Voltammetry at Regular Microband Electrode Arrays: Theory and

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J. Phys. Chem. C 2007, 111, 12058-12066

Voltammetry at Regular Microband Electrode Arrays: Theory and Experiment Ian Streeter,† Nicole Fietkau,† Javier del Campo,‡ Roser Mas,‡ Francesc Xavier Mu˜ noz,‡ and Richard G. Compton*,† Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom, and Centro National de Microelectro´ nica, IMB-CNM. CSIC, Campus de la UniVersidad Auto´ noma de Barcelona, Bellaterra 08193, Spain ReceiVed: April 26, 2007; In Final Form: June 4, 2007

Microband electrode arrays are useful tools for the electrochemist, offering the enhanced sensitivity associated with microelectrodes but with a higher total current output. For optimum performance, the array may be designed such that space is used efficiently but the individual microbands behave as isolated electrodes on the time scale of the experiment. For a linear sweep experiment, the optimum specifications of a microband array depend on the scan rate used and the diffusion coefficient of the electroactive species. A two-dimensional simulation method is used to examine the nature of the diffusion to a regular array of microbands. Cyclic voltammetry of hexaammineruthenium(III)chloride is performed at a regularly spaced microband array to test the theory.

1. Introduction Microelectrodes are popular tools in electroanalysis. High rates of mass transport to the electrode surface produce high current densities and allow electrode kinetics to be studied on a much shorter time scale than on macroelectrodes. When constructed carefully, an array of many microelectrodes wired in parallel can offer the same enhanced sensitivity of a single microelectrode but with the advantage of a higher total current output. Most experimental work to date has used the disc electrode as the repeating unit of the array,1-5 and theoretical work has centered on the optimum packing of the discs while still achieving maximum sensitivity.6-8 The work presented here uses the microband electrode as the repeating unit of the array.9 Microbands are attractive to the electrochemist for their relative ease of fabrication to precise specifications. Interdigitated microband arrays are often used in “redox cycling” experiments in which consecutive bands in the array alternate between anodic and cathodic potentials. The target analyte is electrochemically titrated by measuring its diffusion from the “generator” microbands to the “collector” microbands.10-14 In this paper, the arrays used are regular, meaning all bands have uniform length, width, and distance of separation from their nearest neighbor. In future work, we will consider the effects of random arrays with nonuniform spacing of the microbands. Figure 1 shows a schematic diagram of a small section of a regular microband array. The bands are microscopic in terms of their width in the x-direction but are macroscopic in the y-direction, having a length that is orders of magnitude greater than a typical diffusion layer thickness. They are embedded flush into an insulating surface such that they lie parallel along the y-direction. A challenge in the optimization of a microband array is to pack the bands as closely as possible while retaining their diffusional independence. Any significant overlap of the dif* Corresponding author. Email: [email protected]. Tel: +44(0) 1865 275 413. Fax: +44(0) 1865 275 410. † Oxford University. ‡ Campus de la Universidad Auto ´ noma de Barcelona.

Figure 1. Schematic diagram of a section of a microband array. The theoretical array extends to infinity in both the x- and z-directions.

fusion fields between adjacent bands creates competition between those bands for the diffusing species. This has a “shielding” effect, which decreases the flux density at each individual band, reduces the total current measured, and negates the advantages of using microelectrodes. The size of the diffusion layer and the separation between bands within the array are therefore clearly important considerations. For any band separation and diffusion layer size, we can describe the mass transport to the electrode in terms of the four categories originally defined by Davies et al.15 These categories were initially used to describe the overlap of diffusion layers on partially blocked electrodes; they have also been applied to discuss arrays of microdisc electrodes16 and they are appropriate here for discussing arrays of microbands. For completeness, this work extends the classification to include a fifth category. To illustrate each category of behavior, a computer-simulated concentration profile in the (x, z) plane at a microband array is shown in Figure 2. The numerical simulations used to generate these profiles will be discussed in subsequent sections. Each category will now be discussed in turn. Category 1: In this limit, the diffusion layer thickness is small compared to both the electrode width and the band separation. Mass transport to the band is dominated by linear diffusion, therefore giving the current response expected for a macroelectrode scaled down to match the total area of all the individual bands. Category 2: In this case, the band separation is large enough that the bands continue to behave independently, but diffusion to each band is no longer necessarily linear. Rapid diffusion to

