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Anal. Chem. 1983, 55, 1146-1151
Chronoamperometric Response at Carbon-Based Composite Electrodes Duane E. Welsshaar’ and Dennis E. Tallman” Department of Chemktry, North Dakota State University, Fargo, North Dakota 58105
Potentlal step experiments performed at Kel-F-graphlte composlte electrodes result in nonllnear I vs. t-”* plots. The electrode surface Is considered to consist of an array of microelectrodes, and the devlatlon from Cottreil behavior Is attrlbuted to radial dlffusion occurring at each mlcroelectrode and the interactlon among neighboring mlcroelectrode dlffuslon regimes. By use of a model developed for partlally blocked electrode surfaces, slmpiex optlmlratlon of surface slte parameters leads to good predlctlon of the observed chronoamperometric response. The dlmenslons of actlve and Inactive sltes on the electrode surface can be adjusted by varying Kel-F partlcle slze and carbon content of the composite. Composlte electrodes, as a result of signal enhancement due to radlai dlffusion, are predicted to possess a slgnal-to-noise advantage compared to contlnuous carbon electrodes such as glassy carbon. The extent of slgnal enhancement depends on electrode surface slte dlmenslons and the time scale of the measurement.
Results obtained in this laboratory (1) suggest that carbon-based composite electrodes may possess a signal-to-noise advantage compared to solid carbon electrodes such as glassy carbon when used for detection of analytes in flowing streams. A signal-to-noise advantage has also been demonstrated recently for a detector using an electrode consisting of an array of carbon fibers or microelectrodes (2). In an attempt to better understand the electrochemical behavior of composite electrodes, we have investigated the chronoamperometric response of Kel-F-graphite (Kelgraf) electrodes (3) to a potential step carried out in solutions containing either potassium ferricyanide or 1,l’-bis(hydroxymethy1)ferrocene(BHMF). Deviation from Cottrell behavior is observed over the time range of milliseconds to a few seconds, the extent of deviation being dependent on the percent carbon and on the Kel-F particle size selected for electrode fabrication. We have described the surface of these composite electrodes as islands of graphite in a sea of Kel-F ( I ) . Each island of graphite is in effect a microelectrode, each separated from other microelectrodes by insulating regions of Kel-F. Thus, the electrode surface is considered to consist of an array of microelectrodes. The deviation from Cottrell behavior might then be attributed to radial diffusion occurring at each microelectrode and the interaction among neighboring microelectrode diffusion regimes. From this point of view, the graphite-based composite electrode surface is analogous to that of a partially blocked solid carbon electrode. Studies of the effects of radial diffusion at partially blocked electrode surfaces have been reviewed recently ( 4 ) . There appears to have been only one such study on a composite electrode (5). In that study Landsberg and Thiele (5) calculated the average radii of the active and inactive regions of the electrode surface from rotating disk experiments, although ‘Present address: Department of Chemistry, The Ohio State University, Columbus, OH 43210.
no attempt was made to verify the results. In this report, we describe the application of the model of Gueshi et al. (6) to the chronoamperometric response of Kelgraf composite electrodes. The average radii of the active and inactive regions computed from the model are compared with estimates from scanning electron microscopy. The Model. The electrode surface of one of the models of Gueshi et al. (6) consists of a hexagonal array of circular microelectrodes separated by inactive regions (Figure l),referred to as the type A model. These workers derived an equation for the chronoamperomatric response of such an electrode, making two assumptions to simplify the derivation. First, it was assumed that the diffusion space (hexagonal prism) adjacent to a microelectrode comprising a unit cell could be approximated as a semiinfiiite cylinder of equal cross sectional area. It was also assumed that mass transport from region I1 to region I (Figure 2) at height 2 above the electrode surface was proportional to the difference in the mean concentrations in the two regions at height 2.This approach gives rise to a radial diffusion term (y) which was experimentally determined to be 0.27 (6). Contamin and Levart ( 4 ) confirm that this parameter is a function of the model and not dependent on experimental conditions. The resulting equation for electrodes with greater than 50% of the geometric surface area inactive is given by -I =
where LT is 6 / ( l - e), 6 being the fraction of the surface area that is inactive, t is the time in seconds, 1 is given by
and R is the radius of the diffusion cylinder (Figure 2b). I d is the Cottrell current for the corresponding fully active electrode (0 = 0 )
(3) where q is the geometric area of the electrode and the other parameters have their usual electrochemical definition. Gueshi et al. (6) also derived the equation for a type B model (Figure 1). In this model the circular regions are inactive and the surrounding hexagonal regions are active. Equation 1still applies for type B electrodes, but in this case 1 is given by 1=
20
R20(1 - 6) In (1 + y/&)
0 1983 American Chemical Society 0003-2700/83/0355-1148$01.50/0
(4)
ANALYTICAL CHEMISTRY, VOL. 55, NO. 7, JUNE 1983
MODEL A
MODEL
B
Hexagonal array electrode models of Gueshi et al. (6). Shaded areas are the active regions. Flgure 1.
b
Schematic of the diffusion cylinder. Shaded areas are inactive in model A and active in model B electrodes: (a) side vlew and (b) top view at the electrode surface. Figure 2.
