Langmuir 1990,6, 371-376
371
Passivation of Pinholes in Octadecanethiol Monolayers on Gold Electrodes by Electrochemical Polymerization of Phenol Harry 0. Finklea,' Daniel A. Snider, and John Fedyk Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045 Received March 17,1989. In Final Form: August 10, 1989 An organized monolayer of octadecanethiol on a gold electrode strongly inhibits faradaic reactions except at pinholes in the monolayer. For simple outer-sphere redox couples, the monolayer-coated electrode behaves like a microelectrode array, with pinholes acting as the microelectrodes. The average size and separation of the pinholes can be estimated by fitting the experimental cyclic voltammograms with simulated voltammograms for a microarray electrode. The pinholes are selectively and permanently passivated by electrochemical polymerization of phenol in dilute sulfuric acid. The deposition of poly(phenylene oxide) suppresses the pinhole currents at low overpotential, but residual faradaic currents become visible at large overpotential. The residual currents are assigned to electron tunneling between the electrode and molecules which partially penetrate the monolayer.
Introduction Because organized monolayers have important applications in electronic and optical devices,' there is a need for characterization methods which probe the microstructure of the monolayer, such as the size and distribution of defects in the monolayer. Many established methods like ellipsometry, wetting contact angles, and grazing angle infrared spectroscopy only provide information about the average properties of the monolayer. In contrast, diffusion of molecules through a monolayer is very sensitive to molecular packing, thermal motion, and especially the presence of defects in the structure. Diffusion through an organized monolayer is readily measured if the organized monolayer is deposited on an electrode surface and the voltammetry of solution redox couples is observed. Organized monolayers with sufficient stability for electrochemical experiments have been made by self-assembly of long-chain alkanethiols, octadecyltrichlorosilane, and amphiphilic viol0 and by Langmuir- Blodgett deposition methods.18-26 Octadecanethiol (C,,SH) and silane monolayers are strongly blocking to many redox (1) Swalen, J. D.; Allara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelavchivili, J.; McCarthy, T. J.; Murray, R.; Pease, R. F.; Rabolt, J. F.; Wynne, K. J.; Yu, H. Langmuir 1987,3,932. (2) Finklea, H. 0.; Robinson, L. R.; Blackburn, A.; Richter, B.; Allara, D.; Bright, T. Langmuir 1986,2,239. (3) Finklea, H. 0.; Avery, S.; Lynch, M.; Furtach, T. Langmuir 1987. - - - ., s. -,409. . - -. (4) Sabatini, E.; Rubinstein, I.; Maoz, R.; Sagiv, J. J. Electroanal. Chem. 1987,219,365. (5) Sabatini, E.; Rubinstein, I. J . Phys. Chem. 1987,91,6663. (6) Rubinstein. I.: Steinbern. -. S.:. Tor.. Y.:. Shanzer. A,: Saniv, J. Nature 1988.332. 426.' (7) Port& M: D.; Bright, T. B.; Allara, D.; Chidsey, C. E. D. J. Am. Chem. SOC. 1987,109,3559. (8) Miller, C. J.; Majda, M. J . Am. Chem. SOC.1986,108,3118. (9) Widrig, C. A.; Majda, M. Anal. Chem. 1987,59,754. (10) Widria, C. A.; Miller, C. J.; Majda, M. J. Am. Chem. SOC.1988, 110,2009. (11) Miller, C. J.; Widrig, C. A.; Charych, D. H.; Majda, M. J . Phys. Chem. 1988,92,1928. (12) Goss, C. A.; Miller, C. J.; Majda, M. J. Phys. Chem. 1988,92, 1937. (13) Sugawara, M.; Kojima, K.; Sazawa, H.; Umezawa, Y. Anal. Chem. 1987,59,2842. (14) Facci, J. S.; Falcigno, P. A.; Gold, J. M. Langmuir 1986,2,732. (15) Facci, J. S.Langmuir 1986,3,525. (16) Daifuku, H.; Aoki, K.; Tokuda, K.; Matusda, H. J . Electroanal. Chem. 1982,140,179. .
