random assemblies of microelectrodes (ram™ electrodes) for electrochemical studies

1388-2481/99/$ - see front matter q 1999 published by Elsevier Science S.A. All rights reserved.PII S1388- 2481 (99 )00100 -9

Thursday Sep 30 12:56 PM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 110

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Electrochemistry Communications 1 (1999) 502–512

Random assemblies of microelectrodes (RAMy electrodes) forelectrochemical studies

Stephen Fletcher, Michael David Horne *CSIRO Minerals, Box 312, Clayton South, Vic. 3169, Australia

Received 5 August 1999; received in revised form 20 August 1999; accepted 23 August 1999

Abstract

The application of random assemblies of microdisks (RAMy electrodes) to electrochemical studies is described. These devices haveworking surfaces intersected by hundreds or thousands of disk-shaped microelectrodes that are capacitively, resistively, and diffusivelyindependent. They therefore produce current–time responses of the same form as single microelectrodes, but many times larger. This propertyallows experimental data to be obtained on the benchtop without shielding and without significant mains interference — something that isimpossible with single microelectrodes. The design criteria of random assemblies are summarized, and examples of their utility in a widerange of electrochemical experiments are given. q 1999 published by Elsevier Science S.A. All rights reserved.

Keywords: Microelectrodes; Electrode arrays; Voltammetry; Equivalent circuits

Fig. 1. The concept of a random assembly of microdisks: (a) section view,(b) plan view.

1. Introduction

A decade ago, single microelectrodes promised to revolu-tionize electrochemical research [1,2], but today thispromiseremains largely unfulfilled. The main reasons for this are two-fold: they have low current output, and they have an alarmingsusceptibility to mains interference. In combination, thesefactors are deadly. For example, when currents in the picoamprange must be measured, the faradaic signal is often com-pletely submerged beneath capacitively coupled mains inter-ference, thus rendering the measurements useless. When thishappens, the experimenter has only one recourse — todecrease the interference — but since this typically involvesplacing all apparatus inside earthed screens, and wiring allcircuits in a common ground plane, it greatly adds to thecomplexity of experimental design, and in some cases makesexperiments impossible.

A lateral-thinking solution to this problem, which we haveadvocated for a number of years [3–5], is to make an assem-bly of thousands of microelectrodes wired in parallel, witheach microelectrode independent of its neighbours. Withcareful design, such an assembly may show all the usefulproperties of a single microelectrode, whilst generating asignal which is thousands of times larger. We call such assem-blies ‘random assemblies of microdisks’ or RAMy elec-

* Corresponding author. Tel.: q61-3-9545-8866; fax: q61-3-9562-8919;e-mail: [email protected]

trodes. In what follows we provide a summary of the designcriteria that must be met by these assemblies in order for themto function correctly, and then we provide some illustrativeexamples of their use in electrochemistry.

The random assembly concept is shown in Fig. 1. Notethat we use the word ‘assembly’ in preference to the word‘array’ because the microdisks are not regularly spaced. Typ-ically, the surface of an assembly is inlaid with about 3200randomly dispersed conducting carbon microdisks of 3.5 mmradius, embedded in epoxy resin. The carbon microdisks arethe sectioned ends of carbon fibres, and between 20 and 40%of them are electrically connected to the external circuit.Since the median nearest-neighbour distance of active

S. Fletcher, M.D. Horne / Electrochemistry Communications 1 (1999) 502–512 503


microdisks is approximately 70 mm, and the surface area ofthe assembly is 28 mm2, the fraction of the surface which iselectroactive is only 0.2%. Nevertheless the total resistanceis less than 4 V.

In order to prevent neighbouring microelectrodes frominterfering, it is necessary to ensure that they are far enoughapart to avoid any kind of coupling. In the present work wedo this by calculating bounds on the spacings needed to avoidcapacitive coupling, resistive coupling, and diffusive cou-pling, which we believe exhausts the known possibilities. Wealso derive an expression for the signal-to-noise ratio of awell-spaced assembly. Since the principal source of noise ismains interference, caused by near-field conduction betweenthe assembly and the nearby mains circuitry in the laboratory,we find that the signal-to-noise ratio is proportional to N notN1/2 as one might have expected. As a result, even modestincreases in N produce significant increases in performance.This makes multi-parallel-wired microelectrodes (arrays andassemblies) important candidates for the next generation ofsensors.

Presently, the development of a full theory of diffusion tonon-independent microelectrodes in a spatially randomassembly is stalled by a lack of appropriate mathematicaltools, although the problem could, in principle, be solvednumerically by Brownian dynamics simulation. However, afew papers have been published on the related problem ofmutually interacting regular arrays of microdisks [6–8],which at least provide some qualitative insight into the spa-tially random case. One such paper is by Amatore et al. [6],who investigated by approximate methods the analytical the-ory of cyclic voltammetry in the case of a reversible couplein solution. Two limiting behaviours were predicted:a steady-state response at low sweep rates (or low number of micro-disks per cm2), and a quasi-reversible response at high sweeprates (or high number of microdisks per cm2). As we showlater, similar limits are observed experimentally in the caseof random assemblies.

Another paper on regular arrays of microdisks was pub-lished by Reller et al. [7], who computed cyclic voltammo-grams by digital simulation and then compared them withknown asymptotic formulae in three limits. These were1. at short times, when planar diffusion to individual micro-

disks predominated;2. at intermediate times, when radial diffusion to microdisk

edges became significant; and3. at long times, when planar diffusion was restored, albeit

across the whole face of the electrode (includinginsulator).

In each limit good agreement was found with conventionaltheory.

Finally, a third paper on regular arrays of microdisks waspublished by Shoup and Szabo [8]. These authors simulatedcurrent–time transients on a regular array in response topotential steps, and also developed an interpolation formulaaccurate to better than 2%.

