should be expected as compared with the

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corresponding distribution of reduced sites. Then, also it would be expected that the distribution of oxidised sites reflects electrons more diffusely than the distribution of reduced sites. The linear DR versus uox dependence was interpreted on the basis of the ‘‘size effect’’ theory [15,62]. Considering a thin gold film covered with POAP, the DR (=DrfG0/d) change (see Eq. (6)) during the redox conversion of the polymer, should only reflect interfacial processes at the gold film–polymer film interface. By using Eq. (6), the DR change of the gold film coated with POAP was written as:   3 rb l0 Dp (33) DR ¼
G0 8 d2 where rb and l0 represent the bulk resistivity of the massive gold and the mean free path of the conduction electrons of gold, respectively. On the assumption that the decrease of the specularity parameter (
Dp) of the gold film surface going from the reduced to the oxidised state of POAP is proportional to the degree of oxidation (uox) of the polymer film deposited on it, Dp =
kuox, Eq. (33) can be written as:   3 rb l0 DR ¼ G0 (34) k0 uox 8 d2 As it can be seen from Eq. (34), at constant d, if k0 is a constant independent of uox, a DR versus uox plot should give a linear dependence. Fig. 15 shows, for the different electrolytes, and constant d, a linear DR versus uox dependence within the range 0.10 < uox < 0.98. Also, as it can be seen from Fig. 15, the DR/uox slope increases as d decreases. Thus, Fig. 16 shows, as it is predicted by Eq. (34), a linear DR/u ox versus d
2 dependence. This dependence seems to confirm the existence of a surface scattering process assisted by a size effect, at the gold film–POAP interface during the redox reaction of a POAP film. From the slope showed in Fig. 16 and using in Eq. (34) values of G0 (=l/w = 2), rb (=2.4  10
6 V cm) and l0 (=22 nm at 25 8C) for our gold films, a k0 value about 3.8  10
2 was obtained. As the distribution of redox sites at POAP depends on the solution pH, the DR versus uox dependence also depends on this external variable [41]. In another work [42], the irreversible deterioration suffered by POAP films when the upper positive potential limit (Eupl) is extended to values higher than a threshold value of 0.5 V versus SCE, was studied by using the SR technique together with cyclic voltammetry and rotating disc electrode voltammetry (RDEV). This deterioration is reflected by a strong reduction in both anodic and cathodic voltammetric response of POAP coated gold film electrodes. Again, resistometric measurements were employed to study the process at the gold–POAP interface. A strong attenuation of the gold film resistance within the potential region of maximal electroactivity of POAP, after polymer degradation, allowed to infer that polymer inactive zones are developed at the POAP–gold interface. Distribution of redox sites at the POAP–gold interface, even actives after degradation, becomes more expanded than that present on the gold film surface contacting a freshly prepared POAP film. This was inferred from a more diffuse reflection of the conduction electrons from the inside of the gold film at the POAP–gold interface with increasing POAP degradation. RDEV experiments carried out on both freshly prepared and degraded POAP films contacting a solution containing a redox species able to be discharged at the POAP– electrolyte, allowed to obtain electron diffusion coefficient values De which decrease with polymer degradation. This was explained on the basis of larger distances among adjacent redox sites as the polymer becomes degraded, which is in agreement with the existence of more extended distributions of redox sites in a degraded polymer film as it is detected by SR. In [42], the (DR/uRed) versus uRed,Max dependence, where uRed represents the degree of reduction of the POAP film and uRed,Max is the maximal

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Fig. 15. DR vs. uox dependencies for different gold film thickness d coated with a 2.8 mC cm
2 thick POAP film. Electrolytes: (*) 0.1 M HClO4 + 0.4 M NaClO4; (~) 0.4 M Na2SO4 + 0.1 M H2SO4 and (&) 0.4 M sodium benzenesulphonate + 0.1 M benzenesulphonic acid. From [41].

degree of reduction achieved by the POAP films after being subjected to different degradation treatments, was compared with the De versus u Red,Max dependence. De represents a measure of the electron-hopping rate within the polymer. In this way, an interfacial property (DR/uRed), related to the electron scattering process at the metal–polymer interface, was correlated with a massive transport parameter of the polymer, De, related to the electron motion within the polymer film. Leonidopoulos [181–185] employed the concentric cylindrical electrode method to obtain the surface resistance of different polymeric materials such as polyester [181,182], estrofol [183] and polyethylene [184]. The method works as a voltage divider and it is described by means of an electrical equivalent circuit where the polymer film is represented by a resistance. In a more recent paper [185], Leonidopoulos used the same method to analyse the surface resistance of acetate films. The experimental response for acetate films was compared with the theoretical response, which was developed analytically and expressed mathematically in terms of the different parameters of the system. Theoretical analysis gives, for instance, the depth of the film within which surface phenomena take place. In another two papers [186,187] it was explained why the surface resistance vary during the experimental response of the system.