.
I
0743-7463/90/2406-0371$02.50/0
couples in aqueous electrolyte^.^-' Sabatini et al.4*5have demonstrated that the monolayer-coated electrode behaves like a microelectrode array. Pinholes in the organized monolayer function effectively as microelectrodes. Pinholes can be characterized by several electrochemical methods. The total area fraction of pinholes can be measured by (1)oxide stripping of the gold substrate after anodization in dilute sulfuric acid and (2) faradaic impedance of a redox couple at zero overpotential. Depending on the gold substrate, thiol monolayers exhibit area fractions of pinholes ranging from to lo6.%' We describe here how the average radii and separation of the pinholes can be determined from a quantitative fit of cyclic voltammograms (CVs) of a reversible redox couple to the theory of Amatore et al.26 In order to explore the properties of the ClsSH monolayer away from the pinholes, the pinholes must be selectively passivated. Phenol oxidation in a q ~ e o u s ~ 'or -~~ n o n a q u e ~ u s ~ Oelectrolytes -~~ produces a blocking layer (17) Daifuku, H.; Aoki, K.; Tokuda, K.; Matusda, H. J. Electroanal. Chem. 1985,183,l. (18) Park, S. G.; Aoki, K.; Tokuda, K.; Matusda, H. J. Electroanal. Chem. 1986,195,157. (19) Daifuku, H.; Yoshmura, I.; Hirata, I.; Aoki, K.; Tokuda, K.; Matusda, H.J. Electroanal. Chem. 1986,199,47. (20) Fujihira, M.; Poosittisak, S. J . Electroanal. Chem. 1986,199, 481. (21) Fujihira, M.; Araki, T. J.Electroanal. Chem. 1986,205,329. (22) Memming, R. Discuss. Faraday SOC. 1974,58,261. (23) Arden, W.; Fromherz, P. Ber. Bunsen-Ges. Phys. Chem. 1978, 82,868. (24) Fromherz, P.; Arden, W. J . Am. Chem. SOC.1980,102,6211. (25) Sato, H.; Kawasaki, M.; Kasatani, K.; Higuchi, Y.; Azuma, T.; Nishiyama, Y. J. Phys. Chem. 1988,92,754. (26) Amatore, C.; SavBant, J. M.; Tessier, D. J. Electroanal. Chem. 1983,147,39. (27) Koile, R. C.; Johnson, D. C. Anal. Chem. 1979,51,741. (28) Bejerano, T.;Gileadi, E. J. Electroanal. Chem. 1970,27,69. (29) Zeigerson, E.;Gileadi, E. J . Electroanal. Chem. 1970,28, 421. (30) Finklea, H. 0.; Vithanage, R. S. J. Electroanal. Chem. 1984, 161,283. (31) Bruno, F.; Pham, M.-C.; Dubois, J.-E. Electrochim. Acta 1970, 22,451. (32) Pham, M.-C.; Lacaze, P.-C.; Dubois, J.-E. J. Electroanal. Chem. 1978,86,147. (33) Pham, M X . ; Dubois, J.-E.; Lacaze, P.-C. J. Electroanal. Chem. 1979,99,331. (34) Pham,M.-C.;Tourillon,G.;Lacaze,P.-C.;Dubois, J.-E. J.Electroanal. Chem. 1980,111,385. (35) Dubois, J.-E.; Lacaze, P.4.; Pham, M.4. J. Electroanal. Chem. 1981,117,233. 0 1990 American Chemical Society
372 Langmuir, Vol. 6, No. 2, 1990
of poly(pheny1ene oxide) (PPO). On a C,,SH-coated electrode, deposition of PPO is expected to occur predominately at the pinhole sites. Rubinstein et al.' reported that oxidation of 1-naphthol resulted in the passivation of pinholes in thiol and sulfide monolayers on gold. We show that the pinholes can be selectively and permanently passivated by phenol oxidation in dilute sulfuric acid. The residual currents that appear when the pinholes are blocked are assigned to electron tunneling to molecules which have partially penetrated the monolayer.
