J Electnx+nal Chent, 2(4 (1986) 229-244
229
Elsevier Sequoia S A . Lausanne - Printed in The Netherlands
RECENT IMPROVEMENTS IN THE STUDY OF THE ELECTROCHEMICAL INTERFACE BY SURFACE PLASMON EXCITATION *
A . I ADJEDDINE, 11 . ABRAHAM ** and A . HADJADJ L,boratoere dEledroch,mte Inferfaoa?e du C.N.R.S., 7, Place A Brand, F-92195 Meudon Pnncipal C'edex (France)
(Received ist November 1985)
ABSTRACT A new field for the investigation of the optical properties of interfaces by the surface plasmon excitation technique can be opened by the use of a stratified electrode . This is made of aluminium as a site in the optical plasmon excitation . covered by a thin laver of the material under study . In this paper, we present some results we have obtained on Ag/Al and Pt/Al electrodes in contact with aqueous solutions .
INTRODUCTION
Surface plasmon (SP) excitation has been proved as a suitable probe for the investigation of electrode surfaces . Like other optical techniques, it is a valuable in situ tool for the characterisation of electrochemical interfaces . As pointed out by Kolb [1] the use of SPs for interfacial studies on electrodes is twofold . First, since the dispersion relation depends on the dielectric functions of the media sampled, the SPs offer a sensitive technique for investigating surface and film optical properties . Secondly, structural information on surfaces can be obtained as they act as SP momentum sources . An interesting situation which must be emphasized is the field enhancement which occurs at the metal/ambient interface in the case of SP excitation . This enhancement has been used for the detection and the determination of the properties of overlayers . Since some recent reviews have presented and analyzed the main investigations in the field [1-4] we shall restrict this contribution to new improvements we have made to widen the application of this technique . Due to the conditions of SP resonance (see for example Abeles [5]) only a few materials can be investigated in the spectral energy region where their optical properties are controlled by their free electrons . In electrochemistry, most studies have been performed with silver, a material which is both a good electrode and a good optical * Dedicated to the memory of Professor R .R . Dogonadze. '" Permanent address : TH Ilmcnau, Sektion Phyteb, DDR 6300 Ilmenau . PST 327 . 0022-0728/86/$03 .50
1986 Elsevier Sequoia S .A .
2 30
probe in the IR and visible range . However, the onset of interband transitions of silver (3 .8 eV) does not allow the application of this technique in the UV, where there are interesting electrochemical phenomena to be studied . Aluminium, with three free electrons per atom, should allow the extension of the SP technique up to 9 eV . However, due to its spontaneous irreversible oxidation, bare aluminium cannot be used as the electrode in aqueous solutions . To overcome this difficulty one must split the optical probe and the electrode by using a stratified electrode . Such an electrode allows the SP technique to be extended towards two directions which will be discussed in this contribution . The spectral extension will be illustrated by the silver/aluminium stratified electrode in contact with K,SO, solution, while preliminary data on the platinum/aluminium electrode will be presented to demonstrate the sensitivity of SP to the properties of the transition metal/electrolyte interface . EXPERIMENTAL
As we have discussed previously [6], the electrode must satisfy conditions which are difficult to achieve ; the overlayer (Pt/Ag) must be very thin (1 .5 to 10 nm) in order to cause only a small perturbation and to keep Al/SP sensitive to changes which occur at the ambient interface . The overlayer must be continuous to protect the aluminium film and ensure the stability of the electrode . Our samples were prepared under UHV conditions using a Riber UHV chamber with sorption, ionic, titanium sublimation pumps and a liquid nitrogen cryotrap . Evaporation was performed either by a Riber electron gun (4 kV) or thermally * on cleaned, optically polished SUPRASIL substrate, using high-purity materials . Thickness was measured by a quartz microhalance calibrated by Talystep measurements . Before the electrochemistry. structural characterisation . performed by SIMS, transmission electron microscopy and surface plasmon excitation allowed us to conclude that the silver overlayers were continuous and well-defined, with a rather sharp Ag/Al boundary. Pt/Al samples prepared by thermal evaporation display a more complicated structure which could be due to the thermally stimulated formation of a Pt + Al compound between the platinum overlayer and the aluminium film [7] . SP excitation was studied by attenuated total reflection (ATR) using the Otto configuration where the metal under investigation is separated by a thin electrolyte gap from the ATR device . The SP resonance appears as a minimum in the p-polarized reflected light as a function of the angle of incidence ($) at fixed wavelength (A) (or as a function of A at fixed ¢) . Measurements were performed under focussed ATR conditions described previously [8], using a new experimental set-up, shown in Fig. 1, which will be presented elsewhere . To cover a wide spectral range (800-250 nm) all optical devices are made of quartz and the detector is a
* Thermal evaporation was performed together with Dr . G . Hmcehn . Laboratoue de Physique Apphqude aux lndustnes du Vide et des composants Etectromques du C N .A .M. (Paris).