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Fig. 16. DR/uox slopes as a function of d
2. Slopes values extracted from Fig. 15. From [41].

3. Phenomenological parameters of scattering models determined from surface resistance measurements in electrochemistry In the scattering model, the conduction electrons of the metal are treated with a free-electron model [44], in which the electron gas is characterised by two parameters, the electron density, n0, and a relaxation or scattering time, t. Adsorbates or other surface defects can change n0 by forming local hybridised orbitals with the metallic electronic states, and can change t by acting as scattering centres. Either effect will change the conductivity near the metal film surface. Although the impurity potential is screened within a few lattice constants (1 nm) the electronic conductivity is affected to a much greater depth, on the order of the electron mean-free path l0 (=vFt) where vF is the Fermi velocity. In general, the scattering models assume that adsorbates act as scattering centres affecting the conductivity of the metal sample. However, each adsorbate may also trap some conduction electrons de in localised states (de represents the average number of localised conduction electrons per adsorbate) which also could affect the metal conductivity. Under these considerations, the resistance change of the film induced by adsorption can be written as [188]: Drf Dn0 =n0 þ Dt=t 
d rb

(35)

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143

where d is the film thickness and Drf, Dn0 and Dt represent surface resistivity, electron density and scattering time changes, respectively, caused by the adsorbate. rb is the bulk resistivity. In some cases, the analysis assumes that the scattering introduced by the adsorbates is independent of other sources of scattering in the metal, whether from phonons, bulk impurities, grain boundaries or defects present on the clean surface. This assumption, the Mathiessen’s rule [72], allows one to analyse the changes induced by the adsorbate without knowing the details of the electron dynamics in the metal [189,190]. At a given point the theoretical treatments become entirely phenomenological, since the quantities Dn0 and Dt are not generally known a priori. Then, these quantities are expressed in terms of other phenomenological parameters, such as the Fuchs specularity parameter, p, the scattering cross-section per adsorbate, sa, the Persson–Volokitin friction coefficient, h, and the number of electron lacalized per adsorbate, de. Thus, the different contributions in the last term of Eq. (35) can be considered in the equivalence [188]: Dt 3 3 ¼
ð1
pÞ ¼
s a Na ¼
ðNa MÞðvF mn0 Þ
1 h t 16 16

(36)

Dn0 ¼
Na de ðn0 lB Þ
1 n0

(37)

and

where Na is the surface density of adsorbates, M is the adsorbate mass and lB (lB < d), is the thickness of a surface layer whose conductivity is affected by the adsorbate. Thus, many of the experimentally testable predictions of the theory concern with p (or sa or h) as a purely phenomenological parameter characterising the extent of the diffuse scattering. The different parameters expressed in Eq. (36) are found in the different scattering models. With regard to the specularity parameter, p, in the Fuchs–Sondheimer model [15,62] the surface enters in the theory through it. There have been numerous efforts to refine and improve upon the Fuchs–Sondheimer model [65,67–69,191–194]. In general, theoretical advances have shown that the specularity parameter is dependent on both the electron incident angle and the different environments given by the top and the bottom surfaces [63,70,195]. Lessie and Crosson [196] considered S-wave scatterers distributed randomly on a square lattice located inside an infinite-barrier surface and evaluated p using the average T-matrix approximation. The calculated surface resistivity reproduced the Nordheim (or parabolic) dependence as a function of the coverage of the scatterers. Ishida [197,198] derived an expression of the surface resistivity where he considered the interior of the metal as a Jellium whereas the surface region may have any 3D structures such as isolated adsorbates, ordered atomic layers and surface defects. With the assumption to the probability of diffuse scattering is independent of the direction of the scattered waves the expression of the resistivity coincides with the semiclassical result [197]. Concerning the scattering-cross section, sa, in the Watanabe approximation [102] the potential of the adatom, as seen by the incident electron, has the form of a shielded Coulomb potential located at an infinite barrier representing the metal surface. In this model the metal is considered in terms of a positive Jellium density. In the derivation supplied by Greene and O’Donnell [63] and subsequent modification of Watanabe [102] an expression for the scattering cross-section of adsorbed species sa is obtained in terms of the Bohr radius. The Persson–Volokitin theory interprets h as the damping rate of the adsorbate’s motion parallel to the surface [27]. This aspect of the model provides its connection to friction, sticking, electromigration, diffusion, etc., but it is not without controversy [199,200] and the experimental

