(7.15) A Data Analysis Service for Steady-State Voltammetry via the World Wide Web
A service has been set up via the World Wide Web
(http://physchem.ox.ac.uk/~rgc/datan/datan.htm)
which permits the analysis of steady-state
experimental data (limiting currents or half-wave potentials) at:
* Spherical Electrodes
* Microdisc Electrodes
* Rotating Disc Electrodes
* Channel Electrodes
* Channel Microband Electrodes
This analysis is available for a range of common electrochemical mechanisms (E,
EC, EC2, EC2E, DISP1, DISP2 and EC' processes). The software interpolates the
simulated response from a series of working curves and surfaces. These were
generated from fully-implicit steady-state numerical simulations using
expanding
grids for Channel and Channel microband electrodes[1] and in conformal space
for Microdisc[2], Spherical and Rotating Disc[3] electrodes. The simulations
employed multigrid[4] and preconditioned Krylov subspace[5] methods for the
efficient solution of the large sparse linear systems resulting from finite
difference discretisation and global linearisation via Newton's method.
The user simply selects a geometry and mechanism, enters the cell parameters
and
the limiting current/half-wave potential as a function of radius/rotation
speed/flow rate. Data may be entered directly via a WWW interface, or uploaded
as a file by FTP. For each experimental data set, the theoretical response is
predicted for the chosen mechanism and plotted as a function of mass transport
appropriate to the electrode geometry.
The variance is computed between the experimental and theoretical sets of data.
This may be minimised to 'fit' (i.e. optimise) unknown parameters such as rate
constants or diffusion coefficients. A Golden Section Search[6] may be used to
find a local minimum in one dimension. Downhill Simplex minimisation[6] may be
used for multidimensional searches. One-, two- and multi-dimensional sampling
routines are also available so that the variance curve or surface may be
visualised allowing the global minimum to be discerned from local minima.
Analysis for wall-jet electrodes and heterogeneous chemical and electrochemical
processes at channel electrodes will be added shortly. The service is
available
free of charge.
References
[1] J.A. Alden and R.G. Compton, J.Phys. Chem. B, 101, (1997), 9751.
[2] J.A. Alden and R.G. Compton, J.Phys. Chem. B, 101, (1997), 9606.
[3] R.G. Compton, M.E. Laing, D. Mason, R.J. Northing, P.R. Unwin, Proc. R.
Soc. Lond. A, 481, (1988), 113.
[4] J.A. Alden and R.G. Compton, J. Electroanal. Chem., 415, (1996), 1.
[5] J.A. Alden and R.G. Compton, J.Phys. Chem. B, 101,(1997), 8941.
[6] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Edition, Cambridge University Press, 1992.
(7.22) ELSIM: Program for the simulation of electrochemical transient methods.
ELSIM version 3.0 by Leslaw K. Bieniasz (June 1996)
The third version of the program ELSIM, for the simulation of electrochemical
transient methods, is now freely available for the purposes of scientific
research. Anyone willing to obtain a copy of the program is kindly requested to
contact me at the addresses indicated below (email preferred).
ELSIM is a User-Friendly Problem Solving Environment for the
simulation of transient electrochemical techniques. The program runs on IBM compatible personal computers under MS DOS (including the DOS mode of the Windows 95 or IBM OS / 2 WARP
operating systems). The user simply types in an electrochemical
reaction mechanism and specifies parameter values. The built-
in "reaction compiler" automatically generates the text of the corresponding mathematical governing equations, and comprehensively verifies the correctness of the reaction
mechanisms. If necessary or desired, the user may also directly
type in the text of the mathematical problem definition, using
a conventional mathematical notation. In both cases the text of
the equations serves as input data to the formula translator that automatically generates a solution algorithm and sets up the numerical problem.
The program solves: -------------------
(1) Integral equations for linear potential scan and cyclic
voltammetry, for electrochemical kinetic systems in one space
dimension (must be typed in directly). Choice of four solution
methods.
(2) Governing equations independent of the space coordinates
(sets of algebraic, ordinary differential or differential-
algebraic equations) that arise for electrochemical kinetic
systems characterized by the presence of interfacial species
(localized at the electrodes) of variable concentrations, and
possibly bulk species (distributed in the electrolyte) of
constant concentrations. This permits i.a. the simulation of
adsorption phenomena coupled with electrochemical reactions at
the neglection of bulk transport, simulation of a class of
oscillatory electrochemical systems, or modelling of thin-layer
electrodes. Choice of two solution methods.
(3) Governing equations in one space dimension, that arise for
electrochemical kinetic systems characterized by the presence
of bulk species of variable concentrations and possibly
interfacial species of variable concentrations (sets of partial
differential equations for the concentrations of bulk species,
optionally coupled with the sets of algebraic, ordinary
differential or algebraic-differential equations for the
concentrations of interfacial species). This permits i.a. the
simulation of homogeneous reaction-diffusion problems like many
frequently discussed CE, EC, ECE, etc. models, as well as
adsorption phenomena coupled with electrochemical and
homogeneous reactions, in the presence of bulk transport.
