The Effect of Kinetic Nonlinearity on Battery Electrode Design: A Closer Look at Electrode Processes
Authors: Qi Yanbo , Chen Jerry , Pathak Chintan , Schwartz Daniel T. , Subramanian Venkat R. 
Published: February 2020

The idea of using modeling in battery design was first introduced by W. Tiedemann and J. Newman in 19751. They used an ohmically limited porous electrode model to maximized the cell effective capacity by controlling electrode thickness and porosity. Newman later applied the reaction-zone model to maximize the specific energy of the system by considering mass as well2. V. Ramadesigan et al.3went one step further with the ohmic resistance model in the electrode by including electrode kinetics. They assumed the linear kinetics, and minimized the ohmic resistance in the positive electrode by varying porosity using control vector parameterization (CVP) method. They also introduced the idea of using layered graded electrode to get a porosity distribution to further reduce the ohmic resistance in the system.
Since the introduction of the pseudo-2D (P2D) model3, many efforts have been made in applying the P2D model in battery design. W. Du et al. applied an optimization framework based on surrogate method4. S. Golmon et al. performed the multi-objective and multi-design-parameter optimization problem with adjoint sensitivity analysis5 with expanded P2D model incorporating mechanical stress-strain relationship. S. De and his coworkers6 used a reformulated model developed by the Subramanian group7, to perform simultaneous optimization of multiple design parameters. N. Xue et al. 8 applied the gradient-based algorithm framework to optimize the cell design. More recently, Y. Dai and V. Srinivasan9used a gradient-free direct search method to maximize the specific energy.
Generally, there are two purposes of using models to simulate the battery system; one is to develop a better understanding of the system, and the other is to use the models as guidance to achieve better performance. For the latter purpose, a model with fewer assumptions and more equations capturing as many processes as possible is desired to simulate the system better. However, for a better understanding of the system, it may be worth taking a step back, and examining a simpler model where the effects of different processes can be observed clearly, even though more detailed physical models with much less assumptions would be used to guide the actual design. This is the purpose and idea behind this study.
The model used in this study is an ohmic resistance model, with the assumption that the electrolyte concentration is uniform and double-layer charging can be ignored. Ohm’s law for both solid and electrolyte phases was included in the model, as well as a polarization equation representing the electrode kinetics. The polarization equation describes the charge transfer between the two phases, of which the linear form together with Ohm’s law for the two phases can be found in Ref10. In such a model, the trade-off between ohmic potential drop and reaction kinetics can be captured by current distribution between the two phases.
In this work, we want to quantify the impact of nonlinearity on the architecture design by carefully examining the effect of nonlinearity on the ohmic resistance model. For linear kinetics, the optimal design to minimize overall resistance is independent of operation conditions (Fig. 1). However, for nonlinear kinetics, the optimal porosity is bigger for higher charge/discharge rates. This suggests that for batteries built for different applications, the optimal design varies depending on the operation conditions, especially at high rates, where the kinetics fall outside the linear regime.

Figure
1
. Optimal Porosity under Different Charge/Discharge Rates for Linear and Nonlinear Polarization

Acknowledgements

The authors are thankful for the financial support of this work by the Clean Energy Institute (CEI) at the University of Washington.

References

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4. W. Du, A. Gupta, X. Zhang, A. M. Sastry, and W. Shyy, Int. J. Heat Mass Transf.,53, 3552–3561 (2010)
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8. N. Xue et al., J. Electrochem. Soc., 160, A1071–A1078 (2013)
9. Y. Dai and V. Srinivasan, J. Electrochem. Soc., 163, A406–A416 (2015).
10. J. Newman, K. E. Thomas, H. Hafezi, and D. R. Wheeler, J. Power Sources, 119-121, 838–843 (2003).

Figure 1