For very short times eq 1predicts that I will approach I d ( l
- e), the Cottrell current for an electrode having an active area (1- 8)q. This is to be expected since at sufficiently short times the diffusion layer thickness is small compared to the dimensions of the rnicroelectrodes and nonlinear diffusion will be negligible. At long times eq 1predicts that I will approach I d and the entire geometric area will appear active. As R , decreases (Figure 2) and 8 approaches unity, the microelectrodes become increasingly smaller and the spacing between them increasingly larger, eventually reaching a point where the observation of either of the above limiting cases becomes experimentally inaccessible. Reller et al. (7) have compared the results of a digital simulation of the chronoamperometric response of an ensemble of microelectrodeis to that predicted by eq 1. The simulation agrees quite well with eq 1 a t long times when the entire geometric area appears active. However, at intermediate times the current predicted by eq 1 is lower than that predicted by the simulation and the deviation increases with increasing 8. As indicated by FCeller et al. (7), this is presumably because the steady-state radial diffusion assumption of Gueshi et al. is only approximately correct. In spite of this deviation, we have found that the model of Gueshi et al. (6) can be used to obtain reasonable estimates of the radius of the active and inactive sites on a composite electrode surface.
EXPERIMENTAL SECTION Stock solutions of reagent grade K3Fe(CN)6(Fisher Scientific) were prepared fresh daily in deionized, distilled water. BHMF was prepared by a lithium aluminum hydride reduction of 1,l’ferrocenedicarboxylic acid dimethyl ester (Strem Chemical). Stock solutions of BHMF were prepared in methanol (HPLC grade, Burdick and Jackson) and stored at 0 “C. The supporting
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electrolyte was 1 M KCl in deionized, distilled water. The concentrations of the final ferricyanide and BHMF solutions varied slightly depending on the concentration of the stock solution, but all were approximately 1 mM. All solutions were thoroughly degassed with nitrogen that had been passed through a vanadium scrubber to remove oxygen. The graphite, Ultracarbon “F”purity (Ultracarbon Corp., Bay City, MI) with a particle size of less than 1 pm, was used as received. The powdered Kel-F type 81 plastic (3M Corp., Minneapolis, MN) was sieved through a 40 mesh screen to remove the larger particles. The sieved Kel-F had a particle size range of approximately 150-450 pm. The Halocarbon 19-00 wax (poly(chlorotrifluorethylene),i.e., Kel-F, Halocarbon Products Corp., Hackensack, NJ) was sieved through a 200 mesh screen resulting in particle sizes less than 75 pm. The lower limit of the size distribution was not determined, but approximately half of the particles also passed through a 325 mesh screen (40 pm). The chronoamperometric apparatus and procedure have been published elsewhere (8). For ferricyanide the potential was stepped from +0.35 V to -0.85 V, and for BHMF, from 0.0 V to +0.85 V vs. SCE. A Pt wire counterelectrode was used. Electrode Fabrication. The required amounts of graphite and Kel-F were thoroughly mixed with a mortar and pestle. The mixture was placed in a stainless steel cylindrical die with a diameter of 0.953 crn and the die was inserted in a vacuum chamber (modified chamber from Perkin-Elmer originally used to produce KBr pellets for IR analysis). The chamber and die were then placed in a heater-equipped Carver Laboratory Press. A vacuum was drawn and the press pressure slowly increased to ca. 700 lbs (the vacuum is necessary to remove air from the composite that otherwise gets trapped and produces voids on the electrode surface and throughout the composite). The vacuum and press pressure were then released. The die was removed from the chamber and placed in the press. The die was then wrapped with a heat tape and both the heat tape and heater blocks of the press were activated and ca. 700 lbs of pressure was applied to the die. The die was heated to 300-325 OC for the Kel-F-81 and to 250-275 OC for the 19-00 wax and maintained in the temperature range for 5 min. The temperature was monitored with a Chromel-Alumel thermocouple inserted in the top of the die. The pressure was then increased to 1500 lbs, the heaters were turned off, and the die was cooled quickly to room temperature with distilled water from a plastic squirt bottle while the pressure was maintained a t 1500-2000 lbs. The pellet was then removed from the die. One end of the cylindrical pellet was drilled concentrically to accept a glass tube which was epoxied in place. A mercury pool and copper wire were used to make electrical contact to the electrode. The side of the cylindrical pellet was sheathed with in. i.d. black gum rubber tubing. This tubing a length of effectively sealed the side of the pellet from solution and produced no interferences during the experiments. The sheath could also be slipped back to prevent interference during polishing or roughening of the electrode surface. The resulting Kelgraf disk electrode had a geometric area of 0.713 cm2 (not including the sheath). A smooth electrode surface was prepared by polishing the electrode with moderate hand pressure on a lapping wheel (ca. 90 rpm) with a slurry of 1 pm alumina for 2 min. The rough electrode surface was prepared by hand “polishing”the electrode on 600 grit sand paper (3M wet or dry). The hand “polishing” consisted of a circular motion (1-2 in. in diameter) with moderate pressure for 50 circles. After either surface preparation the surface was thoroughly rinsed with a stream of deionized, distilled water and dried with a tissue. The symbols S and R will be used to denote smooth and rough, respectively, throughout the remainder of the discussion. Electrodes fabricated with Kel-F-81 will be referred to as 3M electrodes and those fabricated with the 19-00 wax as HC electrodes. Procedures. To determine the influence of composition on chonoamperometric response, step experiments with ferricyanide and BHMF were performed at rough and smooth electrodes of 5 % , 1570, and 25% graphite with each type of Kel-F, i.e., six electrodes and two surface conditions each. The data were collected in two time ranges, 0 to 100 ms and 0 to 10 s, with ca. 100 points collected in each range for each set of conditions.
