Abstract
Reaction rate distribution across porous electrodes in Li-ion battery applications largely determines the overall battery performance. In the present work, expressions for the reaction rate distribution across porous electrodes are analytically derived and analyzed for small current and short time applications. The dependency on the effective ionic and electronic conductivities is systematically investigated and discussed. It is found that in the case of equal effective electronic and ionic conductivities, the reaction rate distribution is symmetric around the electrode mid-point. Small conductivities induce the charge-transfer reaction to preferentially occur at the interface of the current collector and separator, while high conductivities make the reaction rate distribution uniform across the electrode thickness. In the case of unequal conductivities, a decrease in the effective electronic conductivity shifts the reaction rate distribution towards the electrode/current collector interface. In contrast, a decrease in the effective ionic conductivity shifts the reaction rate distribution towards the electrode/separator interface. It is also found that the reaction rate distribution shows saturating behavior when the effective electronic or ionic conductivity grows infinitely. A further increase in the effective ionic or electronic conductivity does not lead to any further reaction rate distribution changes.
Highlights
Lithium-ion batteries (LIB) with high energy density are highly demanded in our present-day society
The effective ionic conductivity of the electrolyte and the effective electronic conductivity of the electrode are proven to be highly responsible for these reaction rate distributions [15,16]
From Eq (19), it can be concluded that a combination of five material-related parameters essentially determines the charge-transfer reaction rate: the thickness of the porous electrode (L − δ), the effec tive ionic conductivity of the electrolyte inside the porous electrode, porous electrode is plotted from the normalized position x = 0.26 on wards to x = 1 for the case where κC = σC
Summary
Lithium-ion batteries (LIB) with high energy density are highly demanded in our present-day society. The charge-transfer reaction rate and current distribution across the porous electrodes are analytically derived, and explicit closed-form solutions are obtained, considering a linear approximation of the Butler-Volmer expression at low overpotentials and short-time interval. With this analytical solution, it was possible to study the separate effects of the effective conductivities of solid elec trode matrixes and electrolytes on the reaction rate and current distri bution inside porous electrodes. These analyses are highly useful for further optimizing the electrolyte and electrode properties of LIB and as interesting limiting cases for testing battery modeling software
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