Design considerations in the development and applicationof microdisc electrode arrays (MDEAs) for implantablebiosensors

Abdur Rub Abdur Rahman & Anthony Guiseppi-Elie

Published online: 23 January 2009# Springer Science + Business Media, LLC 2009

Abstract The use of microlithographically fabricatedMicrodisc Electrode Arrays (MDEAs) in the developmentof implantable voltammetric biosensors necessitates designcriteria that balances the overall footprint of the device withthe advantages to be derived from large separation distancesbetween non-interacting microdisc elements. Using thedynamic electroanalytical techniques of Multiple Scan RateCyclic Voltammetry (MSRCV) experiments with finiteelement simulations and Electrochemical Impedance Spec-troscopy with equivalent circuit modeling, three uniqueMDEA designs; MDEA 050 (r=25 μm, 5,184 discs),MDEA 100 (r=50 μm, 1,296 discs) and MDEA 250 (r=125 μm, 207 discs) of constant critical dimensions (center-to-center d/r=4) and area (A=0.1 cm2) were studied in1.0 mM ferrocene monocarboxylic acid (FcCO2H) solution(in 0.1 M Tris/0.1 M KCl buffer, pH=7.2). The criticaldisc-to-disc spacing (d/r) required to archive 67% ofmaximal current response was defined as optimal. Basedon the predictive model, new MDEA designs; MDEA 001(r=0.5 μm, 127,324 discs), MDEA 002.5 (r=1.25 μm,20,372 discs), MDEA 005 (r=2.5 μm, 5,093 discs), MDEA

010 (r=5 μm, 1,273 discs), MDEA 015 (r=7.5 μm, 566discs), MDEA 020 (r=10 μm, 318 discs) were simulated at10 and 100 mV/s. The final disc count of each MDEA wasdictated by the need to maintain a comparable electroactivearea between the MDEAs, which was chosen to be0.001 cm2, which in turn was dictated by the need togenerate sufficient electrochemical current to be comfort-ably measured by common electrochemical detectors.

Keywords Ultramicroelectrodes .Microelectrode arrays .

Voltammetry . Impedance . Biosensors . Simulation

1 Introduction

Microfabricated electrochemical biosensors are gainingpopularity due to their small footprint, enhanced electro-chemical detection limits (Logrieco et al. 2005, Kermanet al. 2004) and the relative ease with which they may beintegrated into lab-on-a-chip devices (Nyholm 2005,Lingerfelt et al. 2007). The superior mass transportcharacteristics of ultramicroelectrodes (one dimension lessthan 25 μm) that results from a steady state current that isindependent of slew rate, the high signal to noise ratio andthe possibility for small sample sizes have established theultramicroelectrode as a superior electroanalytical transduc-er (Xie et al. 2004, Basha and Rajendran 2006). Enhancedmass transport influences sensor performance character-istics such as limit of detection and sensitivity. Onedisadvantage of the ultramicroelectrode is the extremelysmall currents which result when these transducers areintegrated with biorecognition layers in the construction ofbiosensors. Compromised by a reduction in diffusioncoefficient (Justin et al. 2008) and low abundance of thebiologically relevant analyte, the performance of the ultra-

Biomed Microdevices (2009) 11:701–710DOI 10.1007/s10544-008-9283-3

A. R. A. Rahman :A. Guiseppi-Elie (*)Center for Bioelectronics, Biosensors and Biochips (C3B),Clemson University,100 Technology Drive,Anderson, SC 29625, USAe-mail: guiseppi@clemson.edu

A. Guiseppi-ElieDepartment of Chemical and Biomolecular Engineering,Clemson University,Clemson, SC 29634, USA

A. Guiseppi-ElieDepartment of Bioengineering, Clemson University,Clemson, SC 29634, USA

microelectrode biosensor is better served by an array ofultramicroelectrodes, themicroelectrode array (Abdur Rahmanet al. 2008). The microelectrode array allows for the keyadvantages of the ultramicroelectrode to be combined withhigher currents that are readily measured by “low” currentpotentiostats. These challenges are exemplified by thedevelopment of implantable biosensors where biomarker(analyte) levels may be low in relation to the backgroundand the bioanalytical implant footprint and power consump-tion are major constraints.