Unfortunately, none of the above approaches is strictlyapplicable to the case of random assemblies, so in the presentwork we have confined ourselves to the calculation of boundsthat ensure microdisk independence within a few percent ofaccuracy.

Regarding the fabrication of assemblies, literature issparse, and the few papers that have been published tend todescribe widely different manufacturing techniques. Forexample, there are papers on thick film printing coupled withlaser micromachining [9], injection of liquid conductor intoporous insulator [10], injection of liquid insulator intoporous conductor [11], formation of conducting channels inself-assembled monolayers [12,13] and microlithography[14,15]. However, none of these methods has yet produceda product that is both robust and repolishable. The only excep-tion is the epoxy resin impregnation of carbon fibres, whichis the technique we have used in the present work [3–5].

2. Design criteria

In order to obtain readily measurable currents at an assem-bly of microdisks it might be thought desirable to cram asmany microdisks as possible into the available space. How-ever, in order to ensure the independence of the microdisksthere is an upper limit on the number density that can be used.If this number density is exceeded, capacitive, resistive, anddiffusive interferences occur, and ultimately the wholeassembly behaves as a single large electrode. It is thereforeimportant to derive formulae that tell us at what point suchinterferences become significant.

2.1. Capacitive independence

If the microdisks at the surface of an assembly are notsufficiently far apart, the possibility exists that the diffuseparts of their electrical double layers might overlap. This isof special concern in dilute electrolyte solutions wheredoublelayers extend into solution. To explore this possibility, weneed a measure of the thickness of the diffuse part of thedouble layer. Fortunately, an exact solution to this problemis known in the case of planar electrodes, and, to a good levelof approximation, this solution can be applied to microdisksof radius greater than 1 mm in aqueous solutions.

A measure of the thickness of the diffuse part of the doublelayer in dilute electrolyte solutions is the Debye length LD

[16]. This is the characteristic distance at which the electro-static (Coulomb) potential becomes significantly shieldedby the counter ions adjacent to the microdisk surfaces. Solv-ing Gauss’s law in the direction normal to the plane of theelectrode surface, the Debye length is found to be

2 2 1/2L s[́ ´ kT/ r z e ] (1)D 0 i i8i

where ´ is the dielectric constant of the electrolyte solution(78.5 for pure water at 258C), ´0 is the permittivity of free

S. Fletcher, M.D. Horne / Electrochemistry Communications 1 (1999) 502–512504


space (8.854=10y12 Jy1 C2 my1), k is Boltzmann’s con-stant (1.381=10y23 J Ky1), T is the absolute temperature(K), ri is the number density of ions in the bulk of the solution(my3) and zie is the ionic charge (C). The summationextends over all the different ions in solution.

It may be observed that the magnitude of the Debye lengthdepends solely upon the properties of the electrolyte solutionand not upon any properties of the electrode surfaces such astheir charge density or electrode potential. Specifically, for asimple 1:1 electrolyte dissolved in water [16]:

y1/2L f0.304c nm (2)D

where c is the concentration of electrolyte in mol ly1. Itfollows that the maximum size of LD is attained in pure waterat pH 7.0, where the concentration of ions is minimal (i.e.,10y7 M H3O

q, and 10y7 M OHy). Under such conditionsthe Debye length is 960 nm, implying that capacitive (diffuselayer) interferences between microdisks in aqueous solutionscan always be avoided by ensuring that the inter-electrodespacing is greater than 2 mm.

2.2. Resistive independence

The theory of the resistance of an electrolyte solutionbetween a single disk electrode and a large electrode at infin-ity has been presented by Newman [17]. At a long distanceaway from the centre of the disk the resistance increases as

R 2 rf1y (3)≥ ¥R p x`

where

y1R s[4kr] (4)`

and where k is the specific conductance of the electrolytesolution, r is the radius of the microdisk, and x is the distancefrom the centre of the disk.

For present purposes we are concerned with the more com-plex case of the resistance between N microdisks in a randomassembly and a large electrode at infinity. Clearly, when therandom assembly is widely spaced the system behaves as Nresistors in parallel, but when the random assembly is com-pact the total resistance will be larger and will be an extremelycomplex function of the spatial distribution and radii of themicrodisks. In such a scenario it would be very difficult toderive an analytical formula for the smallest average interdiskspacing that would allow the total resistance to remain within10%, say, of the ‘widely-spaced’ limit. Nevertheless, anapproximate method does present itself. This is to consider asingle microdisk in isolation, and then determine the radialdistance at which R/R`s90%, since this represents, roughly,the radius of the zone in which most of the solution resistanceis concentrated. From Eq. (3) we find that this zone radiusis about 6.4r, implying that for 3.5 mm radius microdisks theinterdisk spacing should be at least 12.8r or 45 mm. Computersimulations yield comparable figures [7,18].

2.3. Diffusive independence

When designing random assemblies of microdisks, thehardest problem to avoid is diffusive interference betweenadjacent microdisks. Unfortunately, no exact solution isknown for the extent of diffusive interference between twocoplanar microdisks, let alone a large number of them dis-tributed at random. However, by the standard methods ofmathematical physics, a solution can be derived for thesteady-state diffusion-limited current at two interferingcoplanar microhemispheres, and this can be used to get abound on the problem. By a method similar to that of Alfredand Oldham [19] we obtain

` sinh b(mq1)I s4pnFDCr (y1) (5)2 8 sinh mbms1

which may be compared with the diffusion-limited current attwo independent coplanar microhemispheres, for which

2I s4pnFDCr (6)1

In the above two formulae, I is the steady-state diffusion-limited current, cosh bsd/2r, d is the distance between themicrohemispheres, and r is their radius. It is found that forthe inequality

I 2 G95% (7)2I1

to be achieved (i.e., for diffusive interference to be negligi-ble) requires d/rG20. In our case using carbon fibre micro-disks of 3.5 mm radius, this implies an average spacingbetween the microdisks of greater than 70 mm. Our assem-blies are therefore carefully designed to achieve this value.Of course, in the much more complex case of N microdisksin a random assembly (N42) the time variable also entersthe picture because a steady state is then sandwiched betweentwo Cotrellian relaxations: one at short times due to planardiffusion to individual microdisks, and one at long times dueto planar diffusion to the whole electrode surface.