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evidence is both limited and mixed. Persson used the Newns–Anderson model to give a general expression for the friction coefficient h in terms of the adsorbate-induced density of states at the Fermi level ra(EF) [27,189,190]:   h (38) M
1 Fra ðEF Þhkp2 i h¼ 2p In this model, it is assumed that the adsorbate induces resonance states of width F near the Fermi level. hkp2 i (kp is the wave vector component parallel to the surface) depends on both the matrix element for electron transfer between the adsorbate-induced state and a metallic state and the energy of the state. Despite adsorbate-induced electronic levels near the Fermi energy are not well characterised, this model predicts resistance changes of the right order of magnitude, as well as the tendency of chemisorbed species to give larger effects than physisorbed ones. The model has also been used to account qualitatively for the increasing scattering cross-section and vibrational redshift of CO on Cu(1 1 1) caused by coadsorbed C2H4 [190]. However, the model is unable to explain the effects on CO of coadsorbed Cs [189,190]. In its original form, the Persson’s model applies strictly to atomic adsorbates [27]. Despite many features are also applicable to molecular adsorbates and coadsorption systems, exact quantitative agreement should not be expected. A more general quantum mechanic formulation is also available [201]. With regard to surface resistance in electrochemistry, Rath [18] obtained experimental values of apparent scattering cross-sections (sa) for several upd species and different adsorbing halides on gold film electrodes by using Eq. (39): ! @2 ðDR=RÞT (39) s a ¼ lim k!1 @Na @k
1 where (DR/R)T is the relative change of the total film resistance, Na is the surface density of the adsorbed species and k is the reduced thickness, that is, the ratio of the film thickness to the mean free path of the conduction electrons of gold. The experimental evaluation of Eq. (39) from electrochemical data requires that the electrosorption valency of the species and the roughness factor of the film surface be known. sa values obtained from Eq. (39) were compared with those obtained from Eq. (40) which is derived from the theoretical approach of Greene and O’Donnell [63] modified by the approximation of Watanabe [102]:   Z 3 @p1 ðuÞ 3 du (40) ðu
u Þ sa ¼
4 @Na In Eq. (40), u is the cosine of the incident angle of the conduction electrons to the surface and p1(u) is the specularity parameter corresponding to the upper surface of the film. At low coverages a close fit between theoretical and experimental values was observed. However, relative large departures observed for some upd species were assigned to changed effective distance of interaction between the adsorbate and the adsorbent. Rath and Hansen [50] by employing the scattering hypothesis of Wedler and Wissmann [71] determined the scattering cross-sections of Br
and I
anions on gold film electrodes. On the basis of Eq. (5), the resistivity was written in terms of the induced electrode charge (field effect) and the amount

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of specifically adsorbed species:   K0 Ne s e Na s a rf ¼ rb 1 þ þ þ k k k

145

(41)

where k (=d/l0) is the reduced thickness and K0 includes the constant intrinsic properties of the metal film. Ne and Na are the surface densities of the induced free electrons and adsorbed species of cross-sections se and sa, respectively. The induced electrons from the simple charging are placed into the scattering hypothesis as surface scattering with a constant negative cross-section. rb is the measurable bulk resistivity since the thickness dependence on internal structure has been included as a separate entity. Scattering cross-sections were calculated from the expression:   @as (42) s a ¼
gF lim k ! 1 @k
1 where g is the electrosorption valence, F the Faraday constant and as is the resistance sensitivity coefficient defined as by Eq. (8) (Section 2.2). sa was experimentally obtained from the limiting slope of the as versus k
1 dependence when the thickness film tends to infinity (Eq. (42)). A sa value of 0.015 nm2 was obtained for iodide. With g =
0.81 for bromide an apparent cross-section for this anion about 0.66 times that of iodide was obtained. By using the Perssons theory [29,30] to interpret resistance curves at very small coverages, Hanewinkel et al. [37] estimated the cross-section of lead on Ag(1 1 1) film electrodes. Considering the equivalencies showed in Eqs. (35) and (36) it is possible to express the cross-section of an adsorbed species as:  
1 @rf 2 (43) s a ¼ ð16dn0 e Þð3vF mÞ @Na To calculate sa of lead in [37] the change of coverage, calculated from the initial slope of the current response of Pb upd process, and the change of the dc-resistance per time unit, were employed. A crosssection value around 0.01 nm2 was obtained. This value is about one order of magnitude smaller than that corresponding to the silver atom (0.14 nm2). It is interesting to remark that from atomic scale friction experiments Krim et al. [202] deduced a value sa = 6  10
5 nm2 for the water molecule in a complete monolayer of adsorbed water molecules on silver. Then, under electrochemical environment this last value of the cross-section for diffuse scattering of adsorbed water can be neglected compared to those for other adsorbates. Clavilier and co-workers [76] studied the electrochemical process of oxygen on gold film electrodes with preferential orientation (1 1 1) by surface resistance measurements. From the experimental dependence of the resistivity change per unit of charge (@Drf/@Qa,c) as a function of d
1, and using the Wissmann approximation [87,89], the authors calculated values of the coefficient K3 (=lrbsa) for the different oxide surface structures proposed. For each structure proposed it was assumed that the crosssection sa of the adsorbed oxygen atom remains constant with increasing the coverage. However, the decrease of K3 going from Au2(OH) to Au2O3, surface structures was assigned to a density increase of the oxide surface phase where different interactions between adsorbed oxygen atoms should occur. Also, by employing the Fuchs–Sondheimer theory a Dp change about 0.72 was obtained for the total change of the reflection coefficient corresponding to the film surface contacting the electrolyte. This Dp value was associated to the coverage change from zero to the maximum coverage of oxygen.