231 D, P L
L
11 BS,
m r B
BS
loc in
S
recorder Fig . 1 . Experimental set-up . S,.,,, S uv : visible and UV sources . BS : beam splrtter ; P : polariser ; CH : chopper ; PM : photomultiplier .
photomultiplier . The incident light is split into two beams (A and B) which are individually modulated and polarized . They are mixed together and focussed onto the flat side of a hemicylinder. The reflectance as a function of angle of incidence is detected by moving the photomultiplier across the light cone . A double lock-in amplifier allowed us to record either signal A or B and their ratio . Electrochemical experiments were carried out using classical potentiostatic equipment and a specially designed electrochemical cell [8] . We worked with oxygen-free solutions using a Pt grille as a counter electrode and a saturated K 2 SO,+Hg 2 SO,/Hg reference electrode . Our potentials will be referred to the standard hydrogen electrode (SHE) by adding 0 .65 V. ELECTROCHEMICAL BEHAVIOR OF THE STRATIFIED ELECTRODES
Two main questions have to be answered before using the electrodes : Do they have the same behavior as the massive material and what is their stability under electrochemical cycling? As discussed in previous work [6], the films may break down spontaneously in contact with aqueous solution . This can be prevented by prepolarisating them in the potential range where the electrode is ideally polarizable before immersion. Ag/Al electrodes were studied in 0 .1 M K 2 SO, solution . The potential of immersion was chosen as -0 .25 V and the potential was scanned at a rate of 0 .25 V s -l _ Figure 2 shows the first and the second cycles recorded on an Ag (5 nm)/Al (100 nm) electrode . There is a drastic difference between these cycles during the potential sweep in the positive direction . There is a positive charge around -0 .1 V . 0 .5 V which appears only in the first cycle [6] . The same behavior was observed with all samples, only the quantity of charge being different . To explain this effect, we evaluated the thickness of the silver layer from coulometric measurements (cycle 2 in Fig . 2) and from the negative shift of the SP dispersion curve induced by Ag dissolution (Fig . 3) . We found good agreement between the optical thickness and the thickness measured by the quartz microbalance during the evaporation, while
232
E/v 0
0.5
1,0
Fig . 2 . Current- potential curve of the Ag/K, SO, system . (a) First cycle ; (b) second cycle .
the electrochemical thickness was always smaller . This difference could be accounted for by the positive charge observed during the first cycle . This charge could be due to the dissolution of weakly bound Ag particles, most likely located at the grain boundaries as seen in the Transmission Electron Micrograph presented in Fig . 4 . The Pt/Al electrodes were tested by cyclic voltanunetry in 0 .5 M H 2 SO, solutions . Figure 5 shows a typical i(E) curve recorded after immersion at 0 .75 V . The shape of the curve - especially in the region of hydrogen evolution - is characteristic of the behavior of a polycrystalline platinum electrode, where the crystallite surfaces preferentially have the (111) orientation [9,10] . So a platinum overlayer as thin as 2 nm is continuous, which makes the Pt/Al electrode available for further investigations . The total charge due to hydrogen chemisorption (without correction for the contribution of the double layer) evaluated at ca 250 µC cm -,
. I 2 .3 a 2 .2
/*
2 .1 2 .0 .005 1 .010
K/K l I I . w 1 .025 1,C15 1 .020
Fig. 3 . Surface dispersion curve of Ag (5 nm)/AI (100 nm) before (a) and after (h) silver dissolution .
23 3
Fig . 4 . Transmission electron micrograph of a Ag (5 nm)/Al (100 nm)/quartz sample (after ref . 6) . {Url .Crl
Z
V
Fig . 5 . Current-potential curve of Pi (3 nm)/(Al (100 nm)/0 .S M H 2SO4 . /PA nn 2
Ely
51J,
Fig . 6 . Effect of cycling on the same system as in Fig . 5 . (a) After ca. 200 cycles : (b) further cycles .
