Computing the local ion concentration variations for electric-double-layer-modulation microscopy

Modulation of the electric potential on a conducting electrode is presented to generate an optical contrast for scattering microscopy that is sensitive to both surface charge and local topography. We dub this method electric-double-layer-modulation microscopy. We numerically compute the change in the local ion concentration that is the origin of this optical contrast for three experimentally relevant geometries: nanosphere, nanowire, and nanohole. In absence of plasmonic effects and physical absorption, the observable optical contrast is proportional to the derivative of the ion concentration with respect to the modulated potential. We demonstrate that this derivative depends on the size of the object and, less intuitively, also on its surface charge. This dependence is key to measuring the surface charge, in an absolute way, using this method. Our results help to identify the experimental conditions such as dynamic range and sensitivity that will be necessary for detecting the elementary charge jumps. We conclude that the nanohole is the most suitable geometry of the three for achieving elementary charge sensitivity.