voltammetric sizing and shaping of a cylinder

Available online at www.sciencedirect.comJournal of

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Journal of Electroanalytical Chemistry 611 (2007) 201–207

ElectroanalyticalChemistry

Voltammetric sizing and shaping of a cylinder

Nicole Fietkau a, Ian Streeter a, Javier del Campo b, Andreu Llobera b, Roser Mas b,Francesc Xavier Munoz b, Richard G. Compton a,*

a Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdomb Centro National de Microelectronica, IMB-CNM, CSIC, Campus de la Universidad Autonoma de Barcelona, Bellaterra 08193, Spain

Received 20 July 2007; received in revised form 16 August 2007; accepted 24 August 2007Available online 4 September 2007

Abstract

A reversible electron transfer is studied at a microdisk electrode which is partially blocked by an inert particle at the disk center. Theinert particle is either a cylinder of a sphere. The size of a cylinder located at the center of the microdisk electrode is determined with thehelp of a simple electrochemical procedure. Cyclic voltammograms for the reduction of a reversible redox system are recorded as a func-tion of scan rate and compared to simulations. Excellent agreement between theory and experiment was found. Modelling diffusion to amicrodisk electrode modified with a sphere or cylinder at its center by numerical simulations gives physical support for the transition indiffusion-layer shape and size, therefore allowing to size not only particles of known shape but also, in principle, to determine their shapeand size simultaneously.� 2007 Elsevier B.V. All rights reserved.

Keywords: Particle sizing; Particle shaping; Modified electrodes; Electrochemical analysis; Cyclic voltammetry; Simulation

1. Introduction

In a series of experiments, we have demonstrated the useof electrochemical methodologies in determining the sizeand precise location of inert particles of known shape. Ini-tially, we determined the average size of these particles atabout the micron level by a simple electrochemical proce-dure in which the particles were deposited on a macroelec-trode and cyclic voltammograms of a reversible redoxcouple were recorded as a function of the voltage-scan rate.With a total mass of the particles and a value for their den-sity, the accurate size was calculated [1]. We sized a spher-ical particle placed at the center of a microdisk electrode bycomparing experimental voltammograms of a simple redoxsystem at different scan rates with simulated voltammo-grams [5]. The same concept was extended to three dimen-sions by depositing a sphere adjacent to a microdisk

0022-0728/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jelechem.2007.08.021

* Corresponding author. Tel.: +44 (0)1865 275 413; fax: +44 (0)1865 275410.

E-mail address: [email protected] (R.G. Compton).

electrode; chronoamperometric measurements of a simpleredox system were compared with Lattice Boltzmann sim-ulations to derive the radius of the sphere and its distancefrom the electrode. By using a three-electrode array in a tri-angulation experiment, we were able to pinpoint the exactposition of the sphere [6]. Cyclic voltammetric experimentswere applied to the same system and the resulting voltam-mograms were compared with Lattice Boltzmann simula-tions. Size and distance determinations were derivedmore precisely at the expense of time [7]. Taking this ideafurther, we measured the radius of identical hemisphericalmicrodroplets immobilized on a regular array of hydro-phobic polymer blocks of a partially blocked electrode bycomparing a simple Cottrellian-like potential-step experi-ment with simulations [3]. These experiments build on ideasimplied in scanning electrochemical microscopy and thosedeveloped for measuring film thickness [8,9].

Developing these concepts further, we report herein theuse of linear sweep voltammetry to elucidate not only thesize but also the shape of a single, inert cylinder locatedat the center of a microdisk electrode (Fig. 1). Specifically,

mailto:[email protected]

Fig. 1. Schematic representation of the physical system in which re is theradius of the electrode, rc is the radius of the centered cylinder and hc is theheight of the cylinder.

Table 1Boundary conditions

Boundary Condition

Semi-infinite boundary [A] = [A]bulk

Insulating surface o½A�oz ¼ 0

Symmetry axis o½A�or ¼ 0

Surface of inert block o½A�o�n ¼ 0

Electrode surface ½B�½A� ¼ expð F

RT ðE � E>ÞÞ

202 N. Fietkau et al. / Journal of Electroanalytical Chemistry 611 (2007) 201–207

we examine theoretically whether the shape of voltammo-grams taken at different scan rates is the same for a cen-tered sphere and a centered cylinder. In particular, weattempt to fit simulations of a sphere at the center of amicrodisk electrode with simulations of a cylinder at thecenter of an electrode of the same size. The size of a cylin-der is then determined by comparing experimental cyclicvoltammograms taken at different scan rates with simu-lated voltammograms. Excellent agreement between theoryand experiment is found.