Experimental Section Gold mirror electrodes (lo00 A of gold on float glass with 50 A of TiO, binder) were purchased from Evaporated Metal Films, Inc. The electrodes were cleaned by sonication in chloroform, immersion in hot (>lo0 "C) concentratedsulfuric acid, and cyclic voltammetry in 0.5 M H,SO, between 0.5 and 1.4 V vs SCE at 0.1 V/s. Polycrystalline gold flags (0.8 X 0.8 cm) were heated to incandescence in an air-gas flame. Octadecanethiol monolayers were formed by immersion of the clean gold electrode in a 10-50 mM solution of the thiol in chloroform (HPLC grade, Fisher). After ca. 1 h, the electrode was removed and rinsed with a stream of clean chloroform. Cyclic voltammograms were recorded by using a locally constructed potentiostat connected to a data acquisition system (Zenith PC with a Metrabyte DASH-16 interface board running MacMillan MYSTANT+ software). Ellipsometry was performed at a 70' angle of incidence on a manual nulling ellipsometer with a HeNe laser source. The ellipsometric parameters Q and A were measured on each gold mirror immediately before and after monolayer deposition. Typical values for Q and A for a clean gold mirror are 43.5-43.6' and 108-110". Film thicknesses were calculated from changes in A by assuming an isotropic film with an index of refraction of 1.5. Typically,the C,,SH monolayers were 19-22 thick (A decreased by ca. 2"). However, Q decreased by ca. 0.lo,which is opposite to the change predicted for a transparent film. A better fit to the changes in Q could be obtained if the film index of refraction was assumed to be complex (1.5 - O.li),which implies light absorption by the monolayer. It seems unlikely that the C,,SH monolayer is absorbing at the HeNe laser wavelength; hence, we attribute the discrepancy to a modification of the gold substrate optical constants by the adsorption of the thiol. Results and Discussion Pinhole Mapping with Cyclic Voltammetry. We assume that the area fraction of pinholes is accurately measured by oxide stripping. The potential of the electrode is scanned from 0.5 to 1.4 V vs SCE and back at 0.1 V/s. The integrated charge of the oxide stripping peak near 0.9 V vs SCE is measured for identical electrode areas before and after deposition of the C,,SH monolayer. The oxide stripping peak for a clean gold mirror has an area of 450-500 pC/cm2 under these conditions. The ratio of the charges found for the coated and clean surfaces is the area fraction of pinholes (1 - 8, where 8 is the fractional coverage of the thiol). Typically, 1 - 8 is 0.05-0.001 for both the mirror electrodes and the polycrystalline gold flags. Lower levels of pinholes appear to require ultrasmooth gold surfaces such as evaporated gold films on polished silicon wafers.' Care must be taken in choosing a redox couple for probing the pinholes in a monolayer. The redox couple should be hydrophilic and exhibit simple outer-sphere electron transfer. Ru(NH3):+l2+ has been proposed as a reference redox couple for fast kinetic measurements3' and has a rate constant and transfer coefficient independent (36) Pham, M.-C.; Dubois, J.-E.; Lacaze, P.-C. J.Electrochem. SOC. 1983,130,346. (37) Gennet, T.; Weaver, M. J. Anal. Chem. 1984,56, 1444.
Finklea et al.
\ /
-200.1
-400.
v
.