However, if we apply Shoup and Szabo’s interpolationformula for a regular array [8], assume a diffusion coefficientof reactant of 10y5 cm2 sy1, and a time scale of 1 s, we obtaina similar inequality for d/r.

2.4. Sources of noise

In electrochemistry there are many sources of noise. Inmicroelectrode measurements, however, one source of noisedominates all others: interference from the a.c. mains supply.The origin of this interference is indicated in Fig. 2, where itis shown how the interference current enters the cell via thestray capacitance Cstray. Note that, contrary to popularmythol-ogy, the interference current is not caused by electromagneticradiation, but rather is caused by near-field conduction.

Generally Cstray arises in one of two ways: either as theinput capacitance of the control electronics or as a distributed



Fig. 2. The origin of interference in microelectrode measurements. In effect,the electrochemical cell is at the intersection point of two circuits, the controlcircuit and the interference circuit. The latter is formed by the stray capaci-tance between the cell and the mains source, which in turn is connected tothe control circuit via a common ground.

capacitance associated with the finite dielectric constants ofthe glass, the solution, and the air surrounding the cell. How-ever, irrespective of the physical cause of the stray capaci-tance, the effect is the same: cell currents are contaminatedby interference currents originating in the mains supply.

Naturally, it is of interest to minimize this interference.However, before we can suggest methods of doing this wemust first develop a mathematical model of the interferenceprocess. We begin by assuming that the impedance of thecontrol electronics is high enough for the control circuit notto act as an interference shunt. The problem then reduces tothat of finding the current Iinterference that flows through theinterference circuit in response to the mains voltage:

VsV sin vt (8)0

where V0 is the amplitude of the mains voltage and v is themains frequency. By equating the currents flowing throughCstray and Rcell a differential equation is readily obtainedwhichsolves to yield

V 0I s sin(vtqf) (9)interference NzN

where

2 2 1/2NzNs(R q[1/vC ] ) (10)cell stray

and

y1fscot (vR C ) (11)cell stray

In the above equations NzN is the magnitude of the impe-dance in the interference circuit and f is the negative of thephase angle. The behaviour of Iinterference therefore dependson the relative values of Rcell and 1/(vCstray). If the productof v and Cstray is very large, then Rcell41/vCstray and

V 0I f sin(vt) (12)interference R cell

In this limit the stray capacitance behaves as a short circuitand the interference current is conducted directly into the cell.Alternatively, if the product of v and Cstray is comparativelysmall (the usual case since Cstray is typically a few picofaradswhile v is 50 or 60 Hz), then Rcell<1/vCstray and

I fV C v cos(vt) (13)interference 0 stray

In this limit the stray capacitance is partially blocking sothe interference current is both attenuated and differentiated.As a result any high frequency components in the mainssource tend to be exaggerated in the interference. Furtherdiscussion of this phenomenon may be found in Refs.[20,21].

The melancholy conclusion from Eq. (13) is that, for asingle microelectrode, the only practical method of decreas-ing the interference current is to decrease Cstray, since themains voltage V0 and mains frequency v are not generallyexperimental variables. In theory this can be done by placingan earthed screen around the cell (in the case of distributedstray capacitance) or by placing an earthed screen around thecontrol electronics (in the case of significant input capaci-tance). In practice, however, neither of these strategies is100% effective, which means that some interference currentis always present in single microelectrode measurements. Itis this residual interference current that makes single micro-electrode measurements so difficult at low bulk concentra-tions of electroactive species where faradaic currents aresmall.

Fortunately, this is not the end of our story because whatis of most concern experimentally is not the absolute valueof Iinterference but the magnitude of the signal-to-interferenceratio NIsignalN:NIinterferenceN. By changing to an assembly it ispossible to multiply Isignal by virtually any desired amount,simply by increasing the number N of microdisks in theassembly within the spatial limitations discussed earlier.Thus, at low frequencies, assemblies having N)1000 nec-essarily have more than three orders of magnitude greaterimmunity to mains interference than single microelectrodes.

3. Experimental

Electrochemical measurements were carried out using amodel 175 universal programmer coupled to a model 173potentiostat, both from Princeton Applied Research Corp.(NJ, USA). The current flowing in the working-electrode/counter-electrode circuit was converted to a proportionalvoltage and amplified using a model 176 current follower,also from Princeton Applied Research Corp. Results wererecorded on flatbed X–Y recorders (model 7046A from Hew-lett-Packard Inc., San Diego, USA, and model 3023 fromYokogawa Electric Works, Tokyo, Japan) or on a digitalstorage oscilloscope (model 2232 from Tektronix, Beaver-ton, USA). Anodic stripping voltammetry was performedusing a programmable trace element analyser (model

TEA3000 from Chemtronics Ltd., Perth, Australia).



Fig. 3. Electrochemical currents recorded in response to triangular scans ofapplied potential in 10y3 M K4Fe(CN)6/K3Fe(CN)6, 0.1 M KNO3 (aq).The scan rate was 20 mV sy1. Note that the random assembly (Ns260)produces a steady-state voltammogram; the carbon macrodisk does not.

The reference half-cell was AgNAgClNKCl(saturated),and all applied potentials are quoted with respect to it unlessotherwise specified. It had a potential q0.222 mV withrespect to the standard hydrogen electrode.