Choice of eight solution methods.
Virtually any kind of controlled-potential or controlled- current transients can be simulated, because the actual transient waveforms and other peculiarities of the
electrochemical problems can be freely defined by the users, by entering appropriate mathematical formulae.
A number of tools serving for the post-processing of simulation results and their comparisons with experimental data (e.g. fitting of the simulated transient curves) is integrated with ELSIM. The program involves a comprehensive context-sensitive hypertext "help" facility, and is accompanied by a set of 68
example reaction mechanisms, a set of 70 demonstration examples
of mathematical problem definitions, and a manual (over 250
pages). Extensive error diagnostics are present throughout the program.
Although in the case of complex kinetic models ELSIM 3.0
may suffer from various limitations inherent in the DOS system, this program is the most comprehensive and the most
general of the currently available free and commercial programs
for the simulation of electrochemical transient methods, for kinetic problems in one space dimension.
In contrast to other available simulation programs, ELSIM has been widely described in regular scientific papers, so that the program users have
access to many details regarding the algorithms implemented in the program, properties of the simulation methods, various physico-chemical assumptions accepted, and other technical aspects. The following list of publications may be helpful in locating a subject of interest.
Basic publications about the program: -------------------------------------
1) L. K. Bieniasz
"ELSIM - A User-friendly PC Program for Electrochemical Kinetic
Simulations. Version 1.0 - Solution of Integral Equations for
Linear Scan and Cyclic Voltammetry".
Computers. Chem., vol. 16 (1992) 11.
2) L. K. Bieniasz
"ELSIM - A PC Program for Electrochemical Kinetic Simulations
Version 2.0 -Solution of the Sets of Kinetic Partial
Differential Equations in One-dimensional Geometry, Using
Finite Difference and Orthogonal Collocation Methods".
Computers. Chem., vol. 17 (1993) 355.
3) L. K. Bieniasz
"A Reaction Compiler for Electrochemical Kinetics".
Computers. Chem., vol. 20 (1996) 403.
4) L. K. Bieniasz
"ELSIM - A Problem Solving Environment for Electrochemical
Kinetic Simulations. Version 3.0 - Solution of Governing
Equations Associated with Interfacial Species, Independent of
Spatial Coordinates or in One-dimensional Space Geometry".
Computers. Chem., vol. 21 (1997) 1.
Automatic derivation of mathematical governing equations: ---------------------------------------------------------
1) L. K. Bieniasz
"Automatic Derivation of the Governing Equations that Describe
a Transient Electrochemical Experiment, Given a Reaction
Mechanism of Arbitrary Complexity. Part 1. Problem Parameters
and Initial Conditions".
J. Electroanal. Chem., vol. 406 (1996) 33.
2) L. K. Bieniasz
"Automatic Derivation of the Governing Equations that Describe
a Transient Electrochemical Experiment, Given a Reaction
Mechanism of Arbitrary Complexity. Part 2. Governing Equations
in One-dimensional Geometry".
J. Electroanal. Chem., vol. 406 (1996) 45.
Formula translation and automatic construction of simulation ------------------------------------------------------------ algorithms: -----------
1) L. K. Bieniasz
"A Method-oriented Approach to the Formulation of Algorithms
for Electrochemical Kinetic Simulations".
J. Electroanal. Chem., vol. 340 (1992) 19.
2) L. K. Bieniasz
"A Method-oriented Approach to the Formulation of Algorithms
for Electrochemical Kinetic Simulations. Part 2. Extension to
Kinetic Problems Characterized by the Simultaneous Presence of
Bulk and Interfacial Species".
J. Electroanal. Chem., vol. 404 (1996) 195.
Various simulation methods implemented in the program: ------------------------------------------------------
1) L. K. Bieniasz
"An Efficient Numerical Method of Solving the Abel Integral
Equation for Cyclic Voltammetry".
Computers. Chem., vol. 16 (1992) 311.
2) L. K. Bieniasz
"An Efficient Numerical Method of Solving Integral Equations
for Cyclic Voltammetry".
J. Electroanal. Chem., vol. 347 (1993) 15.
3) L. K. Bieniasz and D. Britz
"Electrochemical Kinetic Simulations of Mixed
Diffusion / Homogeneous Reaction Problems by the Saul=92yev
Finite Difference Algorithms".
Anal. Chim. Acta, vol. 278 (1993) 59.
4) L. K. Bieniasz and D. Britz
"Efficiency of Electrochemical Kinetic Simulations by
Orthogonal Collocation and Finite Difference Methods -
A Comparison".
Acta Chem. Scand., vol. 47 (1993) 757.
5) L. K. Bieniasz and D. Britz
"Efficiency of Electrochemical Kinetic Simulations by
Orthogonal Collocation and Finite Difference Methods - A
Comparison. Responses to the Comments by B. Speiser"
Acta Chem. Scand., vol. 48 (1994) 609.
Numerical stability of finite-difference simulation techniques: