Optimal design of nanoporous materials for electrochemical devices

Unique macroscopic properties of nanoporous metamaterials stem from their microscopic structure. Optimal design of such materials is facilitated by mapping a material's pore-network topology onto its macroscopic characteristics. This is in contrast to both trial-and-error experimental design and design based on empirical relations between macroscopic properties, such as the often-used Bruggeman formula that relates a material's effective diffusion coefficient to its porosity. We use homogenization to construct such a map in the context of materials design that maximizes energy/power density performance in electrochemical devices. For example, effective diffusion coefficients and specific surface area, key macroscopic characteristics of ion transport in a hierarchical nanoporous material, are expressed in terms of the material's pore structure and, equally important, ion concentrations in the electrolyte and externally applied electric potential. Using these microscopic characteristics as decision variables, we optimize the macroscopic properties for two two-dimensional material-assembly templates and several operating conditions. The latter affect the material's performance through formation of an electrical double layer at the fluid-solid interfaces, which restricts the pore space available for ion transport.