Concentration Distributions at Galvanostatically Controlled Micro- and Nanoelectrodes

Galvanostatic (controlled-current) techniques allow electrochemical generation of a species at a known rate. They are particularly useful when the electrode reaction involves the solvent or other abundant species, e.g., using water oxidation and reduction to electrogenerate H+ and OH-, respectively (overall reactions 2H2O -> O2 + 4H+ + 4e- and 2H2O+2e-->H2 + 2OH-). When coupled with the steady-state mass transport of micro- and nanoelectrodes, galvanostatic methods allow for precise control of reactant concentrations at and around the electrode surface. Electrochemical control of the surface concentration allows for the initiation and study of concentration-driven processes, such as phase nucleation of an electrochemically generated product[1] or electro-mineralization[2].
While the surface concentration in galvanostatic measurements at micro- and nanoelectrodes has previously been determined through numerical calculations, or approximated by assuming uniform accessibility, there are no reported expressions that directly relate the surface concentration distribution to the experimental conditions (electrode geometry, electrode reaction, diffusion coefficients, applied current). Such expressions are desirable, as they provide direct and transparent relationships between the experimentally controlled parameters (current) and desired parameters (surface concentrations) without the need to (re-)run numerical simulations requiring access to commercial software. This simplifies experimental design and interpretation and provides direct insight into the relationships. In this work we provide expressions for the concentration distribution at and around disk and ring micro- and nanoelectrodes under galvanostatic control. These expressions are confirmed by comparison to numerical simulations. The expressions offer a link between experimental parameters and measurable quantities, which will be of use in the investigation of concentration-driven electrode processes, e.g., phase nucleation and electromineralization.