In the design of implantable biosensors, several criteriamust be simultaneously satisfied. These criteria may bebroadly classified as physicochemical (assessable in vitro)and pathophysiological (accessible only in vivo) perfor-mance criteria. Amongst the physicochemical performancecriteria are sensitivity and limits of detection appropriate tothe decision criteria for the measurement and a dynamicrange to address the clinically relevant variability in thebiomarker of interest. When a microdisc electrode array is tobe considered as the electrochemical transducer of choice toachieve stated physicochemical performance criteria, itbecomes necessary to arrive at an appropriate device design.In such cases, purely analytical determination of the optimalelectrode geometry is of little use and is seldom undertaken.The availability of finite element tools allows for design andsimulation of complex systems that can model the electro-chemical performance. Using a commercially available FEMtool, COMSOLMultiphysics, this paper develops a predictivemodel for electrochemical characteristics of uncoated MDEAtransducers. First, the model was verified by comparing itsoutput with the experimental data of manufactured MDEAs,then, design criteria were established and these and the modelwere used to design a new set of MDEAs consistent with thedesign criteria.

Microdisc Electrode Arrays (MDEAs) are electrodeswherein the total electrode area is sub-divided intomicrometer sized sub-domains arranged in a specificfashion. Various arrangements have been investigated(Ordeig et al. 2006) and the hexagonal close packed(HCP) arrangement, because of its high packing densityof microdiscs (73%) within a given area, has been favored(Davies and Compton 2005). Individual microdiscs in thearray are intended to behave as independent ultramicroe-lectrodes with separate diffusion zones, which may overlapwith the diffusion zones of neighboring microdiscs undercertain potential scan rate conditions, depending uponspecies diffusivity, and depending upon the critical micro-array dimensions. Figure 1 is an illustration of the diffusionzones of (a) planar electrode, (b) single disc ultramicroelec-trode, and (c) a microelectrode array. Figure 1(c) displaysthe characteristics of both 1(a) and (b) at different scanrates, leading to ambiguity. Four scenarios have beenoutlined that can lead to different voltammetric shapes, (a)complete overlap of diffusion zones, (b) no overlap ofdiffusion zones, (c) partial overlap and (d) linear diffusion(Davies et al. 2005). Finite element analysis based approachsimplifies the process of identification of transport depen-dent design criteria (Rahman et al. 2008). Thus electrodearrays could be tailored to specific performance criteriaunder specific test conditions based upon their criticaldimensions. CV simulations performed by Saito (Saito1968) have shown that the ratio, d/r, (d=center-to-enterdistance between microdiscs and r=radius of the microdisc)can be used to delineate two clearly defined regimes ofdiffusion. The first corresponds to independent behavior ofthe microdisc electrode elements and therefore negates anoverlapping diffusion field. This condition occurs at d/r>12(Lee et al. 2001). Under these conditions radial diffusion

(a)Planar macro electrodes

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Fig. 1 Schematic illustration of(a) linear diffusion at a planarelectrode, (b) radial diffusion ata microdisc electrode, and (c)radial diffusion profiles at amicrodisc electrode array withits scan rate dependent response

702 Biomed Microdevices (2009) 11:701–710

dominates and sigmoidal voltammograms are expected.The second corresponds to behavior wherein the diffusionfields overlap and produce a uniform linear diffusionprofile. Large d/r values while maximizing analyte fluxresults in a large transducer footprint. The need to balancethe physicochemical advantages of the microdisc electrodearray with its footprint, which influences its pathophysio-logical behavior, necessitates design criteria that balancesthe overall footprint of the device with the advantages to bederived from large separation distances between non-interacting microdisc elements.

Three unique MDEA designs; MDEA 050 (r=25 μm,5,184 discs), MDEA 100 (r=50 μm, 1,296 discs) andMDEA 250 (r=125 μm, 207 discs) each with constantcritical dimensions (center-to-center distance (d)/radius(r)=4), constant total electroactive area (A=0.10 cm2) andconstant total plan area (P=0.45 cm2) were studiedexperimentally and simulated. Using the dynamic electro-analytical experimental technique of Multiple Scan RateCyclic Voltammetry (MSRCV) with finite element simu-lations and Electrochemical Impedance Spectroscopy withequivalent circuit modeling, MDEAs were studied in1.0 mM ferrocene monocarboxylic acid (FcCO2H) solution(in 0.1 M Tris/0.1 M KCl buffer, pH=7.2). Followingvalidation of the models, they were used to predict thecritical design parameter, d/r, required to archive 67% ofmaximal current response, defined as optimal, for MDEAdevices; MDEA 001 (r=0.5 μm), MDEA 002.5 (r=1.25 μm), MDEA 005 (r=2.5 μm), MDEA 010 (r=5 μm),MDEA 015 (r=7.5 μm), and MDEA 020 (r=10 μm). TheseMDEA electrodes were investigated at varying d/r valuesand at scan rates corresponding to 10 and 100 mV/s.Optimized responses were selected at 67% of maximalcurrent response and shown to generate currents valuescommensurate with available low current potentiostats.

