Computer Simulation of Charge-Selective Electrochemistry of

Merrimack College, North Andover, Massachusetts 01845 ... Best fit between the computer-calculated and experimental CV waves is obtained for a model ...
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Anal. Chem. 1999, 71, 3712-3720

Computer Simulation of Charge-Selective Electrochemistry of Catechols at High-Surface-Area Carbon Fibers David J. Weiss,† Richard S. Kelly,‡ Milo Cumaranatunge,† and Theodore Kuwana*,†

Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, and Department of Chemistry, Merrimack College, North Andover, Massachusetts 01845

The shape and size of cyclic voltammetric (CV) waves at the ultrahigh surface area carbon fiber are dependent on the pH and the charge of the electroactive species. The high surface area resulted from the fiber being fractured by application of a high anodic potential or current. The CV waves have been computer simulated with a model that assumes the entry of positively charged and, in some cases, neutral ones, but rejection of negatively charged species from the interior of the fractured fibers. Best fit between the computer-calculated and experimental CV waves is obtained for a model containing three components as the source of the current: (a) background capacitive charge, (b) diffusion to the outer cylindricalshaped fiber, and (c) interior thin-layer volume. Simulation results indicate that the values for the inner void volume are in the nanoliter range when electroactive species penetrate the interior. In a recent report,1 we described the electrochemical behavior of ultrahigh surface area carbon fibers (UHSACFs) created from extreme anodic current or potential treatment of one type of highmodulus fiber (DuPont E120). Following fracture, the double-layer capacitance of these fibers had increased by more than 3 orders of magnitude. Scanning electron micrographs showed the presence of deep fissures running along the principal axis of the fiber that were between one-tenth and several micrometers in width, depending on the severity of the treatment. Further, the fracturing process resulted in a structure with a calculated area-to-volume ratio greater than 106 cm2/cm3. Interestingly, the shape and size of cyclic voltammetric (CV) waves recorded at UHSACFs differed dramatically from those recorded at unfractured fibers, changing as a function of solution pH and with the nature of the electroactive species. We observed increased capacitance as the pH of the buffer solution was increased, presumably as acidic surface oxides became deprotonated between pH 2.5-5.0. This resulted in an electrode surface that was neutral at low pH and negatively charged at pH >5. A comparison of the slopes of peak current (Ip) vs square root of * To whom correspondence should be addressed: (phone) 785-864-3015; (fax) 785-864-5396; (e-mail) [email protected]. † University of Kansas. ‡ Merrimack College. (1) Kelly, R. S.; Weiss, D. J.; Chong, S. H.; Kuwana, T. Anal. Chem. 1999, 71, 413-418.

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scan rate (ν1/2) for several charged species revealed a charge dependence, with slopes for positively charged species being much greater than those for negatively charged ones, especially at pH values where the fiber surface was also negatively charged. Additionally, the voltammetric responses for cations and neutrals were enhanced, apparently as species penetrated into the interior void volume produced as a consequence of the fracture process. The increased sharpness of these voltammograms suggested a contribution to the total current from either thin-layer electrolysis or adsorption. In an attempt to explain why the shapes and sizes of the CV waves with UHSACFs varied so markedly with the nature of the electroactive species and pH, a model for the current response at these electrodes has been developed and computer simulated.2 The major assumption of this model is that the electroactive species enters the interior of the UHSACF and resides there either adsorbed onto the large surface area or in the void volume as a thin-layer solution. Contributions to the total voltammetric current from four possible sources are considered: (a) background capacitive charge, (b) diffusion to the outer cylindrical-shaped fiber, (c) interior thin-layer volume, and (d) adsorption on the interior surface area. Dopamine, catechol, and 3,4-dihydroxybenzoic acid (DHBA) were chosen to test the model because they represent a series of structurally similar catechols whose charges span the range from +1 to -1 between pH 2 and pH 7. Computersimulated CV waves that are a composite of the possible sources of current are matched to “best fit” the experimental voltammograms. In this way, the relative contributions to the total current are obtained, and an estimate can be made of the interior void volume. These results are the subject of this report. EXPERIMENTAL SECTION Reagents and Materials. High-modulus, pitch-based carbon fibers (type E120 obtained from DuPont, Chattanooga, TN) with a nominal diameter of 10-12 µm were used. Dibasic sodium phosphate, phosphoric acid, and potassium nitrate were all reagent grade. Dopamine, catechol, and DHBA were used as received from Aldrich. All solutions were prepared with water from a Nanopure water system (Barnstead/Thermolyne Corp., Dubuque, IA), and solutions, except those used to fracture, were thoroughly degassed with argon prior to use. (2) Weiss, D. J. Strategies for Immobilizing Catechols Onto Carbon Electrodes for NADH Catalysis. Ph.D. Dissertation, University of Kansas, 1997. 10.1021/ac990140v CCC: $18.00

