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Theoretical and experimental study of the ECE mechanism at microring electrodes
Journal of
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 578 (2005) 289–299 www.elsevier.com/locate/jelechem
Theoretical and experimental study of the ECE mechanism at microring electrodes Irina Svir a,*, Alexander Oleinick a, Kamran Yunus b, Adrian C. Fisher b, Jay D. Wadhawan c,1, Trevor J. Davies c, Richard G. Compton c,* a
Mathematical and Computer Modelling Laboratory, Kharkov National University of Radioelectronics, 14 Lenin Avenue, Kharkov 61166, Ukraine b Department of Chemical Engineering, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK c Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, UK Received 20 December 2004; accepted 6 January 2005 Available online 23 February 2005
Abstract Microring electrodes are useful for the investigation of reaction kinetics due to their large perimeter to area ratio and compact nature but have hitherto been limited in application due to the absence of the underpinning theory. In this paper, we apply the conformal mapping technique recently developed by Amatore et al. [C. Amatore, A.I. Oleinick, I.B. Svir, J. Electroanal. Chem. 564 (2004) 245] for the simulation of chronoamperometry at very thin microring electrodes, where an ECE-type mechanism is in operation. The simulated results are compared with data obtained from chronoamperometry experiments with bromonitrobenzenes at lithographically fabricated gold microring electrodes. Best fit parameters for the experimental system are determined using an automatic fitting procedure. The dark electrochemical reduction of ortho-bromonitrobenzene (o-BNB) in 0.1 M tetrabutylammonium/acetonitrile solution is consistent with an ECE-type mechanism and a value of 20 s1 is theoretically determined for the unimolecular cleavage of the o-BNB radical anion, in good agreement with that previously reported for similar chemical systems. 2005 Elsevier B.V. All rights reserved. Keywords: Microring electrode; Chronoamperometry; Lithography; Conformal map; Simulation; Bromonitrobenzenes
1. Introduction The microring provides an attractive geometry for microelectrodes as it combines the large perimeter-toarea ratio (PAR) of the microband with the compact form of the microdisk [1]. In addition, the inner core which the electrode material surrounds is a unique fea* Corresponding authors. Tel.: +38 057 702 10 20; fax: +38 057 702 10 13 (I. Svir); Tel.: +44 01865 275430; fax: +44 01865 275410 (R.G. Compton). E-mail addresses: [email protected] (I. Svir), richard.compton @chemistry.ox.ac.uk (R.G. Compton). 1 Present address: Ecole Normale Supe´rieure, Department de Chimie, UMR CNRS 8640 ‘‘PASTEUR’’, 24 rue Lhomond, 75231 Paris Cedex 05, France.
0022-0728/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2005.01.011
ture of the ring geometry and can be exploited. For example, OÕHare and coworkers [2] fabricated a micro-optical ring electrode (MORE) where the inner core of the ring is a strand of fibre optic allowing a simple experimental procedure for the investigation of coupled photochemical homogeneous reactions. Using a similar method, Szunerits and Walt [3] coated over 200 optical fibres with gold and constructed an array of MOREs. Unwin and coworkers [4,5] demonstrated the hydrodynamic possibilities for the microring geometry by using a hollow glass capillary as the inner core through which they forced solution to flow. Placing the electrode above a perpendicular insulating wall resulted in the radial flow microring electrode (RFMRE) [4,5]. Thus, the potential application of microring electrodes
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for electroanalysis and kinetic investigations is very promising. In this work, we demonstrate the ability of microring electrodes to probe homogeneous chemical reactions by combining precise simulations with the results from potential step experiments on a system where an ECE mechanism is in operation. In particular, we use a new method of microring fabrication based on the lithographic technique described by Jackel [6]. At present, the most popular method for ring fabrication is to coat an inner core, a pulled glass capillary, for example, with the electrode material via metal evaporation or painting with an organometallic compound followed by decomposition and metal deposition at high temperatures [1– 6]. Although this results in rings that can be as thin as 200 nm, it is difficult to obtain rings thicker than 500 nm and there is no way of ensuring a specific size prior to fabrication, i.e., the experimentalist has very little control over the ring parameters [4]. On the other hand, with the lithographic technique used in this work, microrings can be made to more or less the exact size and thickness required, with negligible increase in cost (currently, the minimum thickness possible is around 0.5 lm). Such a reliable fabrication technique allows the production of a ‘‘microring toolbox’’ where the electrochemist has available a wide range of microrings of varying thickness. For example, chronoamperometry with a microring toolbox could provide a viable alternative to cyclic voltammetry, where varying the ring thickness, as opposed to the scan rate, achieves the desired range of mass transport coefficients. As such, the use of microrings complements the possibilities offered by variable sized microdisk or microband electrodes. The sequence of all limiting diffusion regimes taking place at microrings of any thickness and their time limits were shown in a recent work by Amatore with coworkers [7]. Also, the difference between ÔbandÕ and ÔringÕ behaviour at steady state was proved [7]. A new approach for the simulation of the microring electrode problem by the conformal mapping technique was introduced in the work of Amatore et al. [7] which we use here for the simulation of an ECE mechanism under chronoamperometry at microring electrodes. The application of the conformal map for microring simulations allows one to investigate rings of any width from very thick to vanishingly thin. In the case of the latter, a precise and efficient simulation is especially important as edge effects play the main role in the concentration distribution and current density. In the simulations in this work, we apply the ADI method which has previously proved extremely efficient in combination with the conformal mappings for different microelectrode geometries such as rings [7], disks [8–11], double bands [12], double hemicylinders [13,14], and the channel double band flow system [15]. Since we simulate chronoamperometry, the exponentially expanding time grid,
initially proposed in [16], can be employed in all our calculations. The best fit parameters of experiments are determined by an automatic fitting procedure in program based on the Nelder–Mead minimisation algorithm [17,18]. In this article, we show good agreement between the theoretical results and experimental data for E- and ECE-mechanisms at lithographically fabricated microring electrodes.
2. Theory The two redox systems of interest are the non-aqueous reductions of para-bromonitrobenzene (p-BNB), which undergoes a simple E step, and ortho-bromonitrobenzene (o-BNB), which undergoes an ECE-type mechanism, as illustrated in Scheme 1 [19–21]. The one
Scheme 1. Reaction scheme for the electrochemical reduction of pBNB and o-BNB in TBAP/acetonitrile solutions. ‘‘HS’’ represents the solvent/supporting electrolyte system and ‘‘rds’’ is the rate determining step.
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electron reduction of p-BNB in dark conditions results in a radical anion that is stable on the timescale of the experiment [19,20]. However, the o-BNB radical anion undergoes a fast C–Br bond cleavage forming a nitrophenyl radical and a bromide anion. The nitrophenyl radical rapidly abstracts a hydrogen atom from the solvent/supporting electrolyte system, producing nitrobenzene which also undergoes a one electron reduction to the corresponding radical anion, resulting in an ECEtype mechanism [19,21]. The rate determining step in the homogeneous reaction sequence is the initial cleavage of the C–Br bond [19–21]. In the works of Amatore and Save´ant [22,23], it has been shown that current responses of ECE and DISP1 mechanisms are very similar when diffusion coefficients of species are almost equal and the value of the rate determining homogeneous rate constant is small enough for the transition from pure diffusion to pure kinetics is observable. However, the literature [19–21] relative to bromonitrobenzenes does not usually consider the alternative DISP1 route. Therefore, to remain consistent with the previous literature and compare our measurements within the same interpretative framework, we will consider only the ECE mechanism. Note that if a DISP1 mechanism is active, considering an ECE analysis should not greatly affect our results owing to the close identity of the two mechanistic behaviours [22,23]. The two-dimensional simulation for the chronoamperometry of a simple E step at a microring electrode (where the potential is stepped from a value where no charge transfer occurs to a potential where the redox reaction occurs at a rapid rate) using conformal mapping approach has been previously reported in [7] and shall be used to analyse our p-BNB experimental data. Concerning the o-BNB system, in the following section we discuss the simulation procedure employed for a potential step experiment at a microring electrode where an ECE mechanism is in operation. 2.1. Mathematical model
2 ocA o cA 1 ocA o2 cA ¼ DA þ 2 ; þ r or ot or2 oz
ð1Þ
2 ocB o cB 1 ocB o2 cB ¼ DB þ 2 k 1 cB ; þ r or ot or2 oz
ð2Þ
2 ocC o cC 1 ocC o2 cC ¼ DC þ þ þ k 1 cB ; r or ot or2 oz2
ð3Þ
where cA, cB, cC denote the concentrations of the species A, B and C; DA, DB, DC are the diffusion coefficients of A, B, C, respectively; t is the time elapsed since the beginning of the potential step; r and z are the cylindrical coordinates describing the semi-infinite space located above the insulating plane in which the electrode is embedded (Fig. 1). The initial and boundary conditions are: t = 0: 8r;
cA ¼ c1 A ; cB ¼ 0; cC ¼ 0;
8z;
ð4aÞ
t > 0: 0 < r < rin ;
z ¼ 0;
ocA ocB ocC ¼ ¼ ¼0 oz oz oz rin 6 r 6 rout ;
z ¼ 0;
z ¼ 0;
r > rout ;
ð4bÞ
ðinsulatorÞ; cA ¼ 0;
ocB ocA ¼ DA ; cC ¼ 0 DB oz oz
ðelectrodeÞ;
ocA ocB ocC ¼ ¼ ¼0 oz oz oz
ð4cÞ
ðinsulatorÞ; ð4dÞ
r ¼ 0;
8z;
ocA ocB ocC ¼ ¼ ¼0 or or or
ðsymmetry axisÞ; ð4eÞ
r ! 1;
We consider the ECE reaction mechanism at the ring electrode surface described by pathway (A1):
291
z ! 1;
cA ! c1 A ; cB ! 0; cC ! 0 ðinfinityÞ; ð4fÞ
where
c1 A
is the bulk concentration of the species A.
Aþe !B k1
B!C C þ e ! D
ðA1Þ
where k1 is the first order (irreversible) rate constant. The conditions of the experiment are such that at t = 0 only species A is present in solution and the applied voltage is stepped from a value where no redox reaction occurs to a potential where the reduction of both A and C is rapid and diffusion controlled. The mathematical model describing the diffusion mass-transport processes for the ECE mechanism is:
Fig. 1. Schematic diagram of a microring electrode indicating the notations and coordinates used in the real space.
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2.2. Normalised model Let us variables: R¼
r rout
introduce
Z¼
;
z zout
;
the
following
dimensionless
r2 k 1 K 1 ¼ out : DA
DA t s¼ 2 ; rout
ð5Þ
2
oC A o C A 1 oC A o C A ¼ þ þ ; R oR os oR2 oZ 2 2 oC B o C B 1 oC B o2 C B ¼ cB þ þ K 1CB; R oR os oR2 oZ 2
ð6Þ
ð7Þ
ð8Þ
s = 0: 8Z;
C A ¼ 1; C B ¼ 0; C C ¼ 0;
ð9aÞ
s > 0: 0 < R < a;
Z ¼ 0;
oC A oC B oC C ¼ ¼ ¼0 oZ oZ oZ
ðinsulatorÞ;
Z ¼ 0;
oC A oC B oC C ¼ ¼ ¼0 oZ oZ oZ R ¼ 0;
ð9cÞ
ðelectrodeÞ;
ðinsulatorÞ;
ð9dÞ
8Z;
oC A oC B oC C ¼ ¼ ¼0 oR oR oR Z ! 1;
ðsymmetry axisÞ;
C A ! 1; C B ! 0;
C C ! 0 ðinfinityÞ;
ð9eÞ
ð9fÞ
where a = rin/rout.
where cB = DB/DA and cC = DC/DA are the normalised diffusion coefficients of species B and C with the corresponding initial and boundary conditions:
8R;
C A ¼ 0;
oC B oC A ¼ ; CC ¼ 0 oZ oZ
R ! 1;
oC C o2 C C 1 oC C o2 C C ¼ cC þ þ þ K 1CB; R oR os oR2 oZ 2
cB
R > 1;
After the normalisations, the mathematical model given by Eqs. (1)–(3) becomes: 2
Z ¼ 0;
a 6 R 6 1;
ð9bÞ
2.3. Conformal mapping approach The conformal mapping for a ring geometry (Fig. 1) can be defined by a function of complex coordinate variables: X = R + iZ, where R and Z are the dimensionless cylindrical coordinates defined in Eq. (5) [7]: 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2 X 2 a2 A x ¼ arcsin @ ; ð10Þ p 1 a2 in which x = n + ig. The complex valued function in Eq. (10) maps the upper semi-infinite plane (Fig. 2(a)) onto the semi-infinite band with vertical insulating boundaries at n p = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 and n = 1 and with the segment ½0; p2 arcsinði a2 =ð1 a2 ÞÞ excluded from it (Fig. 2(b)). Fig. 2(c) illustrates the shape of the grid in real space
Fig. 2. Simulation area in different spaces: (a) real physical space, see Fig. 1; (b) conformal space; (c) computational grid in real space.
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corresponding to a regular rectangular grid in the conformal space (Fig. 2(b)). The back transformation from the simulation space onto the real one is given by the complex-valued function [7]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi p ð11Þ X ¼ ð1 a2 Þsin2 x þ a2 : 2
on og dx ¼ ¼ Re ; oR oZ dX
The mathematical model of the ECE mechanism in the transformed coordinates can be rewritten as: 2 oC A o2 C A o CA ¼D þ os og2 on2 1 oC A on oC A og þ þ ; ð12Þ Rðn; gÞ on oR og oR
dx 2X ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : dX p ðX 2 a2 Þð1 X 2 Þ
2 oC B o C B o2 C B ¼ D cB þ os og2 on2 cB oC B on oC B og þ K 1CB; þ Rðn; gÞ on oR og oR
is
2 oC C o C C o2 C C ¼ D cC þ os og2 on2 cC oC C on oC C og þ þ þ K 1CB; Rðn; gÞ on oR og oR
on og dx ¼ ¼ Im ; ð16bÞ oZ oR dX where the derivative of the complex valued function x(X) is given by ð17Þ
2.4. Current The expression for the current in the real coordinates Z
rout
rin
ð14Þ
ð16aÞ
IðtÞ ¼ 2pF ð13Þ
293
ocA ocC DA þ DC r dr: oz z¼0 oz z¼0
ð18Þ
The transient current can be rewritten as a function of dimensionless variables in the following form: IðsÞ ¼ 2pFc1 A r out DA Z 1 oC A oC C þ cC R dR: oZ Z¼0 oZ Z¼0 a
ð19Þ
The transient current in the conformal space is
where 2 2 on on D ¼ þ : oR oZ
IðsÞ ¼ 2pFc1 A r out DA ! Z 1 oC A oC C Rðn; gÞ dn: þ cC og g¼0 og g¼0 0
The new initial and boundary conditions are:
ð20Þ
s = 0: 8n;
8g;
C A ¼ 1; C B ¼ 0; C C ¼ 0;
ð15aÞ
3. Experiments 3.1. Chemical reagents
s > 0: 0 6 n 6 1; cB
g ¼ 0;
C A ¼ 0;
oC B oC A ¼ ; CC ¼ 0 og og
n ¼ 0;
ðelectrodeÞ;
ð15bÞ
8g;
oC A oC B oC C ¼ ¼ ¼ 0 ðsymmetry axis and insulatorÞ; on on on ð15cÞ n ¼ 1;
8n;
8g;
g ! 1;
oC A oC B oC C ¼ ¼ ¼ 0 ðinsulatorÞ; on on on ð15dÞ C A ! 1; C B ! 0; C C ! 0ðinfinityÞ: ð15eÞ
All partial derivatives in Eqs. (12)–(14) can be defined using the Cauchy–Riemann conditions:
All reagents were of the highest grade available commercially and were used as received without any further purification. These were 1-bromo-4-nitrobenzene (pBNB, 99%, Aldrich), 1-bromo-2-nitrobenzene (o-BNB, 98%, Aldrich) and tetrabutylammonium perchlorate (TBAP, electrochemical grade, Fluka). All solutions were prepared with dried and distilled acetonitrile (Fisher Scientific). In all experiments, the temperature was 298 ± 2 K. All solutions were outgassed with oxygenfree nitrogen (BOC Gases, Guilford, Surrey, UK) for at least 20 min prior to experimentation. During the experiments, the electrochemical cell was kept under a nitrogen atmosphere. 3.2. Instrumentation Voltammetric measurements were carried out using a l-Autolab I (ECO-Chemie, The Netherlands) potentiostat. All experiments were conducted using a three
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electrode configuration where the working electrode was a gold microring. At all times, the counter electrode was a bright platinum wire and a silver wire was employed as the reference.
