A GENERAL-METHOD FOR ELECTROCHEMICAL SIMULATIONS .2. APPLICATION TO THE SIMULATION OF STEADY-STATE CURRENTS AT MICRODISK ELECTRODES - HOMOGENEOUS AND HETEROGENEOUS KINETICS

ILU preconditioned Krylov subspace methods are used with conformal map pings to simulate the steady-state response of microdisk and hemispher ical electrodes with the influence of homogeneous and heterogeneous ki netics. For the microdisk electrode, the conformal mapping of Amatore and Fosset (J. Electroanal. Chem. 1992, 328, 21) is shown to be superi or to that of Verbrugge and Baker (J. Phys. Chem. 1992, 96, 4572), bot h in its efficiency for simple electron-transfer problems and in terms of the conditioning of the matrix it produces. The efficiency improve ment arising from the use of multipoint Taylor series expressions for boundary conditions is investigated and is found to be highly signific ant for these systems where edge singularities are removed by the conf ormal mapping. Convergence at high rate constants is also addressed. T he simulations were used to generate working curves at microdisk and s pherical/hemispherical electrodes for ECE, DISP1, EC2E, DISP2, and EC' mechanisms and a working surface for quasi-reversible heterogeneous k inetics. These allow quantitative mechanistic analysis for these mecha nisms without the need for any further simulation. A suite of programs is available to perform this analysis via the World Wide Web (http:// physchem.ox.ac.uk:8000/wwwda/). Approximate analytical expressions, wh ere available, are compared with simulated results. The approximate 'e quivalence' between microdisk and spherical/hemispherical electrodes i s assessed in the presence of heterogeneous and homogeneous kinetics. The results show that while there is no formal physical basis for an e quivalence relation, an approximation for many common mechanisms can b e generated by treating a microdisk electrode of radius r as if it wer e a spherical electrode of radius 2r/pi. Slightly better results are o btained if the rate constant, k, for a coupled homogeneous reaction at the microdisk electrode is treated as a rate constant of pi k/4 at a spherical electrode of radius pi r/4. Caution is advised, however, sin ce the quality of the approximation is mechanism dependent: the error is reasonably uniform across the ECE, EC2E, and DISP reactions but inc reases significantly with substrate concentration in the EC' reaction.