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The adsorption process of HSO4
anions on thin gold film electrodes was studied in [48] by using cyclic voltammetry and surface resistance measurements. In this work, a cross-section value for the bisulphate anion s HSO4 from the expression: @ðDR=RÞT ¼ ðn0 edÞ
1 þ k0 @s m

(44)

which can be derived from Eq. (19). From the experimental @(DR/R)T/@sm slope (=4.78  10
5 cm2 mC
1) obtained for gold film electrodes contacting acid sulphuric solutions and comparing this value with the theoretical value (n0ed)
1 = 2.11  10
5 cm2 mC
1 for a gold film of thickness d = 50 nm, a k0 = 2.55  10
5 cm2 mC
1 was extracted from Eq. (44). Expressing k0 in the light of the Wissmann approach [87,89] a value ðl0 rb s HSO4 Þ ¼ 0:082  10
27 V cm4 ion
1 results. Considering for gold the corresponding values of the mean free path for the conduction electrons, l0, and the bulk resistivity, rb, a value s HSO4 ¼ 0:0015 nm2 for the cross-section of bisulphate anion was obtained. This cross-section value is very small as compared with those corresponding to other adsorbing species [37,50]. However, it is higher than that the value determined by Krim et al. [202] (sa = 6  10
5 nm2) for the water molecule. Decrease of the specularity parameter,
Dp, upon adsorption of a monolayer of different adatoms (Tl, Cd, Pb and Bi) on gold and silver film electrodes as substrates, respectively, were compared in [79]. Dp changes were directly evaluated from the expression of the resistivity changes given by the Fuchs– Sondheimer theory. The sequence of specularity changes for a given substrate film indicates that the more dense is the surface layer, the more specularly are reflected the conduction electrons. Also, in [79], the change in the number of free electrons, de was used as alternative parameter to interpret resistance changes during adsorption. de values were calculated and compared for the different adsorbed metal atoms above mentioned on both gold and silver films. If resistance changes involve a change in the surface concentration of free electrons, it should be expected a different degree of chemical bond in the case of covalent bonding, or the establishment of an image-induced surface charge in the case of an ionic one. A lower degree of covalent bonding was observed for adsorption on silver as compared with gold for the different adsorbates studied. Because of the difficulty of making absolute quantitative tests in electrochemistry, most of the experimental evidence relating to mechanism of surface resistivity focuses on relative measurements of variations as a function of film thickness, adsorbate coverage and also of the relative magnitudes of resistivity and reflectance changes (Section 2.3.7).