10.1021/jp073224d CCC: $37.00 © 2007 American Chemical Society Published on Web 07/25/2007

Voltammetry at RMAs: Theory and Experiment

J. Phys. Chem. C, Vol. 111, No. 32, 2007 12059

Figure 2. Simulated concentration profiles at a microband array. Category 1: Xgap ) 1, σ ) 1000. Category 2: Xgap ) 1, σ ) 10. Category 3: Xgap ) 1, σ ) 1. Category 4: Xgap ) 1, σ ) 10-3. Category 5: Xgap ) 0.05, σ ) 10. All profiles are for a fast reversible electron transfer and are taken at the peak potential. Labels on the contour lines refer to the normalized concentration, a.

the band edge may be present, behavior typically associated with a single microelectrode. The measured voltammetric response is equal to that of a collection of isolated microbands. This is often considered the ideal behavior for an array of microbands, because it is the presence of edge effects that leads to heightened sensitivity. Category 1 may be thought of as a subset of category 2 because its behavior is that of a collection of isolated microbands at scan rates fast enough to allow only linear diffusion. Category 3: In this situation, the band separation is no longer large enough to prevent overlap of adjacent diffusion fields. The band experiences shielding from its neighbor, and flux density at the band edge is reduced. This is the behavior that an analytical electrochemist would typically like to avoid. Category 4: This represents the limiting situation of category 3 when neighboring diffusion fields overlap to such an extent that the overall concentration profile is linear. The current response is equal to that of a macroelectrode having the same geometric area of the microband array; all of the advantages of using microelectrodes are lost. Category 5: This case also involves the complete overlapping of adjacent diffusion fields to effect overall linear diffusion. However, there is a second condition that the current measured at a single microband is equal to that expected for linear diffusion to an electrode of the same area. This is only possible when the band separation is much smaller than the bandwidth. While this theoretical case is unlikely to ever arise for any sensible design of microband array, we suggest its inclusion as a legitimate category because it provides a link between categories 1 and 4, both of which are concerned with linear diffusion. In a potential sweep experiment at a microband array, the diffusional behavior of the electroactive species will depend on the width and separation of the bands and on the potential scan

rate used. By varying the scan rate, the size of the diffusion layer that forms over the course of an experiment can be controlled. Therefore, even if the dimensions of the array are fixed, we would expect changes in scan rate to induce transitions between different Davies categories. In this paper, we use linear sweep voltammetry of hexaammineruthenium(III)chloride to explore the behavior of a fast electron transfer at a regular array of microbands. Modeling the diffusion to the electrode by numerical simulation allows us to interpret the experimental results. 2. Mathematical Model and Numerical Simulation This section describes the modeling of the simple heterogeneous reduction in eq 1 in a linear sweep experiment at a regular array of microband electrodes.

A + e- a B

(1)

The electron transfer is described by Butler-Volmer kinetics at the electrode surface as

∂[A] F ) k0 [A] exp -R (E - EQf ) + ∂z RT

D

(

(

)

F [B] exp (1 - R) (E - EQf ) RT

(

)) (2)

where D is the diffusion coefficient, assumed equal for both species, k0 is the heterogeneous rate constant, R is the chargetransfer coefficient, E is the electrode potential, EQf is the formal electrode potential, and the terms R, T, and F have their usual meaning. Under the initial conditions, only species A is present with concentration [A]bulk. The potential is swept through reducing potentials with a uniform scan rate, ν. Species A is

12060 J. Phys. Chem. C, Vol. 111, No. 32, 2007

Streeter et al.

Figure 3. (a) Cross section through the (x, z) plane of a microband array. (b) The unit cell in normalized space.

