THEORY OF POLAROGRAPHIC KINETIC CURRENTS FOR SECOND-ORDER REGENERATION REACTIONS AT SPHERICAL ELECTRODES .1. NUMERICAL SOLUTION OF FINITE-DIFFERENCE EQUATIONS

A numerical finite-difference method of solution, for the equations describing homogeneous reactions with kinetic complications as applied to stationary electrode polarography, is extended to include the effects of spherical diffusion at large values of time. The accuracy and speed of computation were improved by the application of the integral equation for the linear combination of concentrations which obeys the pure diffusion equation, and solution by a simultaneous equation, Newton-Raphson iteration method. The best data from both the finite-difference and steady-state integral equation methods of solution are tabulated. Measurements with spherical electrodes in the near steady-state region are shown to give a one electrode equivalent to a thin layer cell, and to permit the determination of rate constants in a nearly time-independent region by comparison with measurements at a planar electrode. © 1969, American Chemical Society. All rights reserved.