A Generic Model for Electric Double Layers in Porous Electrodes

The performance of electric-double-layer capacitors (EDLCs) hinges on microscopic charge distributions near the electrode/electrolyte interfaces. Whereas practical EDLCs consist of electrodes made of amorphous porous materials, theoretical understanding of EDLCs is mostly based on EDL structure near a planar surface or on simplistic models that have little relevance to realistic systems. In this work, we propose a spherical shell model to account for both pore size and curvature effects of amorphous porous materials. The EDL structure in spherical shells has been investigated over a broad range of pore sizes and curvatures by use of classic density functional theory. Theoretical results reveal that the curvature effects on convex and concave EDLs are drastically different and that materials with extensive convex surfaces will lead to maximized capacitance. Like a slit pore, the spherical shell model also predicts oscillatory variation of capacitance with pore size, but the oscillatory behavior is magnified as the curvature increases. The joint effects of pore size and curvature identified in this work give new insight into materials design for porous electrodes with optimal EDLC performance.