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Impedance characteristics of poly-o-aminophenol electrodes
Ekcmchtmica Acta, Vol. 40. No. 8. pp. 1037-1040, 1995 Copyright 0 1995 l?lscvia Bcicma Ltd. Printed in Great Britain. AU ri&tt# tucrwd 0013~4686/9s 59.50 + 0.00
Pergaman
IMPEDANCE CHARACTERISTICS OF POLY-OAMINOPHENOL ELECTRODES C. BARBERO,*~R. I. TUCCFZRI,~ D. POSADAS,~!~ J. J. SILBER~and L.
SERENO~
t lnstituto
de Investigaciones Fisicoquimicas Tebricas y Aplicadas (INIFTA), Fact&ad de Ciencias Exactas, Universidad National de La Plata, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina 1 Universidad National de Rio Cuarto, Departamento de Quimica y Fisica, Estafeta Postal No. 9, 5800, Rio Cuarto, Argentina (Received 6 April 1994) Akatraet-The impedance characteristics of poly-e-aminophenol film electrodes in NaClO, 0.4M + HCIO, 0.1 M electrolyte have been measured in the frequency range 0.01 c f < 10” Hz and at two different thicknesses. The experimental results can be interpreted through a simple charge transfer resistance in parallel with a constant, capacity at high frequencies and the redox capacity in series with the fdm resistance at low frequencies. The analysis of the impedance response allows to the electrochemical rate constant, the concentration of redox centers in the film, the film conductivity and the diffusion coelIicient of the elections to be determined. Key words
: impedance, poly-o-aminophenol,
modified electrodes.
1. INTRODUCTION work In previous we have studied the electrochemical[ 11 and optical[2] properties of poly-o-aminophenol Electrochemical (POAP). impedance spectroscopy (EIS) has proven to be a valuable technique for determining important characteristics of electrochemically active polymers (see Ref. 3 for a review). Since POAP differs both in the electrochemical response as well as in structure from the more investigated polyaniline (PANI) it seems interesting to study the first by EIS in order to determine its characteristic electrochemical parameters.
2. EXPERIMENTAL o-Aminophenol (Fluka) was purified as described previously[l]. Water was obtained from a Mini-Q (Millipore). NaClO, and HClO, (Merck, ar grade) were used without further purification. The poly-o-aminophenol (POAP) modified electrodes were prepared as previously reported[2]. Two different film thickness, d, were used: 30 and 300 nm. The films were grown to the approximate desire thickness by using the reduction charge vs. ellipthickness reported sometric working curve elsewhere[2]. The base working electrode was a Platinum wire (0.52 cm long, o.d. 0.05 cm). A large area Pt counter electrode was employed. The reference electrode was
a hydrogen electrode. The electrolytic solution was 0.1 M HClO, + 0.4 M NaClO, . Impedance measurements at constant applied potential were carried out with a Solartron Model 1286 Potentiostat and a Solartron Model 1250 Frequency Response Analyzer. Data were acquired at seven discrete frequencies, j, per decade in the range 0.01 Hz
3. RESULTS
AND
DISCUSSION
The voltammetric response of the POAP film is shown in Fig. 1 for d = 30nm. The voltammogram shows the characteristic response of a reversible redox film as discussed elsewere[l, 21. It should be emphasized here the appearance of only one voltammetric peak for POAP as opposed to the two main peaks in PANIC41 and poly-o- toluidine (POT)[5].
-80 -0.1
* Present address: Paul Scherrer Institut, Wtirlinggen und Villigen, CH-5232, Villigen, Switzerland. $ Author to whom correspondence should be addressed.