© 1999 American Chemical Society Published on Web 08/04/1999

Apparatus. Experiments were conducted with a standard three-electrode system. Potentials were referenced to a commercial Ag/AgCl electrode, with either a platinum foil or wire serving as the auxiliary electrode. Cyclic voltammetry was performed with either a Huntington Instruments model 200A (Yellow Springs, OH) or a Cypress Systems Omni 90 potentiostat (Lawrence, KS). The resulting voltammograms were collected on an Omnigraphic 2000 X-Y recorder (Houston Instruments, Austin, TX). The Cypress Omni 90 potentiostat was also employed in the fracturing process as previously described.1 Chronocoulometric measurements were performed with a Cypress Systems model CS 1090 computer-controlled electroanalytical system, with the results plotted on a Hewlett-Packard Color Pro plotter. Procedures. The preparation of UHSACF electrodes was described previously.1 Briefly, carbon fiber electrodes (2-cm length) were prepared by mounting one end of an individual fiber onto copper wire with colloidal silver epoxy and galvanostatically fractured by the application of 1 mA for 35 s in 0.1 M KNO3. The electrodes used in the measurements reported here were fractured to a capacitance near 1600 µF/cm2. Computer simulations were performed with a Pentium 120MHz machine using a revised version of the program CVSIM.3 Values of diffusion coefficients for the catechols were obtained from the literature.4 The simulations assumed fast electron-transfer kinetics, with a two-step electron transfer.5-7 The same formal potential was used for both electron-transfer steps. The values of the heterogeneous rate constants were set at khet1 ) 10 cm/s and khet2 ) 1 cm/s. These large values for rate constants ensure that the simulated behavior will appear reversible. The transfer coefficient (R) was assumed to be 0.5, and the formal potentials were obtained experimentally as the average of the two peak potentials observed in cyclic voltammetry. All simulations were run with a catechol concentration of 1.0 mM and a fiber length of 2.0 cm. Standard Nernstian boundary conditions were observed, and diffusion to the microcylinder was assumed to adhere to Fick’s second law evaluated for a cylinder. The contribution to the voltammogram from thin-layer electrolysis in the microchannels was calculated with the current simulated as a dual-electrode, thinlayer cell.8 RESULTS AND DISCUSSION Voltammetry of Catechols at UHSACF. Dopamine, catechol, and DHBA provide a series of structurally similar catechols whose acid dissociation behavior, as a group, allows the study of species possessing charges of +1, 0, and -1 between pH 2 and pH 7. Additionally, the kinetics of electron transfer at carbon electrodes and their thermodynamic properties are expected to be similar, so that any significant differences may be attributed to their charge characteristics as a function of pH. The CV waves for all three catechols have, at pH 2.2, enhanced currents and peak shapes for the voltammograms that are not (3) Gosser, D. K., Jr. Cyclic Voltammetry: Simulation and Analysis of Reaction Mechanisms; VCH: New York, 1993. (4) Gerhardt, G.; Adams, R. N. Anal. Chem. 1982, 54, 2618-2620. (5) Laviron, E. J. Electroanal. Chem. 1983, 146, 15-36. (6) Laviron, E. J. Electroanal. Chem. 1984, 164, 213-227 (7) Deakin, M. R.; Wightman, R. M. J. Electroanal. Chem. 1986, 206, 167177. (8) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley and Sons: New York, 1980.

Figure 1. Cyclic voltammograms of 1 mM dopamine at a scan rate of 100 mV/s in pH 2.2 phosphate buffer (a) and in pH 7.0 phosphate buffer (b).

typical of a diffusion-controlled system at a cylindrical electrode. This behavior suggests that there are adsorptive and/or thin-layer contributions to the total current. Figure 1A shows a representative voltammogram for 1 mM dopamine recorded at a UHSACF in pH 2.2 phosphate buffer. The scan rate was 100 mV/s. At this pH, the surface of the electrode is expected to be neutral, with catechol and DHBA uncharged and DA positively charged. In contrast, at pH 7.0, each of the three catechols has a different charge in solution, with dopamine carrying a positive charge, DHBA carrying a negative charge, and catechol remaining neutral. The acidic surface funtionalities are expected to be fully deprotonated at this pH and the surface negatively charged. Figure 1B shows a voltammogram recorded for 1 mM dopamine at a UHSACF in pH 7.0 phosphate buffer. The scan rate was 100 mV/ s. The formal potential has been shifted cathodically from that at pH 2.2 as expected for an electrode reaction involving two electrons and two protons.9 The CV recorded for dopamine illustrates the trend observed for the voltammetry related to the charge of the species. Dopamine, which is positively charged, has a sharp oxidative wave at this pH compared to the voltammograms recorded for catechol and DHBA.1 The negative charge of DHBA leads to peak currents that are much smaller than those observed for dopamine or for catechol. In addition, the appearance of the DHBA wave suggests that the process is under diffusion control, with a shape that is typical of diffusion to a microcylinder. All of the voltammograms recorded at pH 7.0 have lower peak currents than those observed at pH 2.2. Table 1 gives the anodic peak currents for dopamine, catechol, and DHBA at the two values of pH. The magnitude of the peak current is similar for the three species in pH 2.2 phosphate buffer. The anodic peak current at pH 7 for the positively charged dopamine is larger than for the neutral catechol or negatively charged DHBA. Use of computer simulation (vide infra) to calculate the anodic peak current at an unfractured fiber for these three species shows that the peak currents observed are greatly enhanced at pH 2.2 compared to those expected at an unfractured fiber. The peak currents are also higher than expected for dopamine and catechol at pH 7. The anodic peak current for DHBA in pH 7 buffer was on average less than that expected from simulation at an unfractured carbon fiber. (9) Laitinen, H. A. Chemical Analysis: An Advanced Text and Reference; McGrawHill: New York, 1960; p 291.