TABLE 1: Dimensionless Parameters Used for Numerical Simulation parameter concentration of species A concentration of species B lateral coordinate normal coordinate time band separation

expression

[A] [A]bulk [B] b) [A]bulk x X) xe z Z) xe Dt τ) 2 xe xgap Xgap ) xe a)

2

scan rate potential heterogeneous rate constant

F νxe RT D F θ ) (E - EQf ) RT k0xe K0 ) D σ)

consumed at the electrode surface but is replenished by diffusion through solution. Under conditions where the diffusional behavior falls under categories 1, 4, or 5, the current response is that expected from linear diffusion, which is a relatively trivial one-dimensional problem and its solution has been well documented.17 Diffusional behavior described by category 2 is simply that of an isolated microband, which has also been thoroughly investigated and simulated by a variety of two-dimensional approaches.18-22 Category 3 provides a slightly more complicated two-dimensional problem, because the bands cannot be considered in isolation of each other. However, the problem is simplified by identifying diffusionally independent “unit cells” in an approach analagous to that used for microdisc arrays7,8 and partially blocked electrodes.15,23 A band near the center of a large array will have a plane of symmetry along its central axis. A further plane of symmetry is found at the midpoint between two adjacent bands. For all five categories of diffusion, there must be a condition of zero flux across these planes. These planes of symmetry therefore form the boundaries of a diffusionally independent unit cell, which is repeated across the surface of the array. In a numerical simulation of diffusion to a microband array, only a single unit cell needs to be considered. A cross section of the unit cell is illustrated in Figure 3a. It has a width of (xe + xgap) where xe is half the microband width and xgap is half the band separation. For the purposes of simulation, the model is normalized using dimensionless parameters, which are summarized in Table 1. Space is described by the normalized (X,Z )-coordinate system, species A and B are described by their normalized concentrations, a and b, and time, t, is normalized to the dimensionless τ. The configuration of the microband array is summarized by

a single parameter, Xgap, which is the ratio of the bands’ distance of separation to a single band’s width. Using the normalized parameters, the unit cell boundary is at X ) (1 + Xgap), and the electrode lies in the region 0 e X e 1 (Figure 3b). The cell is semi-infinite in the Z-direction, but simulations are performed within the limits 0 e Z e 6xτ beyond which the effects of diffusion are not important on the experimental time scale.24 Because species A and B are assumed to have equal diffusion coefficients, their concentrations at any point in solution may be described by eq 3:25

[A] + [B] ) [A]bulk

(3)

Hence, it is possible to simulate the concentration profile of species A independently from species B, thus reducing simulation times. Mass transport of species A through the unit cell may be described by Fick’s second law in two dimensions, noting that there is zero net diffusion in the y-direction because the length of the microband is very much larger than the diffusion layer thickness. For the dimensionless model, this is expressed in eq 4:

(

)

∂2a ∂2a ∂a + ) ∂τ ∂X2 ∂Z2

(4)

Table 2 shows the boundary conditions for our model, including three alternative conditions for the electrode boundary, labeled a-c. The first of these is the normalized Butler-Volmer expression from eq 2, expressed in terms of the dimensionless heterogeneous rate constant, K0, and the dimensionless potential, θ, which are defined in Table 1. The second condition describes the electron transfer in eq 1 when the reverse process is completely irreversible. The third condition may be used in place of Butler-Volmer kinetics when the electron transfer is fast and reversible to the extent that the ratio of species A to B at the electrode surface is described at any potential by the thermodynamic Nernst equation. The value of θ is given at any time by eq 5:

θ ) θ0 - στ

(5)

where θ0 is its initial value, and σ is the dimensionless potential sweep rate, also defined in Table 1. The solution of eq 4 subject to these boundary conditions leads to a normalized concentration profile of species A from which the dimensionless diffusional flux through the electrode, j, may be calculated as

j)

∂a ∂X ∫01 ∂Z

(6)

The experimentally measured cathodic current, I, is related to this dimensionless flux by eq 7:

I ) -2NFDl[A]bulk j

(7)

where N is the total number of microbands in the array, and l is their macroscopic length in the y-direction. In this paper, the behavior of different microband arrays will be compared using simulated values of the dimensionless flux. It should be remembered that the value j applies to a single microband; it is not normalized per unit area. Equation 4 and its accompanying boundary conditions are discretized over a geometrically expanding rectangular grid and are solved by the alternating direction implicit finite difference



