An Analytical Method to Determine Tortuosity in Rechargeable Battery Electrodes

In high energy density, low porosity, lithium-ion battery electrodes, the underlying microstructural tortuosity controls the macroscopic charge capacity, average lithium-ion diffusivity, and macroscopic resistivity of the cell, particularly at high discharge rates and power densities. In this paper, an analytical framework is presented to extend widely used empirical tortuosity relations such as the Bruggemann relation to incorporate the effects of the mesoscale tortuosity through analytical integration along the width of the electrode (in the limit of high porosities), and integration along a statistically representative tortuous path (in the limit of low porosities). The framework presented herein enables to establish analytical tortuosity-porosity relations that combine the constitutive properties of the individual components. As an example application, the macroscopic tortuosity-porosity relation of a mixture of two porous particle systems of widely different length scales and well-known individual tortuosity constitutive equations, one displaying mesoscale porosity (the carbon black-electrolyte mixture) and a second one displaying microporosity (the electrochemically active phase), are combined into a self-consistent macroscopic tortuosity expression that is in agreement with recently reported empirical measures of tortuosity.