All solutions were prepared from water purified in a Milli-Qw reagent water system (from Milliporew, Bedford, USA)and from as-received analytical reagent grade chemicals.

All the assemblies in the present work were manufacturedby CSIRO’s patented method [3]. Before each experiment,electrochemically active and reproducible working surfaceswere prepared using the following procedure:1. The working surface was polished using a clean, napped

polishing cloth (Microclothw from Buehler, Lake Bluff,IL, USA) for at least 30 s using 0.3 mm polishing alumina(from Engis Ltd., Melbourne, Australia), dispersed inMilli-Qw water.

2. The surface was thoroughly rinsed with Milli-Qw water.3. The working surface was briefly polished a second time

on clean, damp polishing cloth without alumina to removesurface-bound alumina particles.

4. The surface was thoroughly rinsed again with Milli-Qw

water.5. The working surface was dipped in 10% (v/v) aqueous

nitric acid for 10 s to decontaminate it, to remove adven-titious adsorbates (both specifically and non-specificallyadsorbed) from it, and to form a compact double layer.

6. The surface was thoroughly rinsed a third time with Milli-Qw water.After completing this procedure the working surfaces were

visually inspected under a metallographic microscope havinga resolution better than 1 mm (Nikon Epiphot, Tokyo, Japan)to ensure that all the microdisks were visible, flat, and freefrom polishing detritus. The importance of carefully follow-ing all the steps in the cleaning procedure cannot be over-emphasized — the electrochemical activity of carbon fibremicrodisks is critically dependent on surface preparation.

Random assemblies were used in two overall geometries:cylindrical or flat plate. The former was used in a conven-tional electrochemical cell, while the latter was used in arectangular channel flow cell (Dionex Corporation, Sunny-vale, USA).

4. Results

4.1. Demonstration of steady-state diffusion-limitedcurrents

Perhaps the best-known property of single microelectrodesis their ability to generate steady-state current/voltagecurvesin quiescent solutions. That this property is preserved by ourrandom assemblies is illustrated in Fig. 3 where the voltam-metric response of a 10y3 M solution of potassium ferricya-nide/ferrocyanide in 0.1 M potassium nitrate (aq) can beseen. For comparison, we have also included in Fig. 3 the

response of a 3 mm diameter glassy carbon macrodisk elec-trode under identical conditions.

During the manufacture of random assemblies, we havefound steady-state current/voltage curves of the form shownin Fig. 3 very useful in quality control, because they providequantitative measures of (i) the number of active microdisks,(ii) the cleanliness of the active microdisks, and (iii) thespacing between the active microdisks.

The number of active microdisks N is estimated bydividingthe limiting current at y0.20 V by 1.05 nA. The latter is thelimiting current due to a single microdisk under the sameconditions. The cleanliness of the active microdisks isassessed by measuring the potential difference between thequarter-wave potential E1/4 and the three-quarter-wavepotential E3/4, a measure known as the Tomes Criterion T.ˇAt a clean, uncontaminated, electrode surface T is 56 mV.The existence of sufficient spacing between the activemicrodisks is indicated by a low hysteresis between the for-ward and backward scans: 16 mV is ideal. The use of hyster-esis as a measure of microdisk spacing works as follows. Asanticipated by Amatore et al. [6], when microdisks arepacked closer together their steady-state behaviour trans-forms into a quasi-reversible behaviour due to the loss ofdiffusional independence. Empirically, we have observedprecisely this effect, and we have also observed that the firstsign of its onset is a voltammetric broadening. Hence, thewidth of the voltammogram is a convenient and sensitivemeasure of diffusional overcrowding.

Besides their uses in quality control, steady-state current/voltage curves can also be exploited in analytical applica-tions, where the simple act of differentiating steady-statedatahas been found to significantly enhance the resolution ofoverlapping processes. An example is shown in Fig. 4, whichillustrates the undifferentiated and differentiated currentsrecorded at a random assembly in a solution containing 20ppm nitrite ions and 0.2 M sodium chloride (aq). Despite the



Fig. 4. The undifferentiated current (lower curve) and the differentiatedcurrent (upper curve) recorded using a random assembly in a solutioncontaining 20 ppm nitrite ions and 0.2 M NaCl (aq). Ns390.

Fig. 6. The time dependences of charging currents recorded in response toa 200 mV step in applied potential in Milli-Qw water. Ns590 in the randomassembly used.

Fig. 5. Approximate model network of a single microdisk.

proximity of the oxygen evolution reaction, a well-definedand readily measured peak is obtained in the differentiatedcase. Finally, steady-state conditions can also be exploited inanodic stripping voltammetry, where they produce time-invariant deposition currents without stirring, and also pro-duce drift-free background currents during the strippingprocess.

4.2. Rapid charging of capacitance

Under potentiostatic conditions the capacitive charging ofour random assemblies occurs very rapidly. This means theelectrode potential is established very rapidly, which in turnmeans that very fast reactions can be studied. To understandwhat makes this possible, a model network of a single micro-disk electrode is needed. One such model is shown in Fig. 5.

Strictly speaking, this network is only approximatebecause the solution resistance is not really single-valued;actually, one finds that there is a distribution of values overthe surface of the microdisk, given by the formula:

2 1/2R (d)s[1y(d/r) ] /2kr (14)V

2 1/2s2NR M[1y(d/r) ] (15)V

where r is the radius of the microdisk, RV(d) is the solutionresistance at radial distance d on the surface of the disk(0FdFr), k is the specific conductivity of the solution, andNRVM is the solution resistance averaged over the wholemicrodisk. However, since we are concerned here only withorder-of-magnitude estimates of the time constant of thecapacitive charging process, and since it is apparent from Eq.(15) that RV(d) nowhere exceeds twice its average value,no great error is introduced by replacing the distribution ofvalues of solution resistance with the average value [4kr]y1.