I 0.1
I 0.2
I 0.3
I 0.4
I 0.5
I 0.6
c 0.7
E I V (nhe) Fig. 1. Voltammetric 1037
Et? bO:l-H
I 0
response of POAP, v = 0.034 V s-
C. BARBEROet al.
1038
Impedance measurements were made in the potential range between 0.125 < E < 0.7 V vs. nhe. Typical Nyquist diagrams at several potentials for d = 30nm are shown in Fig. 2. The 2” vs. z’ plots show the response characteristic of a redox couple confined to a finite volume[3, 6, 71. That is, a semi-circle at high frequencies and an increase at low frequencies of the imaginary part associated with the redox capacity. In this case the Z” vs. 2’ plot (Fig. 2), at high w, shows a depressed semi-circle. Depressed semi-circles have been found in alkali-metal doped polyacetylene electrodes[8] and in polypyrrole in acetonitrile[9]. These authors fit their results by shifting the center
of the semi-circle down the real axis and interpreting them in terms of the porosity of the film (see also Ref. 10). The influence of the thickness on the impedance response is shown in Fig. 3. Changing the film thickness apparently does not change the semi-circle radius. As expected, the pseudo-capacitive rise of Z” at low frequencies occurs at larger z’ values for thicker films. In turn this means that the resistance of the film at low frequencies increases with d. 3.1. High frequency parameters 3.1.1. The resistance of the electrolyte, R,. From the extrapolation of the high frequency data to the real axis, the resistance at high frequencies, R, was obtained. Since these values showed no significant potential dependence and were very close to those measured in the absence of the polymer, they were interpreted as the resistance of the electrolyte. No high frequency resistance of the film could be detected within the experimental error. 3.1.2. The charge transfer resistance, e[ll]. Experimental data were fitted to a semi-circle whose center could lie down the real axis. The fit was baaed on successive approximations by least square fitting to a linearized equation of a circle[12]. The output of the fit were the coordinates of the semi-circle’s center. From them the charge transfer resistance, 0, 0 = 2RT(eSb + e-‘*)/An2F2k,,
2
I
I
4
6
,
ZlkR
h C,
(1)
was obtained. p and u are the charge transfer coefflcients for the anodic and cathodic partial processes, respectively, A the electrode area, k,., the standard rate constant for the charge transfer (ems-‘), C, = Co + C, the sum of the concentrations of the oxidized and reduced forms, respectively, and 4 = nF(E -E,)/RT, EO being the standard potential of the redox couple. A plot of 0 as a function of potential is shown in Fig. 4. The curve is symmetric with respect to E, . The 0 values for the different thickness lie on a single curve. No thickness dependence of the semicircle radius was apparent. This points to the
+ +
.
+
0 0
+
ca
+
P kl
+
. . .
+
.
63 y +:.%OHz f .+ l 0
2
4
6
8
Fig. 2. Nyquist diagrams of POAP at different potentials: (a) potential cathodic to the E, = 0.34V---(m) 0.1 V, (+) 0.125V, (A) 0.2 V, (0) 0.250,(0) 0.34V; and (b) anodic to the E,-(O) 0.34V, (0) 0.35V, (A) 0.375V, (x) 0.4V, (+) 0.5 V, (V) 0.6 V.
+ . +* I
I I
2 X/kil
Fig. 3. Nyquist diagrams for POAP at different thickness. (+)d=30nm;(e)d=300nm;E=0.375V
Impedance characteristics of poly-o-aminophenol
0
0.1
0.2
0.3
E I
0.4
0.5
1039
electrodes
0.6
V (nhe) d = 30nm; (V)
Fig. 5. Redox capacity, C,, , of POAF films as a function of potential. (0) d = 30 nm, (v) 300 nm.
absence of mass transport contributions to the impedance at frequencies within the semi-circle region. With the values of Cr from previous work[l, 131 and assuming j3 = tl = 0.5, k,,, was obtained from equation (1). It value turns out to be independent of E (Table 1) and is smaller than those found for other redox polymers[6, 7, 14-161. Even though ks,h is rather small, because D, is very small (see below), the voltammetric response shows a reversible behaviour. 3.1.3. The double layer capacitance at high frequencies, C,, C,, was determined from a linear fitting of (Z”) ’ vs. w in the frequency region corresponding to the first quadrant of the semi-circle. These values are roughly independent of E and d (Table 1).
which is in close agreement with CT = 4.7 x 10-3molcm-3 obtained previously[lJ. Note that although the C,, vs. E curve depends on d, C, results independent of it. The intersection of the extrapolation of the low frequency values of Z” with the real axis defines
Fig. 4. Potential
dependence
of 8. (0)
300nm.