TABLE 2: Boundary Conditions for Eq 4 time

boundary

condition

τ)0

all X, Z

a)1

τ>0

X)0

τ>0

X ) 1 + Xgap

τ>0

∂a )0 ∂X ∂a )0 ∂X

Z ) 6xτ

a)1

τ>0

Z ) 0, X > 1

τ>0

Z ) 0, X e 1

∂a )0 ∂Z ∂a ) K0(ae-Rθ + be(1-R)θ) (a) ∂Z ∂a ) K0ae-Rθ (b) ∂Z a (c) ) eθ b

description initial conditions zero flux across plane of symmetry zero flux across plane of symmetry bulk solution

method26 in conjunction with a generalized form of the Thomas algorithm. The expanding grid used is similar to that developed by Gavaghan for microdisc simulations.27 At any grid point (Xi, Zj), the spacing of mesh lines is hi in the X-direction and kj in the Z-direction, where i ) 0, 1, 2, ..., n and j ) 0, 1, 2, ..., m. The highest mesh density is at coordinates (Xi)s, Zj)0), which is the singularity where the electrode meets the insulating surface. The spacing of mesh lines at this point are given by eqs 8 and 9.

zero flux across insulating boundary Butler-Volmer kinetics irreversible Butler-Volmer kinetics Nernstian electron transfer

for convergence to ensure that the spatial and temporal grids lead to less than 1% variation from the asymptotic peak current. 3. Categorization of Simulated Voltammetry

An example mesh with fX ) fZ ) 1.4 and hlast ) klast ) 0.045 is shown in Figure 4. In the work presented here, the values used are fX ) fZ ) 1.2 and hlast ) klast ) 10-4. A regular temporal grid is used, such that there are 150 time steps per unit value of θ in a linear sweep simulation. The simulation program is tested

This section explains our procedure for assigning a diffusion category to any given simulated voltammogram at a microband array. We focus on electron transfers that are fast and reversible or completely irreversible. These limits of electrode kinetics have the advantage that a linear diffusion current response is easily identified. 3.1. Electrochemically Reversible Electron Transfer. Figure 5 shows a selection of flux-potential plots simulated using the boundary condition for a fast reversible electron transfer with a scan rate of σ ) 0.1 and with varying values of Xgap. The variation in appearance of the voltammetry is attributed to a procession through different categories of diffusion. The peak flux, jp, changes significantly with varying Xgap, and so it is suggested that this feature may be used to determine the diffusional regime of the experiment. Voltammograms were simulated using the Nernstian boundary condition with varying scan rate and band separation across the range -5 e log10 σ e 2 and -2 e log10 Xgap e 3, and their peak flux was recorded. For category 2 diffusion, the peak flux is expected to be equal to j iso p , the peak flux recorded at a single isolated microband. For any scan rate, we can find j iso p as the limiting value of jp as Xgap tends to infinity. Figure 6 shows the variation of the ratio jp/j iso p as a function of Xgap and σ for a reversible electron transfer. It takes a maximum value of 1 when the scan rate is fast and the band separation is large, indicating category 2 behavior. For slower scan rates and for smaller band separations,

Figure 4. Example of a geometrically expanding square grid used for discretization of eq 4. fX ) fZ ) 1.4, hlast ) klast ) 0.045.

Figure 5. Simulated linear sweep voltammetry of an electrochemically reversible electron transfer at a microband array. σ ) 0.1, Xgap varies from 0.01 to 100.

kj)0 ) klast

(8)

hi)s ) hi)s-1 ) hlast

(9)

where the constants hlast and klast may be chosen for an appropriate level of accuracy. The grid expands away from this singularity in the Z-direction with an expansion factor fZ and in both X-directions with an expansion factor fX. The distribution of all other grid points is therefore described by eqs 10-12.

kj ) fZkj-1 for j ) 1, 2, ..., m

(10)

hi ) fXhi+1 for i ) 0, 1, ..., s - 2

(11)

hi ) fXhi-1 for i ) s + 1, s + 2, ..., n

(12)