4. The measurement of the surface resistance in electrochemistry. Instrumentation. Designs and preparation of electrodes To obtain surface resistance in electrochemistry, the resistance R of a thin film electrode is usually measured. While an external ac or dc measuring current, Im, is applied along the electrode, the voltage drop DV, also along it, is continuously monitored during the electrochemical experiment. Since the working electrode must be necessarily a resistive electrode, some special problems of current and potential distributions along the electrode should be take into account. In the presence of a stationary faradaic current, there will be an extra contribution IpR to DV, that should be necessarily eliminated, or at

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147

least minimised. Thus, one can write: DV ¼ Im R þ Ip R

(45)

where Ip is the averaged polarisation current. The problem of current and potential distributions along resistive electrodes was considered by several workers [103,203–207]. Harvey [203] examined distributions of potential and longitudinal currents on an uniform metal wire of radius r and resistivity rw immersed in an electrolytic solution, through whose ends a dc current is applied. Similar considerations were applied to solve the potential distribution problem on a metal strip where the radius r of the wire was replaced by the thickness of the strip. Harvey also discuss the application of his equations to other situations of practical interest. Conway et al. [204] considered the potential distribution problem of a wire of length lc, radius rc and resistivity rc immersed in an electrolytic solution assuming the validity of the Tafel relationship, i.e. high overpotentials, and that the potential distribution can be linearized. These authors find the current density distribution as a function of the distance along the electrode solving the corresponding differential equation. Some inconsistencies of solutions given in this work were treated by Rangarajan et al. [205], who extended the treatment of Conway [204] to more general cases. Unfortunately, the solutions of some equations in the treatment given in [205] are very complicated, except for conditions where the anodic and cathodic Tafel slopes are equal. In this last case, a formal solution for the potential distribution of the resistive electrode can be found in terms of Legendre elliptic functions. However, the solution must be calculated numerically for each particular resistive electrode. Tolkachef [206] studied the current density distribution along a resistive electrode, which is separated from other electrode by an electrolytic solution. The method proposed by Tolkachef for finding the current density along the resistive electrode is completely general. Different expressions for the potential at the electrode–electrolyte boundary corresponding to several resistive electrodes shapes (cylindrical, plate-shaped, etc.) were examined by Tolkachev [206]. Following the treatment of Harvey [203], Dickinson and Sutton [103] assumed a linear relation between the current density and the potential drop along a thin film electrode. They find a general solution for the potential distribution along the electrode. The problem of potential distribution along a thin film electrode was reconsidered by Tucceri and Posadas in [207] by assuming that the electrode process fits a Butler–Volmer current–potential distribution and that the potential within the electrode can be linearized. The possibility of coupling between the faradaic and measuring currents within the electrode was also taken into account in [207]. Under the assumption of not too high electrochemical currents, this coupling effect was found to be negligible. Concerning the technique of monitoring resistivity changes during electrochemical processes, it has been demonstrated that a convenient design for metallic electrodes is the so called ‘‘three contact method’’ [48,91,100,103,207]. In this method, the electrochemical current drain (or feeding) contact is placed as symmetrically as possible at the middle of the voltage measurement contacts (Fig. 17). In this way, the contribution of the polarisation current along each half of the electrode tends to cancel each other out. The theoretical analysis of this electrode design is relatively simple when considers only stationary currents. However, the problem becomes more complicated when transient responses, such as those corresponding to linear scanning potential voltammetry are studied. In this last case, the current may increase (or decrease) during the potential scan. That is, while the central contact being to be at a predetermined potential value E, corresponding to a particular current value Ip(E), one of the ends of the resistive electrode will be at somewhat lower potential value E1, which corresponds to a lower current value Ip(E1), and the other end will be at a potential E2, which should correspond to a higher current value

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Fig. 17. Circuitry to measure electrode resistance using the ‘‘three contact method’’. From [207].

Ip(E2). Then, one can write: DV ¼ Im R þ ½Ip ðE2 Þ
Ip ðE1 ÞR

(46)

For instance, when only double layer phenomena being considered the capacitive current is much smaller than the measuring current (Im > [Ip(E2)
Ip(E1)]) and the three contact design would suffice. The three contact method has been applied to study different electrochemical processes on metallic film electrodes by surface resistance measurements [31–37,43,46–48,51,53,55,59,79,90,91,100,103,108,207,208]. However, when working with semiconductors where there are metal–semiconductor polarizable junctions, special care should be taken into account to minimise them. In this case, the electrode design should include four contact electrodes, which works in a similar way to the well-known ‘‘four contact method’’ for measuring thin film resistance. The method is described by Rath in his thesis [169]. In this connection, Rath [18] used a rectangular geometry of the film electrode that allows the use of the four-probe resistance method where the measurement of the voltage drop resulting from a constant current applied along the length of the film, gives the film resistance, free of any contact resistance. The four-point method was recently employed by Otto and co-workers [38] to detect small resistance changes during lead upd process on epitaxial silver film electrodes. Hansen [101] and Rath and Hansen [50] used a fiveprobe method for monitoring electrode resistance and Hall voltage simultaneously. Concerning Eq. (46), it is interesting to remark that if the second term is larger than ImR, the shape of the resistogram will resemble that of the derivative of the voltammogram. A method to obtain the derivative of the voltammogramm through resistance measurements was described in [209]. The modulated response has the form of a swing and shows higher sensibility that the voltammetric response for determined electrochemical processes occurring on a gold film electrode. A modified version of this ‘‘modulatory resistometry’’ technique and an interpretation of the results of its practical application was given by Valinchius [210]. In a further work, Bigeliene and Valinchius [211] improve the modulation resistometry method to measure the change of the surface resistance of a thin film electrode under potentiodynamic conditions. The method allowed the authors to determine not only the differential change in the relative resistance but also the integral one. The modulatory resistometry was applied to analyse the oxidation process of gold film electrodes [211]. Not only integral but also differential change in the relative resistance of thin film electrodes were determined by this method. Rath and Hansen [50]