3.2. Film parameters at lowfrequencies 3.2.1. The redox capacity of theJilm, C,,. From the slope of the -Z” vs. w- ’ plot at sufficiently low frequencies, the redox capacity of the polymer, C,,, can be obtainedC6, 171. These values are plotted as a function of the electrode potential in Fig. 5 for the two thickness investigated. C,, increases with d. However, the thickness dependence of C,, is not linear (Fig. 5). As d increases the shape of the C,, vs. E plot broadens and flattens. This is characteristic of departures from the ideal behaviour of the redox centers in
RJ173: R,=R,+O+R,f,
(3)
R, is the polymer resistance at low frequencies. A plot of R, as a function of potential is shown in Fig. 6. R,f has been related to the polymer conductivity, a,r[7],
where
bir = d/(&r A).
(4)
Thus the polymer film conductivity should show a potential dependence similar to that of Fig. 6. At E, , qf = 4.55 + 0.2 x lo-‘R-l cm-‘, for both thickness. In this respect POAP differs from other aromatic amines derived polymer films such as PANI
8-
the film[l, 18, 191. The total concentration
of redox sites, C, can be obtained from the integral of C,, over the whole potential range: C, = l/AFd
C,, dE. (2) s From equation (2) a value of CT = 4.8 x 10~3molcm-3 for both thickness is obtained, Table 1. Average parameters resulting from the fit at high frequencies at different potentials
2.8 + 0.5
2.3 + 0.4
8+2
O-
0.1
0.2
0.3
0.5
0.5
0.6
E I V (nhe)
Fig. 6. Low frequency resistance, R,, of the polymer as a function of potential from the impedance measurements, (0) d = 30 nm and (W) d = 300 nm.
C. BARBEROet al.
1040
of potential and film thickness. No high frequency resistance could be detected. The analysis of the pseudo-capacitive behavior at low frequencies allowed to determine the concentration of redox sites and to estimate the low frequency conductivity. The latter is small and has a minimum at the redox couple reversible potential.
I’i;j 0
0.2
0.4
0.6
E I v (n/w)
Fig. 7. Potential
dependence of D, calculated equation (5).
according
to
REFERENCES J. J. Silber and L. Sereno, J. electroanal. Chem. 263, 333 (1989); 291, 81 (1990). 2. C. Barbero, J. Zerbino, L. Sereno and D. Posadas, Electrochim. Acta, 32,693 (1987). 3. M. M. Musiani, .&=crrochim. Acta 35, 1665 (1990). 1. C. Barbero,
and POTCZO]. POAP shows a much lower conductivity as compared to PAN1 and POT. Further, POAP only show a conductivity minimum near E, as compared with the shallow minimum shown by PANI and POT in the potential region comprised between the two main oxidation peaks in their respective voltammetric response. This fact should be related to the existence of the plaronic structures in that potential region for PANI and POT. It has been shown by absorption spectroscopy in the near ir-uis region that for POAP these polaronic structures have a transient existence, peaking at E,, . According to Chidsey and MurrayC18-J (see also Ref. [73 for a more general equation) the diffusion coefficient of the electrons, D,, in the polymer can be obtained from u,r and C,,: D, = e&r.
(5)
Previous workers[lrl, 181 have obtained D, by this route and find it to be potential dependent. However, in this case a value of D, = 1.3 x 10-r’ cm* s- ’ results which is nearly independent of potential (Fig. 7). This value is only slightly smaller than that obtained in our previous voltammetric studies[ 11. 4. CONCLUSIONS The electrochemical impedance spectrum of POAP shows a semi-circle loop a high frequency independent of the film thickness and dependent of potential. This can be assigned to a charge transfer reaction in parallel with a capacitance independent
4. E. M. Genies, M. Lapkowski and C. Tsitavis, New J. Chem. 12, 181 (1988). 5. M. Lecferc, J. Guay and L. H. Dao, 1. Electroanal.