Streeter et al. TABLE 3: Categorization of Diffusion Regimes for a Fast Reversible Electron Transfer category 1 2 3 4 5

Figure 6. Peak heights of simulated linear sweep voltammetry of an electrochemically reversible electron transfer at a microband array; the variation of jp/j iso p with σ and Xgap.

condition 1/2 -1

jp e 0.4463σ AND jp g j iso p jp g jiso p jp < 0.4463σ1/2(1 + Xgap) AND jp < j iso p jp g 0.4463σ1/2(1 + Xgap) jp g 0.4463σ1/2(1 + Xgap) AND jp e 0.4463σ1/2-1

sweep experiment for a reversible electron transfer. The parameter alters how stringent the conditions are: the lower its value, the less stringent the conditions. With a maximum value of ) 1, all behavior will be labeled as category 3 behavior, since the peak fluxes can only ever tend toward their limiting values. It can be seen from the conditions in Table 3 how categories 1 and 5 are subsets of the more general categories 2 and 4, respectively. The zone diagrams in Figure 8 show the behavior that was found from the simulated voltammetry using the conditions in Table 3 and values of ) 0.9 and ) 0.99. Note that with the less stringent conditions there are regions where the diffusional behavior may be described by both categories 2 and 4 or by both categories 1 and 5. 3.2. Electrochemically Irreversible Electron Transfer. Flux-potential curves were simulated using the boundary condition for irreversible electron transfer with varying scan rate and band separation across the range -5 e log10 σ e 2 and -2 e log10 Xgap e 3. Figure 9 shows a selection of the simulated voltammetry with a scan rate of σ ) 0.1 and with varying values of Xgap. The values K0 ) 1 and R ) 0.5 are used, although it should be noted that with an irreversible

Figure 7. Peak heights of simulated linear sweep voltammetry of an electrochemically reversible electron transfer at a microband array; the variation of jp/j lin p with σ and Xgap.

the ratio jp/j iso p is less than 1, indicative of a shielding effect at the electrode due to the overlap of neighboring diffusion fields. When diffusion is described by category 4, the peak height is that predicted by the Randles-Sˇ evcˇ´ık model for linear diffusion to an area the size of the entire array. Equation 13 presents the Randles-Sˇ evcˇ´ık expression for peak flux, j lin p , for a fast reversible electron transfer using our dimensionless variables: 1/2 j lin (1 + Xgap) p ) 0.4463σ

(13)

Figure 7 shows the variation of the ratio jp/j lin p as a function of Xgap and σ. It takes a maximum value of 1 when the scan rate is slow and the band separation is small, indicating category 4 behavior. Values less than 1 are observed at faster scan rates and larger band separations, for which the surface of the array is not uniformly depleted of the electroactive species. The peak fluxes of categories 1 and 5 may also be predicted by the Randles-Sˇ evcˇ´ık model for linear diffusion, but with a smaller effective electrode area:

jp ) 0.4463σ1/2

(14)

Given any values of Xgap and σ, the diffusional behavior can be categorized by comparing the simulated peak flux to the limiting cases described above. Table 3 describes the conditions required for a diffusion category to satisfactorily describe a linear

Figure 8. Fast reversible electron transfer at a microband array. Zone diagram showing the category of diffusional behavior exhibited in a simulated linear sweep for varying σ and Xgap. Categorization is described in Table 3 with (a) ) 0.9 and (b) ) 0.99.



Figure 9. Simulated linear sweep voltammetry of an irreversible electron transfer at a microband array. σ ) 0.1, Xgap varies from 0.01 to 100, K0 ) 1, R ) 0.5.