The work presented here builds on our ongoing studiesinto the feasibility of using electrochemical techniques toyield information on the structure of an electrode surface.The sphere and the cylinder are used as the blocking speciesto illustrate the effects of the particle shape, although weanticipate that in future work we will be able to give anaccount of the current response for a more comprehensiverange of shapes. Linear sweep voltammetry is used as anexperimental method because it allows the study of the cur-rent response under different diffusional behaviours byvarying the scan rate. We note that other electrochemicaltechniques may prove to be more informative as our workdevelops.

2. Mathematical model and numerical simulation

The models under consideration here consist of a micro-disk electrode of radius re with an inert cylinder or spherelocated at its center. We wish to simulate the currentresponse of the simple electron transfer in Eq. (1), assum-ing only species A is present in bulk solution.

A�Bþ e� ð1Þ

The diffusion of species A through solution is expressedusing Fick’s second law in cylindrical polar coordinates:

o½A�ot¼ D

o2½A�or2þ 1

ro½A�orþ o2½A�

oz2

� �ð2Þ

The diffusion coefficient, D, is assumed to be equal for bothspecies, A and B, such that the concentration of species Bmay be found at any point in solution from Eq. (3):

½A� þ ½B� ¼ ½A�bulk ð3Þ

in which [A]bulk is the bulk concentration of species A. Theconcentration profile of species A is found by solving

Eq. (2) subject to the boundary conditions in Table 1.The boundary condition at the block surface is a zero fluxcondition in the direction normal to the surface, and thezero flux condition at the axis of symmetry is only imple-mented in the region above the inert particle. The bound-ary condition at the electrode surface derives from theNernst equation and assumes that the electron transfer isfast and reversible. The Faradaic current, I, is then foundfrom the concentration profile through Eq. (4), where theintegral is taken between the limits 0 6 r 6 re for the sphereor rc 6 r 6 re for the cylinder, where rc is the cylinderradius:

I ¼ 2pFDZ

o½A�oz

� �z¼0

r dr ð4Þ

Eq. (2) is discretised over a simulation grid and solvedusing the alternating direction implicit (ADI) finite differ-ence method [10,11] combined with the Thomas algorithm.The simulation grids used have been previously describedin reference [12] for the case of the cylinder, and reference[6] for the case of the sphere. These grids utilise high meshdensities at the singularities in boundary conditions thatoccur at the surfaces of the inert blocks and at the edgeof the disk. The simulation programme is tested for bothspatial and temporal convergence to ensure that there isless than 0.5% variation from the asymptotic peak currentvalue for all scan rates considered.

3. Experimental

3.1. Chemical reagents and instrumentation

All chemicals used were of analytical grade and used asreceived without any further purification. Hexaamineruthe-nium(III) chloride (Ru(III)(NH3)6Cl3) was purchased fromAldrich and potassium chloride (KCl) was supplied by Rie-del-de-Han. All solutions were prepared with deionisedwater with resistivity of no less than 18.2 MX cm (Milli-pore Water Systems, UK).

Cyclic voltammetric measurements were carried outusing a l-Autolab III (ECO-Chemie, Utrecht, Nether-lands) potentiostat interfaced to a PC using GPES (version4.9) software for Windows. All measurements were con-ducted by using a three-electrode cell, where the workingelectrode was a gold microdisk electrode modified with acylinder in the center of the electrode. The exact character-

Table 2Characteristics of the working electrode

Parameter Size (lm)

Microdisk radius, re 50Block radius, rc 30Block height, zc 5

Table 3Radius of the cylinder, rc in lm that would be necessary to fit a sphere ofdifferent radii, rs

Scan rate, v in V s�1 rs = 10 lm rs = 20 lm rs = 40 lm

0.005 14.0 24.0 45.50.01 13.0 24.0 45.30.1 11.0 22.0 42.70.2 10.7 21.5 41.70.4 10.7 21.5 40.70.6 11.0 21.0 40.51.0 10.5 21.0 40.35.0 11.5 20.7 40.2

N. Fietkau et al. / Journal of Electroanalytical Chemistry 611 (2007) 201–207 203

istics of the physical system (see Fig. 1) are listed in Table 2.The counter electrode was a bright platinum wire and a cal-omel electrode was used as a reference electrode. All exper-iments were carried out at 293 ± 2 K. Before commencingexperiments the working electrode was electrochemicallyactivated by cycling from 0.0 to �1.3 V (vs. SCE) in0.1 M KCl at 0.1 V s�1.