Chem. 251,21 (1988). 6. G. Gabrielli,
0. Haas and H. Takenouti, .I. appl. Electrochem. 17, 82 (1987). 7. G. Gabrielli, H. Takenouti, 0. Haas and A. Tsukada, J. electroanal. Chem. 302, 59 (199 1). 8. T. R. Jow and L. W. Shacklette, 1. electrochem. Sot. 135,54[(1988). 9. R. C. hf. Jakobs,
J. J. J. Janssen
and E. Barendrecht,
Rec. Trav. Chim. Pays-Bas, 103,275 (1984). 10. S. Iseki, K. Ohashi and S. Nagaura, Electrochim. Acta, 17, 2249 (1972). 11. M. Sluyters-Bebach and J. H. Sfuyters, Electroanal. Chem. 4,66 (1970). 12. E. Wittaker and G. Robinson, The Calculus of Obseroations: A Treatise on Numerical Mathematics, p. 209. Blackie, London (1948). 13. R. I. Tucceri, C. Barbero, J. J. Silber, D. Posadas and L. Sereno in preparation. 14. T. B. Hunter,-P. S. Tyler, W. H. Smyrl and H. S. White, J. electrochem. Sot. 134. 2198 (1987). 15. G. Gabrielli, F. Huet, M. Keddarn and 0. Haas, Electrochim. Acta 33, 1371 (1988). 16. B. Lindholm, M. Sharp and R. D. Armstrong, J. electroanal. Chem. 235, 169 ( 1987). 17. C. Ho, I. D. Raistrick and R. A. Huggins, J. electrothem. Sot. 127,343 (1980). 18. C. E. D. Chidsey and R. W. Murray, J. phys. Chem. 90, 1479 (1986). 19. A. P. Brown and F. C. Anson, Anal. Chem. 49, 1589 (1977). 20. P. Ocon and P. Herrasti, New J. Chem. 16, 501 (1992).
Pergaman
IMPEDANCE CHARACTERISTICS OF POLY-OAMINOPHENOL ELECTRODES C. BARBERO,*~R. I. TUCCFZRI,~ D. POSADAS,~!~ J. J. SILBER~and L.
SERENO~
t lnstituto
de Investigaciones Fisicoquimicas Tebricas y Aplicadas (INIFTA), Fact&ad de Ciencias Exactas, Universidad National de La Plata, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina 1 Universidad National de Rio Cuarto, Departamento de Quimica y Fisica, Estafeta Postal No. 9, 5800, Rio Cuarto, Argentina (Received 6 April 1994) Akatraet-The impedance characteristics of poly-e-aminophenol film electrodes in NaClO, 0.4M + HCIO, 0.1 M electrolyte have been measured in the frequency range 0.01 c f < 10” Hz and at two different thicknesses. The experimental results can be interpreted through a simple charge transfer resistance in parallel with a constant, capacity at high frequencies and the redox capacity in series with the fdm resistance at low frequencies. The analysis of the impedance response allows to the electrochemical rate constant, the concentration of redox centers in the film, the film conductivity and the diffusion coelIicient of the elections to be determined. Key words
: impedance, poly-o-aminophenol,
modified electrodes.
1. INTRODUCTION work In previous we have studied the electrochemical[ 11 and optical[2] properties of poly-o-aminophenol Electrochemical (POAP). impedance spectroscopy (EIS) has proven to be a valuable technique for determining important characteristics of electrochemically active polymers (see Ref. 3 for a review). Since POAP differs both in the electrochemical response as well as in structure from the more investigated polyaniline (PANI) it seems interesting to study the first by EIS in order to determine its characteristic electrochemical parameters.
