(Invited) Coupling of Microstructure and P2D Electrochemical Model for Predictive Electrode Designing
Authors: Krewer Ulrike , Laue Vincent , Röder Fridolin 
Published: February 2020

The pseudo-two-dimensional (P2D) Doyle-Newman Model is attractive as it allows to simulate Li ion battery performance and to gain understanding of the cell's intrinsic processes, while still being suitable for mathematical optimisation [Krewer]. To investigate new materials and the impact of electrochemically inactive solid additives [2], those models have to be adjusted and enhanced or complemented by other models, to be able to analyze the effect of such materials and especially additives on the battery performance.
An important objective of mathematical battery modeling is their application for design optimization, such as identification of the role and optimal amount of active material, conducting additive and binder [3], as well as the optimal compression rate during the calendering step [4]. This will allow to reduce development costs compared to extensive experimental studies. However, the classical Doyle-Newman model faces its limitations regarding the prediction of new electrode designs as the crucial influence of conducting additives and binder are not considered sufficiently.
This talk will show the application of microstructure models to identify the effective electric and ionic conductivity and electroactive area of
electrode structures containing additives, and its coupling to electrochemical P2D models to evaluate the respective electrochemical performance. At the example of Li ion battery cathode and all solid state Li battery electrodes, the effect of additive and active material content and additive distribution is demonstrated.
The voxel-based irregular micro-structures are based on a Monte Carlo growth algorithm from randomly distributed initial points. Effective electric and ionic conductivity are determined by transforming the voxel-based structure into a knot-based resistor network. Percolation thresholds and their sensitivity on electrode composition are identified.
The results of the coupled model show a transition from an electrically limited state at low active material volume fraction to a kinetically limiting state at high volume fractions due to a reduced active surface area. The identified optimum is in good agreement with conducted experiments of NMC vs. graphite cells at different compression rates. In contrast, the classical model lacks of predicting this optimum.
The successful identification of the experimentally observed optimum proves the feasibility of the presented model approach. The models are applicable to predict the properties and the performance of electrodes in cells. This enables a design optimization without an extensive experimental studies, which will reduce costs and experimental efforts in the development of next-generation batteries.
[1] Krewer et al., J. Electrochem. Soc. (2018) A3656–73
[2] Qi et al., Carbon 64 (2013) 334-340
[3] H. Zheng et al., J. Phys. Chem. C 116 (2012), 7, 4875−4882
[4] Lenze et al., J. Electrochem. Soc. (2017) A1223-33
Fig.:
Illustration of the simulated micro structures containing active material (red), additives (green) and electrolyte (blue)

Figure 1