2 Experimental

2.1 Materials

2.1.1 Reagents

Ferrocene monocarboxylic acid (FcCOOH, 97%, Sigma-Aldrich) was used as received. A 0.1 M Tris buffer solution(adjusted to pH=7.2 using 1 M HCl) was made from Tris(hydroxymethyl)aminomethane or Trizma® (99.8+%, A.C.S.,Sigma-Aldrich). Trichloroethylene (spectrophotometricgrade, ≥99.5%, Sigma-Aldrich), acetone (≥99.9%, Sigma-Aldrich), 2-propanol (≥99.8%, Sigma-Aldrich), ammoniumhydroxide solution (ACS reagent, 28.0–30.0% as NH3, Sigma-Aldrich), hydrogen peroxide solution (ACS reagent, 30 wt.%in H2O, Sigma-Aldrich), ethanol (CHROMASOLV®,

Sigma-Aldrich) and toluene (anhydrous, 99.8%, Across) wereused as received.

2.1.2 Microdisc Electrode Arrays (MDEAs)

The microdisc electrode arrays were fabricated by overlay-ing a single continuous layer of electrode material (100 nmthick gold on 10 nm thick titanium/tungsten) with a secondlayer of an insulating and passivating material (500 nmthick silicon nitride, Si3N4). The passivating layer was thenphotolithographically defined using a positive photoresistand fluoro-plasma etched to reveal multiple defined circularareas of the underlying gold through the Si3N4. Thediameter of the exposed gold discs and their spacingdistinguished the various MDEAs employed. The MDEA050, MDEA 100 and MDEA 250 (ABTECH Scientific,Richmond, VA) comprise 5184 (50 μm diameter) micro-discs, 1,296 (100 μm diameter) microdiscs and 207(250 μm diameter) microdiscs, respectively The discs werearranged in a hexagonal close packed array with center-to-center distances that were four times the radius of the discradius (100, 200 and 500 μm, respectively). The detailedfabrication procedure of the MDEA electrodes is describedelsewhere (Abdur Rahman et al. 2008). The workingelectrodes were hexagonal arrays of recessed microdiscs,fabricated by photolithographic techniques (Rai-Choudhury1997), each with a 0.1 cm2 collective electrode area.

2.2 Methods

2.2.1 MDEA Surface cleaning

The unpackaged MDEA devices were cleaned by sequen-tial washing in boiling trichloroethylene (3 min, 86.7°C),acetone (1 min; 56.2°C), 2-propanol (1 min; 82.4°C) andthen washed profusely in room temperature (RT) deionizedwater. To remove residual organic/ionic contamination andto produce a uniform, reproducible layer of –OH and –NH2

groups on the surface of the Si3N4 (activation), theelectrodes were immersed in a (5:1:1, v/v/v) 60°C solutionof D.I. H2O:NH4OH:H2O2 (RCA Clean), held for 3 to 5 s,quenched in DI water for 1 min and then washed profuselywith running DI water. To remove adventitious chemi-sorbed organic residues, the MDEAs were treated for10 min in the UV-Ozone cleaner (UV_Clean, BoelkelIndustries, PA, USA), washed by ultrasonication in 2-propanol and then washed profusely in room temperaturedeionized water.

2.2.2 Cyclic Voltammetry

Multiple scan rate cyclic voltammetry (MSRCV) wasperformed using a three-electrode (working, counter and

Biomed Microdevices (2009) 11:701–710 703

reference) electrochemical setup connected to a BAS 100Potentiostat/Galvanostat Electrochemical Analyzer andcontrolled by BAS 100 software (Bioanalytical Systems,West Lafayette, IN, USA). A large surface area platinumgauze (3″×2″) electrode (Alfa Aesar, USA) was used as theauxiliary electrode. The gold multidisc electrode arrays(MDEA250 Au, MDEA100 Au, MDEA50 Au) and microAg/AgCl electrode (3 M Cl−), all from ABTECH ScientificInc. (Richmond, VA), were used as the working andreference electrodes, respectively. Voltammetry was per-formed by scanning over the potential range between 0 to600 mV at variable scan rates (10, 25, 50, 75, 100, 200,250, 300, 400 and 500 mV/s). The MDEA’s werecharacterized by CV at room temperature in solutions of1 mM FcCO2H prepared in 0.1 M Tris/0.1 M KCl buffersolution (pH=7.2).