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 7,
JUNE 1983
To assess the effect of surface treatment, similar measurements were made on six smoooth and six rough surfaces of the 15% 3M electrode. The order of surface treatment was determined by lot, the order selected being R, S, R, S, R, S, S, R, S, R, R, S. The active area of each electrode was determined from the least-squares slope of a Cottrell (i vs. t-lIz) plot of the data in the general time range of 5-30 ms. The minimum time of the range was determined by the first data point for which the current was below the full scale setting of the digital recorder (8). The maximum time of the range was limited by the duration over which the Cottrell plot was linear as evidenced by a minimum constant least-squares slope and maximum linear correlation coefficient. For each set of experimental conditions the data sets from the two time ranges were combined and a least-squares fit t o eq 1 was achieved by means of a modified simplex optimization (9) of appropriate unit cell parameters. The error function for arguments less than 4 was calculated from the Maclaurin expansion (10). The series was truncated when the addition of a term in the summation. For resulted in a change of less than arguments greater than 4 the function was set equal to 1. Due to the approximations inherent in this approach, when the difthe ference in the error functions of eq 1 was less than difference was set to zero. With this approach, the theoretical curves published by Gueshi et al. (6) could be accurately reproduced. The optimization was cmied out on a Tektronix 4051 computer which was also interfaced to a 4662 plotter.
RESULTS AND DISCUSSION Active Area Determinations. Equation 1predicts that the current flowing a t a composite electrode at short times in response to a potential step should exhibit Cottrell behavior, and it should be possible to calculate the true active area of the electrode from such data. A number of factors determine the shortest time at which reliable chronoamperometric data can be obtained (8),which in this study appears to be ca. 1 ms. Depending on the dimensions of the active sites, data collected in the 5-30 ms time range may not necessarily fall within the region where Cottrell behavior is predicted. In an attempt to assess the error in areas calculated by using Cottrell slopes in the 5-30 ms time range, eq 1was used to generate a series of theoretical i vs. t-lIz curves for electrodes with B = 0.85 (15% active area) and several values of R (Figure 2b). For an R of 10 pm or greater, the slope in the 5-30 ms time range was within 10% of the expected active area Cottrell slope. Thus, areas calculated from data in this time range should be within 10% of the true active area for R 1 10 pm. The diffusion coefficient calculated from our data for ferricyanide in 1 M KC1 a t a glassy carbon electrode (7.8 X lo4 cm2/s) is in good agreement with the accepted value (7.63 X lo4 cmz/s) (8). The accepted value was used here. The diffusion coefficient for BHMF (6.34 X lo4 cm2/s) was calculated from our data at glassy carbon. Due to the slight irreversibility of BHMF and the tendency of BHMF to adsorb on glassy carbon, the diffusion coefficient calculated for BHMF is subject to an uncertainty which we estimate to be no greater than &lo%. HC Kelgraf electrodes exhibited higher currents and greater curvature of the Cottrell plot in the 10 ma to 1 s time range than the corresponding 3M Kelgraf electrodes (Figure 3). This suggests that R is smaller for the HC Kelgraf, a suggestion borne out by scanning electron micrographs of the surface (see discussion below). Consequently, data could not be collected at times sufficiently short to permit reliable computation of the active area of HC Kelgraf electrodes. The results of active area determinations for the 3M Kelgraf electrodes are summarized in Table I. These areas exhibit a definite correlation with the percent carbon in the bulk composite. Furthermore, the active areas agree very well with determinations of conducting carbon on the surface by X-ray photoelectron spectroscopy. These results will be discussed
4aa
1
B
I
I
2
3
4
5
6
7
8
Q 1 O
T-lnCS-l">
Flgure 3. Effect of Kei-F particle size on chronoamperometric response. HC particle size
