Analytical Solutions to Characterize Through-Plane Inhomogeneity of Porous Electrodes Using Electrochemical Impedance Spectroscopy

Abstract

Characterization of through-plane inhomogeneity in porous media requires knowledge of the distribution of porosity, tortuosity, and double-layer capacitance across the thickness. The thickness-averaged or apparent values of these parameters may not be sufficient to model the transport processes in batteries and fuel cells accurately. Cleverly designed through-plane inhomogeneities can improve the performance of electrochemical systems (e.g., graded-porosity electrodes for batteries or gas diffusion media for fuel cell). In some cases, inhomogeneity can result from manufacturing steps; for example, tortuosity variation due to binder migration in the fast slurry-drying step. In this work, we extend the impedance-based approach to characterize the inhomogeneity of a porous electrode in the through-plane direction. We derive analytical expressions for the impedance response of an electrode having three types of inhomogeneities (step-wise, linear, and inverse-linear variation) in a symmetric cell setup having non-reacting electrode/electrolyte interface (blocking electrode or electrolyte method). We also provide perturbation-theory based approximate solutions and expressions for semi-infinite domain to enable the development of an impedance-based fitting tool for inhomogeneous electrodes. In the end, we provide an impedance-based experimental investigation of gas diffusion media (composite layer) using symmetric cell setup to demonstrate the applicability of the theory and understanding derived in this work.