If a potential step is now applied between points P1 and P3

of the model network, the potential across the interphase (i.e.between points P1 and P2) does not respond immediately, buttakes a certain time to reach its new, steady value. If wedenotethe time-varying potential between points P1 and P2 as Ec(t),

and write the applied potential between P1 and P3 asEappliedH(t), where H(t) is Heaviside’s unit step functionapplied at ts0, we obtain the required result in the form:

R fE (t)s E [1yexp(ykt)]H(t) (16)c appliedR qRf V

where k is the potential step time constant given by

1 1ks q (17)

R C R Cf V

Clearly, this time constant is determined by the smaller ofthe two terms RfC and RVC, which explains the rapid charg-ing. For example, a rough calculation of the capacitance C ina concentrated electrolyte gives

y2 2Cf[10 mF cm ]=pr f4 pF

and a similarly rough calculation of the resistance RV gives

y1R s[4kr] f7 kVV

where the conductivity k of the solution has been taken asequal to that of 1.0 M KCl (aq). Hence, the product RVC forone of our assemblies is approximately 30 ns, which is neg-ligible compared with the time scale of ordinary electrochem-ical experiments ()20 ms). An experimental determinationof the difference in response times of the capacitive chargingcurrents on an assembly and a glassy carbon macrodisk elec-



Fig. 7. Anodic stripping voltammograms recorded on a mercury-coatedrandom assembly. Ns390. The solution, a simulated industrial effluent,contained 100 ppb of lead.

Fig. 8. The effect of current leakage on the shape of a voltammogramrecorded using a random assembly in 0.5 M KNO3. Ns1640. The scan ratewas 200 mV sy1.

trode (As7 mm2) in an extreme case (Milli-Qw water) isshown in Fig. 6. The amplitude of the potential step was 200mV. The superiority of the assembly is evident.

The speed of potentiostatic charging may be contrastedwith the speed of galvanostatic charging. If we denote acurrent step driven through the points P1 and P3 of the modelcircuit by IappliedH(t), then the current through the capacitorC is

I (t)sI exp(yjt)H(t) (18)C applied

and the current step time constant j is given by

1js (19)

R Cf

In this case, the resistance of the solution has no effect onthe speed of the capacitive charging of the electrode. The timeconstant jFk, and therefore the electrode capacitance in thegalvanostatic case always charges more slowly than it doesin the potentiostatic case.

Because capacitive charging on random assemblies is alsovery rapid under conditions of linear potential scan (see Eq.(22) later on) voltammetry can be carried out at very highscan rates. This is particularly advantageous in anodic strip-ping voltammetry (ASV) where peak heights or peak areasare the standard measures used to determine the concentra-tions of analytes. Fig. 7 shows some examples of anodicstripping voltammograms recorded on a mercury-coatedassembly using different scan rates of applied potential.Clearly, the possibility exists of raising the ASV techniqueto new levels of sensitivity, and we are actively pursuing thisidea in our laboratories.

4.3. Immunity to leakage currents

The response of a microdisk assembly to continuous tri-angular scans of applied potential is shown in Fig. 8.

This figure also illustrates an artefact that commonly dis-torts measurements on single microelectrodes at ultra-lowcurrent levels (-1 pA) — a skewed baseline. We have tracedthis phenomenon to the occurrence of leakage currents thatflow through (or over the surface of) an electrode’s insulationand into its back contact. (Note: By a leakage current wemean any current that flows from the counter electrode to theworking electrode lead, whilst bypassing the working elec-trode surface. Such a current can arise because of a poormechanical seal between the microelectrode and the sur-rounding insulation, or because of a conducting film of mois-ture on the microelectrode body, or simply because of aparasitic conduction pathway through any of the materials ofthe electrochemical cell.) Purely for the purposes of illustra-tion, we deliberately generated a leakage current by providinga resistive path of value 40 MV across the total electrodeimpedance of one of our random assemblies. We did this bytouching the metal contact at the back of the assembly ontothe solution-wetted internal glass wall of the electrochemicalcell. It is obvious from the figure that even a comparatively

high resistance (40 MV) still has a dramatic effect on theexperimental output.

Of course, a leakage path of 40 MV can easily be remedied,but on the picoamp scale the situation is not so straightfor-ward, as a simple Ohm’s law calculation demonstrates. Forexample, given a faradaic current of 1 pA, and a potentialdifference of 1 V between a single microelectrode and asolution, a resistance of 1012 V must be engineered betweenthe internal body of the working electrode and the externalsolution to prevent a leakage current equal to that of thefaradaic current! This is quite difficult to achieve, as designersof capacitors well know. Indeed, the penetration of moistureinto microporous ceramics, plastics, etc., is a perennial prob-lem in the microelectronics industry. Thus, the hydrophobi-zation of insulation is an important consideration in thedesignof microelectrodes for picoamp sensitivity. It is also interest-ing to explore other strategies that might be adopted to over-



Fig. 9. A model network that simulates the effect of a leakage path (RL)around a random assembly. N is the number of microdisks in the assembly.

come this problem. To this end, we have found a modelnetwork useful (Fig. 9).