3.2.1. Microring fabrication Glass wafers were cleaned using an acid wash of ‘‘piranha solution’’ [24] and rinsed in milli-Q water several times, before being blown dry using a supply of
Fig. 3. Illustration of the steps involved in (a) fabricating the photoresist patterns and (b) coating with gold film to produce a microring electrode.
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nitrogen. A photolithographic technique, based on a projection-printing system, was used to produce the gold microring patterns on the glass substrates [25–28]. The process involved using a technical drawing software package to create a scaled black and white artwork of the microrings that were then transferred onto highresolution millimask negative plates (Agfa) using standard photography techniques. Thin films of approximately 5 lm Shipley S1828 Photoresist (Chestech) were coated over the glass substrates using a spin coater and were pre-baked on a hot plate at 115 C for 1 min. The millimask negative plates were used to project an ultraviolet (UV) light source (340 nm) from a mask aligner (Karl Suss, model MJB 3) onto the substrates coated with the film of photoresist. The exposed films of photoresist were developed using a developer solution (AZ351, Chestech) to reveal the desired photoresist microring patterns. After the developing process, the substrates were washed with milli-Q water thoroughly before being blow dried in a clean supply of nitrogen and post-baked on a hot plate. Fig. 3(a) illustrates the steps involved in fabricating the photoresist patterns. The patterned substrates were then put through a metal coating cycle using an Edwards Auto 306 metal evaporator to give a titanium/gold film. The coated substrates were then immersed in acetone to lift off the photoresist to reveal the pattern of the microring gold films. Fig. 3(b) demonstrates the steps involved. A schematic diagram of a microring fabricated via this process is illustrated in Fig. 4. The thickness of the gold film was determined to be 80 nm by atomic force microscopy (AFM) conducted in contact mode with a Digital
295
Instruments (now a division of Veeco) Multimode SPM. As observed in Fig. 4, the pattern also includes a gold contact pad connected to the ring via a narrow gold band. Another layer of Shipley S1828 Photoresist was coated over the surfaces of the microring electrodes with the spin coater. Using another mask and photolithography process, a pattern of the photoresist was left over the contact lines leaving the microring electrodes and the contact pads as the only active regions. The photoresist pattern was then hard baked at 200 C for 30 min to create a chemically resistant insulated region over the contact gold contact lines. The microring electrodes were then ready to use once electrical contact was made via the contact pads.
4. Simulations 4.1. Computing All programs were written in Borland Delphi 7 Enterprise Edition and executed on a PC equipped with Intel Pentium 4 processor at 3.00 GHz and 512 Mb of RAM. In all simulations, we used a uniform spatial grid in the conformal space (Fig. 2(b)) of the size Nn · Ng = 100 · 100. The ADI method was applied for the discretisation of the partial differential Eqs. (12)–(14), since in our recent works this proved very efficient when coupled to simulations in conformal spaces [7–15]. Although the mathematical model described in this article allows setting different values to the diffusion coefficients, in all our calculations here the diffusion coefficients of all species were assumed equal. 4.2. Non-uniform time grid When simulating a chronoamperometry experiment, due to the singularity occurring in the concentration distributions at the moment when the potential is applied to the electrode, special care must be taken at the initial times of electrolysis. For this reason, we use the exponentially expanding time grid [16]: Dskþ1 ¼ ð1 þ lÞDsk ;
ð21Þ
where Dsk is the time step at kth time iteration and l is the expansion coefficient (l > 0). The strategy for the determination of the Ds0 and l values was discussed in detail in previous works [7,11,16]. The parameters used for the non-uniform time grid were chosen to be (see definitions in [16]): initial step, Ds0 = 106; grid expansion parameter, l = 2 · 103. 4.3. Fitting Fig. 4. Schematic diagram of a lithographically fabricated gold microring electrode.
An automatic fitting procedure based on the Nelder– Mead minimisation method [17,18] was employed for
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the determination of the best fit parameters (the diffusion coefficient, D, and the first order rate constant, k1) to the experimental data. In our case, the function to be minimised is the weighted sum of squared deviations between the experimentally measured ðI exp k Þ and simulated theoretical ðI sim k Þ currents: X sim 2 SSQ ¼ wk ðI exp ð22Þ k Ik Þ ; k
where wk is the weighting coefficient given by: 1 I sim k wk ¼ 1 þ exp ITe
ð23Þ
and I exp T e is the experimental current value at the time Te, i.e., at the end of the observation period.
5. Results and discussion 5.1. E mechanism Fig. 5 illustrates a cyclic voltammogram recorded in dark conditions at 0.1 V s1 for the reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile solution where the working electrode is a gold microring with parameters rin = 285 lm and rout = 315 lm. Both forward and back peaks are observed, consistent with a simple E step mechanism. In the forward scan, p-BNB is reduced to the radical anion (cathodic peak potential, Ep = 1.16 V vs. Ag) which is stable on the timescale of the experiment and is subsequently oxidised back to p-BNB on reversing the direction of potential sweep. Raising the scan rate, v, gave I-E signals with more pro-
Fig. 5. Cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile at a gold microring with rin = 285 lm and rout = 315 lm.
nounced peaks, whilst a decrease in v led to increasingly steady state like behaviour. Next in chronoamperometric experiments, the potential was stepped from 0 V vs. Ag, where no charge transfer occurs, to 1.3 V vs. Ag, where the reduction of p-BNB to the radical anion is rapid such that [p-BNB] at the electrode surface is zero, in accordance with the boundary conditions for the simulations. Fig. 6 shows the chronoamperometric response for the diffusion controlled reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile solution at a gold microring electrode with inner radius rin = 150 lm and outer radius rout = 210 lm. Overlaid as squares is the simulated response, generated using the theory discussed above using k1 = 0, for the given electrode parameters where the diffusion coefficient is Dp-BNB = 2.4 · 105 cm2 s1 (assuming that the diffusion coefficient of p-BNB and its radical anion are equal). In general, a good fit between experiment and theory was observed for a number of microrings of different sizes which gave a value for the diffusion coefficient of p-BNB to be Dp-BNB = (2.4 ± 0.2) · 105 cm2 s1. This value agrees with those previously reported [19,20] and should be similar to the diffusion coefficient for o-BNB, Do-BNB. Interestingly, the steady state current in Fig. 6 is approximately twice that calculated on the assumption that the ring acts as a ‘‘thin’’ microband electrode [29], confirming the essential need for simulations in this case. 5.2. ECE mechanism Fig. 7 illustrates a cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM o-BNB in 0.1 M TBAP/acetonitrile where the working electrode is the same as that in Fig. 5. As observed, there is a significant
Fig. 6. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of p-BNB at a ring with geometry rin = 150 lm and rout = 210 lm.