2 34
(very close to the theoretical value of 226 1tC cm - ' in ref. 9) is indicative of the very smooth surface of the electrode . The second point to be answered was the stability of the samples during the experiments . This point was checked via the effect of the potential cycles (0-1 .25 V, 0 .05 V s -1 ) on the i(E) curves . During the first 200 cycles there was only a small change in the curve which appeared as a shoulder in the positive scan, before the oxygen adsorption (Fig . 6a) . Further cycling gave rise to a drastic change in the curve (Fig. 6b), followed by a breakdown of the sample . The curve displays a large positive current during both the positive and the negative potential sweep, the onset of which is shifted towards a lower potential after each cycle . Despite this evolution which could be indicative of a Pt dissolution ; no effect is observed on the hydrogen evolution, STUDY OF THE Ag/Al/ELECTROLYTE SYSTEM
Potential dependence of the SP dispersion Figure 7 shows the variation of the p-polarized reflectance versus the angle of incidence recorded at A = 550 mn for several values of the potential electrode (Ag (5 nm)/Al (100 nm), 0 .5 M K,SO,) . This result gives a clear indication of the sensitivity of the AI/SP to changes which occur at the Ag/electrolyte interface . The effects of the electrical potential on the interfacial properties can he analysed within the model discussed previously [11] . In this model any modification located in the vicinity of the plasma interface adds a contribution K-= K i + iK 2 to the wave-vector K., (K,,, is the SP wave vector of bare Al) . This contribution can
45
46
47
48
Fig . 7 . p-Polarized reflectance factor versus the angle of incidence of Ag (5 nm)/Al (100 am) in 0.5 M K 2 SO, at three different electrode potentials: ( } E=-0 .25 V ; (- •- .-) F=0 V ; (- -) F = 0 .25 Y . A = 475 am.
235
be replaced by an effective film of thickness d 1 and dielectric constant Z t = f t - is t , . Since the thickness of each film (including the Ag layer) is much smaller than the wavelength, their contribution is additive and given by K2,[1 AKt=( K0 _EE+)Ey
cc,]dr
[c t
(1)
K O =2ir/X is the wave-vector of the homogeneous wave, c, the dielectric constant of the bulk solution and E the dielectric constant of Al . At the pzc the SP resonance occurs for K R =KAI +AKAR AKA, being the contribution of the Ag overlayer obtained from eqn . (1) . where ft-CAR and d l .=dAK . At a potential E the electrical polarization induces perturbations in both the ionic and metallic phases which cause a change AK(E) : K(E) =K R +AK(E) The potential dependence of the real part AK 1 (E) and the imaginary part AK2 (E), plotted in Figs . 8 and 9, displays the same behavior as the systems studied previously and can be analyzed in the same way [ll] . The damping AK,(E) depends on the electrode charge and vanishes for negative charge, which allows us to evaluate the pzc as lying around -0 .45 V, close to the value measured by Valette et al . on Ag (111) electrodes [12] . The shift AK1 (E) is the same as the shift measured on Ag (111) electrodes [13] in a wide potential range (-0 .5 V to 0 V) . The
1 ° z aK/ Ke
2 .0
.0 1
i
y yLr' A
-0 .5 t
0
t t p
0 .5
Ely
Fig . 8 . Shift of the surface plasmon wave vector with the electrode potential : (a) Ag (5 nm)/Al (100 nm)/0.5 M K 2 S0a ; (b) Ag (111)/0 .5 M NaCIO4 [131 . A=475 rm .
2 36 A01i2
-0.2
A A
-0.1
1
EJV
-f At I I I I I 11 1 0 .5 0 0.5 Fig. 9. Potential dependence of the surface plasmon damping for Ag (5 nm)/AI (100 mm/0 .5 M K 2 SO4 solution . 1-475 nm . (Arrow indicates the pzc of the Ag (111) electrode .)
difference observed at more positive potentials could be accounted for by a specific adsorption which is stronger for SO than for CIO, , or by the polycrystallinity of the samples_ Effects
of the
electrochemical roughening on the SP dispersion
of the
Ag/Al electrode
Our aim with this investigation is to follow the surface properties of the electrode and their changes under electrochemical roughening, using the high sensitivity of the SP technique . The originally flat electrode was immersed at a controlled potential (-0 .25 V) in the double-layer region and a SP dispersion curve was measured . The surface was then roughened by anodic dissolution and subsequent partial redeposition of silver using cyclic voltammetry . Three positive limits, which correspond to three roughening processes, were applied and SP dispersion curves were measured at -425 V after each process. The results are presented in Fig. 10 and have been discussed briefly elsewhere [14] . The dispersion curve of a flat electrode ( Fig . 10a) is monotonic, which is indicative of its smooth surface . Figure l0b shows the dispersion curve measured after one cycle up to 0 .65 V, corresponding to the dissolution and subsequent redeposition of a small amount of silver . There is a drastic change in the curve, which exhibits negative dispersion in a wide spectral range . The third curve (Fig . 10c) was measured after one cycle up to 0 .7 V, where only part of the dissolved silver is redeposited . We observed negative dispersion and weak oscillations at low energy . Figure l0d was recorded after one cycle up to 0 .8 V . In this process silver is quasi-totally dissolved and partially redeposited in the form of clusters of different sizes actually seen in transmission electron micrographs . The dispersion curve is shifted to smaller wave vectors due to the smaller thickness of the effective silver layer . There is no negative dispersion and oscillations appear in the low (< 2 eV) and high (> 2_75 eV) energy region [15] . These results demonstrate
23 7
35! 30 25 20 15
,30 -
40
,45
. ixK/Ko165
Ftg 10 . Surface plasmon dispersion curves of Ag/AI/0 .l 61 K 2 SO, electrolyte measured at -0 . 2 5 V. (a) After immersion ; (b) electrochemical cycle up to 0 .65 V : (c) electrochemical cycle up to 0 .70 V, (d) electrochemical cycle up to 0 .98 V (after ref. 15) .
clearly the sensitivity of the SPs to surface topology since, for example, curves a and h correspond to the same amount of silver on the aluminium . Only the structure of the silver overlayer is different . Indeed, during the negative potential sweep the Ag atoms do not all return to their original positions in the surface lattice, which increases the surface roughness ; this effect is probably enhanced by the rather poor stability of the stratified thin layers compared to bulk materials . There are two kinds of experimental features which can be associated with two different surface structures . Negative dispersion (which can be seen as a splitting of the surface dispersion curve, since resonance occurs for 2 energies at the same wavevector) is observed only on a slightly roughened electrode . Small oscillations of the dispersion curve appear on a strongly roughened electrode where almost all the silver layer is removed during the positive potential sweep . The first effect can be analyzed within the general optical theory of rough surfaces, as we have proposed before [14] . Recent theoretical studies have shown that in the presence of surface roughness the dispersion curve of surface plasmon consists of two branches, in contrast with the dispersion curve on a flat surface, which consists on a single branch . In the large wave-vector region [16-18] Koetz et al . [19] observed such a splitting on Ag (111) by electroreflectance spectroscopy . In the low vector region [20-23] the dispersion relation for a rough surface has been discussed mainly in connection with the broadening of the surface plasmon resonance and the increase of the wave vector . However, in a small roughness limit Toigo et al . [23] deduced the occurrence of a splitting in the A(K) curve from their dispersion relation for periodic and randomly rough surfaces, the frequencies on the sides of the gap being dependent on the surface profile and the wave vector . Figure 11 shows the variation of the gap energy with the wave vector we measured after processes b and c (the K-axis refers to the threshold of the splitting for each curve) . Our results are consistent with the above theory and show for the first time the splitting of the dispersion curve in a low wave-vector range due to a submicroscopic roughness induced by electrochemical treatment of the same kind as the treatment used in Surface Enhanced Raman studies . However, for further analysis we need an actual surface profile, which is difficult to approach since this effect does not appear
238
a ."ev
i 0 .s
s
0 .4 0 .3
0 .2 0 .1
(K-K t)/K u 0 .01
0 .03
0 .04
Fig . 11, Difference Aw of the frequencies of the two branches of the surface plasmon dispersion curves after processes b and c of Fig . 10, (K, corresponds to the onset of the splitting .)