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introduced a dynamic approach when the time derivative of the resistance is compared to the voltammetric current in periodic linear sweep voltammetry. This avoids errors inherent with integral measurements of the electrode charge and resistance. The representation of the normalised current i/n versus the derivative resistance (dDR/dE) was termed dRi method (n = dE/dt is the potentiodynamic scan rate) [50]. Derived resistance curves (dDR/dE) as a function of potential were recently used to study the deposition process of lead [37] on gold film electrodes and thallium [36] and cadmium [35] on epitaxial silver film electrodes. Rath [18,169] discuss the problem associated with measuring the electrode resistance by using dc and ac techniques. For this propose, either dc or ac resistance bridges as well as dc polarisation methods have been employed [31–33,46,47,53,59,90,91,208,212]. Monitoring changes of the electrode resistance by the dc method is suitable for most electrochemical studies and in most of recent experiments resistance changes were in general measured by using Wheatstone bridges and dc current [35–38,109]. Resistance measurement with ac currents has several advantages over the dc method, such as superior instrumentation giving an increased sensitivity with better stability and noise discrimination, and a zero current through the film, so that the dc limitations are avoided. However, the double-layer can no longer confine the ac current to the electrode, making the measurement sensitive to changes in the double-layer impedance when the solution is highly conducting [31–33,213,214]. Thus, different circuitry was employed in resistance measurements in electrochemistry. Bockris et al. [71] used a resistance bridge. The maximum tolerable potential drop across the film electrode was 100 mV (if the electrode contact is made at the centre of the film electrode, then the electrode potential will may only 50 mV). A nullmeter, capable of measuring 5 mV deflections was employed. Fujihira and Kuwana [53] measured the resistance of the thin film electrode, R, by using a bridge. The working electrode contact was made at the centre of R. The coupling by the potential dependent faradaic current was avoided by using very slow scan rates (ca. 0.001 Hz). The electrode potential was controlled by a potentiostat whose ground was isolated from the ground of the bridge circuit. Relative change in conductance of 10
4 was the limit of sensitivity with this system. Niki and Shirato [59] used a Kelvin double bridge in their resistance measurements. The current across the gold film was 230–240 mA so that the potential difference between the ends of electrode was 0.06–0.07 mV and then, the working electrode was considered as an equipotential. Ganon et al. [76] measured resistance changes employing a Wheastone bridge. The potential drop along the film results less than 10 mV. In [79], the potential drop at the extremes of the film was measured with a voltmeter. Measuring dc currents between 2  10
3 and 5  10
3 A were supplied by a constant current source. A voltage compensator was applied to the analog output of the multimeter and the signal was send to a X–Y1–Y2 plotter. This cancel a large portion of the resistance voltage, thereby increasing the sensitivity of the measurement (10
6 V/cm). The percent precision was 10
4 V/ cm. In [35], a constant current source and a voltmeter were used for the four-point probe measurement of the thin film electrode’s resistance. For measurements of very small resistance changes a constant current source, a Wheatstone bridge and an amplification unit was used. In this set-up the difference DV between the two branches of the Wheatstone bridge was amplified by a factor of 100 and measured by the voltmeter. Ko¨ rwer et al. [108] used a potentiostat connected to the middle of a silver film in order to minimise the voltage drop length caused by the electrochemical current. The direction of the current of the resistance circuit could be reversed. So from two measurements with both current directions a result free from interference of the potentiostat could be achieved by subtraction. The electrochemical set-up consisted of a potentiostat, a voltage scan generator and a voltage integrator. A symmetrical geometry of the electrode used by Otto and co-workers [36] allowed them to cancel the voltage drop along the film