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297
difference between the two I–E signals for o-BNB and pBNB. In addition to an increased peak cathodic current, occurring at Ep = 1.39 V vs. Ag, the back peak corresponding to the oxidation of the o-BNB radical anion is absent. Raising the scan rate above 0.1 V s1 did result in the occurrence of an anodic peak, which grew for increasing scan rates. These observations are consistent with an ECE type mechanism where the homogeneous chemical reaction is fast. The C–Br bond of the oBNB radical anion undergoes a fast cleavage eventually producing nitrobenzene which is also reduced, resulting in an increased cathodic peak current, the magnitude of which resembles that of a two electron reduction.
Fig. 8 depicts the chronoamperometric response for the diffusion controlled reduction of o-BNB in the same solution used in Fig. 7, where the working electrode is a ring with parameters rin = 570 lm and rout = 630 lm. The potential was stepped from 0 V vs. Ag, where no charge transfer occurs, to 1.6 V vs. Ag, where the reduction of o-BNB and nitrobenzene is diffusion controlled, in accordance with the simulations. Overlaid as solid squares is the simulated response for an ECE mechanism obtained as a result of running the fitting procedure discussed above. The fitting was carried out assuming two variable parameters: the diffusion coefficient (assumed equal for all species: A, B, C in terms of Section 2.1 [30]) and the first order rate constant of the homogeneous chemical step. Given reasonable ranges of variation for each parameter, the best fit was obtained for the values Do-BNB = 2.8 · 105 cm2 s1 and k1 = 20 s1. The maximum deviation between the experimental and simulated currents given in Fig. 8 is less than 2%, except for very short times when experimentally measured current is inaccurate due to the response time of the potentiostat used. For this system, we can compare the steady state current with that for a simple E step to obtain the effective number of electrons transferred, Neff, which is equal to 1.83. Fig. 9 shows the experimental and simulated chronoamperometric currents for the same potential step experiment in Fig. 8 where the working electrode is a ring with rin = 285 lm and rout = 315 lm, and the values Do-BNB = 2.8 · 105 cm2 s1 and k1 = 20 s1 have been used for the simulation. Again, there is good agreement between experiment and theory with less than a 3.8% deviation between the two and an Neff value of 1.77. Fig. 10 compares the experimental and simulated potential step transients for the rings with (a) rin = 150 lm
Fig. 8. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometry rin = 570 lm and rout = 630 lm.
Fig. 9. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometry rin = 285 lm and rout = 315 lm.
Fig. 7. Cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM o-BNB in 0.1 M TBAP/acetonitrile at a gold microring with rin = 285 lm and rout = 315 lm.
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6. Conclusion Using precision made microring electrodes and a relatively simple voltammetric technique combined with efficient simulations, we have determined the kinetic parameters of an ECE-type system. Our results agree well with those previously obtained from similar systems and suggest that lithographic gold film microrings could be used as an alternative to those currently available. One glass slide could contain a variety of lithographic microrings of differing size and thickness, a microring ‘‘toolbox’’, allowing easy access to a range of mass transfer coefficients, which should prove useful when investigating reaction kinetics. Furthermore, because of the nature of the conformal mapping employed in this work, the simulations are accurate for a large range of ring thicknesses.
Acknowledgements In Kharkov, this work was supported by KNURE in the network of the research plan (project no. 158). The authors thank the EPSRC for a project studentship for T.J.D. We further thank Michael Hyde for his assistance with the AFM work. T.J.D. thanks Lincoln College and the Lord CreweÕs Society for a scholarship 2003–2004.
References Fig. 10. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometries (a) rin = 150 lm and rout = 210 lm and (b) rin = 1230 lm and rout = 1290 lm.
and rout = 210 lm and (b) rin = 1230 lm and rout = 1290 lm, where the values of Do-BNB and k1 are the same as above. The Neff values are 1.83 for both (a) and (b), and the maximum deviation between the experimental and simulated currents is less than (a) 5% and (b) 3%. Overall, the comparison of experimental results with theory gave values of Do-BNB = (2.8 ± 0.2) · 105 cm2 s1 and k1 = 20 ± 2 s1. The experimentally determined diffusion coefficients of o-BNB and p-BNB are similar and the value of k1 = 20 s1 for the cleavage of the C–Br bond of the oBNB radical anion agrees well with that previously determined in acetonitrile solutions by Nelson et al. [21] via cyclic voltammetry and chronoamperometry at platinum macroelectrodes. Thus, the lithographic gold microring electrodes appear to be viable probes for the study of coupled homogeneous reactions.
[1] U. Kalapathy, D.E. Tallman, S. Hagen, J. Electroanal. Chem. 325 (1992) 65. [2] G.I. Pennarun, C. Boxall, D.O.Õ Hare, Analyst 121 (1996) 1779. [3] S. Szunerits, D.R. Walt, Anal. Chem. 74 (2002) 1718. [4] J.V. Macpherson, P.R. Unwin, Anal. Chem. 70 (1998) 2914. [5] J.V. Macpherson, C.E. Jones, P.R. Unwin, J. Phys. Chem. B 102 (1998) 9891. [6] J.P. Jackel, Microtechnology 36 (1996) 707. [7] C. Amatore, A.I. Oleinick, I.B. Svir, J. Electroanal. Chem. 564 (2004) 245. [8] I.B. Svir, A.I. Oleinick, J. Electroanal. Chem. 499 (2001) 30. [9] I.B. Svir, A.I. Oleinick, A.V. Klimenko, J. Electroanal. Chem. 513 (2001) 119. [10] A. Oleinick, C. Amatore, I. Svir, Electrochem. Commun. 6 (2004) 588. [11] O.V. Klymenko, R.G. Evans, C. Hardacre, I.B. Svir, R.G. Compton, J. Electroanal. Chem. 571 (2004) 211. [12] I.B. Svir, A.I. Oleinick, R.G. Compton, J. Electroanal. Chem. 560 (2003) 117. [13] C. Amatore, A.I. Oleinick, I.B. Svir, J. Electroanal. Chem. 553 (2003) 49. [14] C. Amatore, A. Oleinick, I. Svir, Electrochem. Commun. 5 (2003) 989. [15] C. Amatore, A. Oleinick, I. Svir, Electrochem. Commun. 6 (2004) 1123. [16] C. Amatore, I. Svir, J. Electroanal. Chem. 557 (2003) 75. [17] D.M. Himmelblau, Applied Nonlinear Programming, McGrawHill, New York, 1972.