We define Rf as the faradaic resistance of a singlemicrodisksurface, C as its interfacial capacitance (assumed to be inde-pendent of potential), RV as the local uncompensated resis-tance of the solution, RL as the resistance of the leakage path,and N as the number of microdisks. The full effect of RL cannow be understood by deriving the current–time responseI(t) of the model network in response to a triangular scan ofapplied potential E(t), where

nE(t)s {t[H(t)yH(tyT)]q[2Tyt][H(tyT)

T

yH(ty2T)]} (20)

In this equation n is the linear scan rate of applied potential,T is the time taken to reach the furthest excursion point ofE(t), and H(t) is Heaviside’s unit step function applied atts0. Using the Laplace transform method we obtain thesolution in the form:

2R fI(t)s nNC[1yexp(ykt)]µ ≥ ¥R qRf V

N 1qn t q H(t)f≥ ¥∂R qR RV L

2R fy2 nNC[1yexp(yk[tyT])]µ ≥ ¥R qRf V

N 1qn[tyT] q H(tyT)≥ ¥∂R qR Rf V L

2R fq nNC[1yexp(yk[ty2T])]µ ≥ ¥R qRf V

N 1qn[ty2T] q H(ty2T) (21)≥ ¥∂R qR Rf V L

where21 1 R qRV Lks q (22)≥ ¥≥ ¥R C R C Rf V L

The first term in I(t) is the response to the forward scan,the second term is the response to the backward scan, and thethird term is the decay of the current to a steady value afterthe end of the backward scan. From the formula for I(t) itcan readily be deduced that the maximum height of the hys-teresis between the forward and backward currents in the plotof current versus applied potential is

2R fI yI s2nNC (23)f b ≥ ¥R qRf V

which is independent of RL, whereas the minimum slope ofboth currents is

DI N 1s q (24)

DE R qR Rf V L

which is a strong function of RL, at least for RL<[RfqRV].

Thus, it follows from this latter equation that, for a fixed valueof N, the magnitude of the leakage current can be diminishedonly by improving the quality of the insulation between theback contact and the working face of the electrode. Con-versely, for fixed RL, it follows that the ratio of faradaiccurrent to leakage current can be increased in proportion toN, thus making it clear that a random assembly of microdiskshas higher immunity to leakage currents than a singlemicrodisk.

4.4. Uses in nucleation studies

Random assemblies are particularly useful in studies ofnucleation and growth phenomena because, at low overpo-tentials, it is possible to deposit individual crystals on indi-vidual microdisks, so that crystals grow independently. Inthis way the two most serious impediments to the precisestudy of nucleation phenomena on large electrodes — theocclusion of active sites by the diffusion zones of growingcrystals, and competition for reactant between adjacent crys-tals — are avoided. Furthermore, the total observed electricalcurrent at a random assembly is the linear superposition ofthe electrical currents from all crystals considered indepen-dently; a property which allows the time dependence of thenumber of nucleated crystals to be derived directly from onecurrent–time transient [4] instead of having to carry outhundreds of separate experiments on a single microelectrode.

Some current–time transients for the nucleationandgrowthof lead crystals on a random assembly are shown in Fig. 10.This figure also illustrates another advantage of randomassemblies for nucleation studies, namely, the wide separa-tion along the time axis between the capacitive charging ofthe electrode and the growth of the crystals. The resolutionof these phenomena in Fig. 10 is, indeed, unprecedented; andconfirms that non-steady-state phenomena in electrochemicalnucleation, which are normally obscured by double-layercharging, are now accessible to scientific enquiry [5].

4.5. Uses in flow cells

Random assemblies of microdisks can be readily adaptedfor use in rectangular channel flow cells, where their prop-erties of fast response, ease of polishing, and ability to operate



Fig. 10. Nucleation and growth of lead crystals on a random assembly inresponse to negative steps of applied potential in an aqueous solution of10y2 M Pb(Ac)2 in 0.1 M NaAcq0.1 M HAc. Ns2500.

Fig. 11. Currents recorded at a random assembly in a rectangular channelflow cell during linear scans of applied potential. Ns500. The solution was10y3 M K3Fe(CN)6, 0.5 M KNO3 (aq) and the scan rate was 10 mV sy1.The thickness of the spacer is as shown. The corresponding cell volumeswere 2.7 ml (upper curves) and 10.7 ml (lower curves). The volume flowrates were: (A) 0.00 ml miny1, (B) 0.06 ml miny1, (C) 0.51 ml miny1,(D) 1.73 ml miny1, (E) 4.00 ml miny1. The combined reference/counterelectrode was a plate of stainless steel in the same solution (SSSS). Notethat the oscillations at non-zero flow rates were caused by deliberatelyintroduced flow rate pulses, not noise pickup.

Fig. 12. Voltammograms recorded on a random assembly in a rectangularchannel flow cell, in the presence and absence of supporting electrolyte.Ns500. The scan rate was 200 mV sy1, the cell volume was 5.35 ml, andthe flow rate was 3.0 ml miny1. Top traces: Reduction of K3Fe(CN)6.Bottom traces: Oxidation of K4Fe(CN)6. The three traces correspond to:(A) 10y4 M of each electroactive species plus 0.5 M KNO3 (aq), (B) 10y4

M of each electroactive species, and (C) Milli-Qw water (no electroactivespecies).

in the absence of supporting electrolyte, make them extraor-dinarily attractive for sensing.

Considering a conventional rectangular channel flow cellof area A and height H, in which one entire face is a planarelectrode of area A, the limiting current at high volume flowrates is [22]

2/3DA 1/3I s1.47nFc V (25)lim b f≥ ¥H

where Vf is the volume flow rate (cm3 sy1), D is the diffusioncoefficient of the reactant (cm2 sy1), cb is its bulk concen-tration (mol cmy3), and Vf4DA/H. Unfortunately, at lowvolume flow rates, no such limiting current is observedbecause of the depletion of reactant at the electrode surface,and instead an unwanted time dependence appears in meas-urements. Random assemblies avoid this complication byproducing steady-state current/voltage curves even at zeroflow rates (Fig. 11). This happens because of the high sta-bility of the diffusion zones surrounding individual micro-disks. As a result, our assemblies generate steady-statelimiting currents at all flow rates below turbulence.

