Highly accurate, inexpensive procedures for computing theoretical chronoamperometric currents at single straight electrode edges and at single microband electrodes

Abstract

Theoretical considerations of potential step chronoamperometry for electrochemical systems involving straight electrode edges lead to a number of analytical or semi-analytical expressions, or special functions, describing current-time dependences. Unfortunately the functions are hard to evaluate accurately on a computer, due to numerical difficulties or high computational costs. In this work computationally inexpensive procedures have been developed, for two special functions describing chronoamperometry at a single straight edge and for one special function expressing chronoamperometric current at a single microband electrode (two straight edges). The concept of the minimax approximation has been employed. The procedures are highly accurate, ensuring relative errors close to, or even smaller than 10− 16, which is the machine accuracy for standard double precision variables. In addition, computing a single function value requires less than a microsecond of the processor time on currently available personal computers. The procedures can be useful for the purposes of experimental data analysis, and for the testing/validation of diverse mathematical and numerical modelling techniques designed for electroanalytical chemistry.