2.2.3 Electrochemical impedance spectroscopy

Three-electrode electrochemical impedance spectroscopywas performed using a Solartron Instruments Model 1260Frequency Response Analyzer (FRA; Solartron Analytical,Hampshire, UK) in conjunction with Princeton AppliedResearch M283 Potentiostat/Galvanostat. Measurementinstruments were controlled by ZPLOT impedance mea-surement software (Scribner Associates, Southern Pines,NC, USA). The impedance data was viewed in Zview(Scribner Associates, Southern Pines, NC, USA) imped-ance plotting and visualization software. Impedance wasmeasured between the working electrode of the MDEA’sand a large surface area platinum gauze (3″×2″) counterelectrode (Alfa Aesar, USA). The AC sine-wave excitationvoltage amplitude was 10 mV, over the frequency range0.1 Hz to 1 MHz. The probing electroactive specie was1.0 mM FcCO2H in a supporting electrolyte of 0.1 M TRISbuffer/0.1 M KCl (pH=7.2) solution at 20°C.

2.2.4 MSRCV simulation by finite element modeling (FEM)

Finite element modeling of the dynamic electrochemicalresponses of MDEA electrodes was performed in COMSOLMultiphysics software. The reaction considered in thesimulation is a simple, single electron transfer electrochemicalmechanism:

Oþ e� k !R ð1Þ

where O and R are the oxidized and reduced species,respectively. The initial and bulk concentrations of species Owere 1 mM and the reduced species R was assumed to beinitially absent in the bulk solution. The transport processrelated to Eq. (1) can be described by the Nernst–Planck

equation, neglecting the migration, convection and bulkreaction terms,

@ci@t¼ Dir2ci ð2Þ

where, ci=concentration of the ith species and Di=diffusioncoefficient. The diffusion coefficient of both the oxidized andreduced species was taken as 4.61×10−10 m2/s for FcCO2H asdetermined from MRSCV data of a 25 μm diameter ultra-microelectrode (UME) in a 1 mM FcCO2H in 0.1 M Tris/0.1 M KCl solution. This value is close to 5.73×10−10 m2/sthat is reported in the literature (Bartlett and Taylor 1998).

The concentration–overpotential relationship given bythe Butler–Volmer equation (Bard and Faulkner 2001) wasused to solve for the electrode surface reactions

kf ¼ k0 expaF E � E0ð Þ

RT

� �ð3Þ

kb ¼ k0 exp1� að Þ E � E0ð Þ

RT

� �ð4Þ

where kf and kb are the forward and reverse reaction rateconstants, respectively, and k0 is the heterogeneous rateconstant, taken as 1.4×10−2 m/s for the FcCO2H redoxreaction. The value of α was assumed to be 0.5. The standardpotential, E0, was fixed at 300 mV for the purpose of thissimulation. R is the universal gas constant (8.314 J/K),T (temperature) was set at room temperature (298 K) and F isthe Faraday’s constant (96,487 C/mol).

The simulation geometry used is shown in Fig. 2.Hexagonal close packed arrays of recessed microdiscs weresimulated using the domain wall approximation approach(Davies and Compton 2005). The domain wall approxima-tion approach dramatically reduces the computation time byreducing the 3D problem to a 2D one (Lavacchi et al.2006). The radius of the circle inscribed in the hexagon inFig. 3(a) is the simulation geometry, which is illustrated inFig. 3(b). The Nernst–Plank relationship without electro-neutrality application mode with Lagrange triangularquadratic meshing elements was used to solve the problem.The appropriate mesh size was determined by repeatedmesh refinements until the results did not change. Thesimulation cell height, h, was set at 1,300 μm based on therequirement that the simulation cell height be larger thanthe diffusion length of the electroactive species over thetime course of the experiment. The cell height wasdetermined by the following expression (Brookes et al.2003, Lavacchi et al. 2006):

h ¼ 6ffiffiffiffiffiffiffiDtc

pð5Þ

704 Biomed Microdevices (2009) 11:701–710

where, h is the simulation cell height or distance above theelectrode surface, D is the diffusion coefficient of theelectroactive species and tc is the maximum time requiredto perform one half of a CV scan. The recess depth wastaken as 0.5 μm; dictated by the thickness of the nitridelayer of the MDEA. All boundaries were assigned theinsulation/symmetry boundary condition (BC) except forthe boundary corresponding to the microdisc electrode–solution interface (recessed region in Fig. 2), which wasassigned a flux BC, with the flux given by the followingrelationship:

M ¼ Cox � kf � Cred � kb ð6Þwhere Cox and Cred are the surface concentrations of theoxidized and reduced species, and kf and kb are the forwardand reverse reaction rate constants, respectively. Geometricsingularities were particularly meshed at a higher density

than other areas. Simulations were performed for all scanrates corresponding to the experimental scans.

