Quantifying the Role of Electrode Thickness in Battery Rate Performance
Authors: Horvath Dominik Valter , Coelho João , Tian Ruiyuan , Coleman Jonathan N 
Published: December 2020

Batteries are increasingly used in energy-storage applications where a high power is needed in tandem with a high capacity, with electric vehicles being a great example. These batteries ideally deliver large amounts of current for extended periods with no compromise in capacity. However, as the rate is increased, the capacity that can be delivered rapidly decreases. This effect is generally not described using quantitative metrics. In this work, we use a simple semi-empirical equation to model and fit capacity-rate data, allowing us to extract a characteristic time (τ) for charge/discharge that describes rate behavior (Fig. 1).
In a recent publication Tian et al. proposed a link between τ, electrode kinetics and the physical parameters of an electrode (e.g. electrode thickness, LE).1 This equation has accurately described the rate behavior of a large variety of electrodes found in literature, for both Na and Li-ion batteries. It is possible to rearrange this equation such that τ equals a quadratic polynomial in LE, with constants a, b and c depending on tunable parameters (inset equation in Fig. 1). These parameters provide a reasonably comprehensive description of the rate performance of the material. With them we can assess the importance of solid-state diffusion, estimate the electrode capacitance and even calculate values for the liquid diffusion coefficient. Our aim is to further verify this equation and to quantitatively describe rate performance as a function of LE.
We used chronoamperometry (CA) as an alternative to galvanostatic charge-discharge (GCD) to record capacity-rate curves.2,3 This method combined with the previously described fitting process provides a quicker and easier way of obtaining rate information when compared to GCD. Our results show τ to be a quadratic function of LE, confirming the relationship proposed in Ref. 1. The measurements were repeated with a different separator thickness (LS). As predicted by the equation in Fig. 1, the τ vs LE curve for the thicker LS follows the same behavior as the thinner LS, albeit with varied constants. The difference agrees with that predicted by the rate equation.
Our results highlight the potential of the equation described by Tian et al. We have used the equation to describe how rate performance varies with LE. However, it is also possible to quantify the effects of other parameters such as the out-of-plane electrical conductivity (σE)4 or LS. This level of analysis provides the means for better understanding rate performance and the means for designing electrodes for high-rate applications.
In the future we hope to use the rate equation to design battery electrodes which possess very small values of τ and thus, excellent rate performance. We aim to achieve this by using optimization techniques such as design of experiments for the minimization of τ. The understanding gained from the equation would provide us with instructions on what parameters (LE, LS, σE, etc.) to refine for maximized rate performance.

References:

1 – https://www.nature.com/articles/s41467-019-09792-9

2 – https://arxiv.org/abs/1911.12305

3 – https://www.sciencedirect.com/science/article/abs/pii/S0378775318300776?via%3Dihub

4 – https://pubs.acs.org/doi/abs/10.1021/acsaem.0c00034

Quantities for the rate equation in Fig. 1:

LE – electrode thickness
LS – separator thickness
CV,eff – effective volumetric capacitance of the electrode
σE – out-of-plane electrical conductivity of the electrode material
PE, Ps – porosities of the electrode material and separator, respectively
σBL – overall (anion and cation) conductivity of the bulk electrolyte
DBL, DAM – ion diffusion coefficients in bulk-liquid electrolyte and active material, respectively
tc – characteristic time of reaction

Figure 1