after the strongest roughening process (d) and has to he correlated to surface structures of size smaller than 5 mm In the case of the latter process the small oscillations observed on the dispersion curve originate from so-called surface shape resonances at silver clusters, with sizes of 5 nun and greater, built up in the electrochemical cycle, as we have proposed [16j . The problem is to describe the dielectric behavior of a layer of silver bumps of different shapes and its effect on the SP dispersion . This behavior is mainly influenced by the dielectric dipole of the oscillations of the bumps, which couples with the electric field of the SP, giving rise to resonant states . Using the model of hemispheroidal protrusions on a flat surface proposed by Das and Gersten [24] and their normalized data, we have obtained the dipole-type bump resonance as a
too 40
eor~ 20
s 60 40 20
40 700
600
500
A/nm Fig . 12 . Calculated e, and c 2 spectra for a silver
bump
effective film
239
700
600
500
400
T/nm Fig . 13 . Calculated wave-vector shift of a smooth Ag/Al sample relative to the measured (points) and calculated (continuous line) Ag "hump" layer .
function of the semiaxis ratio q of the silver bump in contact with water . Assuming a Gauss distribution P(q) around a mean value q n : P(q)
=-exp
- Q r (q - qo) 2
(2)
and neglecting the intrinsic damping of the bump material, it is possible to describe the imaginary part c h, (w) of the total dielectric function of bump resonances as a superposition of the resonances of each one . The real part c h (w) is then calculated by Kramers-Kronig transformation . Figure 12 shows the dielectric function obtained with the parameters a, q0 and c (c accounts for the concentration of bumps) chosen to locate the C, absorption peaks in the vicinity of the measured structures in the SP dispersion curve, Fig . 10d . The effect of this layer on the SP dispersion is then calculated by eqn . (1) where C h , e b , and d t stand for the dielectric constant and the thickness of the effective film . In Fig. 13 we have drawn the wave vector shift AK, (relative to a calculated smooth 4 .5 nm Ag/Al), observed and calculated for a Ag bump layer . We observe a good agreement between the experimental and the calculated data . Pt/Al/H,/H,S04 SYSTEM
In a previous paper [25] we have shown the sensitivity of A]/SP to changes which occur at the Pt/ambient interface . Measurements have been performed ex situ on bare and Cu-covered Pt, the amount of Cu being monitored by the electrode
2 40
potential in 0 .5 M H,SO,+10 -2 M CuSO, solution . Here we report preliminary data obtained in situ in 0 .5 M solution F1 2 SO, . SP dispersion of Pt electrodes in contact with the solution Figure 14 shows the SP dispersion curve recorded on Pt (3 nm)/Al (100 nm) at E = 0 .85 V immediately after immersion . As we have pointed out for the Ag/Al electrode, the dispersion curve is rather monotonic, indicating the smooth surface of the electrode . Figure l4b shows the dispersion curve recorded (at the same potential) after 1, 2 and 3 potential cycles between 0 and 1 .175 V . We observe a shift of
A/nm
.
. . . 60G
700
s
w Bon
46
47
48
Fig. 14 Surface plasmon dispersion curve of Pt (3 nm)/Al (100 nm)/0 .5 M H,SO, solution . (a) First cycle; (b) second, third and fourth cycles .
241
the curve towards a high wave vector and the appearance of small oscillations which can be due to superficial structural changes induced by the electrochemical treatment . Such experimental features have already been observed on different systems [26] and can be analyzed in connection with SP dispersion on rough surfaces . Indeed, the structure of Pt and gold electrode surfaces can be modified by electrochemical oxidation-reduction cycling [27,28] . Recent analysis of the variation of the LEED spot profiles with electrochemical treatment has shown that excursions to oxidation potentials of Pt single crystals followed by reduction induce the formation of up-and-down steps of monoatomic height with a rather broad distribution of terrace widths in all crystallographic directions . leading to a randomly rough surface [29] . Such structural effects are probably enhanced on stratified electrodes, one oxidation-reduction cycle being sufficient to change the electrode's surface topology . Potential dependence
of the
SP dispersion curve
The sample was immersed at 0 .8 V. The shape of the curve depends on the sweep direction followed during the measurement . Figure 15a shows the shift of AK 1 (E) recorded with the potential decreasing from 0 .8 to 0 .05 V and curve b that with the potential changing in the opposite direction . Both curves are stable for at least two potential cycles . When recorded with decreasing potential . 2iK 1 (E) displays the "classical" behavior observed on gold and silver electrodes [13] . For potentials more negative than E„=0 .15 V, no shift in the dispersion curve is observed . At more positive potentials OK,(E) increases . Curve b, recorded with increasing potential, presents some differences . The plateau observed up to E o is shifted toward a higher wave vector (AK,/K t , - 0 .002) . Kf indicates the appearance of an effective film which does not exist at the same negative-going potentials . A second plateau appears for more positive potentials
15 2 dK t /K o
∎ s
0.9
b as
r a
0 .3 E/V
•t i f t t t t ' 0.5
I
Fig. 15 . Potential dependence of the surface plasmon resonance for the Pt (3 nm)/Al (100 am)/0 .5 M H 2 SO, system . (a) Negative change of electrode potential ; (b) positive change of electrode potential .
