Accurate Simulations of Electric Double Layer Capacitance of Ultramicroelectrodes

This paper aims to develop rigorous and accurate numerical tools for simulating electric double layers formed near ultramicroelectrodes. It also aims to assess the validity of existing models and to identify the dominant physical phenomena that must be accounted for. The electric double layer capacitance was numerically predicted for spherical ultramicroelectrodes of various radii in aqueous electrolyte. The model accounted for the Stern and diffuse layers, the finite size of ions, and the dependency of the electrolyte dielectric permittivity on the local electric field. This study reveals that models reported in the literature suffer from severe limitations. First, it demonstrates that the electrolyte field-dependent dielectric permittivity significantly affects the predicted Stern layer and total specific capacitances and must be accounted for. The finite ion size and the Stern layer also need to be considered in simulating electric double layers under high concentrations and surface potential. This study also establishes that the Helmholtz model predicts the Stern layer capacitance for all electrode radii if the electrolyte permittivity is assumed to be constant. However, it underestimates the Stern layer capacitance for sphere radii less than 40 nm when accounting for field-dependent permittivity. The electrode curvature was found to have negligible effect on the predicted specific capacitance for sphere radii larger than 40 nm. Then, the latter is equal to that of planar electrodes. Results of this study can be used to design electrodes for electrochemical sensors and electrical energy storage.