I. Svir et al. / Journal of Electroanalytical Chemistry 578 (2005) 289–299 [18] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: the Art of Scientific Computing, second ed., Cambridge University Press, Cambridge, 1992. [19] J.D. Wadhawan, T.J. Davies, A.D. Clegg, N.S. Lawrence, J.C. Ball, O.V. Klymenko, N.V. Rees, D. Bethell, M.P. Woolfall, R.R. France, R.G. Compton, J. Electroanal. Chem. 533 (2002) 33. [20] R.G. Compton, R.A.W. Dryfe, J. Electroanal. Chem. 375 (1994) 247. [21] R.F. Nelson, A.K. Carpenter, E.T. Sao, J. Electrochem. Soc. 120 (1973) 206.
[22] [23] [24] [25] [26] [27] [28] [29] [30]
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C. Amatore, J.-M. Save´ant, J. Electroanal. Chem. 86 (1978) 227. C. Amatore, J.-M. Save´ant, J. Electroanal. Chem. 107 (1980) 353. C.S. OÕBrien, Chemistry Society Review (1996) 393. J. Okazaki, J. Vacuum Sci. Technol. B 9 (1991) 2829. H.J. Jeong, D.A. Markle, G. Owen, F. Pease, A. Grenville, R. von Bu¨nau, Solid State Technol. 37 (1994) 39. M.D. Levenson, Solid State Technol. 38 (1995) 57. L. Geppert, IEEE Spectrum 33 (1996) 33. K. Aoki, K. Tokuda, J. Electroanal. Chem. 237 (1987) 163. R.G. Compton, B.A. Coles, R.A. Spackman, J. Phys. Chem. 95 (1991) 4741.
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 578 (2005) 289–299 www.elsevier.com/locate/jelechem
Theoretical and experimental study of the ECE mechanism at microring electrodes Irina Svir a,*, Alexander Oleinick a, Kamran Yunus b, Adrian C. Fisher b, Jay D. Wadhawan c,1, Trevor J. Davies c, Richard G. Compton c,* a
Mathematical and Computer Modelling Laboratory, Kharkov National University of Radioelectronics, 14 Lenin Avenue, Kharkov 61166, Ukraine b Department of Chemical Engineering, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK c Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, UK Received 20 December 2004; accepted 6 January 2005 Available online 23 February 2005
Abstract Microring electrodes are useful for the investigation of reaction kinetics due to their large perimeter to area ratio and compact nature but have hitherto been limited in application due to the absence of the underpinning theory. In this paper, we apply the conformal mapping technique recently developed by Amatore et al. [C. Amatore, A.I. Oleinick, I.B. Svir, J. Electroanal. Chem. 564 (2004) 245] for the simulation of chronoamperometry at very thin microring electrodes, where an ECE-type mechanism is in operation. The simulated results are compared with data obtained from chronoamperometry experiments with bromonitrobenzenes at lithographically fabricated gold microring electrodes. Best fit parameters for the experimental system are determined using an automatic fitting procedure. The dark electrochemical reduction of ortho-bromonitrobenzene (o-BNB) in 0.1 M tetrabutylammonium/acetonitrile solution is consistent with an ECE-type mechanism and a value of 20 s1 is theoretically determined for the unimolecular cleavage of the o-BNB radical anion, in good agreement with that previously reported for similar chemical systems. 2005 Elsevier B.V. All rights reserved. Keywords: Microring electrode; Chronoamperometry; Lithography; Conformal map; Simulation; Bromonitrobenzenes
1. Introduction The microring provides an attractive geometry for microelectrodes as it combines the large perimeter-toarea ratio (PAR) of the microband with the compact form of the microdisk [1]. In addition, the inner core which the electrode material surrounds is a unique fea* Corresponding authors. Tel.: +38 057 702 10 20; fax: +38 057 702 10 13 (I. Svir); Tel.: +44 01865 275430; fax: +44 01865 275410 (R.G. Compton). E-mail addresses: [email protected] (I. Svir), richard.compton @chemistry.ox.ac.uk (R.G. Compton). 1 Present address: Ecole Normale Supe´rieure, Department de Chimie, UMR CNRS 8640 ‘‘PASTEUR’’, 24 rue Lhomond, 75231 Paris Cedex 05, France.
0022-0728/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2005.01.011
ture of the ring geometry and can be exploited. For example, OÕHare and coworkers [2] fabricated a micro-optical ring electrode (MORE) where the inner core of the ring is a strand of fibre optic allowing a simple experimental procedure for the investigation of coupled photochemical homogeneous reactions. Using a similar method, Szunerits and Walt [3] coated over 200 optical fibres with gold and constructed an array of MOREs. Unwin and coworkers [4,5] demonstrated the hydrodynamic possibilities for the microring geometry by using a hollow glass capillary as the inner core through which they forced solution to flow. Placing the electrode above a perpendicular insulating wall resulted in the radial flow microring electrode (RFMRE) [4,5]. Thus, the potential application of microring electrodes
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for electroanalysis and kinetic investigations is very promising. In this work, we demonstrate the ability of microring electrodes to probe homogeneous chemical reactions by combining precise simulations with the results from potential step experiments on a system where an ECE mechanism is in operation. In particular, we use a new method of microring fabrication based on the lithographic technique described by Jackel [6]. At present, the most popular method for ring fabrication is to coat an inner core, a pulled glass capillary, for example, with the electrode material via metal evaporation or painting with an organometallic compound followed by decomposition and metal deposition at high temperatures [1– 6]. Although this results in rings that can be as thin as 200 nm, it is difficult to obtain rings thicker than 500 nm and there is no way of ensuring a specific size prior to fabrication, i.e., the experimentalist has very little control over the ring parameters [4]. On the other hand, with the lithographic technique used in this work, microrings can be made to more or less the exact size and thickness required, with negligible increase in cost (currently, the minimum thickness possible is around 0.5 lm). Such a reliable fabrication technique allows the production of a ‘‘microring toolbox’’ where the electrochemist has available a wide range of microrings of varying thickness. For example, chronoamperometry with a microring toolbox could provide a viable alternative to cyclic voltammetry, where varying the ring thickness, as opposed to the scan rate, achieves the desired range of mass transport coefficients. As such, the use of microrings complements the possibilities offered by variable sized microdisk or microband electrodes. The sequence of all limiting diffusion regimes taking place at microrings of any thickness and their time limits were shown in a recent work by Amatore with coworkers [7]. Also, the difference between ÔbandÕ and ÔringÕ behaviour at steady state was proved [7]. A new approach for the simulation of the microring electrode problem by the conformal mapping technique was introduced in the work of Amatore et al. [7] which we use here for the simulation of an ECE mechanism under chronoamperometry at microring electrodes. The application of the conformal map for microring simulations allows one to investigate rings of any width from very thick to vanishingly thin. In the case of the latter, a precise and efficient simulation is especially important as edge effects play the main role in the concentration distribution and current density. In the simulations in this work, we apply the ADI method which has previously proved extremely efficient in combination with the conformal mappings for different microelectrode geometries such as rings [7], disks [8–11], double bands [12], double hemicylinders [13,14], and the channel double band flow system [15]. Since we simulate chronoamperometry, the exponentially expanding time grid,
initially proposed in [16], can be employed in all our calculations. The best fit parameters of experiments are determined by an automatic fitting procedure in program based on the Nelder–Mead minimisation algorithm [17,18]. In this article, we show good agreement between the theoretical results and experimental data for E- and ECE-mechanisms at lithographically fabricated microring electrodes.