242
(E > 0 .45 V) after a region where OK, increases, as during sweep in the opposite direction . As pointed out by Llopis et al . [30], no detailed picture of the double-layer structure on Pt has so far been elaborated, since the problem is complicated by oxygen and hydrogen adsorption . The effect of hydrogen has been proved to be very important and has to be taken into account in our data . Specific adsorption of HSO, has been widely studied on both platinized and smooth Pt electrodes using radiotracers [31,32] and potentiodynamic pulses [33] and from the decrease in surface coverage of the electrode by adsorbed oxygen . Specific adsorption starts around 0 .2 V and increases up to 0 .7 V. The change in concentration through five orders of magnitude hardly affects the potential dependence . Our data, recorded during a negative-going potential change . are in a good agreement with these results . OK, (E) decreases with HSOa surface coverage and remains constant during hydrogen adsorption . HSO4 adsorption decreases linearly and vanishes at 0 .15 V . At this energy, adsorption of a monolayer of hydrogen induces a very small shift (- i0 - `, calculated from eqn, 1) which cannot be detected in our experiments . When recorded with increasing potential (Fig . 15b) . the data cannot be explained by the same process . The positive shift of the wave vector in the low potential region could be accounted for by many processes such as impurity adsorption or formation of a surface Pt-H compound . The former assumption can be ruled out since it does not explain such a sharp change of the wave vector at 0 .05 V . The latter process seems more probable . since hysteresis between data recorded at negative and positive potential changes disappears when the negative potential limit is shifted from 0 .05 to 0 .1 V to prevent hydrogen loading of the electrode . Such behavior is consistent with previous studies [34 36] which have shown the drastic effect of hydrogen on the double-layer properties of Pt electrodes (see Llopis et al . [30]) . However, these preliminary data are still sparse and do not yet allow further analysis . CONCLUSION
The surface plasmon technique has been proved as a suitable probe in the study of the electrode/electrolyte interface . This method is applicable in situ, is non-destructive and is a very sensitive tool for studying surface and film optical properties . However, SP can be excited only at a few material interfaces (mainly Au and Ag in electrochemistry) which restricts its field of application drastically . In this paper we have proposed an extension of this technique by the use of stratified systems where the plasma site (we have chosen Al because of its three free electrons per atom) is split off from the electrode . It is then possible to study any material evaporated onto oxide-free Al in ultra-high vacuum . 'Ib give support to our proposal we have studied Ag/Al and Pt/Al in contact with an electrolyte. The former system has been studied mainly in connection with the electrochemically induced surface roughness involved in phenomena like Surface Enhanced Raman Spectroscopy . Due to its natural instability, the surface topology of stratified electrodes is very sensitive to electrochemical treatment and can be
24 3
