|
Electrochemical sensors have a wide range of applications in a variety of
fields including clinical medicine, environmental monitoring and pollution
control. Mathematical modelling of such sensors is used to test new
designs and modes of operation by simulation rather than the traditional
yet costly "build and test" approach.
A chemical sensor is made up of two parts. The first is where the chemical
reaction takes place when an excitation function is applied and this
produces some kind of signal, e.g. a change in electrical potential, a
flow of electrons or a colour change. The second part is the transducer
which measures the magnitude of the signal. The aim is to obtain
information about the system based on the excitation function and the
measured response and also on appropriate models for the system. For
example, the excitation function may be an applied potential at an
electrode and the response function may be a flow of current there; the
current is proportional to the concentration and can thus be translated
into a measure of the amount of chemical present.
The governing equations for such problems model mass transfer and chemical
reactions and hence these equations are typically (systems of)
reaction-convection-diffusion equations. This research makes use of a
variety of numerical and analytical techniques including finite difference
and finite element methods, mesh refinement techniques and the use of
locally valid series expansions. Our current research is focused in two
main areas: frequency domain voltammetry and the simulation of processes.
at microelectrodes.
Frequency domain voltammetry
Linear sweep voltammetry (DC voltammetry) involves sweeping the potential
applied to an electrode over a range of interest and recording the
current. A more powerful approach is to superimpose a periodic waveform
onto the waveform used in linear sweep voltammetry; we consider the
superimposition of both a sine wave and a square wave. The resulting
signal (the current) may then be studied in the frequency domain so that
the DC term and the harmonics due to the periodic waveform may be
considered separately. It has been observed both experimentally and
numerically that different system input parameters (double layer
capacitance, uncompensated resistance etc.) affect different harmonics in
different ways. Our aim is to use this information to enable us to solve
the inverse problem, namely: given a current response, determine the
system input parameters which produced that response.
References
- D.J. Gavaghan and A.M. Bond. A complete numerical simulation of the
techniques of alternating current linear sweep and cyclic voltammetry:
analysis of a reversible process by conventional and fast Fourier
transform methods. J. Electroanal. Chem. 480 (2000) 133-149.
- D.J. Gavaghan, D. Elton, K.B. Oldham and A.M. Bond. Analysis of ramped
square-wave voltammetry in the frequency domain. J. Electroanal. Chem. 512
(2001) 1-15.
- D.J. Gavaghan, D. Elton and A.M. Bond. A comparison of sinusoidal, square
wave, sawtooth and staircase forms of transient voltammetry when a
reversible process is analysed in the frequency domain. J. Electroanal.
Chem. 513 (2001) 73-86.
- Anna A. Sher, Alan M. Bond, David J. Gavaghan, Kathryn Harriman, Stephen
W. Feldberg, Noel W. Duffy, Si-Xuan Guo and Jie Zhang. Resistance,
Capacitance and Electrode Kinetic Effects in Fourier Transformed Large
Amplitude Sinusoidal Voltammetry: The Emergence of Powerful and
Intuitively Obvious Tools for Recognition of Patterns of Behaviour. Anal.
Chem. (submitted for publication)
Collaborators
The Bond Group at Monash University
Simulation of processes at microelectrodes
Microelectrodes have at least one dimension on the order of a few
micrometers making them possible candidates for in vivo analysis. They can
also be used to study fast chemical reactions since the rate of mass
transport to and from the electrode surface is inversely proportional to
the electrode size. In many experiments at microelectrodes the quantity of
interest is the current flowing at the electrode surface: mathematically
this is a linear functional of the solution to the governing equations.
Microelectrodes are modelled using 2D equations and the difficulty when
solving these equations numerically is that the solutions exhibit boundary
singularities (i.e. there are points on the boundary at which the normal
derivative of the solution is discontinuous). This means that on regular
meshes the solution (and hence the functional) converge much more slowly
than the optimal rate for smooth problems meaning that the accurate
estimation of currents is very expensive. The aim of our research is to
generate finite element meshes on which the current may be approximated to
within a prescribed error tolerance using a minimum of computing
resources. This entails the derivation of an a posteriori error bound for
the functional - a computable upper bound on the error in the numerical
approximation of the current - and using this bound to determine where the
mesh should be refined to improve the accuracy. After each mesh refinement
step the finite element solution and a posteriori error bound are
recomputed until the error bound, and hence the actual error, are less
than the prescribed tolerance.
References
- K. Harriman, D.J. Gavaghan, P. Houston, and E. Süli. Adaptive Finite
Element Simulation of Currents at Microelectrodes to Guaranteed Accuracy.
Application to a Simple Model Problem. Electrochem. Commun. 2 (2000)
150-156.
- K. Harriman, D.J. Gavaghan, P. Houston, and E. Süli. Adaptive Finite
Element Simulation of Currents at Microelectrodes to Guaranteed Accuracy.
Theory. Electrochem. Commun. 2 (2000) 157-162.
- K. Harriman, D.J. Gavaghan, P. Houston, and E. Süli. Adaptive Finite
Element Simulation of Currents at Microelectrodes to Guaranteed Accuracy.
First Order EC' Mechanism at Inlaid and Recessed Discs. Electrochem.
Commun. 2 (2000) 163-170.
- K. Harriman, D.J. Gavaghan, P. Houston, and E. Süli. Adaptive Finite
Element Simulation of Currents at Microelectrodes to Guaranteed Accuracy.
An E Reaction at a Channel Microband Electrode. Electrochem. Commun. 2
(2000) 567-575.
- K. Harriman, D.J. Gavaghan, P. Houston, D. Kay, and E. Süli. Adaptive
Finite Element Simulation of Currents at Microelectrodes to Guaranteed
Accuracy. ECE and EC2E Mechanisms at Channel Microband Electrodes.
Electrochem. Commun. 2 (2000) 576-585.
- K. Harriman, D.J. Gavaghan, and E. Süli. Adaptive Finite Element
Simulation of Chronoamperometry at Microdisc Electrodes. Electrochem.
Commun. 5 (2003) 519-529.
- K. Harriman, D.J. Gavaghan, and E. Süli. Time dependent EC', ECE and EC_2E
mechanisms at microdisc electrodes: simulations using adaptive finite
element methods. J. Electroanal. Chem. (In press)
Alternatively see the Technical Reports
- K. Harriman, D.J. Gavaghan, P. Houston, and E. Süli. Adaptive Finite
Element Simulation of Steady State Currents at Microdisc Electrodes to a
Guaranteed Accuracy. Technical report NA99/19.
- K. Harriman, D.J. Gavaghan, P. Houston, D. Kay and E. Süli. Adaptive
Finite Element Simulation of Currents at Microelectrodes to a Guaranteed
Accuracy. Application to Channel Microband Electrodes. Technical report
NA00/09.
Collaborators
The Compton Group at the University of Oxford
People involved
Back to CBG homepage
|
![[Oxford Spires]](/im/spires.gif){kind=small}
oucl