  In this paper, we introduce a density-based topology optimization framework
to design porous electrodes for maximum energy storage. We simulate the full
cell with a model that incorporates electronic potential, ionic potential, and
electrolyte concentration. The system consists of three materials, namely pure
liquid electrolyte and the porous solids of the anode and cathode, for which we
determine the optimal placement. We use separate electronic potentials to model
each electrode, which allow interdigitated designs. As the result, a
penalization is required to ensure that the anode and cathode do not touch,
i.e. causing a short circuit. We compare multiple 2D designs generated for
different fixed conditions, e.g. material properties. A 3D design with complex
channel and interlocking structure is also created. All optimized designs are
far superior to the traditional monolithic electrode design with respect to
energy storage metrics. We observe up to 750% increase in energy storage for
cases with slow effective ionic diffusion within the porous electrode.