' - . i o 0 ' - . 5 0 0 ' - . 3 0 0 '-,io0 '
.io7
V v s SCE
Figure 1. Cyclic voltammograms at a clean and a coated gold electrode: 1.3 mM Ru(NH3):+ in 1 M KC1, gold flag electrode with geometric area of 1.3 cm2, sweep rate of 0.1 V/s. Solid curve, clean electrode; dashed curve, CIsSH monolayer on electrode; asterisks,simulation of microarray electrode CV (seetext and Table I). of the electrode metal in 1 M K F e l e ~ t r o l y t e .Figure ~~ 1 illustrates how a C,,SH monolayer affects the CV of Ru(NH3);+ in 1 M KC1. Peak currents are diminished, and peak separation is increased relative to the CV obtained by using a clean gold electrode (Table I). These effects are qualitatively rationalized in terms of the increased current density flowing at an array of
pinhole^.^,^ More quantitative information can be extracted by fitting the CVs with the theoretical treatment of an array of microelectrodes.26 The electrode is assumed to be covered with disk-shaped active sites with an average radius of R,. Each active site is surrounded by an inactive area with an average radius of R,; hence, the distance between active sites is 2R,. For small area fractions of pinholes, R, and R, are related to 1 - 8 by 1- 8 = ~
,2/~,2
(1) By considering only the case in which the diffusion layer thickness is lar er than the distance between active sites, Amatore et al.2 8were able to derive an integral equation which could be solved numerically to generate a simulated CV:
ll, = Ae"'[(l -Ill,
- ll,/B)- (Ill,
+ ll,/A)e-']
$ = i/[nFAC*(FDv/RT)'/']
(2)
(3)
= -(F/RT
) ( E- P)
(4)
Ill, = i T-'/'J$/(t
- ~ ) l / dT '
(5)
A = ko(l - 8)(RT/DFv)"'
(6)
t
B = (DRT(1- ~ ) / F v ) " ~ / ( O . ~ R , ) (7) ll, is the dimensionless current, e is the dimensionless potential, and Ill, is the convolution integral of #. A and B are dimensionless parameters defined by the geometry of the pinholes (1 - 8 and R,), the properties of the redox couple (rate constant ko and diffusion coefficient D), and the experiment (sweep rate u ) . A and B determine the shape of the simulated voltammogram. All other parameters have their usual meaning. (38) Iwasita, T.; Schmickler, W.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 138.
Langmuir, Vol. 6, No. 2, 1990 373
Passivation of Pinholes in Monolayers
Table I. Experimental and Simulated Peak Parameters for Figures 1 and 2.
EPC, mV
EPa,mV
mV Figure 1, 0.1 V/s
A B C
clean Au flag coated Au flag simulation for B
-246 -307 -307
-187 -139 -141
D
coated Au mirror simulation for D simulation for D simulation for D
-230 -236 -231 -230
-163 -158 -164 -164
coated Au mirror simulation for H simulation for H simulation for H
-238 -252 -240 -238
-156 -144 -156 -157
E F G
IUPI?
59 168 166
ipC, MA
ipa, MA
1-8
R,, cm
-381 -130 -129
299 79 64
0.005
6 X IO4
-214 -192 -213 -215
155 137 157 159
0.03 0.03 0.03
1 x 10-4 I x 10-5 1 x 10"
-630 -481 -638 -658
412 0.03 0.03 0.03
1 x 10-4 1 x 10-6 1 x 10"
Figure 2A, 0.1 V/s 67 I8 67 66
Figure 2B,1.0 V/s H I
J K
82 108 84 81
310 462 482
"See Figures 1 and 2 for experimental conditions. Superscript c represents cathodic and a anodic; anodic current is positive. Uncertainties in experimental peak potentials are fl mV; uncertainties in peak currents are fl MA. Kinetic (ko = 1.0cm/s, a = 0.5) and mass-transfer parameters (D = 6 X lo4 cm2/s) from ref 38.
