Dynamic diffuse double-layer model for the electrochemistry of nanometer-sized electrodes

A dynamic diffuse double-layer model is developed for describing the electrode/electrolyte interface bearing a redox reaction. It overcomes the dilemma of the traditional voltammetric theories based on the depletion layer and Frumkin's model for double-layer effects in predicating the voltammetric behavior of nanometer-sized electrodes. Starting from the Nernst-Planck equation, a dynamic interfacial concentration distribution is derived, which has a similar form to the Boltzmann distribution equation but contains the influence of current density. Incorporation of the dynamic concentration distribution into the Poisson and Butler-Volmer equations, respectively, produces a dynamic potential distribution equation containing the influence of current and a voltammetric equation containing the double-layer effects. Computation based on these two equations gives both the interfacial structure (potential and concentration profiles) and voltammetric behavior. The results show that the electrochemical interface at electrodes of nanometer scales is more like an electric-double-layer, whereas the interface at electrodes larger than 100 nm can be treated as a concentration depletion layer. The double-layer nature of the electrode/electrolyte interface of nanometer scale causes the voltammetric responses to vary with electrode size, reactant charge, the value of formal redox potential, and the dielectric properties of the compact double-layer. These voltammetric features are novel in comparison to the traditional voltammetric theory based on the transport of redox molecules in the depletion layer.