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Table 1. Comparison of Anodic Peak Currents for Simulated Unfractured Fibers vs Fractured Fiber Experimental Results

compound

unfractured simulateda

dopamine catechol DHBA

5.26 5.26 5.26

fractured experimentalb pH 2.2 pH 7.0 12.14 14.17 16.95

9.84 7.38 4.02

a Simulations assumed a cylinder with a surface area of 6.28 × 10-3 cm2 at a scan rate of 100 mV/s. b Data were collected at a scan rate of 100 mV/s at galvanostatically fractured fibers. Concentrations for simulations and experiments were 1.0 mM. Current in µA.

Table 2. Slope Data for the Plots of Anodic Peak Current as a Function of the Square Root of the Scan Rate for Dopamine, Catechol, and DHBA slope [µA/(V s-1)1/2] compound

pH 2.2

pH 7.0

dopamine catechol DHBA

39.2 38.5 52.4

21.0 15.4 10.7

Scan rate studies for the three catechols show a similar dependence on solution pH and charge of the electroactive species. Slope data for the plots of anodic peak current as a function of the square root of scan rate between 20 and 250 mV/s are given in Table 2 for dopamine, catechol, and DHBA at pH 2.2 and pH 7. Only the linear portions of these plots were used as a diagnostic indicator of the electrochemistry, with the slopes becoming nonlinear at longer times as expected for microelectrodes. The slopes for dopamine and catechol at pH 2.2 are close to each other, while the slope for DHBA is greater than either at this pH. The enhanced currents for DHBA are believed to be from the formation of a more easily oxidized triol via addition of water followed by tautomerization.2 At pH 7, the slopes follow the same trend as the peak currents in Table 1. When the fiber is negatively charged, positively charged dopamine has the largest slope, with an intermediate value for neutral catechol, and the smallest value being observed for the negatively charged DHBA. Investigation of Source of Current Enhancement. The peak shapes and current enhancements observed as a function of pH and charge apparently result from species penetration into the interior of the UHSACF, where both adsorption and thin-layer effects may be operative. The large increases in capacitance and surface area observed following fracture almost certainly require the interconnectivity between interior voids and channels with appropriate volume to produce thin-layer voltammetry. Thus, experiments were performed to determine whether surface adsorption of the catechols was occurring at the UHSACF. The first experiment was aimed at demonstrating that electroactive species penetrated into the microchannels of the fiber. If catechol was present at the interior of the fiber during a voltammetric scan in a solution of the species, a finite amount of the species should remain after removal of the electrode from that solution. To support this hypothesis, following experiments where the CVs were obtained in solutions of the catechol at pH 2.2, the fibers were rinsed in buffer, immersed in a fresh solution 3714 Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

of buffer, and then scanned again. The initial scans in buffer for each of the three catechols showed redox waves characteristic of the compound but with decreased current that further decreased following multiple scans. This suggests that catechol was initially present at the interior upon removal from solution but was lost upon further potential scanning. Similar experiments with unfractured fibers showed no significant catechol waves upon transfer to buffer solution. Chronocoulometry was next performed in 1 mM catechol at pH 2.2. The total charge recorded during the potential step was expected to be the sum of the contributions from the following: (1) the double-layer charging of the electrode; (2) diffusional mass transport to the electrode surface; (3) charge resulting from thinlayer electrolysis at the interior of the electrode; (4) charge arising from oxidation of any adsorbed analyte. The charge (Q) vs t1/2 relationship is expected to be linear at short times for diffusion to both the inner and outer electrode surfaces. In addition, if there is adsorption of a species onto the electrode, there will be an increase in the charge measured above the double-layer capacitance when the Q vs t1/2 curve is extrapolated to time zero. The chronocoulometric experiments involved a step from 0.00 to +0.80 V and then back to 0.00 V with a step time of 0.50 s. The Q vs t1/2 plots obtained were not linear, as would be expected for a macroelectrode, but rather showed a steep increase in charge for approximately the first 20 ms of the step, followed by a region of decreased slope. This is characteristic of electrolysis initially of solution confined in a fixed volume,with depletion followed by diffusion of the electroactive species from the bulk to the outer cylindrical electrode at longer times. When the forward step was plotted on the same axes as a step recorded in buffer prior to the voltammetric scans in catechol, a significant increase in charge over the double-layer background was observed at times longer than 2 ms. The charge, associated with thin-layer electrolysis and corrected for background, can be found by extrapolating the flat portions of the Q vs t1/2 curves for buffer and for the electrode following voltammetric scans in catechol. In this way, the total charge attributable to microchannel electrolysis was found to correspond to ∼1.7 × 10-11 mol of catechol and a microchannel volume of ∼17 nL. While data were sampled for a total of 2000 points over 500 ms, electrolysis of an adsorbed species that may have taken place at very short times would not have been seen as the first 250 µs of the step was not recorded. Even so, extrapolation of the Q vs t1/2 plots for t > 250 µs back to time zero showed no excess charge assignable to adsorption of the catechol onto the surface of the electrode. Additional experiments were performed to support the finding that no significant adsorption of the catechols was occurring at the surface of the UHSACF. Chronocoulometric experiments were carried out for a freshly fractured fiber immersed in 10 mM dopamine. The potential was stepped oxidatively every minute for 10 min and the response observed over that 10-min period. For a slow adsorption process, a change in the chronocoulometric plots would be expected over time with increasing adsorption. The plots of Q vs t1/2 in this experiment did not change significantly with time, suggesting that adsorption, if it is present, occurs rapidly to

a constant value that is insignificant compared to the size of the thin-layer contribution described above. The response of the electrode to an adsorbed species is a function of the surface area of the electrode and the amount of coverage of the species on the surface. Assuming that the average double-layer capacitance at a clean glassy carbon electrode10 is 10 µF/cm2, the total surface area of a UHSACF electrode whose fractured capacitance was measured to be 1879 µF/cm2, normalized to the area of the unfractured fiber, would be ∼1.17 cm2. If the cross-sectional area of a catechol molecule is taken to be 100 Å2, the surface coverage for a monolayer would be close to 1.7 × 10-10 mol/cm2, which correlates to 2.0 × 10-10 mol of the catechol on the surface of the fiber. The peak current for an electroactive species adsorbed onto an electrode is proportional to the area of the electrode and the surface coverage of the immobilized species8 according to

ip ) (n2F2/4RT)νAΓ*

(1)

The variables in eq 1 have the usual significance with F ) 96 485 C/equiv, R ) 8.314 J/(mol K), T is temperature (in K), and Γ* is surface coverage of the electrode (in mol/cm2). If a monolayer of catechol were adsorbed onto the UHSACF with a surface area of 1.17 cm2, the peak current calculated from eq 1 for a scan rate of 100 mV/s would be ∼75 µA. The magnitude of currents presented in Table 2 is between 10 and 20 µA. While adsorption cannot be conclusively ruled out, the time for depletion observed in chronocoulometry (∼20 ms) is closer to that expected for thin layer and not adsorption. In simulations that follow for cyclic voltammetry, contributions from thin layer and adsorption give similar responses. From the evidence presented, we have assumed that thin layer predominates and is modeled as such in the simulations. Approach to CV Simulations for HSACFs. The model used to simulate the current response of catechols at UHSACF electrodes assumes that there is diffusion of the catechol to the outer portion of the microcylindrical electrode. This process is governed by Fick’s second law for diffusion to a cylinder. It is further assumed that an electroactive species enters the interior of the fiber by transport into the microchannels of the fractured fiber and resides there in the void volume as a thin-layer solution. These microchannels can be thought of as “beakers” where a fixed volume of solution may be present. The microchannels are assumed to be “filled” and in equilibrium with the bulk solution at the beginning of the experiment prior to the initiation of the scan. The dimensions of the channels are such that all of the electroactive species in the channel can undergo electrolysis as the potential is scanned at the electrode. The model for the simulations can be visualized as shown in Figure 2. Cylinder a represents the dimensions of the unfractured fiber (10-µm diameter, 2-cm length). Cylinder b represents the dimensions of the cylinder after fracture necessary to match the diffusion-controlled portion of the experimental voltammograms. The difference in the volume of the two cylinders represents the void volume created upon fracture, which can be attributed to (10) McCreery, R. L. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1991; Vol. 17, pp 221-374.

Figure 2. Idealized model for the fractured fiber, assuming that the carbon fiber is a cylinder. Cylinder a represents the unfractured fiber (10-µm diameter, 2-cm length). Cylinder b represents the electrode modeled as a cylinder after fracture. The microchannels are not shown; however, their total volume is assumed to be the difference in the volumes of the fractured and unfractured fibers.