When the monolayer markedly affects both the peak currents and the peak separation in the CV of a reversible redox couple, then R, and 1 - 8 may be uniquely determined from a single CV. Simulations are performed with R, and 1 - 8 being varied until both the peak separation and the peak current on the forward scan are closely matched. The simulation fit on row C of Table I was determined in this fashion. The fitting process is aided by the monotonic increase in hE, and decrease in i as either 1 - 8 decreases or R, increases. An overlay pfot of the simulation with the experimental CV provides a check on the accuracy of the simulation parameters. In Figure 1,the simulation is plotted as asterisks (*) every 20 mV; the actual calculation produces a point every 0.2 mV. The overall fit is generally good, but a characteristic discrepancy appears in Figure 1; the experimental CV exhibits larger absolute currents at potentials well past the formal potential of the redox couple. The cause of the discrepancy will be discussed later. The value for 1- 8 obtained from the simulation (0.005) agrees reasonably well with the value obtained from oxide stripping (0.002). The simulation indicates that the monolayer of Figure 1 has pinholes that are on the average 0.8 pm in diameter and 1 2 pm apart. The preceding fitting process is not valid if the experimental CV appears to be quasi-reversible; Le., i, and aE have values close to those found on a clean electroze (Figure 2 and Table I). A unique combination of 1 - 0 and R, cannot be determined, and it is necessary to obtain 1 - 8 (0.03) from oxide stripping measurements. The simulation is then fitted by varying only R,. Table I illustrates that even with data at two sweep rates a unique R, cannot be found. The simulated and actual peak positions and peak currents match within expericm or smaller. The mental error for a R, value of problem arises because for sufficiently small R, the simulated CV becomes independent of R,; the simulated CV is identical with the CV at a clean electrode of a redox couple with an effective rate constant of h0(l - e). In Figure 2, the asterisks mark the simulated CV with 20mV resolution; the simulations for R, = and lo4 cm are indistinguishable on the scale shown. The excellent fit between experiment and simulation is typical for quasi-reversible CVs, although again there is a slight discrepancy at the negative potential extreme. For R, = cm, the average pinhole diameter and separation are 350 and 2000 A, respectively; both values would be smaller for a smaller R,.
(a,)
200.1
A
100..
.
UA
.ooo.
i
,
-.SO0
,
-.300
,
,
-.io0
,
,100
,
,
,300
,
,
V vs SCE
640.1
-.ooo-
-320. .
-640.
-.SO0 -.300 -.lo0
v
,100
.300
vs SCE
Figure 2. Cyclic voltammo r a m s at a coated gold mirror electrode: 1.03 mM Ru(NH,),~' in 1 M KCl, C,,SH-coated gold mirror electrode with geometric area of 1.03 cm2, sweep rates of (A) 0.1 V/s and (B)l.O.V/s. Solid curve, experimental CV; asterisks, simulation of microarray electrode CV (see text and Table I).
There is no a priori reason to expect pinholes in a monolayer to exhibit uniform diameter and separation; diameters that vary from microns down to the angstrom level are possible, depending on the morphology of the gold substrate and postdeposition treatment. Nor is it reasonable to partition the monolayer-coated electrode into
,
Finklea et al.
374 Langmuir, Vol. 6, No. 2, 1990 1600
1
400..
io0 ' , 3 0 0 ' V
.io0 VI
.io0
'
200.
.
UA
.
,900
e.600
SCE
Figure 3. Poly(pheny1ene oxide) deposition on a gold electrode: 50 mM phenol in 0.5 M H2S0,, clean gold mirror with geometric area of 1.0 cm2, sweep rate of 0.1 V/s. Solid curve, 1st scan; short dashes, 2nd scan; long dashes, 90th scan. two exclusive regions, one in which the surface is totally blocked and the other in which the metal is completely exposed to the electrolyte. Nevertheless, the simulations provide an insight into the probable magnitude of pinhole dimensions. A more detailed description of pinholes in thiol monolayers will require techniques with a lateral resolution of at least 0.1 pm.