3 Results and discussion

3.1 Cyclic voltammetry of MDEA 050, 100 and 250

Multiple scan rate cyclic voltammetry (MSRCV) measure-ments were performed on the three MDEAs of differinggeometries (variable microdisc diameter and density), but ofsimilar electroactive surface area (A=0.10 cm2), fixed d/r=4,and fixed total plan area (P=0.45 cm2). Consistent withexpectations, the MDEA 050 (50 μm microdiscs) wasassociated with the largest oxidation peak currents, followedby the MDEA 100 (100 μm microdiscs) and then the MDEA250 (250 μm microdiscs), for all scan rates (Fig. 3 top row).

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Fig. 3 Experimental (top row)and simulated (bottom row)voltammograms of uncoatedMDEA 050 (r=25), MDEA 100(r=50), MDEA 250 (r=125) offixed d/r=4 and fixedA=0.1 cm2 over the range 0 to600 mV and over the scan rate10 to 500 mV/s in 1.0 mMFcCO2H prepared in0.1 M Tris/0.1 M KCl buffer(pH=7.2) at RT

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Fig. 2 Illustration of (a) hexag-onal closed packed microdiscarray layout, (b) domain wallapproximation of the microdiscgeometry for the finite elementsimulation

Biomed Microdevices (2009) 11:701–710 705

The voltammograms were hysteresis envelopes with clearlydefined redox peaks at all scan rates, indicating a diffusiondomain overlap at the measured scan rates. Simulations ofthe cyclic voltammograms were performed for MDEAs 050,100 and 250 using the procedures described above. Figure 3(bottom row) shows the simulated voltammograms of theMDEA electrodes. All the voltammograms displayed“peaked” behavior characteristic of reversible reactions,which is in agreement with the experimental results. Thereversibility of the FcCOOH oxidation–reduction reaction isclearly illustrated by the theoretical results.

The differences between FcCOOH peak currents; partic-ularly the reduction peak current, Ipc, becomes lesspronounced with increasing scan rate, υ, as higher scanrates become associated with overlapping diffusion fieldsresulting in an approach to semi-infinite linear diffusionbecoming dominant. As a result, the voltammograms of allthree electrodes become more similar with respect to thepeak currents. The behavior of these three MDEA designs,with respect to their voltammetric current response,therefore, provides insight into the evolving diffusionprofiles of the redox probe molecule at the surface of thesedevices. Each individual microdisc of the MDEA 050approaches the characteristic ultramicroelectrode (UME)behavior; a UME normally being defined as an electrodewith at least one dimension (such as the radius) that is lessthan 25 μm (Bard and Faulkner 2001). For an UME, radialdiffusion predominates over linear diffusion at each of themicrodiscs, resulting in a larger flux and increased masstransport to the electrode surface. Microdisc electrodearrays; however, demonstrate a more complex behavior

than a single microdisc The disc-to-disc distance (d) and theradius of the microdiscs (r) are important parameters thatinfluence the type of diffusion (radial, linear or mixedmode). Also of importance is the scan rate, υ, which revealstime dependence for the diffusion of electroactive species tothe microdisc arrays. Using the validated simulationconditions, the cyclic voltammograms of six MDEAs[MDEA 001 (r=0.5), MDEA 002.5 (r=1.25), MDEA 005(r=2.5), MDEA 010 (r=5.0), MDEA 015 (r=7.5), MDEA020 (r=10.0)] of similar fixed d/r=4 but of reduced totalelectroactive area, A=0.001 cm2 were simulated over therange −500 to 500 mVand over the scan rate 10 to 100 mV/sin 1.0 mM FcCO2H at RT and are shown in Fig. 4.