Figure 3. (A) Computer simulation of double-layer current envelope (a), diffusion to the outer portion of the cylindrical electrode (b), thinlayer voltammetry (c), and the composite voltammogram (dashed line) of all three current contributions (d). (B) Simulation composite (dashed line) overlaid on the experimental voltammogram for a fractured fiber scanned in a pH 2.2 solution of 1.0 mM dopamine. Simulations were performed by assuming a scan rate of 100 mV/s for a 2-cm fiber of geometric area 0.0160 cm2.

microchannels. These microchannels may have additional pores and channels inside them that may contribute to the high surface area of the electrode. To computer simulate the cyclic voltammetric response at UHSACFs, each of the currents that make up the voltammogram needs to be considered. Conceptually, the UHSACF can be represented as a cylindrical microelectrode with large striations and with microchannels along the cylindrical portion of the electrode. To provide an example of the simulation procedure, the voltammetry of dopamine in pH 2.2 phosphate buffer will be simulated and matched with the experimental results as shown in Figure 3. In the procedure, Ibackground is assumed to be purely capacitive, where the capacitance, C, is independent of cell potential. Thus, the background current envelope, Ibackground is given (in µA) by

Ibackground ) 2AνC

(2)

where A is the apparent geometric area (in cm2), ν is the scan Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

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Table 3. Experimentally Determined Parameters Used for Computer Simulationsa dopamine

E°′ (V) Cdl (µF/cm2) D0 (cm2/s) C* (mol/cm3)

catechol

DHBA

pH 2.2

pH 7.0

pH 2.2

pH 7.0

pH 2.2

pH 7.0

0.47 1.9 × 103 6.0 × 10-6 1.0 × 10-6

0.18 1.8 × 103 6.0 × 10-6 1.0 × 10-6

0.47 1.6 × 103 6.0 × 10-6 1.0 × 10-6

0.20 1.4 × 103 6.0 × 10-6 1.0 × 10-6

0.58 1.6 × 103 6.0 × 10-6 1.0 × 10-6

0.26 2.0 × 103 6.0 × 10-6 1.0 × 10-6

a The formal potentials are determined from the average peak potentials of the voltammograms. The double-layer capacitance (C ) is normalized dl to the area of the unfractured fiber. The value of the diffusion coefficient for dopamine in 0.1 M phosphate is used for all the above compounds. The value is taken from ref 2.

rate (in V/s), and C is the capacitance (in µF/cm2).11 Ithin layer and Icylindrical have been simulated using parameters that were determined from (a) the best match to the experimental voltammograms, and (b) experimental or literature values. Table 3 lists the experimentally determined parameters used in the simulations. Each component of the total CV current is simulated independently and is shown in Figure 3A. Then, the individual contributions are added together to form a “composite” voltammogram (see Figure 3A, curve d) which is then matched against the experimental result. The parameters chosen to create the “best fit” match between the experimental and simulated CVs have to fit both the magnitude of the current and the location of the current with respect to the potential. First, the current envelope that results from cycling the potential at the UHSACF in buffer was considered. The doublelayer capacitance for the electrode, whose simulated voltammetry is shown in Figure 3, was 1879 µF/cm2 as normalized to the area of the unfractured fiber. Figure 3A (curve a) presents the current envelope calculated for the UHSACF scanned in buffer. Contributions from the iR drop were neglected. After the background current was calculated, the current from diffusion to the outer cylindrical portion of the electrode was modeled. Simulations were performed using the composite of the current contributions from the background current (Figure 3A, curve a) and the diffusion of the catechol to the outer cylindrical portion of the electrode (Figure 3A, curve b). Contributions from dopamine that may come from penetration into the microchannels were neglected while this component of the voltammogram was simulated. To simulate the portions of the voltammogram that were governed by diffusion, the simulation parameter for the area of the fiber (assuming it to be a cylinder) was adjusted until a best fit was found with the diffusion-controlled portion of the experimental result. Specifically, the portion of the voltammogram between the anodic peak and the end of the forward scan was selected for matching. The voltammogram modeled for diffusion to the outer portion of the cylinder has a well-defined diffusioncontrolled current from mass transport of the catechol to the outer cylindrical portion of the electrode. Figure 3A (curve c) shows the simulation of the voltammogram when dopamine penetrates into the microchannels of the fiber to produce a thin-layer contribution to the current. The voltammetric response is analogous to that of a twin-electrode, thin-layer cell.8 The voltammetric waves are sharp and symmetrical, indicating the electrolysis of a solution in a confined volume. (11) Swain, G. M.; Kuwana, T. Anal. Chem. 1992, 64, 565-568.