changed easily with the positive limit potential which controls the amount of silver dissolved and redeposited onto the electrode during potential cycling . Two kinds of experimental features have been found and linked to slight and strong roughening processes . The second system shows that this technique can be used to study transition metal.electrolyte interfaces, which are of great interest in many electrochemical fields such as electrocatalysts . Even if the preliminary data presented here are sparse, they shown the high sensitivity of the optical properties of platinum electrodes to hydrogen and oxygen . ACKNOWLEDGEMENTS
The experiment on Ag/Al was carried out with Dr . M . Abraham as a guest of the CNRS (1983-1984) . Pt/Al was studied with A . Hadjadj . We thank Dr . M. Costa for his critical reading of the paper. REFERENCES
I D.M . Kolb in V.M . Agranovitch and D .L . Mills (Eds.), Modern Problems in Condensed Matter Sciences- Surface Polaritons, North Holland, Amsterdam, 1982 . Ch 8, p . 299. 2 A . Otto, Surf_ Sc, ., 101 (1980) 99. 3 F. Chao, M. Costa and A . Tadjeddine, Electron . Acta, 24(2) (1981,82) 179 . 4 A .M . Brodsky, L.I . Datkhin and M.I . Urbakh, J. Electroanal . Chem ., 171 (1984) 1 . 5 F. Abeles, J . Phys ., C5 (1977) 67 . 6 7 8 9 10 11 12 13 14
M . Abraham, J.P. Rolland, A . Tadjeddine and G. Schiffinacher, Surf . Set ., 146 (1984) 351 A . Had)adj, G. Hmcelin and A. Tadjeddine . in preparation. A . Tadjeddine, Thin Solid Films, 82 (1981) 103 . AT. Hubbard, RM . Ishikawa and J . Katekaru, J. Electroanal . Chem . . 86 (1978) 271 . J . Clavdier, J. Electroanal. Chem ., 107 (1980) 211 . A . Tadjeddine, J. Electroanal . Chem, 169 (1984) 129 . G . Valette, A . Hamelin and R. Parsons, Z . Phys . Chem ., N.F ., 117 (1978) 71 . A . Tadjeddine, D .M . Kolb and R . Koetz, Surf . Set. . 101 (1980) 277 . A . Tad)eddine and M . Abraham, Phys . Rev . 8, 32 (1985) 5496 . 15 M . Abraham and A. Tadjeddine, submitted . 16 E. Kretchmanm, T.L . Ferrel and J.C. Ashley, Phys . Rev . Lett., 42 (1979) 1312 . 17 T.S . Rahman and A .A. Maradudm, Phys . Rev, B, 21 (1980) 2137 IN G .A . Fanas and A .A . Maradudin, J . Phys., CIO (1983) 375 ; Phys. Rev . B. 28 (1983) 5675 . 19 R. Koetz, H .J . Leverentz and E . Kretschmann, Phys . Lett., 70A (1979) 452. 20 E. Krueger and E. Kretschmann, Phys . Status Solidi B, 76 (1976) 515 . 21 R .H . Ritchie, F .T. Arakawa, J .J . Cowan and R .N . Hanum . Phys. Rev. Lett ., 21 (1968)'1530. 22 AA . Maradudin and W . Zierau, Phys. Rev. B, 14 (1976) 484. 23 F. Toigo, A . Marvin- V. Celh and N .R . Hill, Phys . Rev . B . 15 (1977) 5618 . 24 P.C . Das and J .1. Gersten, Phys . Rev . B, 25 (1982) 6281 . 25 A . Tadjeddme, M . Abraham, A . Hadjadj and J.P. Rolland, Surf. Sci ., 162 (1985) 809 . 26 A . Tadjeddine and D .M . Kolb, J. Electroanal . Chem .. 111 (1980) 119. 27 S . Gilman, J. Electroanal. Chem., 9 (1965) 276 28 F. Chao, M . Costa and A . Tadjeddine . Surf. Sci . . 46 (1974) 265; CR . Acad . Sct . (Paris), 272 (1971) 821 . 29 F.T . Wagner and P .N . Ross, Surf. Sci ., 160 (1985) 305 .
244 30 J.F. Llopis, I .M . Tordesillas and F . Colom in A.J . Bard (Ed .), Encyclopedia of Electrochemistry of Elements. Vol . 6 . Marcel Dekker . New York . Basel, 1976. p . 169 . 3l I .1 . Labkovskaya, V .I . Luk'yanicheva and V .S . Bagotzky, Sov . Electrochcm . . 5 (1969) 535 . 32 C Horany,, J. Soft and F . Nagy, J . Electroanal . Chem ., 31 (1971) 95 . 33 V .S . Bagotzky, Y .B . Vassilvev and J .N . Pirtskmalava, J . Electroanal . Chem ., 27 (1970) 31 . 34 'I .B . Warner and S. Schuldiner, Electrochim . Acta . 11 (1966) 307 . 35 D .J. Bendamel and F .G . Will, J . Electrochem. Soc . . 114 (1967) 909 36 J.O'M. Bockris, S .D . Argade and E. Gilead,, Electrochim. Acta, 14 (1969) 1259 .