3.2. Fabrication of microdisk electrodes

SU-8 2005 and 2025 negative photoresists were used tobuild the cylinder-like structures in the center of the elec-trode. The procedure was as follows: A series of microelec-trodes were fabricated on a 0.5 mm thick pyrex wafer usingstandard photolithographic techniques as described else-where [2–4]. After cleaning it by rinsing with DI water

Fig. 2. Fitting the simulated current response of a microdisk modified with a spcylinder. Note that the height of the cylinder was twice its radius to account fparameters were used: [Abulk] = 1 · 10�6 mol cm�3, DA = 6.2 · 10�6 cm2 s�1, r

(a) 0.01 V s�1, (b) 0.1 V s�1, (c) 0.6 V s�1 and (d) 1.0 V s�1.

the wafer was dehydrated. A SU-8 layer (SU-8 2005 and2025, Microresist Technology GmbH, Germany) is thenspun over the substrate with a spinning speed profile of400 rpm · 15 s, followed by 3000 rpm · 60 s and finishingwith 640 rpm · 4 s. Then, the wafers are left on a flat sur-face to level the SU8 layer and any remaining air bubblesare carefully removed with a pin. The substrates are thenbaked at 95 �C for 10 min, exposed during 10 s to UV lightusing the appropriate mask and post-exposure-baked(PEB) for 15–20 min at 95 �C as to cross link the polymericstructures. When they reach room temperature again, they

here at the center of the electrode to that of a disk modified with a centeredor the symmetrical shape of the sphere. For the simulation the following

e = 50 lm, rs = 40 lm, Estart = 0.2 V, Estop = � 0.5 V, E0 = 0.2 V and v =


are immersed in propylen glycol methyl ether acetate(PGMEA, MicroChem Corporation, Newton, MA,USA), which dissolves the non-exposed SU-8. Last, thewafers are thoroughly rinsed with isopropanol and driedunder a nitrogen stream. The final cylinder-like structurespresented a thickness of 5 lm. Finally, the wafers are dicedinto individual chips which are subsequently mounted andencapsulated on individual PCBs.

4. Results and discussion

The influence of the shape of the particle was investi-gated theoretically by attempting to fit simulated voltam-

Fig. 3. Concentration profiles for a microdisk modified with a centered spheresystem at (i) �0.15 V, (ii) �0.26 V and (iii) �0.40 V. For the simulatDA = 6.2 · 10�6 cm2 s�1, re = 50 lm, rs = 40 lm, Estart = 0.2 V, Estop = �0.5 V

mograms of a reduction of a simple and reversible redoxsystem of a microdisk electrode modified with a sphere atthe center of the electrode with simulations of a cylinderat the center. Simulated voltammograms for different radiiof the sphere, rs, positioned at the center of the electrodewere generated for a range of scan rates (0.005–5.0 V s�1). These voltammograms were then attempted tofit by using a simulation program for a cylinder at the cen-ter of an electrode. All parameters that do not define theshape of the particle—the radius of the electrode, re, thediffusion coefficient, D, and the bulk concentration, c—were kept the same in both simulations. Note that theheight of the cylinder, zc, was assumed to be twice the

illustrating the increase of scan rate on the mass transport properties of theion the following parameters were used: [Abulk] = 1 · 10�6 mol cm�3,, E0 = 0.2 V and v = (a) 0.005 V s�1, (b) 0.1 V s�1 and (c) 1.0 V s�1.


radius of the cylinder to account for the symmetrical shapeof the sphere and that a fit is regarded as a best fit when thepeak currents of the two simulations match. In Table 3 theradius of the cylinder that would be necessary to produce abest fit are listed for a range of scan rates and sphere radii.For all sphere radii, the radius of the cylinder that is neces-sary to produce a best fit increases with decreasing scanrates. Fig. 2 shows the comparison between the simulatedvoltammograms for a centered sphere and a centered cylin-der. Although at high scan rates similar radii for the sphereand cylinder are observed to match the peak currents, thedecline of the current after the peak potential differs for

Fig. 4. Concentration profiles for a microdisk modified with a centered cylindproperties of the system at (i) �0.15 V, (ii) �0.26 V and (iii) �0.40 V. For the siDA = 6.2 · 10�6 cm2 s�1, re = 50 lm, rc = 40 lm, zc = 40 lm, Estart = 0.2 V, E

1.0 V s�1.

both systems. This effect together with the decreasing cylin-der radii for increasing scan rates indicates the contrastingmass transport properties to the electrode caused by thedifferently shaped particles; hence resulting in different dif-fusion fields.

To further examine the nature of the difference in thevoltammetric responses, concentration profiles for bothsystems were generated at different potentials and scanrates (Figs. 3 and 4). The profiles clearly demonstrate theeffects of the sphere and the cylinder on the mass transportproperties of the system. In the case of the sphere, Fig. 3,the concentration profile starts in the confined space

er illustrating the effect of an increasing scan rate on the mass transportmulation the following parameters were used: [Abulk] = 1 · 10�6 mol cm�3,

stop = �0.5 V, E0 = 0.2 V and v = (a) 0.005 V s�1, (b) 0.1 V s�1 and (c)

Fig. 5. SEM image of a microdisk electrode of 50 lm radius modified witha cylinder of 30 lm radius and 5 lm height.