-.400
-.200
,200
,000
v vs SCE 4. Cyclic voltammograms of a clean and a PPO-coated
Figure gold electrode: 1.8 mM Ru(NH3)2+in 1 M KC1, gold mirror with geometric area of 1.0 om2, sweep rate of 0.1 V/s. Solid curve (A), clean electrode; dashes (B),coated with 90-A PPO film.
80.01
Poly(phenylene oxide) Deposition on Bare Gold.
+
Cyclic voltammetry of bare gold in 50 mM phenol 0.5 M H,SO, results in rapid passivation of the phenol oxidation (Figure 3). On the initial scan, phenol oxidation starts at +0.75 V vs SCE and reaches a peak current density of over 1 mA/cm2 at 0.1 V/s, On the second scan, the current drops 10-fold, and by the 10th scan all signs of faradaic reactions are absent. The PPO deposition is continued for 30 min, with a total of 90 complete scans between 0.0 and +1.0 V vs SCE. The deposition yields a PPO film with a thickness of 80-100 A (change in A of 8-10', assumed index of refraction 15), in contrast to the much thicker films generated by oxidation of phenol in alkaline nonaqueous ~ o l v e n t s . ~ ~ - ~ ' An electrode coated with just a PPO film is strongly blocking toward Ru(NH3):+ (Figure 4). At 0.1 V/s, the faradaic current is totally masked by the charging current; only at slower scan rates is a mass-transfer-limited current of ca. 1 pA/cm2 observed. The current is limited by diffusion of the redox couple through the polymer. The permeability (the product of the polymer diffusion coefficient and partition coefficient) of the PPO film to Ru(NH3):+ depends on the number of scans used to deposit the film. The permeability decreases rapidly during the first 10 scans into the phenol oxidation region and then slowly decreases over the next 80 scans. The permeabilit of the PPO film in Figure 4 is estimated to be 5 X lo-' cmz/s. Poly(pheny1ene oxide) Deposition on a C,,SHCoated Electrode. When a monolayer-coated electrode is cycled in 50 mM phenol 0.5 M H,SO,, rapid passivation of the phenol oxidation is again observed. The anodic currents are smaller than the currents obtained on a clean gold electrode. A 30-min deposition time resyts in an apparent increase of surface film thickness of ca. 5 A (change in A of 0.59; assumed index of refraction 1.5 for both the ClsSH and the PPO). The 5-A change probably represents an average of thicker deposits covering a small fraction of the electrode surface rather than a
B
+
'-.Boo '-.400 ' - . 2 0 0 ' .do0 v vs SCE
.
,200
*
Figure 5. Cyclic voltammograms of a PPO-coated and a C, SH + PPO coated electrode: 1.8 mM Ru(NH3)2+in 1 M K& gold mirror with geometric area of 1.0 cm2,sweep rate of 0.1 V/s. Solid curve (A), C,,SH-coated electrode; dashes (B), C,$H + PPO coated electrode. uniformly thick film. For structures which are small compared to the wavelength of the incident light beam,changes in A are roughly linear with coverage.99 However, details about the actual morphology of the PPO film cannot be obtained solely from ellipsometry. The effect of the PPO deposits on the CVs of Ru(NH,):+ is striking. The CV characteristic of pinholes (Figure 5A) is replaced with currents that increase continuously with overpotential (Figure 5B). Most notably, the cathodic currents at the C,,SH + PPO coated electrode are larger at -0.6 V than the currents at the PPO-coated electrode (Figure 4). Equivalent results are obtained with another redox couple (ferrocyanide). A PPO film deposited on top of a ClsSH monolayer suppresses the current peaks at low overpotential which are attributed to pinholes. Residual currents appear which increase in magnitude as the overpotential increases. In contrast, a pure PPO film suppresses faradaic current uniformly at all potentials. (39) Azzam, R.M.A.; B a a h a , N. M.Ellipsometry and Polarized Light; North Holland: Amsterdam, 1977;p 360.
Langmuir, Vol. 6, NO.2, 1990 375
Passivation of Pinholes in Monolayers
-5.00.
