Methods—Understanding Porous Electrode Impedance and the Implications for the Impedance Analysis of Li-Ion Battery Electrodes
Robert Morasch, Josef Keilhofer, Hubert A. Gasteiger, Bharatkumar Suthar
Abstract
Two of the main factors influencing the performance of Li-ion battery (LIB) electrodes are the kinetic losses due to the charge transfer resistance of the active material ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ct</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) and the ionic transport resistance in the electrolyte phase within the electrode pores ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ion</mml:mi> </mml:mrow> </mml:msub> </mml:math> ). Seeking to increase the energy density of LIBs, ever higher active material loadings are applied, resulting in thicker electrodes for which <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ion</mml:mi> </mml:mrow> </mml:msub> </mml:math> becomes dominant. As electrochemical impedance spectroscopy is commonly used to quantify <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ct</mml:mi> </mml:mrow> </mml:msub> </mml:math> of electrodes, understanding the impact of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ion</mml:mi> </mml:mrow> </mml:msub> </mml:math> on the impedance response of thick electrodes is crucial. By use of a simplified transmission line model (TLM), we simulate the impedance response of electrodes as a function of electrode loading. This will be compared to the impedance of graphite anodes (obtained using a micro-reference electrode), demonstrating that their impedance response varies from purely kinetically limited at 0.6 mAh cm −2 to purely transport limited at 7.5 mAh cm −2 . We then introduce a simple method with which <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ct</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">ion</mml:mi> </mml:mrow> </mml:msub> </mml:math> can be determined from the electrode impedance, even under transport limited conditions. Finally, we show how the initially homogenous ionic current distribution across porous electrodes under kinetically limited conditions becomes severely inhomogeneous under transport limited conditions.