ABSTRACT
The Crank-Nicolson (CN) simulation method has an oscillatory response to sharp initial transients. The technique is convenient but the oscillations make it less popular. Several ways of damping the oscillations in two types of electrochemical computations are investigated. For a simple one-dimensional system with an initial singularity, subdivision of the first time interval into a number of equal subintervals (the Pearson method) works rather well, and so does division with exponentially increasing subintervals, where however an optimum expansion parameter must be found. This method can be computationally more expensive with some systems. The simple device of starting with one backward implicit (BI, or Laasonen) step does damp the oscillations, but not always sufficiently. For electrochemical microdisk simulations which are two-dimensional in space and using CN, the use of a first BI step is much more effective and is recommended. Division into subintervals is also effective, and again, both the Pearson method and exponentially increasing subintervals methods are effective here. Exponentially increasing subintervals are often considerably more expensive computationally. Expanding intervals over the whole simulation period, although capable of satisfactory results, for most systems will require more cpu time compared with subdivision of the first interval only.
ABSTRACT
A systematic approach to the construction of finite difference formulae for the approximation to first and second derivatives with respect to space on an arbitrarily spaced grid is presented. The finite difference formulae, combined with backward implicit (BI) and extrapolation methods, are used for electrochemical simulations and tested for efficiency. Excellent results are obtained with second and third order discretisations even for very small space intervals in the vicinity of the electrode and strongly expanding grid spacings. This ensures efficient simulation of kinetic-diffusion systems where, due to a fast homogeneous reaction, a thin reaction layer is formed adjacent to the electrode.
ABSTRACT
The application of fourth-order finite difference discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined further. In the bulk of the diffusion space, a central 5-point scheme is used, and 6-point asymmetric schemes are used at the edges. In this paper, four Runge-Kutta schemes have been used for the time integration. The observed efficiencies, for the Cottrell experiment and chronopotentiometry, are satisfactory, going beyond those for the 3-point scheme. However, it is third-order Runge-Kutta, rather than the fourth-order scheme, which is the most efficient, the two resulting in practically the same errors. This is probably due to the computational procedure where a constant ratio of delta(t)/h2 was used.
ABSTRACT
The application of fourth order discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined. In the bulk of the diffusion space, a central five-point scheme is used, and six-point asymmetric schemes are used at the edges. In this paper, the scheme is applied to the extrapolation technique, based on the backward implicit (BI) algorithm for temporal integration, which (with extrapolation) allows higher orders in time as well. The method is found to be stable, using both the von Neumann and matrix methods. Exceptional efficiency is obtained both for Cottrell and chronopotentiometry simulations, requiring as few as 3-5 steps in time, starting at the dimensionless time t = 0 to gain four-decimal accuracy at t = 1.
ABSTRACT
The application of fourth order discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined. In the bulk of the diffusion space, a central five-point scheme is used, and six-point asymmetric schemes are used at the edges. In this paper, the scheme is applied to the extrapolation technique, based on the backward implicit (BI) algorithm for temporal integration, which (with extrapolation) allows higher orders in time as well. The method is found to be stable, using both the von Neumann and matrix methods. Exceptional efficiency is obtained both for Cottrell and chronopotentiometry simulations, requiring as few as 3-5 steps in time, starting at the dimensionless time t = 0 to gain four-decimal accuracy at t = 1.
ABSTRACT
The application of fourth-order discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined. In the bulk of the diffusion space, a central five-point scheme is used, and six-point asymmetric schemes are used at the edges. In this paper, the scheme is applied to the BDF technique which allows higher orders in time as well. The method is found to be stable, using both the Neumann and matrix methods. Performance with BDF is not, however, optimal, levelling off at three-point BDF, as does the usual three-point approximation. This is shown to be due to startup problems inherent with BDF.
ABSTRACT
In order to establish an experimental basis for exploring the reactivity of membrane-bound redox enzymes using electrochemistry at an organic/aqueous interface, the reactivity of glucose oxidase adsorbed at the dichloroethane/water interface has been studied. Turnover of glucose in the aqueous phase mediated by dimethyl ferricenium electrogenerated in the organic phase was measured by measuring the feedback current caused by recycling the mediator as the generator electrode approached close to the interface from the organic side. An unexpected self-exchange reaction of the ferrocene at the interface was suppressed by adsorption of a surfactant. The interfacial enzyme reaction could be distinguished from reaction within the bulk of the aqueous phase. Reaction within a protein-surfactant film formed at the interface is conjectured.