3716 Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

The thin-layer current is a function of the volume of the thinlayer element.8 To determine the appropriate amount of thin-layer contribution to add, the composite of all three current contributions was used. The thin-layer volume was adjusted in the composite simulation until the anodic peak shape and current height of the simulated composite closely fit the experimental one. Figure 3B shows the simulated voltammogram (dashed trace) overlaid onto the experimental voltammogram (solid trace) for 1 mM dopamine in pH 2.2 phosphate buffer at a scan rate of 100 mV/s. The current envelope for the background of the fiber in buffer is a reasonable match with that of the experiment. The experimental CV has a slight dependence on the capacitance with the electrode potential. However, the current envelope was calculated under the assumption that the current is independent of potential. The slight differences in the calculated and experimental CVs of the current envelope may result from this assumption. In addition, the simulated anodic wave has a peak current and potential profile that match well with the experimental result. The deviation observed for the cathodic scan may arise from slight chemical irreversibility observed in the experimental CV. As discussed previously, if the solid portions of unfractured and fractured fibers are assumed to have equal density, and the dimensions of the unfractured fiber are increased to match that of the fractured fiber, an internal void volume is created. This void volume is the volume element of the microchannels of the fractured fiber. The thin-layer contribution to the current by this volume is so large that, in order to match the anodic peak position and current of the experiment, the area calculated previously for diffusion to the outer cylindrical portion of the fiber needs to be increased. The volume of the thin-layer current cannot be greater than the volume of the cylinder. Considering all of these factors, the area of the outer cylindrical portion of the cylinder was calculated from the simulations of the diffusion-controlled portions of the voltammogram to be 0.0160 cm2. This area corresponds to a 2-cm-long carbon fiber with a diameter of ∼26 µm. Assuming that the diameter has changed from 10 to 26 µm, the area of the outer cylindrical portion of the fiber increases from 0.0063 to 0.0160 cm2. A change in volume for the carbon fiber was calculated to be 9.6 nL, which was taken as the volume of solution trapped in microchannels. Simulations of Catechols at pH 2.2 with Comparison to Experimental Results. Simulations of the individual current contributions to the CV responses for all three catechols at pH 2.2 are shown in Figure 4. For dopamine, catechol, and DHBA at pH 2.2, the thin-layer contribution is a significant portion of the

Figure 4. Computer-simulated voltammograms for 1 mM dopamine (A), catechol (B), and DHBA (C) in pH 2.2 phosphate buffer at a scan rate of 100 mV/s. The composite voltammogram is simulated (d) as well as the background envelope (a), diffusion to the outer portion of the cylinder (b), and thin-layer contribution (c).

Figure 5. Experimental (solid traces) overlaid with composite simulated (dashed traces) voltammograms for 1.0 mM dopamine (A), catechol (B), and DHBA (C) in phosphate buffer pH 2.2 at fractured fibers at a scan rate of 100 mV/s.

total CV current. Figure 5 shows the overlay of the simulated voltammograms (dashed traces) and the experimental CVs (solid traces) using the composite of the individual voltammograms in Figure 4. The anodic peak positions in both current and potential for the simulation and the experimental voltammograms of dopamine and catechol (Figure 5A and B, respectively) are in good agreement. As in Figure 3, slight deviations are seen in the cathodic wave, most likely the result of a chemical step following electron transfer.12 Figure 5C presents the overlay of the experimental and computer-simulated CVs for DHBA. While the anodic peak current of the simulation composite matches the experimental CV, there are deviations in the peak position, particularly for the reverse wave. As mentioned earlier, a current enhancement for the forward scan for DHBA has been observed at this pH and is thought to indicate a follow-up reaction involving the oxidized form of the catechol to form triol.2 To confirm this possibility, the fractured (12) Adams, R. N.; Hawley, M. D.; Feldberg, S. W. J. Phys. Chem. 1967, 71, 851-855.

fiber was scanned first anodically in DHBA, and then the potential was held at 800 mV for 1 min. Upon resuming the scan cathodically, redox waves appeared for the reduction of a more easily oxidized species, believed to be hydroxy-p-quinone formed in the oxidation of triol.2 Therefore, the reduction in the peak height and a shift in the potential of the experimental cathodic wave may be due to the formation of triol from the quinone produced from the oxidation of DHBA. Table 4 lists the parameters found from the best fit composite simulations of the CVs at pH values of 2.2 and 7.0. The areas listed in Table 4 were found from the simulation of the diffusioncontrolled portions of each voltammogram and represent the outer area of the fiber available for diffusion. The diameter was calculated from the area found through simulation. The main mismatch in the simulation results in Figure 5 comes from the inability to model precisely the Ibackground, and the inaccuracy of the cylindrical diffusion, since the outer surface of the UHSACF has openings due to the microchannels. The effects on the current of these imperfections at the cylindrical surface should be Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

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Table 4. Parameters Determined from Computer-Simulated Voltammograms for 1 mM Catechols at Fractured Fibers in pH 2.2 and 7.0 Phosphate Buffera dopamine