2. EXPERIMENTAL o-Aminophenol (Fluka) was purified as described previously[l]. Water was obtained from a Mini-Q (Millipore). NaClO, and HClO, (Merck, ar grade) were used without further purification. The poly-o-aminophenol (POAP) modified electrodes were prepared as previously reported[2]. Two different film thickness, d, were used: 30 and 300 nm. The films were grown to the approximate desire thickness by using the reduction charge vs. ellipthickness reported sometric working curve elsewhere[2]. The base working electrode was a Platinum wire (0.52 cm long, o.d. 0.05 cm). A large area Pt counter electrode was employed. The reference electrode was
a hydrogen electrode. The electrolytic solution was 0.1 M HClO, + 0.4 M NaClO, . Impedance measurements at constant applied potential were carried out with a Solartron Model 1286 Potentiostat and a Solartron Model 1250 Frequency Response Analyzer. Data were acquired at seven discrete frequencies, j, per decade in the range 0.01 Hz
3. RESULTS
AND
DISCUSSION
The voltammetric response of the POAP film is shown in Fig. 1 for d = 30nm. The voltammogram shows the characteristic response of a reversible redox film as discussed elsewere[l, 21. It should be emphasized here the appearance of only one voltammetric peak for POAP as opposed to the two main peaks in PANIC41 and poly-o- toluidine (POT)[5].
-80 -0.1
* Present address: Paul Scherrer Institut, Wtirlinggen und Villigen, CH-5232, Villigen, Switzerland. $ Author to whom correspondence should be addressed.
I 0.1
I 0.2
I 0.3
I 0.4
I 0.5
I 0.6
c 0.7
E I V (nhe) Fig. 1. Voltammetric 1037
Et? bO:l-H
I 0
response of POAP, v = 0.034 V s-
C. BARBEROet al.
1038
Impedance measurements were made in the potential range between 0.125 < E < 0.7 V vs. nhe. Typical Nyquist diagrams at several potentials for d = 30nm are shown in Fig. 2. The 2” vs. z’ plots show the response characteristic of a redox couple confined to a finite volume[3, 6, 71. That is, a semi-circle at high frequencies and an increase at low frequencies of the imaginary part associated with the redox capacity. In this case the Z” vs. 2’ plot (Fig. 2), at high w, shows a depressed semi-circle. Depressed semi-circles have been found in alkali-metal doped polyacetylene electrodes[8] and in polypyrrole in acetonitrile[9]. These authors fit their results by shifting the center
of the semi-circle down the real axis and interpreting them in terms of the porosity of the film (see also Ref. 10). The influence of the thickness on the impedance response is shown in Fig. 3. Changing the film thickness apparently does not change the semi-circle radius. As expected, the pseudo-capacitive rise of Z” at low frequencies occurs at larger z’ values for thicker films. In turn this means that the resistance of the film at low frequencies increases with d. 3.1. High frequency parameters 3.1.1. The resistance of the electrolyte, R,. From the extrapolation of the high frequency data to the real axis, the resistance at high frequencies, R, was obtained. Since these values showed no significant potential dependence and were very close to those measured in the absence of the polymer, they were interpreted as the resistance of the electrolyte. No high frequency resistance of the film could be detected within the experimental error. 3.1.2. The charge transfer resistance, e[ll]. Experimental data were fitted to a semi-circle whose center could lie down the real axis. The fit was baaed on successive approximations by least square fitting to a linearized equation of a circle[12]. The output of the fit were the coordinates of the semi-circle’s center. From them the charge transfer resistance, 0, 0 = 2RT(eSb + e-‘*)/An2F2k,,
2
I
I
4
6
,
ZlkR
h C,
(1)
was obtained. p and u are the charge transfer coefflcients for the anodic and cathodic partial processes, respectively, A the electrode area, k,., the standard rate constant for the charge transfer (ems-‘), C, = Co + C, the sum of the concentrations of the oxidized and reduced forms, respectively, and 4 = nF(E -E,)/RT, EO being the standard potential of the redox couple. A plot of 0 as a function of potential is shown in Fig. 4. The curve is symmetric with respect to E, . The 0 values for the different thickness lie on a single curve. No thickness dependence of the semicircle radius was apparent. This points to the
+ +
.
