Effective Transport Properties of Porous Electrochemical Materials — A Homogenization Approach

This study concerns the determination of effective transport coefficients for multiscale composite materials used in various electrochemical systems. The effective transport coefficients are indispensable in macroscale modeling of such systems. We propose an integrated approach which for a given two-phase or three-phase microstructure allows us to systematically determine the exact values of different effective transport coefficients such as diffusivity of a species or electric conductivity. In addition to electron microscopy, this approach combines state-of-the-art techniques of mathematical homogenization, image processing and numerical computation. When only partial information about the microstructure is available, rigorous upper and lower bounds are available on the effective transport coefficients and we demonstrate that the commonly used Bruggeman's formula may in fact violate the lower bound in some regimes. These upper bounds also allow one to quantify how much the transport properties of the material with a given composition could be improved. The proposed approach is illustrated by analyzing a three-phase electrode material of an actual Li-ion battery. We also quantify the uncertainty of the effective transport coefficients resulting from possibly imprecise information about the material properties of the individual phases and address the question concerning the importance of resolving all three phases.