The use of random assemblies of microdisks in rectangularchannel flow cells also makes possible the observation ofdouble-layer effects (Kryukova effects [23]) with unprec-edented clarity. This is because of the speed with whichsolutions can be exchanged via flow-switching valves, cou-pled with the intrinsic advantage of massively decreased IRdrop. Double-layer effects, which are associated with a sig-nificant potential drop f2 across the diffuse part of the doublelayer in dilute electrolyte solutions, are generally manifestedin two ways: (i) as decreases in the electron transfer rate,since the potential difference between the working electrodeand the plane of closest approach of reactants is (Eappliedyf2) rather than Eapplied, and (ii) as changes in the concentra-tions of charged species, relative to their bulk values, becausethe electrostatic potential in the diffuse part of the doublelayer modifies the local population of ions. Two examples ofdouble-layer effects are shown in Fig. 12, where voltammo-

grams for the reduction of ferricyanide FeIII(CN and3y)6

oxidation of ferrocyanide FeII(CN are shown. It can be4y)6

seen that as supporting electrolyte is removed (curves B) anasymmetry develops; at positive potentials the oxidation offerrocyanide continues because the reactant ions are electro-statically attracted to the electrode surface, whereas at nega-tive potentials the reduction of ferricyanide ‘switches off’because of the electrostatic repulsion of the negatively



Fig. 14. Currents recorded on a random assembly after 20 successive trian-gular scans of applied potential in 10y3 M bis[cyclopentadienyl] iron(II)(ferrocene), 0.1 M LiClO4 in MeCN. Ns1095. Note that the currentsrecorded at potentials negative to q0.35 V are caused by the reduction ofproduct accumulated after the scans to potentials positive to q0.35 V.

Fig. 13. Current/voltage curves for 7,7,8,8-tetracyanoquinodimethane(TCNQ) immobilized beneath a layer of Nafionw on the surface of a randomassembly in a rectangular channel flow cell. Ns620. The four differentcurves were recorded in aqueous solutions of potassium chloride at theindicated concentrations.

charged ferricyanide ions. Many similarly fascinating phe-nomena related to multiply charged ions surely await discov-ery via this new method. (For a further discussion, see Ref.[24].)

A final example of the use of random assemblies in flowcells is in the measurement of concentration dependences,especially of surface-immobilized species. An example isgiven in Fig. 13, which shows the behaviour of nanocrystal-line 7,7,8,8-tetracyanoquinodimethane (TCNQ) immobi-lized on an assembly beneath a layer of Nafionw, in responseto four different concentrations of potassium chloride. Thepeaks shift by approximately 60 mV per decade, proving thatthe reduction of TCNQ to K(TCNQ) is first order in Kq.Most notably, a much wider range of potassium chlorideconcentrations can be used than on a conventional macro-electrode, because the high flux of Kq to the individualmicrodisks, and the absence of any solution contribution tothe IR drop, minimize the impact of diffusive and resistivedistortions.

4.6. Detection of back reactions

A remarkable property of random assemblies is that, if theproduct of a forward reaction is soluble and electroactive, aback reaction can sometimes be detected even though it mightnot be detected at a single microdisk in isolation. This ispossible because the diffusion of product away from a randomassembly occurs in two stages: at first, roughly hemisphericaldiffusion zones develop around each microdisk just as theywould if all the microdisks were independent, but later on —if sufficient time is allowed to elapse — some diffusive coa-lescence occurs. As a result, the escape of product is slightlyinhibited and this makes it possible for the back reaction tobe detected.

An example of the detection of a back reaction is shownin Fig. 14, which was recorded after 20 triangular scans ofpotential were applied to a random assembly in a solution of10y3 M ferrocene. Note that the back reaction that has built

up at potentials negative to q0.35 V could easily be mistakenfor a baseline offset. Clearly, one must be careful to avoidthis mistake when analysing data obtained from randomassemblies.

5. Conclusions

Design criteria for random assemblies of microdisks havebeen derived. Theoretical analysis shows that the most impor-tant factor is a wide spacing between microdisks, which isneeded to guarantee capacitive, resistive and diffusive inde-pendence. When this is successfully arranged, assembliesexhibit all the advantages of individual microelectrodes,whilst being able to provide high currents, high immunity tomains interference, and high immunity to leakage currents.Furthermore, when assemblies are made by potting carbonfibres in epoxy resin, they are robust and can be repolishedmany times.

The advantages of random assemblies can now besummarized:

(1) Random assemblies of 1 cm2 can pass currents thatare about 1000 times greater than those that pass through asingle microelectrode. This removes the need for special low-noise amplifiers, and allows conventional electronics to beused for all laboratory work.

(2) Random assemblies allow electrochemical measure-ments to be carried out in highly resistive media, such asdilute aqueous solutions. The total current at an assembly isgenerally much smaller than that at a macrodisk electrode —roughly one hundredth the value — and, consequently, dis-tortion of voltammograms by IR drop is easier to avoid.

(3) Random assemblies allow diffusion coefficients ofelectroactive species to be measured in viscous media. Unlikerotating disk electrodes, or dropping mercury electrodes,assemblies have no moving parts. Steady-state diffusion-lim-ited currents can therefore be observed in motionless solu-tions, or in very viscous media.



(4) Random assemblies are comparatively immune toleakage currents. At ultra-low current levels (- 1 pA) singlemicrodisk measurements are prone to distortion by leakagecurrents that bypass the microdisk surface and flow to thecurrent collector via the solvent-wetted side walls of the elec-trode body or through poorly sealed gaps between the micro-disk and the matrix material. These leakage currents manifestas skewed, ohmic, baselines in current/voltage curves. Leak-age currents around assemblies are made insignificant in threeways: the electrochemical current multiplier effect of themany microdisks, the hydrophobized side walls of the elec-trode body, and the strong chemical bonds between thecarbonfibres and the epoxy resin.

