Dual microband electrodes: current distributions and diffusion layer 'titrations'. Implications for electroanalytical measurements

The simulation of transport to double microband electrodes in generator-collector mode is reported focusing especially on the 'titration curve' approach to electroanalysis in which a titrant is electrogenerated from a redox active precursor on the generator electrode and reacts homogeneously with the target analyte. The current on the detector electrode reflects the amount of titrant 'surviving' passage between the two electrodes. The form of the titration curve - plots of detector current as a function of generator current - is shown to be highly sensitive to the electrode kinetics of the redox couple driven at the generator electrode. Accordingly the natïve use of such methodology for analysis without accompanying simulation and kinetic analysis is fraught with danger. Use of the conformal mapping approach in combination with the ADI method for investigation of the 'titration' current distributions at the double band system gives fast and precise simulation of this and similar problems. Convergence analysis is described which allows for the automatic selection of the simulation grid size so as to obtain a chosen accuracy (for example 1%) of the current for all experimentally meaningful values of the geometrical and physico-chemical parameters of the system to be investigated. © 2003 Elsevier B.V. All rights reserved

Solution of ring electrode problems in spherical coordinates: An application to near-steady-state linear sweep voltammetry

We report on the simulation of ring electrode problems in spherical coordinates and apply it to the problem of near-steady-state linear sweep voltammetry at a ring electrode. The results are compared with those given by traditional methods

Diffusion with moving boundary on spherical surfaces.

In this work, we illustrate two approaches to the simulation of surface diffusion over a sphere coupled with the formation of a cluster by reactive particles as a paradigm of a wide variety of problems occurring in many areas of nanosciences and biology. The problem is treated using a Brownian motion approach and a numerical solution of the corresponding continuous Fick’s laws of diffusion. While being computationally more expensive, the Brownian motion approach allows one to consider a wider range of situations, particularly those corresponding to relatively high concentrations of diffusing particles and the ensuing problem of particle overlap when they are ascribed finite sizes

KinFitSim: A powerful kinetic simulator and mechanism fitting tool

© 2003 IEEE.The mathematical package for simulation of kinetic mechanisms and fitting experimental data (KinFitSim) is presented. The KinFitSim package consists of two major parts. The first part is the kinetic simulator (KS) featuring an advanced kinetic mechanism compilation algorithm and an automatic simulation procedure itself, and the second part is the fitting simulator (FS) for automated fitting of the simulated response of a chemical system with the experimental one

Theory of long-range diffusion of proteins on a spherical biological membrane: application to protein cluster formation and actin-comet tail growth.

Breaking of symmetry is often required in biology in order to produce a specific function. In this work we address the problem of protein diffusion over a spherical vesicle surface towards one pole of the vesicle in order to produce ultimately an active protein cluster performing a specific biological function. Such a process is, for example, prerequisite for the assembling of proteins which then cooperatively catalyze the polymerization of actin monomers to sustain the growth of actin tails as occurs in natural vesicles such as those contained in Xenopus eggs. By this process such vesicles may propel themselves within the cell by the principle of action-reaction. In this work the physicochemical treatment of diffusion of large biomolecules within a cellular membrane is extended to encompass the case when proteins may be transiently poised by corral-like structures partitioning the membrane as has been recently documented in the literature. In such case the exchange of proteins between adjacent corrals occurs by energy-gated transitions instead of classical Brownian motion, yet the present analysis shows that long-range movements of the biomolecules may still be described by a classical diffusion law though the diffusion coefficient has then a different physical meaning. Such a model explains why otherwise classical diffusion of proteins may give rise to too small diffusion coefficients compared to predictions based on the protein dimension. This model is implemented to examine the rate of proteins clustering at one pole of a spherical vesicle and its outcome is discussed in relevance to the mechanism of actin comet tails growth

Electrochemical determination of flow velocity profile in a microfluidic channel from steady-state currents: numerical approach and optimization of electrode layout.

In this article, the numerical approach for flow profile reconstruction in a microfluidic channel equipped with band microelectrodes introduced previously by the authors, based on transient currents, is extended to the exclusive use of steady-state currents. It is shown that, although the currents obey steady state, the flow velocity profile in the channel may be reconstructed rapidly with a high accuracy, provided a sufficient number of electrodes performing under steady state are considered. The present theory demonstrates how the electrode widths and sizes of gaps separating them can be optimized to achieve better performance of the method. This approach has been evaluated theoretically for band microelectrode arrays embedded into one wall of a rectangular channel consisting of three, four, or five electrodes, all of which are operated in the generator mode. The results prove that the proposed approach is able to accurately recover the shape of the flow profile in a wide range of Peclet numbers and flow types ranging from the classical parabolic Poiseuille flow to constant electro-osmotic-type flow

A new strategy for simulation of electrochemical mechanisms involving acute reaction fronts in solution under spherical or cylindrical diffusion

In this paper we present a combined simulation approach for solving complex electrochemical kinetic problems at (hemi)spherical and (hemi)cylindrical electrodes based on the simultaneous application of analytical conformal coordinate transformations to accurately treat the diffusional transport and adaptive grid compression to locally increase the accuracy of the approximation of acute reaction fronts. This strategy is shown to be very efficient and leads to extremely accurate results both for steady state and transient situations and is equally powerful for both pure diffusion and that complicated by severe kinetic distortions. © Pleiades Publishing, Ltd., 2012

A new strategy for simulation of electrochemical mechanisms involving acute reaction fronts in solution under spherical or cylindrical diffusion

In this paper we present a combined simulation approach for solving complex electrochemical kinetic problems at (hemi)spherical and (hemi)cylindrical electrodes based on the simultaneous application of analytical conformal coordinate transformations to accurately treat the diffusional transport and adaptive grid compression to locally increase the accuracy of the approximation of acute reaction fronts. This strategy is shown to be very efficient and leads to extremely accurate results both for steady state and transient situations and is equally powerful for both pure diffusion and that complicated by severe kinetic distortions. © Pleiades Publishing, Ltd., 2012

Reconstruction of hydrodynamic flow profiles in a rectangular channel using electrochemical methods of analysis

We propose a theoretical method for reconstructing the shape of a hydrodynamic flow profile occurring locally within a rectangular microfluidic channel based on experimental currents measured at double microband electrodes embedded in one channel wall and operating in the generator-collector regime. The ranges of geometrical and flow parameters providing best conditions for the flow profile determination are indicated. The solution of convection-diffusion equation (direct problem) is achieved through the application of the specifically designed conformal mapping of spatial coordinates and an exponentially expanding time grid for obtaining accurate concentration and current distributions. The inverse problem (the problem of flow profile determination) is approached using a variational formulation whose solution is obtained by the Ritz’s method. The method may be extended for any number of electrodes in the channel and/or different operating regimes of the system (e.g. generator-generator). © 2007 Elsevier Ltd. All rights reserved