2. Theory The two redox systems of interest are the non-aqueous reductions of para-bromonitrobenzene (p-BNB), which undergoes a simple E step, and ortho-bromonitrobenzene (o-BNB), which undergoes an ECE-type mechanism, as illustrated in Scheme 1 [19–21]. The one
Scheme 1. Reaction scheme for the electrochemical reduction of pBNB and o-BNB in TBAP/acetonitrile solutions. ‘‘HS’’ represents the solvent/supporting electrolyte system and ‘‘rds’’ is the rate determining step.
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electron reduction of p-BNB in dark conditions results in a radical anion that is stable on the timescale of the experiment [19,20]. However, the o-BNB radical anion undergoes a fast C–Br bond cleavage forming a nitrophenyl radical and a bromide anion. The nitrophenyl radical rapidly abstracts a hydrogen atom from the solvent/supporting electrolyte system, producing nitrobenzene which also undergoes a one electron reduction to the corresponding radical anion, resulting in an ECEtype mechanism [19,21]. The rate determining step in the homogeneous reaction sequence is the initial cleavage of the C–Br bond [19–21]. In the works of Amatore and Save´ant [22,23], it has been shown that current responses of ECE and DISP1 mechanisms are very similar when diffusion coefficients of species are almost equal and the value of the rate determining homogeneous rate constant is small enough for the transition from pure diffusion to pure kinetics is observable. However, the literature [19–21] relative to bromonitrobenzenes does not usually consider the alternative DISP1 route. Therefore, to remain consistent with the previous literature and compare our measurements within the same interpretative framework, we will consider only the ECE mechanism. Note that if a DISP1 mechanism is active, considering an ECE analysis should not greatly affect our results owing to the close identity of the two mechanistic behaviours [22,23]. The two-dimensional simulation for the chronoamperometry of a simple E step at a microring electrode (where the potential is stepped from a value where no charge transfer occurs to a potential where the redox reaction occurs at a rapid rate) using conformal mapping approach has been previously reported in [7] and shall be used to analyse our p-BNB experimental data. Concerning the o-BNB system, in the following section we discuss the simulation procedure employed for a potential step experiment at a microring electrode where an ECE mechanism is in operation. 2.1. Mathematical model
2 ocA o cA 1 ocA o2 cA ¼ DA þ 2 ; þ r or ot or2 oz
ð1Þ
2 ocB o cB 1 ocB o2 cB ¼ DB þ 2 k 1 cB ; þ r or ot or2 oz
ð2Þ
2 ocC o cC 1 ocC o2 cC ¼ DC þ þ þ k 1 cB ; r or ot or2 oz2
ð3Þ
where cA, cB, cC denote the concentrations of the species A, B and C; DA, DB, DC are the diffusion coefficients of A, B, C, respectively; t is the time elapsed since the beginning of the potential step; r and z are the cylindrical coordinates describing the semi-infinite space located above the insulating plane in which the electrode is embedded (Fig. 1). The initial and boundary conditions are: t = 0: 8r;
cA ¼ c1 A ; cB ¼ 0; cC ¼ 0;
8z;
ð4aÞ
t > 0: 0 < r < rin ;
z ¼ 0;
ocA ocB ocC ¼ ¼ ¼0 oz oz oz rin 6 r 6 rout ;
z ¼ 0;
z ¼ 0;
r > rout ;
ð4bÞ
ðinsulatorÞ; cA ¼ 0;
ocB ocA ¼ DA ; cC ¼ 0 DB oz oz
ðelectrodeÞ;
ocA ocB ocC ¼ ¼ ¼0 oz oz oz
ð4cÞ
ðinsulatorÞ; ð4dÞ
r ¼ 0;
8z;
ocA ocB ocC ¼ ¼ ¼0 or or or
ðsymmetry axisÞ; ð4eÞ
r ! 1;
We consider the ECE reaction mechanism at the ring electrode surface described by pathway (A1):
291
z ! 1;
cA ! c1 A ; cB ! 0; cC ! 0 ðinfinityÞ; ð4fÞ
where
c1 A
is the bulk concentration of the species A.
Aþe !B k1
B!C C þ e ! D
ðA1Þ
where k1 is the first order (irreversible) rate constant. The conditions of the experiment are such that at t = 0 only species A is present in solution and the applied voltage is stepped from a value where no redox reaction occurs to a potential where the reduction of both A and C is rapid and diffusion controlled. The mathematical model describing the diffusion mass-transport processes for the ECE mechanism is:
Fig. 1. Schematic diagram of a microring electrode indicating the notations and coordinates used in the real space.
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2.2. Normalised model Let us variables: R¼
r rout
introduce
Z¼
;
z zout
;
the
following
dimensionless
r2 k 1 K 1 ¼ out : DA
DA t s¼ 2 ; rout
ð5Þ
2
oC A o C A 1 oC A o C A ¼ þ þ ; R oR os oR2 oZ 2 2 oC B o C B 1 oC B o2 C B ¼ cB þ þ K 1CB; R oR os oR2 oZ 2
ð6Þ
ð7Þ
ð8Þ
s = 0: 8Z;
C A ¼ 1; C B ¼ 0; C C ¼ 0;
ð9aÞ
s > 0: 0 < R < a;
Z ¼ 0;
oC A oC B oC C ¼ ¼ ¼0 oZ oZ oZ
ðinsulatorÞ;
Z ¼ 0;
oC A oC B oC C ¼ ¼ ¼0 oZ oZ oZ R ¼ 0;
ð9cÞ
ðelectrodeÞ;
ðinsulatorÞ;
ð9dÞ
8Z;
oC A oC B oC C ¼ ¼ ¼0 oR oR oR Z ! 1;
ðsymmetry axisÞ;
C A ! 1; C B ! 0;
C C ! 0 ðinfinityÞ;
ð9eÞ
ð9fÞ
where a = rin/rout.
where cB = DB/DA and cC = DC/DA are the normalised diffusion coefficients of species B and C with the corresponding initial and boundary conditions:
8R;
C A ¼ 0;
oC B oC A ¼ ; CC ¼ 0 oZ oZ
R ! 1;
oC C o2 C C 1 oC C o2 C C ¼ cC þ þ þ K 1CB; R oR os oR2 oZ 2
cB
R > 1;
After the normalisations, the mathematical model given by Eqs. (1)–(3) becomes: 2
Z ¼ 0;
a 6 R 6 1;
ð9bÞ
2.3. Conformal mapping approach The conformal mapping for a ring geometry (Fig. 1) can be defined by a function of complex coordinate variables: X = R + iZ, where R and Z are the dimensionless cylindrical coordinates defined in Eq. (5) [7]: 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2 X 2 a2 A x ¼ arcsin @ ; ð10Þ p 1 a2 in which x = n + ig. The complex valued function in Eq. (10) maps the upper semi-infinite plane (Fig. 2(a)) onto the semi-infinite band with vertical insulating boundaries at n p = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 and n = 1 and with the segment ½0; p2 arcsinði a2 =ð1 a2 ÞÞ excluded from it (Fig. 2(b)). Fig. 2(c) illustrates the shape of the grid in real space
Fig. 2. Simulation area in different spaces: (a) real physical space, see Fig. 1; (b) conformal space; (c) computational grid in real space.
