Analytical Model for Predicting the Discharge Performance of Thick Battery Electrodes
Authors: Wang Fan , Tang Ming 
Published: February 2020

There is an increasing interest in using thick electrodes in Li-ion batteries to improve the energy density and lower the cost by reducing the amount of inactive components. However, increasing electrode thickness usually leads to inferior rate performance. Currently there lacks a quantitative understanding of the trade-off between the power and energy density for thick electrodes, which is essential for optimizing electrode structures for specific applications and developing novel thick electrode designs. Addressing this deficiency, here we present a simple and yet accurate analytical model for predicting the discharge performance of battery cells containing thick electrodes. Compared to the traditional porous electrode simulations, this model offers a more transparent understanding of the kinetic limitations of thick electrode configurations and the effects of various cell-level structural parameters on battery performance. Computation-wise, the model is substantially more efficient than the numerical pseudo-2D discharge simulation, and provides a powerful tool for performing the optimization of thick electrodes within the multi-dimensional design space.
Our model is motivated by two important observations from numerical simulations and experiments, namely, the capacity utilization of thick electrodes is limited by electrolyte transport and a pseudo-steady state of electrolyte transport is established during discharge. Accordingly, we derived analytical expressions for the electrolyte distribution across the electrode and the discharge capacity at termination based on the steady state assumption. As shown in Figure 1a, the predicted distribution of Li ion concentration in electrolyte agrees well with the numerical simulation. The depth of discharge (DoD) calculated from the analytical model provides excellent approximations to the simulation results for various electrode thickness and cell configurations (half vs full cells) without any adjustable parameters, Figure 1b. This model is generally applicable to electrodes that display solid-solution intercalation behavior such as the layer oxide cathodes paired with the graphite anode at low to moderately high discharge rates.
An important insight we obtained from the analytical model is that the discharge capacity of half and full cells exhibit qualitatively different scaling relation with electrode thickness and discharge current. As such, the half cell configuration with Li metal anode exhibits markedly improved DoD at large electrode thickness over full cells containing the graphite anode. This finding explains the seemingly scattered results from various thick electrode experiments reported in literature. It cautions against the practice of using the half cell testing as an indicator of the rate performance of full cells with thick electrodes. On the other hand, it suggests that the combination of a thick cathode with a high capacity anode such as Li metal, silicon and tin is an effective strategy to enable thick electrode designs with higher capacity utilization.
Figure 1: a) Li ion concentration distribution in electrolyte during discharge calculated from the porous electrode simulation (solid lines) and steady-state analytical model (dashed line).

Figure 1