+
0 0
+
ca
+
P kl
+
. . .
+
.
63 y +:.%OHz f .+ l 0
2
4
6
8
Fig. 2. Nyquist diagrams of POAP at different potentials: (a) potential cathodic to the E, = 0.34V---(m) 0.1 V, (+) 0.125V, (A) 0.2 V, (0) 0.250,(0) 0.34V; and (b) anodic to the E,-(O) 0.34V, (0) 0.35V, (A) 0.375V, (x) 0.4V, (+) 0.5 V, (V) 0.6 V.
+ . +* I
I I
2 X/kil
Fig. 3. Nyquist diagrams for POAP at different thickness. (+)d=30nm;(e)d=300nm;E=0.375V
Impedance characteristics of poly-o-aminophenol
0
0.1
0.2
0.3
E I
0.4
0.5
1039
electrodes
0.6
V (nhe) d = 30nm; (V)
Fig. 5. Redox capacity, C,, , of POAF films as a function of potential. (0) d = 30 nm, (v) 300 nm.
absence of mass transport contributions to the impedance at frequencies within the semi-circle region. With the values of Cr from previous work[l, 131 and assuming j3 = tl = 0.5, k,,, was obtained from equation (1). It value turns out to be independent of E (Table 1) and is smaller than those found for other redox polymers[6, 7, 14-161. Even though ks,h is rather small, because D, is very small (see below), the voltammetric response shows a reversible behaviour. 3.1.3. The double layer capacitance at high frequencies, C,, C,, was determined from a linear fitting of (Z”) ’ vs. w in the frequency region corresponding to the first quadrant of the semi-circle. These values are roughly independent of E and d (Table 1).
which is in close agreement with CT = 4.7 x 10-3molcm-3 obtained previously[lJ. Note that although the C,, vs. E curve depends on d, C, results independent of it. The intersection of the extrapolation of the low frequency values of Z” with the real axis defines
Fig. 4. Potential
dependence
of 8. (0)
300nm.
3.2. Film parameters at lowfrequencies 3.2.1. The redox capacity of theJilm, C,,. From the slope of the -Z” vs. w- ’ plot at sufficiently low frequencies, the redox capacity of the polymer, C,,, can be obtainedC6, 171. These values are plotted as a function of the electrode potential in Fig. 5 for the two thickness investigated. C,, increases with d. However, the thickness dependence of C,, is not linear (Fig. 5). As d increases the shape of the C,, vs. E plot broadens and flattens. This is characteristic of departures from the ideal behaviour of the redox centers in
RJ173: R,=R,+O+R,f,
(3)
R, is the polymer resistance at low frequencies. A plot of R, as a function of potential is shown in Fig. 6. R,f has been related to the polymer conductivity, a,r[7],
where
bir = d/(&r A).
(4)
Thus the polymer film conductivity should show a potential dependence similar to that of Fig. 6. At E, , qf = 4.55 + 0.2 x lo-‘R-l cm-‘, for both thickness. In this respect POAP differs from other aromatic amines derived polymer films such as PANI
8-
the film[l, 18, 191. The total concentration
of redox sites, C, can be obtained from the integral of C,, over the whole potential range: C, = l/AFd
C,, dE. (2) s From equation (2) a value of CT = 4.8 x 10~3molcm-3 for both thickness is obtained, Table 1. Average parameters resulting from the fit at high frequencies at different potentials
2.8 + 0.5
2.3 + 0.4
8+2
O-
0.1
0.2
0.3
0.5
0.5
0.6
E I V (nhe)
Fig. 6. Low frequency resistance, R,, of the polymer as a function of potential from the impedance measurements, (0) d = 30 nm and (W) d = 300 nm.