Ipa (µA) area (cm2) diam (µm) Vthin-layer (nL) Ithin-layer (µA) Idiffusion (µA) Icomposite (µA) % thin layer % diffusion

catechol

DHBA

pH 2.2

pH 7.0

pH 2.2

pH 7.0

pH 2.2

pH 7.0

13.19 0.016 25.5 9.6 3.61 9.75 13.19 27 73

12.7 0.0195 31.0 1.2 0.44 11.39 12.68 3.7 96

15.63 0.020 32.0 12.0 4.51 11.68 15.63 28 72

10.4 0.0155 25.0 0.15 0.058 9.45 10.37 0.6 99

17.55 0.021 33.0 16.5 6.22 12.09 17.55 34 66

6.2 0.0069 11.0 0.0 0.0 4.90 6.15 0.0 100

a Values of current (I) are those determined from the anodic peaks of the simulated voltammograms. The scan rate for the simulation was 100 mV/s. The calculated percentages for the thin-layer and diffusional contributions to the total current did not include contributions from background capacitance currents.

significant at short times, or at the foot of the CV wave, but not at times when the peak current is reached or beyond. The microchannel volumes listed in Table 4 were found from the amount of thin-layer current added into the composite voltammograms. These values are of the same order of magnitude as the volume of the microchannels calculated from chronocoulometric experiments (∼17 nL). The amount of catechol oxidized in the thin-layer volumes obtained from simulation experiments was between 1 × 10-11 and 1.6 × 10-11 mol, in good agreement with that obtained from step experiments. This agreement between experiment and simulation lends credence to the essential correctness of the model for UHSACF electrodes. The contributions to the current from thin layer and diffusion to the outer portion of the cylinder, and the percentage of the total current to which these contributions correspond, are also listed in Table 4. On average, ∼70% of the total current was due to diffusion to the outer portion of the cylinder, while some 30% of the total current was current from the electrolysis in the thin layer of the microchannels at pH 2.2. Results in Table 4 also show that the internal volume of the microchannels of the fiber increases from dopamine to DHBA. The increase was not compound dependent, but was due to the corresponding difference in the areas of the fibers, as each fiber fractured to a different extent. Scan Rate Dependence of Simulated and Experimental CV Response for Unfractured Cylindrical Fibers. The case for peak current that arises from diffusion of electroactive species to a microcylindrical electrode has been described by Matsuda and co-workers.13 The peak current density is given by

(ipa)/(nFC*D) ) 0.446p + 0.335p0.15

(3)

p ) {(nFa2ν)/(RTD)}1/2

(4)

where

The symbols in eqs 3 and 4 have their usual significance, where (13) Aoki, K.; Honda, K.; Tokuda, K.; Matsuda, H. J. Electroanal. Chem. 1985, 182, 267-279.

3718 Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

Figure 6. Scan rate study of 0.5, 1.0, 2.0, 5.0, and 10.0 mM dopamine at a fractured fiber.

D is the diffusion coefficient (in cm2/s) and C is the concentration (in mol/cm3). In this equation, a is the radius of the cylinder (in cm) and p is defined as a function of the radius of the cylinder as described in eq 4. Matsuda used Pt microcylindrical electrodes with a ) 10-100 µm and scan rates from 10 to 200 mV/s in order to examine the validity of these equations. The second term, 0.335p0.15, expresses the deviation from linear diffusion at a microcylindrical electrode. Equation 3 can be approximated as

(ipa)/(nFC*D) ) 0.446p + 0.336

(5)

when p has values between 0.2 and 5.13 If the diameter of a UHSACF is 26 µm (radius 13 µm), p has a value of 1.48. Rearranging eq 5 into linear form gives

ip ) 0.446{(nFC*D)/a}p + 0.336{(nFC*D)/a}

(6)

where ip is directly proportional to the square root of the scan rate. The second term in eq 6 is the y intercept, the value of which is concentration dependent. The simulated CV response of a 1 mM catechol solution at a cylindrical electrode with dimensions of the UHSACF showed the peak current to be directly proportional to the square root of the scan rate between 10 and 250 mV/s, as predicted by eq 6 for diffusion to a cylindrical microelectrode. However, when plotted as a function of the scan rate, the experimental current was found not to be directly proportional to the scan rate, with the data curving downward with increasing scan rate. A positive intercept was normally observed for plots of peak current vs square root of the scan rate for both simulated and experimental data at UHSACF electrodes. This behavior is typical for diffusion to a cylinder as described by Matsuda.13 The deviation from linearity of these plots as a function of the cylindrical

Figure 7. Computer-simulated voltammograms for 1 mM dopamine (A), catechol (B), and DHBA (C) in pH 7.0 phosphate buffer obtained at a scan rate of 100 mV/s. The background envelope (a), diffusion to the outer portion of the cylinder (b), and thin-layer contribution (c), as well as the composite voltammogram (d) are simulated.

