Current calculation of irreversible electrode reaction mechanismsin linear sweep voltammetry

Application of exponential infinite series gives highly accurate analytical solution contributing to the theory of linear sweep voltammetry for single scan experiments. We have calculated theoretical dimensionless current function (usually denoted as π1/2χ(bt)) at relevant potentials for irreversible charge transfer without a coupled chemical reaction. For this purpose several transformation techniques were used, which convert the derived infinite series into summable sequences. Since infinite series of further electrochemical mechanisms with irreversible electrode reaction have similar features (particularly those comprising preceding and catalytic chemical reaction), the same approach can be successfully applied also for further electrochemical mechanisms. The respective infinite series are divergent in the most important potential region at and after voltammetric peak therefore their transformation by Epsilon and Levin transform techniques was used. Necessary arbitrary precision arithmetic (APA) was implemented by UBASIC. The results were compared to the customary solution of Nicholson and Shain, who computed the current-potential curves by means of numerical solution of the integral equations but with a much lower precision. Our results were obtained in a broad potential range including the potential regions where the series are divergent. Obtained current functions are precise to 12 valid decimal numbers, which is utilizable for evaluation of the results achieved by various faster but less precise digital simulation techniques.