-15.0. UA
.
-25.0.
-35.0.
-45.0.
‘-.Zoo
‘-,600 ‘-.io0
v
’
,000
’
,200
v s SCE
Figure 6. Comparison of a “synthesized”voltammogram with residual currents on a C ,SH + PPO coated electrode. Solid curve, CV from Figure 5h;asterisks, “synthesized”voltammogram with five active sites (see Figure 7).
We assert that the currents due to pinholes are reduced to neglible levels. If the pinhole model is retained, then the simulation parameters required to fit the residual currents include pinhole diameters on the order of angstroms or smaller. In effect, the pinhole model reduces to penetration of the redox couple through the monolayer. Furthermore, we conclude that no new pinholes appear after the PPO film is deposited on the monolayer. Pinholes must be static entities which are permanently blocked by PPO deposition. We cannot yet assert that pinholes are static in size and location prior to PPO deposition. Finally, we propose that the PPO deposits are predominately localized around pinhole sites and not spread across a sizable fraction of the monolayer. If the PPO deposits were uniform with a thickness of ca. 5-10 A across most of the monolayer, then PPO deposits at the pinholes would not be sufficiently thick to strongly inhibit the pinhole currents. However, direct observation of the polymer deposits will be necessary to settle the question of PPO morphology. The residual faradaic currents at the C,,SH + PPO coated electrode are assigned to electron transfer to redox molecules at sites other than the pinholes. The residual currents are effectively masked prior to PPO deposition by the large faradaic currents flowing at the pinholes, although as noted in the first section currents exceeding the curves obtained by the simulation are observed over the same potential region as the residual currents. Once the pinholes are blocked, faradaic currents at more intact areas of the monolayer dominate the CV. The redox molecules are prevented from reaching the electrode surface, and electron transfer must proceed by a tunneling mechanism. Tunneling is expected to cause the apparent rate constant for the redox couple to decrease exponentially with tunneling distance.’ If the redox couple approaches no closer than a well-defined plane a constant distance away from the electrode surface (Le., the outer edge of the monolayer), then tunneling would yield an irreversible CV characteristic of a uniform rate constant. With an extremely small rate constant, the CV would exhibit the exponential current-overpotential dependence given by the Butler-Volmer equation and would be independent of the scan rate. However, the residual currents (Figure 5 ) , while
pseudoexponential in shape,do not fit normal Tafel behavior; i.e., the current does not increase 1 order of magnitude for every 120-mV increase in overpotential. Tafel plots with anomalously low slopes are also observed at monolayer-coated electrodes for the Fez+/’+ redox couple in sulfuric acid.’ Also, CVs using the C&H + PPO coated electrodes are sweep-rate dependent, with larger faradaic currents appearing a t faster scan rates. The shapes of the voltammograms on the CIsSH + PPO coated electrodes can be explained by assuming that electron transfer occurs only a t small localized active sites, with electron-transfer rate constants for the different active sites varying over a wide range. To illustrate this point, we employ a simple model in which each active site is isolated in terms of diffusion. Each active site is characterized by an area A , a mass-transfer-limiting current Zim*’, and an apparent rate constant k:. If only the oxidized form of the redox couple is present (cathodic currents are positive in the equations but negative in the figures) and the currents at all sites are steady-state, then ri
+ (l/Zf)] zim= zimJ/(1+ e‘)
= l/[(l/Zi?
Zf = nFAik:C*ea‘
(8) (9)
(10)
ljm is the mass-transfer current component and I: the kinetic current component at each active site. While Zf is directly proportional to the area of the active site, no explicit dependence is shown for the area in the masstransfer current; for example, a disk-shaped active site at steady state in an unstirred solution would have a current proportional to the square root of the area. The total current is obtained by summing over all active sites: ~t
=
C(zi)
(11)
If the currents a t all active sites are under kinetic control ( Z:
