Geometric Effects on the Transient Charging of Electric Double Layers in Nanopores

Porous electrodes are common in electrochemical devices. To that end, much continuum research focuses on simplifying pore networks as simple stacks of cylinders. In reality, the structure of these porous electrodes exhibits a highly tortuous and interconnected morphology. To enhance the modeling of these devices, it is essential that the model reflects the shape-changing and interconnected nature of these electrodes.

Previously, we linearized the Poisson-Nernst–Planck equations to develop an equivalent model of ionic transport in a network of straight cylindrical pores. This study expands our model to account for variations in pore radius along the axial direction and develops an equivalent circuit model for this system. We investigate linearly converging and diverging pores and find that convergence leads to faster charging times. The underlying mechanisms are analyzed, highlighting the effects of double-layer thickness and entrance resistance. We also reveal the interplay between diffusive and electromigrative forces and show how the rotation of the electric field plays a key role in determining the transient timescale. Our work opens opportunities to study networks of shape-changing pores, which will more accurately model porous electrodes and aid in their future design. timescale. Our work opens opportunities to study networks of shape-changing pores, which will more accurately model porous electrodes and aid in their future design.