Analytical solutions for fast and straightforward study of the effect of the electrode geometry in transient and steady state voltammetries: Single- and multi-electron transfers, coupled chemical reactions and electrode kinetics

•Accurate analytical solutions reported for voltammetry of key electrochemical systems•Expressions enable fast and direct analysis of transient and steady-state responses.•Multi-electron transfers and coupled homogeneous chemical reactions are considered.•A wide variety of electrode size and shape is covered, including microdisks.•The arrays of submicroelectrodes and liquid|liquid microinterfaces are discussed.

We survey recently-reported, analytical solutions for the study of simple and complicated charge transfer reactions by means of any voltammetric technique with electrodes of very different geometries under conditions where the mass transfer takes place only by diffusion, that is, in fully-supported media where migration can be neglected. Under transient conditions, expressions are reported for one-electron and multi-electron reversible transfers, electrode reactions coupled to homogeneous chemical equilibria and the first-order catalytic mechanisms with electrodes of any geometry.The steady-state voltammetric response of the above systems will also be considered at submicro- and nanoelectrodes of very different shapes and arrays. Also, a universal approach to the steady-state voltammetry of sluggish electron transfer processes is presented. Finally, solutions for ion transfer processes across (sub)micrometric liquid|liquid interfaces is discussed.

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