Impact of Li+ Ion Diffusion Coefficient and Grain Size of Active Material on Overpotential
Authors: Ando Keisuke , Kanamura Kiyoshi 
Published: December 2024

Introduction

The charge–discharge reaction focusing on the lithium insertion material has two steps: (1) the charge transfer process and (2) the ion diffusion process within the particle. The Butler–Volmer equation is valid when ion diffusion is sufficiently fast and charge transfer is dominant. However, when ion diffusion dominates, the Butler–Volmer equation is inapplicable. Nevertheless, the effect of ion diffusion in active material particles is not well understood.
We investigated the effect of the active material diffusion coefficient on the electrochemical response, particularly the overpotential, using Battery Design StudioⓇ (BDS), a one-dimensional lithium-ion battery performance simulator using the Newman model, to create a single-particle measurement model with the exchange current density and diffusion coefficient as parameters.[1] In this paper, we discuss the effect of the active material particle size, in addition to the active material exchange current density and diffusion coefficient, on the electrochemical response by simulating pulse application tests and generating Tafel plots.

Experimental

A single-particle measurement model with the area, thickness, porosity, and specific surface area reproducing spherical LiCoO2 inside a cubic working electrode was set up in the BDS. A flat Li metal electrode was used as the counter electrode. To minimize the overpotential, the parameters of the counter electrode and electrolyte were set significantly higher than their actual values.
We experimented with combinations of three different exchange current densities (1 × 10−4, 1 × 10−3, and 1 × 10−2 A cm− 2), eight different diffusion coefficients (1 × 10−5, 1 × 10−6, 1 × 10−7, 1 × 10−8, 1 × 10−9, 1 × 10−10, 1 × 10−11, and 1 × 10−12 cm2 s−1), and three different diameters (1, 10, and 100 μm) for LiCoO2. The Tafel plots were obtained using the overpotential from the simulated pulse application at 50% state of charge. The setup model is described in detail in our previous study [1].

Results and discussion

Fig. 1 shows the Tafel plots for different grain sizes and the same parameters (exchange current density = 1 × 10−3 A cm−2, different diffusion coefficient = 1 × 10−9 cm2 s−1). When the current density is not excessively small, the aforementioned parameters demonstrate a linear relationship between the current density (log i) and the overpotential (η), indicating a Tafel region lying on the dashed straight line. This indicates that charge transfer is dominant. As the current density (log i) increases, the overpotential (η) deviates from the dashed line, the gap of which is attributed to the effect of ion diffusion. Compared to the 1 and 100 μm grain sizes, the shape of the Tafel plots is different, although the parameters (exchange current density and diffusion coefficient) are the same except for the grain size. The plots for the 100 µm grain size fall out of the Tafel region at the current density (log i) of -2.2 or higher, which is earlier than those for the 1 µm grain size. In other words, a larger grain size causes the diffusion coefficient to become dominant at lower current densities. In the presentation, we discuss the real parameters of LiCoO2.

Acknowledgement

This study was partially funded by JSPS KAKENHI under Grant Numbers JP20K14729 and JP23K13327.

Reference

[1] K. Ando, et al. Journal of Electroanalytical Chemistry, 948 (2023) 117802.

Figure 1