Nanoporous materials are used in the variety of fields, ranging from medicine and biosensors to clean energy and purification. Technological advances have enabled one to manufacture nanoporous materials with a prescribed pore structure. This raises a possibility of using controllable pore scale properties (e.g., pore size distribution, pore connectivity and tortuosity) to design materials with desired macroscopic properties (e.g., porosity, effective diffusion coefficient and effective electrical conductivity). Upscaling techniques, such as homogenization via multiple-scale expansions, provide a framework to connect these two scale. This research uses such techniques to optimize macroscopic properties of a material by using its microscopic properties as decision variables.

This research aims to obtain qualitative understanding and quantitative predictions of macroscopic properties of nanoporous materials to transmit solutes that undergo non-equilibrium adsorption and local electrochemical surface reactions at the fluid-solid interface. The first part of this work focuses on the design of hierarchical nanoporous materials with optimal permeability and sorption capacity. A class of nanoporous materials whose pore space consists of ordered nanopores interconnected by nano-channels is considered. Anisotropic effective diffusion coefficients and adsorption coefficients of such materials are expressed in terms of pore properties and connectivity Nano-channels can significantly alter diffusive properties and increase its adsorbing capacity.

The second part of this work contains a macroscopic model of ion transport in electrically charged nanoporous materials. The corresponding effective diffusion coefficients, electric conductivity and transference numbers account for dynamic changes in the electrical double layer (EDL), possible overlap of EDLs in nanopores, and electrochemical conditions (i.e., concentration of ions in the electrolyte). Our effective coefficients are derived from the first principles and vary with a range of electrochemical conditions (e.g., initial concentration of ions in the electrolyte). The resulting model predictions of the EDLC voltage response match the experimental data better than the original model does.

The last part of this work is devoted to derivation of macroscopic properties of three-dimensional dendritic spines. The effective diffusion coefficient estimated with this analysis is used to quantify travel time of electric signal through the spine.