Optimizing transient transport in materials having two scales of porosity

Porous materials having multiple scales of porosity afford the opportunity to combine the high surface area and functionality of nanopores with the superior charge/discharge characteristics of wider transport channels. However, the relative volume fractions assigned to nanopores and transport channels must be thoughtfully balanced because the introduction of transport channels reduces the volume available for nanopore functionality. In the present paper, the optimal balance between nanopore capacity and system response time is achieved by adjusting the aperture and spacing of a family of transport channels that provide access to adjacent nanopores during recharge/discharge cycles of materials intended for storage of gas or electric charge. A diffusive transport model is used to describe alternative processes of viscous gas flow, Knudsen gas flow, and ion diffusion or electromigration. The coupled transport equations for the nanopores and transport channels are linearized and solved analytically for a periodic variation in external gas pressure, ion concentration, or electric potential using a separation-of-variables approach in the complex domain. Optimization of these solutions yields closed-form expressions for channel apertures and spacing that provide maximum discharge of gas or electric charge for a fixed system volume and a desired discharge time.