The rate of charge transfer at the electrochemicalinterface during CV experiments is determined by theapplied potential. As this potential increases, the chargetransfer rate increases, reaches a peak and decreasesthereafter. At the peak, all available electroactive speciesat the electrochemical interface are oxidized (or reduced).Further increase in potential, does not lead to an increase incurrent due to the unavailability of species at the interface,which now must be replenished by diffusion from the bulkelectrolyte. This gives rise to a diffusion zone within whichthe profile of species increases with increasing scan rate. Asthe time scale of the voltammetric experiment lengthens, thecurrent response of the microdisc arrays are controlled byfour different diffusion domains (Davies and Compton 2005,Davies et al. 2005): (1) at short time scales, the microdisccurrent response is controlled entirely by linear diffusion(category-1); (2) at longer time scales, the microdisc arraysachieve a steady-state current controlled by radial diffusion

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and fixed A=0.001 cm2 over the range −500 to 500 mV and over thescan rate 10 to 100 mV/s in 1.0 mM FcCO2H at RT. (Note similarity ofscales)

706 Biomed Microdevices (2009) 11:701–710

(category-2); (3) at still longer time scales, the diffusionlayers enlarge and begin to overlap, so that the disc arrayscease to function completely as individual working electro-des, thus showing elements of both linear and radialdiffusion (category-3); and (4) eventually, complete overlapof the diffusion fields occur between the microdiscs, resultingin a linear diffusion behavior and a current responsecharacteristic of macroelectrodes (category-4). Figure 5shows the relationship between the oxidation peak currentdensity vs. the square root of the scan rate in Randles–Sevcik-like plots for the MDEA 050, MDEA 100 andMDEA 250 as determined by experiment and FEM

simulations and for uncoated MDEA 005, MDEA 010,MDEA 015 and MDEA 020 as determined by FEMsimulations.

Saito (1968) has studied the relationship between the d/rratio and its effect on the voltammetric shape usingsimulations. In the cited study it was shown that the ratio,d/r, can be used to delineate two clearly defined regimes ofdiffusion. Under one regime the individual discs in thearray have overlapping diffusion domains with the neigh-boring discs. Under the second regime, which prevailswhen d/r>12, the individual discs have independentdiffusion domains, thus acting as several isolated singlediscs in parallel (Lee et al. 2001). Under these conditionsradial diffusion dominates and sigmoidal voltammogramsare expected. For our MDEA devices, this critical ratio, d/r,has a fixed value of 4 and thus all registered cyclicvoltammograms are expected to be peak-shaped (lineardiffusion). Moreover, while a d/r>12 assures the fullbenefits of ultramicroelectrode performance in a microelec-trode array, it nonetheless demands a large plan area thatmay be inappropriate for an implantable device.

The purpose of the aforementioned experiments andsimulation of CVs at MDEAs 050, 100 and 250, was toestablish a reliable finite element model for simulating thevoltammetric performance of smaller dimensioned micro-disc electrode arrays. The successful demonstration of sucha model (Figs. 3, 4, and 5) then allows its use to predict thebehavior of MDEAs 001 to 020 of different d/r values. Thispredictive model provides the ability to simulate variouscombinations of disc diameters and disc-to-disc spacing atdifferent voltammetric scan rates and with different currentrequirements. This approach allows for transducer optimi-zation without incurring the upfront cost of microfabrica-tion. To study the interdependence of voltammetric scan

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Fig. 5 Relationship between the oxidation peak current density andsquare root of scan rate (Randles–Sevcik-like plots) for uncoatedMDEA 050, MDEA 100 and MDEA 250 as determined byexperiment and FEM simulations and for uncoated MDEA 005,MDEA 010, MDEA 015 and MDEA 020 as determined by FEMsimulations

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Fig. 6 Simulated half CVs ofindividual discs (a) MDEA 001(r=0.5), (b) MDEA 002.5(r=1.25), (c) MDEA 005(r=2.5), (d) MDEA 010(r=5.0), (e) MDEA 015 (r=7.5),(f) MDEA 020 (r=10.0) as afunction of increasingdisc-to-disc separation and fixedA=0.001 cm2 over the range−500 to 500 mV and at the scanrate of100 mV/s in 1.0 mMFcCO2H at RT (D=4.61e−10 m2/sand kf=kb=1.4e−102 m/s)

Biomed Microdevices (2009) 11:701–710 707

rate and disc-to-disc separations, half CVs were simulatedat various scan rates and for various disc-to-disc separa-tions. These results are displayed in Fig. 6. It was foundthat by increasing the disc-to-disc separation, the currentincreases and reaches saturation level consistent with theunderstanding that, beyond a certain disc to disc spacing,the individual discs are no longer within the diffusiondomains of each other and hence act independently. This is

summarized in Fig. 7 as a plot of response current vs. d/rfor an exampled slow scan rate (10 mV/s) and an exampledfast scan rate (100 mV/s).