Fig. 6. Cyclic voltammograms for the reduction of 1 mM (Ru(III)(NH3)6-Cl3) in 0.1 M KCl recorded at scan rates ranging from 0.01 V s�1 to 1.0V s�1 for the electrode corresponding to Fig. 5.

Fig. 7. Comparison between the experimental and theoretical currentresponse at 0.1 V s�1 and 0.2 V s�1. For the simulation the follow-ing parameters were used: [Abulk] = 1 · 10�6 mol cm�3, DA = 5.6 ·10�6 cm2 s�1, re = 50 lm, rc = 30 lm, zc = 5 lm, Estart = 0.2 V, Estop =� 0.5 V, E0 = 0.19 V.

Fig. 8. Comparison between experimental and theoretical results for acylinder placed in the center of a microdisk electrode. The parameters usedfor the simulations were as follows: [Abulk] = 1 · 10�6 mol cm�3,DA = 5.6 · 10�6 cm2 s�1, re = 50 lm, rc = 30 lm, zc = 5 lm, Estart =0.2 V, Estop = �0.5 V, E0 = 0.19 V.


between the sphere and the electrode surface, almost alongthe whole length of the electrode, as a nearly flat layerbefore changing into the hemispherical shape associatedwith a steady-state current at a microdisk electrode atlonger times. Whereas the concentration gradient at veryhigh scan rates, Fig. 3c (i)–(iii), is located within the con-fined space between the sphere and the electrode, it is verysteep and surmounts the sphere at low scan rates, Fig. 3a(i)–(iii). In the case of the cylinder, Fig. 4, the diffusion pro-file changes from a almost flat layer near the uncoveredpart of the electrode surface into the hemispherical shapealso observed for the sphere. The concentration profile ofthe two systems resemble each other at slow scan ratesand high potentials in which the diffusion-layer thickness,approximately given by

ffiffiffiffiffiffiffiffi2Dtp

, is big compared to the sizeof the electrode and sphere or cylinder. However, at med-ium and high scan rates the concentration profiles of the

two systems differ sufficiently from each other to cause adifference in the voltammetry as observed in Fig. 2. Hence,by varying the timescale of the experiment not only the sizeof particles of known shape can be deduced from cyclic vol-tammetric measurements but also their shape.

Fig. 5 shows a SEM image of a microdisk electrodemodified with a centered cylinder. The image showing thevolume of the structure were taken with the sample andthe electron beam at a 45� angle. Subsequent analysis ofthe image resulted in an electrode radius of 50 ± 1 lm, acylinder radius of 30 ± 1 lm and a cylinder height of5 ± 0.5 lm.


Cyclic voltammograms were then recorded as a functionof scan rate (0.01–1.0 V s�1) for the reduction of 1 mMRu(III)(NH3)6Cl3 in 0.1 M KCl aqueous solution (Fig. 6).Using the simulation program described in Section 2, thecurrent responses of the modified electrode were simulatedand compared to the experimental data. Only the forwardscan of the cyclic voltammogram is used in this comparison.Fig. 7 illustrates a representative comparison of simulatedand experimental current responses in which the peak cur-rents as well as the peak shape agree. The plot of peak cur-rent vs. the square root of the scan rates exhibits a goodagreement between theory and experiment (Fig. 8) and con-firm the dimensions of the cylinder obtained independentlyby SEM.

5. Conclusions

We have theoretically shown that it is possible to elec-trochemically shape a particle located at the center of amicrodisk electrode by comparing voltammetric simula-tions for a centered sphere to those of a centered cylinder.For all sphere radii investigated there is not one set ofparameters that fit the whole range of scan rates; withincreasing scan rate the radius of the cylinder that wouldbe necessary to fit the voltammetric response of a spheredecreases. This together with the different decline of thecurrent response after the peak potential prove that it isnot only possible to size a particle of known shape but alsoto distinguish electrochemically between the shape of theparticle based on the different mass transport propertiesto the electrode caused by the differently shaped particles.We note that the redox couple used in such an experimentwould have to be carefully chosen to avoid any unwantedadditional contributions to the current in the decliningregion of the voltammogram, for example from a secondelectron transfer process.

We have also shown that the size and shape of a ‘‘real’’cylinder at the center of a microdisk electrode can be deter-mined by a simple electrochemical procedure in which vol-tammograms of a simple redox couple are recorded andcompared to simulated ones. Work to extend this conceptto differently shaped particles as well as the tracking ofmoving particles is currently under way in our lab.

Acknowledgement

N.F. and I.S. thank the EPSRC for project studentships.

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voltammetric sizing and shaping of a cylinder

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