TABLE 4: Categorization of Diffusion Regimes for an Irreversible Electron Transfer category

condition

1 2 3 4 5

jp e 0.4966σ R AND jp g j iso p jp g j iso p jp < 0.4966σ1/2R1/2(1 + Xgap) AND jp < j iso p jp g 0.4966σ1/2R1/2(1 + Xgap) jp g 0.4966σ1/2R1/2(1 + Xgap) AND jp e 0.4966σ1/2R1/2-1 1/2 1/2 -1

boundary condition changes in K0 do not affect the shape of the voltammogram, only its position on the potential axis. The curves in Figure 9 are broader than their reversible counterparts in Figure 5 with slightly lower peak currents, as is typical of irreversible linear sweeps.24 A shift in peak potential is observed as Xgap is varied and is much more significant than for the corresponding reversible voltammetry in Figure 5. The Randles-Sˇ evcˇ´ık expression for peak flux for an electrochemically irreversible electron transfer under conditions of linear diffusion is given in eq 15 using our dimensionless variables.24 Note this is the equivalent of eq 13 for identifying category 4 diffusion. 1/2 1/2 j lin (1 + Xgap) p ) 0.4966σ R

Figure 10. Irreversible electron transfer at a microband array. Zone diagram showing the category of diffusional behavior exhibited in a simulated linear sweep for varying σ and Xgap. Categorization is described in Table 4 with (a) ) 0.9 and (b) ) 0.99. K0 ) 1, R ) 0.5.

(15)

As for the electrochemically reversible case, category 2 diffusional behavior may be identified by comparison with the peak current simulated for an isolated microband. The conditions required for a diffusion category to satisfactorily describe a linear sweep experiment for an irreversible electron transfer are summarized in Table 4. The zone diagrams in Figure 10 show the behavior that was found from the simulated voltammetry using the conditions in Table 4 and values of ) 0.9 and ) 0.99. We note the similarity in shape of Figures 8 and 10, although they are not identical. The nature of the electron-transfer clearly has little influence on the category of diffusional behavior induced by a linear sweep experiment. 4. Experimental Methods 4.1. Chemical Reagents and Instrumentation. All chemicals employed were of analytical grade and used as received without any further purification. Hexaammineruthenium(III)chloride (Ru(III)(NH3)6Cl3) was purchased from Aldrich and potassium chloride (KCl) was supplied by Riedel-de-Hae¨n. All solutions were prepared with deionized water with resistivity of no less than 18.2 M Ω cm (Millipore water systems, U.K.).

Figure 11. (a) Schematic of the regular microband array (RMA) with interdigitated arrangement and (b) enlargement of the RMA illustrating the electrode width, we, and the gap width, wgap.

Cyclic voltammetric measurements were carried out using a µ-Autolab III (ECO-Chemie, Utrecht, Netherlands) potentiostat interfaced to a PC using GPES (version 4.9) software for Windows. All measurements were conducted using a threeelectrode cell in which the working electrode was a gold regular microband array (RMA). This consists of two sub-arrays, each consisting of 250 microbands, in an interdigitated arrangement (Figure 11). When a potential is applied to only one of the subarrays, we refer to the configuration as RMA-1. When the same potential is applied to both sub-arrays, we refer to the configuration as RMA-2. A microband length, l, of 2 mm was obtained by covering both connecting tracks along the whole length of


Streeter et al.

Figure 13. Graph illustrating the good match between SEM image and perfilometric data. Note that the electrode sits at the bottom of a trench enclosed between two oxinitride walls.

Figure 12. Schematic of the mask used in the fabrication process of an a regular microband electrode array with interdigitated structure. Parts a-c are discussed in the text.

the silica plate by a 1.5 mm wide strip of silicone. The counter electrode was a bright platinum wire and a saturated calomel electrode (SCE) was used as a reference electrode. All experiments were carried out at 298 ( 2 K. To ensure that all microband electrodes were electrochemically active, copper metal was deposited onto the array by holding the potential at -1.2 V for 600 s in a solution of 0.05 M CuSO4/0.1 M Na2SO4 (pH ) 3, adjusted with HCl). After plating, the microband array was studied with a microscope; this allowed us to take a visual count of the active microband electrodes. Before commencing experiments, the working electrode was electrochemically activated by cycling from 0.0 to -1.3 V (versus SCE) in 0.1 M KCl at 0.1 V s-1. 4.2. Fabrication of the Microband Array. The array of gold microband electrodes was produced by standard photolithographic techniques on a pyrex wafer. The electrodes consisted of two sets of 250 fingers, 20 µm wide and 3 mm long. The electrodes do not sit flush with the insulating surface but are recessed by 1 µm. This recess is small compared to the electrode width and compared to a typical diffusion layer thickness, and so the decrease in current due to the recession is sufficiently small as to be neglected.21 The fabrication procedure has been described previously.28 Here, we present a short summary for the reader’s convenience. A 4 inch diameter and 1 mm thick pyrex wafer was first thermally oxidized at 1400 K until the oxide layer was 1 µm thick. This oxide layer served to improve the adhesion of the photoresist to the pyrex. After coating with a positive photo-

