Theory of Impedance Spectroscopy for Lithium Batteries

Abstract

In this article, we derive and discuss a physics-based model for impedance spectroscopy of lithium batteries. Our model for electrochemical cells with planar electrodes takes into account the solid-electrolyte interphase (SEI) as porous surface film. We present two improvements over standard impedance models. Firstly, our model is based on a consistent description of lithium transport through electrolyte and SEI. We use welldefined transport parameters, e.g., transference numbers, and consider convection of the center-of-mass. Secondly, we solve our model equations analytically and state the full transport parameter dependence of the impedance signals. Our consistent model results in an analytic expression for the cell impedance including bulk and surface processes. The impedance signals due to concentration polarizations highlight the importance of electrolyte convection in concentrated electrolytes. We simplify our expression for the complex impedance and compare it to common equivalent circuit models. Such simplified models are good approximations in concise parameter ranges. Finally, we compare our model with experiments of lithium metal electrodes and find large transference numbers for lithium ions. This analysis reveals that lithium-ion transport through the SEI has solid electrolyte character.

Operando Electrochemical Kinetics in Particulate Porous Electrodes by Quantifying the Mesoscale Spatiotemporal Heterogeneities

“…The calculated capacitances (C SEI = 20.5 µF and C CT = 214 µF) were then used to determine the associated dielectric constants via C = ε r ε 0 A edge /d, where A edge = 1.459 cm 2 is the total area of the edge planes based on image analyses, d is the thickness of the respective capacitors (assuming 10 nm for the SEI layer and 1 nm for the electrical double layer), ε 0 is the permittivity of vacuum, and ε r is the dielectric constant. The resulting dielectric constants (161.2 and 167.5) are surprisingly very close to each other, but much higher than the dielectric constants for liquid electrolyte (<90) we used in the operando cells, [57] yet consistent with the reported values for the solid electrolyte interphase [58] and solid polymer electrolytes. [59] This quantitative physical confirmation validates our hypothesis on the microstructure of the equivalent circuit model.…”

Solid–Electrolyte Interphase During Battery Cycling: Theory of Growth Regimes

“…However,t here were some inconsistenciesi nt he modeling approach.F irst, recent models show that the SEI is as ingle-ion solid electrolyte. [58] Therefore, the lithium ion concentration inside the SEI should remain constant due to chargec onservation. Second, the modeled conduction of electrons and lithium ions leads to counterpropagating fluxes.T hus, SEI formation should be fully suppressed during deintercalation.…”

“…However, there were some inconsistencies in the modeling approach. First, recent models show that the SEI is a single‐ion solid electrolyte . Therefore, the lithium ion concentration inside the SEI should remain constant due to charge conservation.…”

Wetting Phenomena and their Effect on the Electrochemical Performance of Surface‐Tailored Lithium Metal Electrodes in Contact with Cross‐linked Polymeric Electrolytes

“…η arc , however, comprises significant influences by the diffusion properties of the systems (Figure S11). By analysis of the Warburg impedance ( Z W ) in EIS at low frequencies (<10 Hz), additional information about mass transport properties can be derived . As illustrated in Figure d, the low‐frequency region (<10 Hz) reveals a distinct diffusion contribution with a phase angle of − π / 4 (45° slope) which indicates that solid‐state diffusion processes play a crucial role for understanding the ongoing complex electrochemical behaviors at the Li|PE interface .…”