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caused by the electrochemical current. The contact for the potentiostat was in between two silver stripes. The resistance was measured with four contacts directly at the electrode. The electrical signals for the resistance measurements, the electrochemical current and the potential were digitised. The same experimental set-up was used in [109]. In [38], the resistance was obtained by passing a constant current Im through the film electrode and measuring the voltage whit a four-point method in order to detect small resistance changes. The experimental set-up used in [37] to measure the electrode resistance was similar to that described in [108]. Additional instrumentation is necessary in some cases. To apply the five-probe Hall method in [101,169] an electromagnet was used to provide the magnetic field. A Gaussmeter was used to measure the magnetic field with a precision of 0.01%. The ac and dc Hall voltage was measured with a lock-in amplifier and a nanovoltmeter, respectively. When Rath [169] and Rath and Hansen [50] applied the dRi method, the ac resistance time derivative was measured with a standard differentiating circuit consisting of a low noise operational amplifier, a capacitor and a fixed resistor. Anderson and Hansen monitored together in situ surface conductance and electroreflectance measurements in [46,47]. In this case, a Wheastone bridge was used to monitor the conductance change of the gold film electrode. The reflectance measurements were made on a Cary 14 spectrophotometer, used a expanded adsorbance slidewire at 4800. When capacitance–potential response was recorded together with current–potential and resistance–potential curves in [51,55], a lock-in amplifier and an oscillator level were used as additional instrumentation. With regard to electrode configurations, Bockris et al. [91] used a film strip with three electrical contacts as thin film electrode, two for resistance measurements and one for electrochemical contact, the ˚ ). For a later being made at the centre of the film. Electrical contacts were thick platinum films (>103 A strip 2 cm long by 0.2 cm wide, a resistance of 160 V was obtained. Fujihira and Kuwana [53] employed thin platinum films prepared by vacuum vapour deposition. The Pt films were annealed at 350 8C for 2 h prior to use. Three electrical contacts were made to the Pt film. Platinum foils, which were pressure contacted to the film electrode, were employed for masking electrical connections to the external circuit. Ganon et al. [76] used electrodes of rectangular geometry of 10 mm2 area. Anderson and Hansen [100] used a special electrode configuration, useful when the potential sweep rate exceeds 5 V/s. Romeo et al. [79] used gold and silver film electrodes obtained by high vacuum deposition of evaporated metals onto optically polished Pyrex glass or acrylic substrates at room temperature. The topography of the deposited films were investigated by transmission electron microscopy and the structure by electron diffraction. Polycrystalline gold films with crystallite sizes of about 0.1–0.5 mm resulted from this preparation method. The crystallites were preferentially oriented in the (1 1 1) direction. Silver film had lower crystallite sizes, i.e. between 0.01 and 0.1 mm and also had a preferential (1 1 1) orientation. Electrodes of rectangular shape 0.2 cm width, 1.62 cm cm long and 25 nm thick were obtained through the use of appropriate masks. Film thickness were determinated by weighting samples obtained at the same time, i.e. under the same evaporating conditions as the electrode. These values agree within 5% with those calculated from the deposition conditions: a source–substrate distance is about 10 cm and an evaporation rate is 0.1 nm s
1 were employed. Electrodes had an initial resistance value of about 10 V. In order to have a rough estimation about the quality of the metal film surfaces the specularity parameter for both Ag gold and silver films was calculated in [79]. Initial values of about pAu i = 0.57 and pi = 0.63 for gold and silver films, respectively, were obtained. These small pi values result surely from the small crystallite size of samples prepared in [79] and thus they are indicative of a relative large amount of surface defects on an atomic scale. On the other hand, the rugosity factor of the film surface was evaluated during the electrochemical measurements by comparing the differential capacity of the metal film at the cathodic