character of the electrode was investigated for unfractured fibers and for the UHSACF as a function of concentration and of the diameter of the cylindrical electrode. Figure 6 shows the scan rate study for a UHSACF as the concentration of dopamine was increased from 0.5 to 10 mM. The y intercept increased in a linear fashion as a function of dopamine concentration according to eq 6. Nonzero y intercepts were reported by Nicholson in an early study of diffusion to cylindrical electrodes.14 A value for p of 0.56 was obtained from eq 4 using the average diameter of 10 µm for an unfractured fiber. Plots of the steadystate current vs the square root of scan rate for different concentrations of dopamine were observed to have positive y intercepts. The values for these intercepts were also found to be directly proportional to dopamine concentration. The peak voltammetric current that results from electrolysis in a thin layer is a function of the volume of the thin layer8 according to

ip,tl ) (n2F2 νVC*)/(4RT)

(7)

where V is the volume of the thin layer (in cm3) and ν is the scan rate (in V/s). All other variables have their usual significance. When the simulated thin-layer peak voltammetric currents obtained for a UHSACF in a solution of 1 mM catechol were plotted vs the scan rate, the data were observed to be linear as predicted by eq 7. However, when the simulated thin-layer peak current was plotted vs the square root of the scan rate, the data were observed to curve upward. The total currents resulting from composite simulation, where the double-layer charging, diffusion to the outer cylindrical portion of the electrode, and contributions from thin-layer voltammetry are all combined, were expected to show characteristics of both scan rate and square root of scan rate dependence as described above. This was indeed the case. A plot of simulated peak current vs the square root of the scan rate for the composite simulation between 10 and 250 mV/s was observed to curve slightly upward with increasing scan rate. With close to 30% of the current total from thin layer, the slight curvature results from the nonlinearity of this component as a function of the square root of the scan rate. (14) Nicholson, M. M. J. Am. Chem. Soc. 1954, 76, 2539-2544.

Conversely, the plot of peak current vs scan rate for the simulated composite bends slightly downward, as was previously observed for the purely diffusional case. Thus, the simulation composite showed behavior consistent with both thin-layer and cylindrical diffusion. Simulation of Catechol Voltammetry at pH 7 with Comparison to Experimental Results. We have previously reported results for DHBA that demonstrated the charge repulsion between the negatively charged fiber surface and the like-charged catechol at pH 7.1 This charge repulsion appeared to prevent DHBA from entering the interior of the fiber and thereby limited the current to that resulting from diffusion to the outer electrode surface. The charge-selective properties of UHSACF electrodes were further explored by the computer simulation of the voltammetric responses of dopamine, catechol, and DHBA at pH 7 and by comparison of the simulation results with experimental voltammograms. The individual contributions to the observed current at pH 7 obtained from simulation, as well as the composite voltammograms for the three catechols, are shown in Figure 7. Only a small contribution to the total current from thin layer was observed for dopamine while no thin-layer current was needed in order to match the simulated and experimental voltammograms for catechol or DHBA. Essentially, only the area available for diffusion to the outer surface of the electrode needed to be simulated to match the experimental results. Additionally, the area of the fiber did not need adjustment for the UHSACF scanned in DHBA at this pH. The parameters necessary to match successfully the simulated to the experimental voltammograms for the three catechols at pH 7.0 are also listed in Table 4. The diameters of the fractured fibers increased to values similar to those at pH 2.2 for dopamine and catechol, while the electrode diameter for the simulation of DHBA was nearly the same as that of the unfractured fiber. This result is unexpected since the double-layer capacitance following fracture had increased to a value higher than either electrode used for dopamine or catechol. Thus, the CV wave shape and peak height can be accounted by diffusion of DHBA from solution to the outer surface of an unfractured cylindrical electrode. The overlay of the composite simulated CV waves with the experimental ones at pH 7.0 is shown in Figure 8. The match between the simulated and experimental CVs is nearly quantitative Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

3719

Figure 8. Experimental (solid traces) overlaid with composite simulation (dashed traces) voltammograms for 1.0 mM dopamine (A), catechol (B), and DHBA (C) in phosphate buffer pH 7.0 at fractured fibers at a scan rate of 100 mV/s.

in all three cases except for the reverse cathodic wave for catechol. The reason for this difference has not been elucidated. The mismatch in the potential region beyond +0.4 to +0.5 V is most likely due to oxidative processes of the carbonaceous electrode, which is not taken into account in the simulated backgrounds. One significant feature of the fractured fibers is the magnitude in the change of the current when electroactive species penetrate into the interior void volume. Simulation indicates that this interior volume is dependent on the pH and the nature of the electroactive species. Thus, volumes in the order of nanoliters are found from simulations of the CV waves, as matched to the experimental ones. Work is in progress to include many other compounds so that differences in ionic charge, size, and redox mechanisms can be evaluated at fibers before and after fracture. We hope that such

3720 Analytical Chemistry, Vol. 71, No. 17, September 1, 1999

studies will provide greater insight to explain observed pH effects at various carbon electrodes. ACKNOWLEDGMENT We gratefully acknowledge support for this project from the National Science Foundation (University of Kansas, Macro-ROA Program; T.K., R.S.K.) and from a Merrimack College Faculty Development Grant (R.S.K).

Received for review February 15, 1999. Accepted June 15, 1999. AC990140V