Quantifying the Dependence of Battery Rate Performance on Common Physical Parameters

The demand for batteries to deliver high capacities at fast charge/discharge rates is rapidly increasing. Electric vehicles are required to cover large distances and to have short recharge times between stops. These types of applications seek to simultaneously maximise capacity and power. While the charging rate can be increased without impacting the capacity, this is only possible until a threshold charge/discharge rate, R_T, is reached. Past R_T the capacity begins to rapidly decline. Understanding the factors influencing this capacity-rate trade-off is crucial for designing systems with exceptional rate performance.<br/><br/>In this work, we use a simple semi-empirical model to extract a characteristic time, τ for charge/discharge which quantifies the rate behaviour of the investigated system. It has been proposed by Tian <i>et al.</i> that τ is linked to electrode kinetics and the physical parameters (e.g. out-of-plane electrode conductivity, σ_E, electrode thickness, L_E) of the system.[1] This multi-mechanistic model is based on solid- and liquid-phase diffusion processes, as well as electrical and electrochemical effects. The equation for τ has been demonstrated to accurately describe a large variety of electrodes found in literature, for both Na and Li-ion batteries. Since τ is a function of common physical parameters, it is possible to predict how rate performance will be affected by a given property. We investigated the rate performances of model battery systems in which only one parameter is varied (L_E, and separator thickness, L_S), and we found that the outputs of the rate model are in close agreement with experimental data.<br/><br/>To gather rate data, we used chronoamperometry (CA), a recently reported alternative to traditional galvanostatic charge-discharge (GCD) measurements.[2] Current transients are converted to capacity-rate curves, which were fitted with the previously described fitting method. We firstly investigated the effects of L_E on rate performance by obtaining τ-L_E curves over a wide L_E range (10-252 μm).[3] The results clearly show a quadratic dependence of τ on L_E, a result that is not explained by simple models that only incorporate solid or liquid-phase diffusion, but is in full agreement with our rate equation. Furthermore, electrochemical impedance spectroscopy measurements indicate that the electrochemical and solid-state diffusion contributions to τ are in line with our model.<br/>In a similar manner, we examined the rate behaviour of systems where only L_S is varied through stacked separator films. The rate model predicts a linear τ-L_S curve, which is confirmed by experimental data at separator thicknesses &lt;100 μm. Our results highlight the potential of the rate equation proposed by Tian <i>et al.</i> We used the equation to describe how rate performance varies with L_E and L_S and it has been used to analyse τ-σ_E data as well.[4] This in-depth analysis further builds the understanding of rate performance and importantly, quantifies the effects which influence it. We believe it is a tool that can be used for designing electrodes for high-rate applications and for identifying emerging materials for energy storage.<br/><br/>In the future, our aim is to apply the rate equation to battery systems and to design electrodes which have very small values of τ and thus, excellent rate performance. For a given system we aim to use optimization techniques such as design of experiments to minimize τ. The insights gained from the equation would provide use with the necessary instructions on what parameters to tune for maximised rate performance.<br/> <br/>[1] – https://doi.org/10.1038/s41467-019-09792-9<br/>[2] – https://doi.org/10.1016/j.jpowsour.2020.228220<br/>[3] – https://dx.doi.org/10.1021/acsaem.0c01865<br/>[4] – https://doi.org/10.1021/acsaem.0c00034