I. Svir et al. / Journal of Electroanalytical Chemistry 578 (2005) 289–299
corresponding to a regular rectangular grid in the conformal space (Fig. 2(b)). The back transformation from the simulation space onto the real one is given by the complex-valued function [7]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi p ð11Þ X ¼ ð1 a2 Þsin2 x þ a2 : 2
on og dx ¼ ¼ Re ; oR oZ dX
The mathematical model of the ECE mechanism in the transformed coordinates can be rewritten as: 2 oC A o2 C A o CA ¼D þ os og2 on2 1 oC A on oC A og þ þ ; ð12Þ Rðn; gÞ on oR og oR
dx 2X ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : dX p ðX 2 a2 Þð1 X 2 Þ
2 oC B o C B o2 C B ¼ D cB þ os og2 on2 cB oC B on oC B og þ K 1CB; þ Rðn; gÞ on oR og oR
is
2 oC C o C C o2 C C ¼ D cC þ os og2 on2 cC oC C on oC C og þ þ þ K 1CB; Rðn; gÞ on oR og oR
on og dx ¼ ¼ Im ; ð16bÞ oZ oR dX where the derivative of the complex valued function x(X) is given by ð17Þ
2.4. Current The expression for the current in the real coordinates Z
rout
rin
ð14Þ
ð16aÞ
IðtÞ ¼ 2pF ð13Þ
293
ocA ocC DA þ DC r dr: oz z¼0 oz z¼0
ð18Þ
The transient current can be rewritten as a function of dimensionless variables in the following form: IðsÞ ¼ 2pFc1 A r out DA Z 1 oC A oC C þ cC R dR: oZ Z¼0 oZ Z¼0 a
ð19Þ
The transient current in the conformal space is
where 2 2 on on D ¼ þ : oR oZ
IðsÞ ¼ 2pFc1 A r out DA ! Z 1 oC A oC C Rðn; gÞ dn: þ cC og g¼0 og g¼0 0
The new initial and boundary conditions are:
ð20Þ
s = 0: 8n;
8g;
C A ¼ 1; C B ¼ 0; C C ¼ 0;
ð15aÞ
3. Experiments 3.1. Chemical reagents
s > 0: 0 6 n 6 1; cB
g ¼ 0;
C A ¼ 0;
oC B oC A ¼ ; CC ¼ 0 og og
n ¼ 0;
ðelectrodeÞ;
ð15bÞ
8g;
oC A oC B oC C ¼ ¼ ¼ 0 ðsymmetry axis and insulatorÞ; on on on ð15cÞ n ¼ 1;
8n;
8g;
g ! 1;
oC A oC B oC C ¼ ¼ ¼ 0 ðinsulatorÞ; on on on ð15dÞ C A ! 1; C B ! 0; C C ! 0ðinfinityÞ: ð15eÞ
All partial derivatives in Eqs. (12)–(14) can be defined using the Cauchy–Riemann conditions:
All reagents were of the highest grade available commercially and were used as received without any further purification. These were 1-bromo-4-nitrobenzene (pBNB, 99%, Aldrich), 1-bromo-2-nitrobenzene (o-BNB, 98%, Aldrich) and tetrabutylammonium perchlorate (TBAP, electrochemical grade, Fluka). All solutions were prepared with dried and distilled acetonitrile (Fisher Scientific). In all experiments, the temperature was 298 ± 2 K. All solutions were outgassed with oxygenfree nitrogen (BOC Gases, Guilford, Surrey, UK) for at least 20 min prior to experimentation. During the experiments, the electrochemical cell was kept under a nitrogen atmosphere. 3.2. Instrumentation Voltammetric measurements were carried out using a l-Autolab I (ECO-Chemie, The Netherlands) potentiostat. All experiments were conducted using a three
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electrode configuration where the working electrode was a gold microring. At all times, the counter electrode was a bright platinum wire and a silver wire was employed as the reference.
3.2.1. Microring fabrication Glass wafers were cleaned using an acid wash of ‘‘piranha solution’’ [24] and rinsed in milli-Q water several times, before being blown dry using a supply of
Fig. 3. Illustration of the steps involved in (a) fabricating the photoresist patterns and (b) coating with gold film to produce a microring electrode.
I. Svir et al. / Journal of Electroanalytical Chemistry 578 (2005) 289–299
nitrogen. A photolithographic technique, based on a projection-printing system, was used to produce the gold microring patterns on the glass substrates [25–28]. The process involved using a technical drawing software package to create a scaled black and white artwork of the microrings that were then transferred onto highresolution millimask negative plates (Agfa) using standard photography techniques. Thin films of approximately 5 lm Shipley S1828 Photoresist (Chestech) were coated over the glass substrates using a spin coater and were pre-baked on a hot plate at 115 C for 1 min. The millimask negative plates were used to project an ultraviolet (UV) light source (340 nm) from a mask aligner (Karl Suss, model MJB 3) onto the substrates coated with the film of photoresist. The exposed films of photoresist were developed using a developer solution (AZ351, Chestech) to reveal the desired photoresist microring patterns. After the developing process, the substrates were washed with milli-Q water thoroughly before being blow dried in a clean supply of nitrogen and post-baked on a hot plate. Fig. 3(a) illustrates the steps involved in fabricating the photoresist patterns. The patterned substrates were then put through a metal coating cycle using an Edwards Auto 306 metal evaporator to give a titanium/gold film. The coated substrates were then immersed in acetone to lift off the photoresist to reveal the pattern of the microring gold films. Fig. 3(b) demonstrates the steps involved. A schematic diagram of a microring fabricated via this process is illustrated in Fig. 4. The thickness of the gold film was determined to be 80 nm by atomic force microscopy (AFM) conducted in contact mode with a Digital
295
Instruments (now a division of Veeco) Multimode SPM. As observed in Fig. 4, the pattern also includes a gold contact pad connected to the ring via a narrow gold band. Another layer of Shipley S1828 Photoresist was coated over the surfaces of the microring electrodes with the spin coater. Using another mask and photolithography process, a pattern of the photoresist was left over the contact lines leaving the microring electrodes and the contact pads as the only active regions. The photoresist pattern was then hard baked at 200 C for 30 min to create a chemically resistant insulated region over the contact gold contact lines. The microring electrodes were then ready to use once electrical contact was made via the contact pads.
4. Simulations 4.1. Computing All programs were written in Borland Delphi 7 Enterprise Edition and executed on a PC equipped with Intel Pentium 4 processor at 3.00 GHz and 512 Mb of RAM. In all simulations, we used a uniform spatial grid in the conformal space (Fig. 2(b)) of the size Nn · Ng = 100 · 100. The ADI method was applied for the discretisation of the partial differential Eqs. (12)–(14), since in our recent works this proved very efficient when coupled to simulations in conformal spaces [7–15]. Although the mathematical model described in this article allows setting different values to the diffusion coefficients, in all our calculations here the diffusion coefficients of all species were assumed equal. 4.2. Non-uniform time grid When simulating a chronoamperometry experiment, due to the singularity occurring in the concentration distributions at the moment when the potential is applied to the electrode, special care must be taken at the initial times of electrolysis. For this reason, we use the exponentially expanding time grid [16]: Dskþ1 ¼ ð1 þ lÞDsk ;
ð21Þ
where Dsk is the time step at kth time iteration and l is the expansion coefficient (l > 0). The strategy for the determination of the Ds0 and l values was discussed in detail in previous works [7,11,16]. The parameters used for the non-uniform time grid were chosen to be (see definitions in [16]): initial step, Ds0 = 106; grid expansion parameter, l = 2 · 103. 4.3. Fitting Fig. 4. Schematic diagram of a lithographically fabricated gold microring electrode.