resist, a dark field mask (similar to the one shown in Figure 12a) is used to uncover the areas where a thin Pt layer is to be deposited by lift-off. After removing the photoresist in an acetone bath and with it the Pt from the unwanted areas, a metal triple layer consisting of 50 nm of titanium, 50 nm of nickel, and 100 nm of gold was depositioned by sputtering. Next, the gold-coated wafer was coated with a photoresist prior to insulation with a clear field mask (as the one depicted in Figure 12b). After development of the photoresist, the gold was removed from the unwanted areas in a wet etching step. The last phase of the fabrication involved passivating the side pads of the interdigitated structure and patterning the electrodes. This was achieved by growing a mixed layer composed of silicon oxide and silicon nitride over the entire chip. This passivating layer was produced by plasma-enhanced chemicalvapor deposition and was approximately 1 µm thick. An important feature to note of this passivating layer is its homogeneity and the way it follows the profile of the substrate, as shown by the perfilometry data shown in Figure 13. Next, a new layer of photoresist was cast over the wafer and was insulated through a dark field mask containing the final electrode patterns (as shown in Figure 12c). Once the photoresist was developed, the exposed oxinitride was removed from the electrode areas in a dry reactive ion-etching step. After this, the remaining photoresin was removed in an acetone bath. The wafers were then diced to the size of individual chips, which are subsequently glued, wire-bonded, and encapsulated to suitable print-circuit boards. 5. Results and Discussion Figure 14a,b presents scanning electron microscopy (SEM) images of a regular microband array whose characteristics are summarized in Table 5. Cyclic voltammograms for the reduction of 1 mM Ru(III)(NH3)6Cl3 in 0.1 M KCl for the electrode array, RMA-1 (250 microband electrodes, which are separated from each other by a gap of 60 µm) were recorded at scan rates varying from 0.01 to 3 V s-1 at a temperature of 298 ( 2 K (Figure 15a). Numerical simulation was then used to determine the theoretical response of RMA-1 by using the following values for Ru(III)(NH3)6Cl3 in 0.1 M KCl: 0.05 cm s-1 for the heterogeneous rate constant, k0, and 6.3 × 10-6 cm 2 s-1 for the diffusion coefficient, D; these values are in good agreement with the values reported in the literature.28-30 Because of capacitative currents that are difficult to account for, only the


J. Phys. Chem. C, Vol. 111, No. 32, 2007 12065 TABLE 5: Characteristics of the Regular Microband Electrode Arrays RMA-1 and RMA-2 parameter electrode width we/µm electrodelength l/cm distance between two microbands wgap/µm number of microbands N

Figure 14. (a) SEM image of the regular microband array with interdigitated structure. (b) Close-up of the electrode ends.

Figure 15. (a) Experimental voltammetry for the regular microband electrode array RMA-1 at scan rates varying from 0.01 to 3 V s-1 in 1.0 mM Ru(NH3)63+/0.1 M KCl solution. (b) Comparison between experimental and theoretical results for RMA-1. The parameters used for the simulation are as follows: [A]bulk ) 1.0 mM, D ) 6.3 × 10-6 cm2 s-1, k0 ) 0.05 cm s-1, we ) 20 µm, l ) 0.2 cm, wgap ) 60 µm, and N ) 250.

forward scan is considered when comparing experiment to theory. The analysis of the forward peak currents, Ip, versus the scan rates, V, shows excellent agreement between experimental and theoretical results (Figure 15b). To illustrate the deviation of the current response of RMA-1 from 250 inde-