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end with that of the mercury electrode in solutions of the same concentration. All the electrochemical parameters, where the area was required, were corrected by the roughness factor. This value ranged between 1.3 and 1.8 depending of the previous history of the electrode. Ko¨ wer et al. [108] used film silver electrodes of 20–30 nm thickness prepared by evaporating silver onto a glass substrate under vacuum conditions (pressure: <5  10
4 Pa). The typical resistance of the 20 nm films was about 10 V. Otto and co-workers [36] used as electrodes thin epitaxial silver film prepared under UHV conditions and they were controlled in situ by LEED. Ag(1 0 0) films were grown on air-cleaved MgO(1 0 0) single-crystal substrates. The procedure results in smooth, continuos Ag(1 0 0) films with sharp LEED patterns demonstrating a remarkable stability when used as film electrodes under electrochemical conditions. Ag(1 1 1) films were grown on TiO2(1 1 0) and Si(1 1 1) substrates and also these electrodes demonstrated to have an excellent stability under electrochemical conditions. The epitaxial silver film electrodes consisted of two parallel stripes of 20–25 nm thickness. The same electrodes were used in [109]. Epitaxial Ag(1 1 1) films about 26 nm grown on Si(1 1 1) were used as electrodes in [38]. Also, silver thin film epitaxially grown onto single-crystal silicon substrates under UHV conditions were employed as working electrodes in [37]. The silver was evaporated onto the substrate at 300 K with an evaporation rate of about 0.7 nm/min until a total thickness of approximately 20 nm was reached. Annealing these thin films at 400 K for 1 h led to smooth Ag(1 1 1) films. For the electrode preparation in [35], process steps of silicon planar technology were employed. Silicon wafers with an h1 0 0i surface orientation served as substrates for the 15 nm thick polycrystalline gold film electrodes, which were deposited by electron-beam evaporation under high vacuum conditions. Patterning of the metal structures was achieved by optical lithography. Via 200 nm thick conducting tracks, current and voltage were supplied to the electrodes. Each electrode consisted of two identical parts which were connected in series by a metallic pad that serves also as the connection of the electrode to the potentiostat. This arrangement ensures that electrochemical currents do not influence the resistance measurements. A processed silicon wafer contains a number of square chips, each of them carrying several thin film electrodes. For measurements in electrolyte solutions they were mounted onto a batch cell made of PTFE, in a such way that only the gold film electrodes were exposed to the electrolyte.

5. Concluding remarks Surface resistance changes of thin film electrodes provide a powerful technique to study quantitatively different electrochemical phenomena: double layer charging, ionic and molecular adsorption and different oxidation and reduction processes. In this way, new information about the microscopical structure of the metal–electrolyte interface, particularly concerning to the role played by the conduction electrons of the metal on the different electrochemical processes, can be obtained. This technique coupled with simultaneous observation of electroreflectance and Hall effect represent a superior mean of investigating the metal–solution interface where an independent sets of data of the changes at the electrode surface can be compared. Resistance measurements were also used to monitor double layer process during electrode emersion. In this connection the underpotential deposition of lead on gold has been used to demonstrate that the double layer is removed intact with the electrode. This feature of resistance measurement provides an important link between the electrochemistry, where the sample can be precisely controlled, and the experimentation in gas phase, where numerous structure sensitive techniques are now accessible.

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Resistance measurements can serve as a sensitive probe to detect the presence of lattice imperfections and surface roughness on samples freshly prepared and also surface structural changes produced during the electrochemical manipulation. Concerning practical applications, it was recently demonstrated that surface resistance measurements might represent an interesting supplement or even an alternative to conventional electroanalytical methods. Also, its applicability to study the redox conversion and degradation of an electroactive polymer was recently demonstrated. Bluvshtein and co-workers demonstrated the applicability of this technique to study electrochemical processes in semimetal films. Experimentally, several difficulties arise to prepare thin film without imperfections useful to study adsorption processes. With regard to the interpretation of resistometric data, the model of free electrons with random point scatterers (FERPS) assumes randomly distributed, non-interacting adsorbates, so it is expected to be valid at low coverages, for adsorbates that do not form ordered islands. In this limit, the surface resistivity change varies linearly with adsorbate coverage. It is not obvious what should happen at higher coverages, especially if the adsorbate forms an ordered layer. In this connection, for a perfectly smooth surface, translational symmetry guarantees that only specular reflection is possible, giving no contribution to the resistivity (for fields parallel to the surface). Randomly distributed adsorbates (or defects) break the translational symmetry, permitting diffuse scattering and increased surface resistivity; this is the case considered in the FERPS models. An ordered array of adsorbates restores translational symmetry, but typically with a larger unit cell than that of the clean surface. Despite the important theoretical contribution of Persson revealing the connection of surface resistance with friction, sticking, electromigration and diffusion, more quantum theories need to be developed to explain different effects that probably contribute to the conductance change as creation of chemical bonds at the surface, surface states originated by the adsorbed particles, electron tunnelling across grain boundaries, etc. Theoretical improvements and more knowledge of the specific properties of the thin films will aid to understand more completely the resistance response to electrode processes.

Acknowledgements The author gratefully acknowledge to the Consejo Nacional de Investigaciones Cientı´ficas y Te´ cnicas (CONICET) and also to the Facultad de Ciencias Exactas, National University of La Plata (UNLP).

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