Figure 7 shows that for each scan rate as the d/r valuesincrease, the current increases and approaches a saturationlimit beyond which further separation of the micro discsproduces no further current enhancements. The approach tothis limit is itself scan rate dependent and is achieved athigher d/r values at higher scan rates.

3.2 Electrochemical Impedance Spectroscopy (EIS)

Figure 8(a) is the experimentally determined Bode magni-tude and phase of the MDEA 050, MDEA 100, MDEA 250transducers along with the simulated Bode magnitude andphase of MDEA 005, MDEA 010, MDEA 015 and MDEA020 in 1.0 mM FcCO2H (aq) made up in 0.1 M TRIS/0.1 MKCl solution. Figure 8(b) are the equivalent Cole–Cole orcomplex plane plots. Both experiments and simulationswere performed on MDEAs with d/r=4. However, MDEA050, MDEA 100, MDEA 250 transducers were of electro-active area, A=0.1 cm2, while transducers MDEA 005,MDEA 010, MDEA 015 and MDEA 020 were of area, A=0.001 cm2, accounting for the differences in data groupings.The MDEAs show a charge transfer characteristic that isassociated with the presence of a redox active specie in thesolution and is indicated by the phase angle tendingtowards lower values at low frequencies. This tendencytowards lower phase angle scales with the diameter of the

0 50 100 1500

1

2

3

4

5

d/r

Cur

rent

µA

001-10mv001-100mv002.5-10mv002.5-100mv005-10mv005-100mv010-10mv010-100mv015-10mv015-100mv020-10mv020-100mv

Fig. 7 Current as a function of d/r for (●) MDEA 001 (r=0.5), (▪)MDEA 002.5 (r=1.25), (◂) MDEA 005 (r=2.5), (▾) MDEA 010(r=5.0) (▸) MDEA 015 (r=7.5), ( ) MDEA 020 (r=10.0) of A=0.001 cm2. Open markers are at a slow scan rate (10 mV/s) and filledmarkers are at a high scan rate (100 mV/s)

Fig. 8 Electrochemical impedance spectra; (a) Bode Plots and (b)Cole–Cole Plots for uncoated (Δ) MDEA 050 (r=25), (□) MDEA 100(r=50), (○) MDEA 250 (r=125) as determined by experiment andFEM simulations and for uncoated (▾) MDEA 005 (r=2.5),

(▪) MDEA 010 (r=5), (●) MDEA 015 (r=7.5) and (♦) MDEA 020(r=10) as determined by equivalent circuit model simulations. Insertshows the behavior of the MDEA 050, MDEA 100 and MDEA 250

708 Biomed Microdevices (2009) 11:701–710

disc and increases with decreasing microdisc diameter(enhanced flux). This is consistent with the voltammetricobservations of higher current densities for lower discdiameters (Justin et al. 2008). The impedance data of theMDEAs 050 to 250 was parameterized using an equivalentcircuit comprising a parallel combination of constant phaseelement and charge transfer resistance in series with thesolution resistance (Rahman et al. 2008). The impedance ofthe four MDEAs (005 to 020) was simulated using thesame equivalent circuit model that was used to parameterizethe experimental data from MDEAs 050, 100 and 250. Theimpedance simulation parameters for MDEAs 005, 010,015 and 020 were derived from equivalent circuit fitparameters of MDEAs 050 to 250 and the cyclic voltam-metry data from these MDEAs.

The solution resistance parameter, which was found tobe almost unchanged for the MDEAs 50 to 250 wasaveraged and used to extract the solution resistivity, whichis a material constant. This resistivity was then used tocalculate the solution resistance of the new MDEAs using

the expression R=ρ /2*d, where ρ is the solution resistivityand d is the disc diameter. The n factor of the CPE, which is aquantity reflective of the physical characteristics of thetransducer’s surface and is linked to the manufacturingprocess, was the same for all of the MDEAs used in thisstudy and was parameterized based on the n-factor of theCPE that was obtained for MDEAs 50 to 250. The Qparameter of the CPE was calculated from the directrelationship between Q and the surface area of the MDEAs.From the experimental data of MDEAs 50 to 250, anormalized, dimensionless Q value was obtained by dividingby the area of the MDEAs (0.1 cm2), which was thenmultiplied by the area of the new MDEAs (0.001 cm2) toyield the desired Q values. The calculation of Rct for the newMDEAs, however, is more involved. Here, we employ theStern–Greary relationship, which relates the charge transferresistance to the charge transfer current, given as follows.