RMA-1 RMA-2 20 0.2 60 250

20 0.2 20 500

error (1 (0.02 (2 0

pendent microband electrodes of the same size, the theoretical response of 250 isolated microbands was simulated. Only for scan rates below 0.05 V s-1 does the experimental data deviate from the simulated current response of the isolated microbands, showing that on the time scale of the voltammetric experiment the diffusion layers start to lightly overlap. This deviation indicates the transition from category 2 to category 3 diffusional behavior. Figure 16a shows the cyclic voltammograms for RMA-2 in which both sets of microbands in the interdigitated structure are connected, hence, resulting in gap width between microbands of 20 µm. As for RMA-1, the analysis of Ip versus V for RMA-2 shows an excellent agreement between experimental and theoretical results (Figure 16b). Overlaid as a dashed line is the electrochemical response for a macroelectrode of area, A, in which A is the sum of the area of 500 microband electrodes and the area of the separating gaps. Note that linear diffusion is observed for small scan rates (0.01-0.02 V s-1), where the diffusion layers of adjacent microbands heavily overlap, whereas for high scan rates (0.4-3.0 V s-1) the current response resembles the response of 500 independent microband electrodes. This is consistent with an overall change in diffusional behavior from category 4 to category 2. Figure 17 illustrates the good fit between simulated and experimental linear sweep voltammetry for both electrodes,

Figure 16. (a) Experimental voltammetry for the regular microband electrode array RMA-2 at scan rates varying from 0.01 to 3 V s-1 in 1.0 mM Ru(NH3)63+/0.1 M KCl solution. (b) Comparison between experimental and theoretical results for RMA-2. The parameters used for the simulation are as follows: [A]bulk ) 1.0 mM, D ) 6.3 × 10-6 cm2 s-1, k0 ) 0.05 cm s-1, we ) 20 µm, l ) 0.2 cm, wgap ) 20 µm, and N ) 500.


Streeter et al. while retaining category 2 diffusion. The optimum specifications may be found from our model with knowledge of the diffusion coefficient and range of scan rates to be used in experiment. By using potential sweep experiments at variable scan rates, we have illustrated that the overlap of the diffusion layers of individual microband electrodes depends on the time scale of the experiment. The excellent agreement between theory and experiment confirms that our modeling approach can be used to predict the electrochemical response of microband electrode arrays. Acknowledgment. N.F. and I.S. thank the EPSRC for studentships. References and Notes

Figure 17. Experimental and simulated voltammetry for the regular microband electrode arrays, RMA-1 and RMA-2, at 400 mV s-1. The parameters used for the simulation are as follows: [A]bulk ) 1.0 mM, D ) 6.3 × 10-6 cm2 s-1, k0 ) 0.05 cm s-1, we ) 20 µm, l ) 0.2 cm, wgap ) 60 µm, and N ) 250 for RMA-1, and wgap ) 20 µm and N ) 500 for RMA-2.

Figure 18. Comparison between the experimental data, RMA-1 and RMA-2, and the simulated current of the equivalent number of independent microband electrodes, illustrating the deviation of both electrodes from same number of independent microband electrodes. The parameters used for the simulations are as follows: [A]bulk ) 1.0 mM, D ) 6.3 × 10-6 cm2 s-1, k0 ) 0.05 cm s-1, we ) 20 µm, l ) 0.2 cm and N ) 250 or 500.

RMA-1 and RMA-2. The deviation of the current response of RMA-1 and RMA-2 from 250 and 500 independent microband electrodes, respectively, is shown in Figure 18. It can clearly been seen that for the smaller gap width, the diffusion layers of adjacent microbands start to overlap at shorter timescales, whereas for the bigger gap width, the diffusion layers of adjacent microbands only overlap at longer timescales. 6. Conclusions The nature of diffusion in a linear sweep experiment has been shown to depend on the ratio of band separation distance to electrode width, Xgap, and on a normalized scan rate, σ, whose value depends on the electrode width and the diffusion coefficient of the electroactive species (Table 1). When fabricating an array of microbands, it is desirable to optimize the electrode bandwidth and separation distance in terms of space efficiency

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Voltammetry at Regular Microband Electrode Arrays: Theory and

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