An automatic fitting procedure based on the Nelder– Mead minimisation method [17,18] was employed for
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the determination of the best fit parameters (the diffusion coefficient, D, and the first order rate constant, k1) to the experimental data. In our case, the function to be minimised is the weighted sum of squared deviations between the experimentally measured ðI exp k Þ and simulated theoretical ðI sim k Þ currents: X sim 2 SSQ ¼ wk ðI exp ð22Þ k Ik Þ ; k
where wk is the weighting coefficient given by: 1 I sim k wk ¼ 1 þ exp ITe
ð23Þ
and I exp T e is the experimental current value at the time Te, i.e., at the end of the observation period.
5. Results and discussion 5.1. E mechanism Fig. 5 illustrates a cyclic voltammogram recorded in dark conditions at 0.1 V s1 for the reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile solution where the working electrode is a gold microring with parameters rin = 285 lm and rout = 315 lm. Both forward and back peaks are observed, consistent with a simple E step mechanism. In the forward scan, p-BNB is reduced to the radical anion (cathodic peak potential, Ep = 1.16 V vs. Ag) which is stable on the timescale of the experiment and is subsequently oxidised back to p-BNB on reversing the direction of potential sweep. Raising the scan rate, v, gave I-E signals with more pro-
Fig. 5. Cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile at a gold microring with rin = 285 lm and rout = 315 lm.
nounced peaks, whilst a decrease in v led to increasingly steady state like behaviour. Next in chronoamperometric experiments, the potential was stepped from 0 V vs. Ag, where no charge transfer occurs, to 1.3 V vs. Ag, where the reduction of p-BNB to the radical anion is rapid such that [p-BNB] at the electrode surface is zero, in accordance with the boundary conditions for the simulations. Fig. 6 shows the chronoamperometric response for the diffusion controlled reduction of 1.6 mM p-BNB in 0.1 M TBAP/acetonitrile solution at a gold microring electrode with inner radius rin = 150 lm and outer radius rout = 210 lm. Overlaid as squares is the simulated response, generated using the theory discussed above using k1 = 0, for the given electrode parameters where the diffusion coefficient is Dp-BNB = 2.4 · 105 cm2 s1 (assuming that the diffusion coefficient of p-BNB and its radical anion are equal). In general, a good fit between experiment and theory was observed for a number of microrings of different sizes which gave a value for the diffusion coefficient of p-BNB to be Dp-BNB = (2.4 ± 0.2) · 105 cm2 s1. This value agrees with those previously reported [19,20] and should be similar to the diffusion coefficient for o-BNB, Do-BNB. Interestingly, the steady state current in Fig. 6 is approximately twice that calculated on the assumption that the ring acts as a ‘‘thin’’ microband electrode [29], confirming the essential need for simulations in this case. 5.2. ECE mechanism Fig. 7 illustrates a cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM o-BNB in 0.1 M TBAP/acetonitrile where the working electrode is the same as that in Fig. 5. As observed, there is a significant
Fig. 6. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of p-BNB at a ring with geometry rin = 150 lm and rout = 210 lm.
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difference between the two I–E signals for o-BNB and pBNB. In addition to an increased peak cathodic current, occurring at Ep = 1.39 V vs. Ag, the back peak corresponding to the oxidation of the o-BNB radical anion is absent. Raising the scan rate above 0.1 V s1 did result in the occurrence of an anodic peak, which grew for increasing scan rates. These observations are consistent with an ECE type mechanism where the homogeneous chemical reaction is fast. The C–Br bond of the oBNB radical anion undergoes a fast cleavage eventually producing nitrobenzene which is also reduced, resulting in an increased cathodic peak current, the magnitude of which resembles that of a two electron reduction.
Fig. 8 depicts the chronoamperometric response for the diffusion controlled reduction of o-BNB in the same solution used in Fig. 7, where the working electrode is a ring with parameters rin = 570 lm and rout = 630 lm. The potential was stepped from 0 V vs. Ag, where no charge transfer occurs, to 1.6 V vs. Ag, where the reduction of o-BNB and nitrobenzene is diffusion controlled, in accordance with the simulations. Overlaid as solid squares is the simulated response for an ECE mechanism obtained as a result of running the fitting procedure discussed above. The fitting was carried out assuming two variable parameters: the diffusion coefficient (assumed equal for all species: A, B, C in terms of Section 2.1 [30]) and the first order rate constant of the homogeneous chemical step. Given reasonable ranges of variation for each parameter, the best fit was obtained for the values Do-BNB = 2.8 · 105 cm2 s1 and k1 = 20 s1. The maximum deviation between the experimental and simulated currents given in Fig. 8 is less than 2%, except for very short times when experimentally measured current is inaccurate due to the response time of the potentiostat used. For this system, we can compare the steady state current with that for a simple E step to obtain the effective number of electrons transferred, Neff, which is equal to 1.83. Fig. 9 shows the experimental and simulated chronoamperometric currents for the same potential step experiment in Fig. 8 where the working electrode is a ring with rin = 285 lm and rout = 315 lm, and the values Do-BNB = 2.8 · 105 cm2 s1 and k1 = 20 s1 have been used for the simulation. Again, there is good agreement between experiment and theory with less than a 3.8% deviation between the two and an Neff value of 1.77. Fig. 10 compares the experimental and simulated potential step transients for the rings with (a) rin = 150 lm
Fig. 8. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometry rin = 570 lm and rout = 630 lm.
Fig. 9. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometry rin = 285 lm and rout = 315 lm.
Fig. 7. Cyclic voltammogram recorded at 0.1 V s1 for the reduction of 1.6 mM o-BNB in 0.1 M TBAP/acetonitrile at a gold microring with rin = 285 lm and rout = 315 lm.
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6. Conclusion Using precision made microring electrodes and a relatively simple voltammetric technique combined with efficient simulations, we have determined the kinetic parameters of an ECE-type system. Our results agree well with those previously obtained from similar systems and suggest that lithographic gold film microrings could be used as an alternative to those currently available. One glass slide could contain a variety of lithographic microrings of differing size and thickness, a microring ‘‘toolbox’’, allowing easy access to a range of mass transfer coefficients, which should prove useful when investigating reaction kinetics. Furthermore, because of the nature of the conformal mapping employed in this work, the simulations are accurate for a large range of ring thicknesses.
Acknowledgements In Kharkov, this work was supported by KNURE in the network of the research plan (project no. 158). The authors thank the EPSRC for a project studentship for T.J.D. We further thank Michael Hyde for his assistance with the AFM work. T.J.D. thanks Lincoln College and the Lord CreweÕs Society for a scholarship 2003–2004.
References Fig. 10. The experimental (solid line) and simulated (symbols) chronoamperometric currents for the diffusion controlled reduction of o-BNB at a ring with geometries (a) rin = 150 lm and rout = 210 lm and (b) rin = 1230 lm and rout = 1290 lm.
and rout = 210 lm and (b) rin = 1230 lm and rout = 1290 lm, where the values of Do-BNB and k1 are the same as above. The Neff values are 1.83 for both (a) and (b), and the maximum deviation between the experimental and simulated currents is less than (a) 5% and (b) 3%. Overall, the comparison of experimental results with theory gave values of Do-BNB = (2.8 ± 0.2) · 105 cm2 s1 and k1 = 20 ± 2 s1. The experimentally determined diffusion coefficients of o-BNB and p-BNB are similar and the value of k1 = 20 s1 for the cleavage of the C–Br bond of the oBNB radical anion agrees well with that previously determined in acetonitrile solutions by Nelson et al. [21] via cyclic voltammetry and chronoamperometry at platinum macroelectrodes. Thus, the lithographic gold microring electrodes appear to be viable probes for the study of coupled homogeneous reactions.
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