(5) Random assemblies have very small RVC time con-stants under potentiodynamic conditions, a property thatallows voltammograms to be recorded using very fast scanrates of applied potential — hundreds of volts per second.For disk-shaped electrodes the RVC time constant for estab-lishing the electrode potential at the disk surface is propor-tional to the radius of the disk. Consequently, the electrodepotential at an assembly is established thousands of timesfaster than the electrode potential at a macroelectrode.

(6) Random assemblies achieve steady-state diffusion-limited currents much faster than macroelectrodes. The timetaken to reach a steady-state current is proportional to thesquare of the radius of the individual microdisks, sincetssf400r2/D where r is the radius of a microdisk and D isthe diffusion coefficient of the reactant. Hence, at assemblies,steady-state diffusion-limited currents can be recorded with-out stirring the solution. In anodic stripping voltammetry(ASV) this same property produces drift-free backgroundcurrents and steady-state deposition currents.

(7) Random assemblies are remarkably insensitive tocapacitively coupled interference from nearby equipment.The amplitude of capacitively coupled interference currentsis independent of N, the number of microdisks. But the meas-ured current is directly proportional to N. Hence, the signal-to-interference ratio is proportional to N. In manyapplicationsthis removes the need for metallic screens around theapparatus.

(8) Random assemblies require less than one hundredththe amount of mercury than macroelectrodes during ASV.This property is important in environmental situations wherelegislation requires low mercury loading. It arises becausethe active surface area of an assembly is less than one hun-dredth that of a macroelectrode of comparable overalldimensions.

(9) Random assemblies are flat, robust, and can be repol-ished many times. Most other assemblies of microelectrodesthat have been reported have been made by microlithographictechniques. These are not flat, are not robust, and cannot berepolished. Assemblies, by contrast, can be repolished andreused several hundred times.

(10) Random assemblies can operate potentiostatically intwo-electrode cells. Just like single microelectrodes, assem-blies can operate potentiostatically in two-electrode cells pro-vided the counter electrode is large enough.

Acknowledgements

The authors thank the following for experimental assis-tance: Ms C.M. Calle, Dr R.L. Deutscher, Ms S. Ghosh, MrR.A. Pillig, Mr P.G. Symons, Mr A.J. Urban and Dr V.A.Vicente-Beckett. They also thank the following for theoreti-cal discussions: Professor S. Feldberg and Professor K.B.Oldham. Financial support from DIST, Chemtronics Ltd.,Melbourne Water, and CSIRO Minerals is gratefullyacknowledged.

References

[1] M. Fleischmann, S. Pons, D.R. Rolison, P.P. Schmidt, Ultramicro-electrodes, Datatech Systems Inc. Scientific Publishing Division,Mor-ganton, USA, 1987.

[2] M.I. Montenegro, M.A. Queiros, J.L. Daschbach (Eds.), Microelec-´trodes: Theory and Applications, Kluwer, Dordrecht, 1991.

[3] Int. Patent Applic. No. PCT/AU94/00466.[4] R.L. Deutscher, S. Fletcher, J. Electroanal. Chem. 239 (1988) 17.[5] S. Fletcher, in: M.I. Montenegro, M.A. Queiros, J.L. Daschbach´

(Eds.), Microelectrodes: Theory and Applications, Kluwer, Dor-drecht, 1991, pp. 341–355.

[6] C. Amatore, J.M. Saveant, D. Tessier, J. Electroanal. Chem. 147´(1983) 39.

[7] H. Reller, E. Kirowa-Eisner, E. Gileadi, J. Electroanal. Chem. 161(1984) 247.

[8] D. Shoup, A. Szabo, J. Electroanal. Chem. 160 (1984) 19.[9] B.J. Seddon, Y. Shao, H.H. Girault, Electrochim. Acta 39 (1994)

2377.[10] C.A. Huber, T.E. Huber, M. Sadoqi, J.A. Lubin, S. Manalis, C.B.

Prater, Science 263 (1994) 800.[11] B.K. Davis, S.G. Weber, A.P. Sylwester, Anal. Chem. 62 (1990)

1000.[12] R. Bilewicz, T. Sawaguchi, R.V. Chamberlin, M. Majda, Langmuir

11 (1995) 2256.[13] J.K. Schoer, Interface 4 (1995) 56.[14] R.S. Glass, D.R. Ciarlo, S.P. Perone, K. Ashley, Extended Abstracts

of the E.C.S. (Fall Meeting), Hollywood, FL, USA, 15–20 Oct. 1989,p. 969.

[15] R. John, M.G. Boutelle, M. Berness, personal communication, 1994.[16] J.N. Israelachvili, Intermolecular and Surface Forces, 2nd ed., Aca-

demic Press, London, 1994, p. 238.[17] J. Newman, J. Electrochem. Soc. 113 (1966) 501.[18] A.C. West, J. Electrochem. Soc. 140 (1993) 134.[19] L.C.R. Alfred, K.B. Oldham, J. Electroanal. Chem., in press.[20] S. Fletcher, M.D. Horne, J. Electroanal. Chem. 297 (1991) 297.[21] S. Fletcher, in: M.I. Montenegro, M.A. Queiros, J.L. Daschbach´

(Eds.), Microelectrodes: Theory and Applications, Kluwer, Dor-drecht, 1991, pp. 243–257.

[22] R.G. Compton, R.A.W. Dryfe, R.G. Wellington, J. Hirst, J. Elec-troanal. Chem. 383 (1995) 13.

[23] T.A. Kryukova, Dokl. Akad. Nauk SSSR 65 (1949) 517.[24] M.J. Palys, Z. Stojek, M. Bos, W.E. van der Linden, J. Electroanal.

Chem. 383 (1995) 105.

random assemblies of microelectrodes (ram™ electrodes) for electrochemical studies

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