C. BARBEROet al.
1040
of potential and film thickness. No high frequency resistance could be detected. The analysis of the pseudo-capacitive behavior at low frequencies allowed to determine the concentration of redox sites and to estimate the low frequency conductivity. The latter is small and has a minimum at the redox couple reversible potential.
I’i;j 0
0.2
0.4
0.6
E I v (n/w)
Fig. 7. Potential
dependence of D, calculated equation (5).
according
to
REFERENCES J. J. Silber and L. Sereno, J. electroanal. Chem. 263, 333 (1989); 291, 81 (1990). 2. C. Barbero, J. Zerbino, L. Sereno and D. Posadas, Electrochim. Acta, 32,693 (1987). 3. M. M. Musiani, .&=crrochim. Acta 35, 1665 (1990). 1. C. Barbero,
and POTCZO]. POAP shows a much lower conductivity as compared to PAN1 and POT. Further, POAP only show a conductivity minimum near E, as compared with the shallow minimum shown by PANI and POT in the potential region comprised between the two main oxidation peaks in their respective voltammetric response. This fact should be related to the existence of the plaronic structures in that potential region for PANI and POT. It has been shown by absorption spectroscopy in the near ir-uis region that for POAP these polaronic structures have a transient existence, peaking at E,, . According to Chidsey and MurrayC18-J (see also Ref. [73 for a more general equation) the diffusion coefficient of the electrons, D,, in the polymer can be obtained from u,r and C,,: D, = e&r.
(5)
Previous workers[lrl, 181 have obtained D, by this route and find it to be potential dependent. However, in this case a value of D, = 1.3 x 10-r’ cm* s- ’ results which is nearly independent of potential (Fig. 7). This value is only slightly smaller than that obtained in our previous voltammetric studies[ 11. 4. CONCLUSIONS The electrochemical impedance spectrum of POAP shows a semi-circle loop a high frequency independent of the film thickness and dependent of potential. This can be assigned to a charge transfer reaction in parallel with a capacitance independent
4. E. M. Genies, M. Lapkowski and C. Tsitavis, New J. Chem. 12, 181 (1988). 5. M. Lecferc, J. Guay and L. H. Dao, 1. Electroanal.
Chem. 251,21 (1988). 6. G. Gabrielli,
0. Haas and H. Takenouti, .I. appl. Electrochem. 17, 82 (1987). 7. G. Gabrielli, H. Takenouti, 0. Haas and A. Tsukada, J. electroanal. Chem. 302, 59 (199 1). 8. T. R. Jow and L. W. Shacklette, 1. electrochem. Sot. 135,54[(1988). 9. R. C. hf. Jakobs,
J. J. J. Janssen
and E. Barendrecht,
Rec. Trav. Chim. Pays-Bas, 103,275 (1984). 10. S. Iseki, K. Ohashi and S. Nagaura, Electrochim. Acta, 17, 2249 (1972). 11. M. Sluyters-Bebach and J. H. Sfuyters, Electroanal. Chem. 4,66 (1970). 12. E. Wittaker and G. Robinson, The Calculus of Obseroations: A Treatise on Numerical Mathematics, p. 209. Blackie, London (1948). 13. R. I. Tucceri, C. Barbero, J. J. Silber, D. Posadas and L. Sereno in preparation. 14. T. B. Hunter,-P. S. Tyler, W. H. Smyrl and H. S. White, J. electrochem. Sot. 134. 2198 (1987). 15. G. Gabrielli, F. Huet, M. Keddarn and 0. Haas, Electrochim. Acta 33, 1371 (1988). 16. B. Lindholm, M. Sharp and R. D. Armstrong, J. electroanal. Chem. 235, 169 ( 1987). 17. C. Ho, I. D. Raistrick and R. A. Huggins, J. electrothem. Sot. 127,343 (1980). 18. C. E. D. Chidsey and R. W. Murray, J. phys. Chem. 90, 1479 (1986). 19. A. P. Brown and F. C. Anson, Anal. Chem. 49, 1589 (1977). 20. P. Ocon and P. Herrasti, New J. Chem. 16, 501 (1992).