Staircase, cyclic and differential voltammetries of the nine-member square scheme at microelectrodes of any geometry with arbitrary chemical stabilization of the three redox states

Simple analytical expressions are deduced for the cyclic (staircase) and differential cyclic (staircase) voltammetric responses of the nine-member square scheme at the most widely used microelectrode geometries: disc, (hemi)spheres, cylinders and bands. The generality of the reaction scheme considered enables us to tackle many different and common electrochemical situations where the oxidized, intermediate and/or reduced species of a two-electron transfer also take part in homogeneous chemical equilibria such as protonations, complexations, or ion pairings. The effect of the coupled chemical processes on the voltammograms is analyzed at electrodes of different size and shape under a variety of conditions depending on which redox state is chemically stabilized most significantly. Also, working curves for the determination of the formal potentials and the chemical equilibrium constants are given for macroelectrodes, microelectrodes and ultramicroelectrodes in cyclic voltammetry and differential cyclic voltammetry.