Rct ¼ 1

2:3030b1

i

where, Rct is the charge transfer resistance, i is the chargertransfer current, and beta is the system constant. From theRct values available from circuit fitting of experimental dataof MDEAs 50 to 250 and i values available from the CVdata (peak currents), beta values were calculated for MDEAs50 to 250. These beta values were then extrapolated to yieldbeta values for the new MDEAs. These were then used inconjunction with the simulated CV peak currents of MDEAs005 to 020 to yield the Rct values for the new electrodes.The experimental EIS data of MDEAs 50 to 250 and thesimulated EIS data of MDEAs 005 to 020 are show in Fig. 8.

4 Conclusions

The geometric design parameters for electrochemical trans-ducers that are based on the hexagonal close packedmicrodisc array are; (a) the disc diameter, (b) the disc-to-

0 10 20 30 40 500

20

40

MDEA Microdisc Radius, r (µm)

d/r

0 10 20 30 40 500

0.1

0.2

Pla

n A

rea,

P (

cm2 )

d/r-10mvd/r-100mvP-10mvP-100mv

Fig. 9 The optimized d/r ratio (left) and plan area, P, (right) as afunction of selected microdisc radius, r, for a fixed electroactive area,A=0.001 cm2 at 10 mV/s and 100 mV/s

Table 1 Critical geometric design parameters for optimized MDEA performance at the 67% peak current efficiency for MDEAs that were offixed A=0.001 cm2

10 mV/s scan rate 100 mV/s scan rate

MDEA Ndisc 67% of Ipk Plan area (cm2) d/r 67% of Ipk Plan area (cm2) d/r

1 127,324 2.49E−11 1.46E−01 23 2.58E−11 3.97E−02 122.5 20,372 9.39E−11 9.95E−02 19 9.58E−11 2.75E−02 105 5,093 2.35E−10 6.20E−02 15 2.41E−10 1.35E−02 710 1,273 5.29E−10 2.75E−02 10 5.46E−10 6.89E−03 515 566 8.71E−10 1.76E−02 8 9.05E−10 4.41E−03 420 318 1.17E−09 1.35E−02 7 1.26E−09 2.48E−03 350 51 3.18E−09 4.40E−03 4 4.36E−09 1.10E−03 2

Ipk currents listed in column 2 and 6 are the results of simulations of single disc electrodes

Biomed Microdevices (2009) 11:701–710 709

disc spacing, and (c) the number of discs. Abundant, smalldisc diameters are either difficult to manufacture or arequite expensive. A large number of discs leads todifficulties in the mask generation process for photolithog-raphy due to the conversion of small circular geometries,that are piecewise linear, into associated data files.Likewise, it is impractical to fabricate MDEAs with largedisc-to-disc separations as this will violate the plan areaconstraint, producing bulky transducers. A suitable com-promise has been reached by defining the peak currentoptimum at 67% of the peak current that corresponds todisc-to-disc separations that define infinite separation.Based on this definition, the disc-to-disc separation for thesix simulated MDEAs were found and are tabulated inTable 1 alongside the plan area and the governing currents asdictated by two voltammetric scan rates, 10 and 100 mV/s.The relationship between the d/r and the plan area as afunction of the microdisc diameter is illustrated in Fig. 9.

The important constraints in the implementation of thesedesigns for implantable biosensor applications are; (a) thetotal electroactive surface area of the transducer to supporttargeted current values, (b) the total plan area to limitoverall size of the transducer, and (d) the voltammetric scanrate or amperometric transient electrochemical response tomaximize current response. While all interrelated, the firstconstraint of total electroactive area may be set, as in thiscase (0.001 cm2), by the application, which could be in vivoor in vitro, that yields current values that are readilymeasured by the specified instrumentation. In the case ofin vivo applications, the second constraint (total plansurface area) should be minimized in order to reduceattendant tissue scarring and discomfort to the subject. Thefinal constraint is governed by sensor update frequencyrequirements and power demands on the instrumentation.

Acknowledgments This work was supported by the US Departmentof Defense (DoDPRMRP) grant PR023081/DAMD17-03-1-0172 andby the Consortium of the Clemson University Center for Bioelec-tronics, Biosensors and Biochips.

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