Smoothed Boundary Method Simulations of Electrochemical Impedance Spectroscopy for Energy Materials with Complex Microstructures

Abstract

Electrochemical impedance spectroscopy (EIS) is commonly utilized to measure ionic and electronic conductivities in energy materials (e.g., battery and solid oxide fuel cell electrodes), which are often represented as equivalent circuits that contain capacitors and resistors. Although effective capacitance and resistance can be calculated with the simplified representation as circuits, such representation cannot incorporate microstructural characteristics (e.g., porosity, tortuosity, grain boundary density, etc.) that strongly influence the performance of these energy materials. For example, the grain boundary network can enhance or hinder the overall transport of ions and electrons, which in turn influence polarization. Such a microstructural effect cannot be captured with the simplified representation as circuits. As such, a comprehensive model of EIS should take into account the microstructural characteristics that play a crucial role in determining material properties and device performance. In this work, we develop an innovative approach based on the smoothed boundary method, which allows us to simulate EIS behavior of materials with complex microstructures. Using a continuous domain parameter to define the geometry of a porous electrode, different physical mechanisms, such as surface transport along irregular particle surfaces, electrochemical reaction at the particle surfaces, and diffusion through the tortuous complex bulk of the electrode, are coupled and taken into account in the simulation of the ion concentration responding to oscillating loadings. In addition, using multiple domain parameters, each of which defines a primary cathode particle, transport through complex grain boundary networks in secondary particles is simulated and accounted for in the simulation of the EIS response. From the simulation results, the effects of microstructures and the impact of interface/boundary transport on EIS behavior are elucidated. This work is supported by the NorthEast Center for Chemical Energy Storage (NECCES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award Numbers DE-SC0012583.