Use of conformal maps to model the voltammetric response of collector-generator double-band electrodes

Fosset, Bruno; Amatore, Christian; Bartelt, Joan E.; Michael, Adrian C.; Wightman, R. Mark

doi:10.1021/ac00004a003

Cited by 81 publications

(137 citation statements)

References 28 publications

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“…By digital simulation, they demonstrated the preponderate influence of the gap size on the collection efficiency. Conformal maps for modelling the collector-generator behavior as a function of the widthto-gap ratio for a double [2] and a triple band configuration [3] have shown a good agreement between models and experimental data. Later, the application-specific modelling based on conformal mapping was successfully adopted for simulating the current distribution at dual microband electrodes and their efficiency in electrochemical titrations [4,5].…”

Section: Introductionmentioning

confidence: 69%

Theoretical treatment and computer simulation of microelectrode arrays

Morf¹,

Koudelka‐Hep²,

Rooij³

2006

Journal of Electroanalytical Chemistry

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New relations for and interrelations between the current responses of different microelectrode arrays are presented. Interdigitated microelectrode arrays (IDAs: alternating cathodes and anodes) and uniform microband electrode arrays (MEAs: only cathodes or anodes) are treated, and miniaturized systems with planar band electrodes or hemicylinder electrodes are discussed. A common basis was found for the specific response characteristics of IDAs and MEAs. The theoretical expressions were verified by results from computer modelling. The numerical simulations made use of finite-element procedures to evaluate steady-state and time-dependent mass fluxes and concentration profiles of electroactive species at the surfaces of different microelectrode arrays. It was shown that the response behavior of a given array can be exactly predicted from the current data of other arrays.

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Section: Introductionmentioning

confidence: 69%

Theoretical treatment and computer simulation of microelectrode arrays

Morf¹,

Koudelka‐Hep²,

Rooij³

2006

Journal of Electroanalytical Chemistry

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“…Two series of ultramicroelectrode assemblies were constructed along the same ªsandwich º technique [7] pictured in Figure 1. A gold foil (thickness: w 10 mm, length: l 3 mm, Goodfellow, 99.95 %) was placed on a flat glass substrate, covered by a mylar insulating film (thickness: g 10 mm) and then by a PTFE sheet a few millimeters wide (operating assembly).…”

Section: Methodsmentioning

confidence: 99%

Micrometrically Controlled Surface Modification of Teflon ^® by Redox Catalysis: Electrochemical Coupling between Teflon ^® and a Gold Band Ultramicroelectrode

Amatore

Combellas

Kanoufi

et al. 2000

Chemistry A European J

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Carbon-fluorine bonds of Teflon (polytetrafluoroethylene, PTFE) can be reduced electrochemically with the purpose of modifying its adhesive and wetting surface properties by micrometrically controlled surface carbonization of the material. This can be performed adequately by redox catalysis provided that the redox mediator couple has a sufficiently negative reduction potential. The process is investigated kinetically with benzonitrile as the mediator and a gold-band ultramicroelectrode mounted adjacent to a PTFE block, though separated from it by an insulating micrometric mylar gap. For moderate fluxes of reduced mediator, the whole device behaves as a generator-collector double-band assembly with a constant current amplification factor. This is maintained over long periods of time, during which the carbonized PTFE zones extends over distances that are much wider than the slowly expanding cylindrical diffusion layer generated at the gold-microband electrode. This establishes that the overall redox catalysis proceeds through electronic conduction in the n-doped carbonized material. Thus, carbonization progresses at the external edge of the freshly carbonized surface in a diffusion-like fashion (dependence on the square root of time), while the redox-mediator oxidized form is regenerated at the carbonized PTFE edge facing to the gold ultramicroelectrode, so that the overall rate of carbonization is controlled by solution diffusion only. For larger fluxes of mediator, the heterogeneous rate of reduction and doping of PTFE becomes limiting, and the situation is more complex. A conceptually simple model is developed which predicts and explains all the main dynamic features of the system under these circumstances and allows the determination of the heterogeneous rate constant of carbon-fluorine bonds at the interface between the carbonized zone and the fresh PTFE. This model can be further refined to account for the effect of ohmic drop inside the carbonized zone on the heterogeneous reduction rate constants and henceforth gives an extremely satisfactory quantitative agreement with the experimental data.

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“…The conformal space grid is adjusted more parallel to the equiconcentration lines than the grid in the original space. We apply a conformal map similar to the one used by Amatore et al [34,35]. The conformal map is de®ned by…”

Section: The Model Problemmentioning

confidence: 99%

Digital Simulation of Two-Dimensional Mass Transfer Problems in Electrochemistry Using the Extrapolation Method

Strutwolf

Williams

1999

Electroanalysis

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In this article we report the application of the extrapolation method to electrochemical problems involving two-dimensional mass transfer. The extrapolation method is based on a combination of fully implicit difference schemes and was previously successfully used in solving electrochemical processes including linear diffusion. The diffusion equation to a microband electrode under diffusion controlled conditions is solved by the extrapolation method and the alternating implicit direction technique. The results are compared. Both ®nite difference methods have the same order of accuracy but the extrapolation technique has a higher order of stability making it preferable for stiff relaxation problems and for an accurate simulation of short time behavior.

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Use of conformal maps to model the voltammetric response of collector-generator double-band electrodes

Cited by 81 publications

References 28 publications

Theoretical treatment and computer simulation of microelectrode arrays

Theoretical treatment and computer simulation of microelectrode arrays

Micrometrically Controlled Surface Modification of Teflon ^® by Redox Catalysis: Electrochemical Coupling between Teflon ^® and a Gold Band Ultramicroelectrode

Digital Simulation of Two-Dimensional Mass Transfer Problems in Electrochemistry Using the Extrapolation Method

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Use of conformal maps to model the voltammetric response of collector-generator double-band electrodes

Cited by 81 publications

References 28 publications

Theoretical treatment and computer simulation of microelectrode arrays

Theoretical treatment and computer simulation of microelectrode arrays

Micrometrically Controlled Surface Modification of Teflon ® by Redox Catalysis: Electrochemical Coupling between Teflon ® and a Gold Band Ultramicroelectrode

Digital Simulation of Two-Dimensional Mass Transfer Problems in Electrochemistry Using the Extrapolation Method

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Micrometrically Controlled Surface Modification of Teflon ^® by Redox Catalysis: Electrochemical Coupling between Teflon ^® and a Gold Band Ultramicroelectrode