Bending Stress Analysis of All Solid State Flexible Lithium Battery
Authors: Chang Tsen-An , Chen Kuo-Ching 
Published: February 2020

Wearable electronic devices like smart watches and smart bracelets are promising products in the market. Batteries that are implanted to these devices are required to be thin-layered, light, powerful, and the most importantly, safe. It will also be more convenient for users to wear if the devices are bendable. All solid state lithium battery (ASSLB) can play a good role as the power source of wearable devices due to its high energy density, noninflammability and flexibility. Along with the growing applications of ASSLB, it is important to fully understand its characteristics. With the help of a physical model of ASSLB, this study attempts to establish a relationship between the performance of battery and the bending stress.

In the past, several studies constructing a mathematical model for ASSLB have been reported.  Danilov et al.
1 first presented an ASSLB model in 2011. Even this model provides a good agreement between simulation and experiment, several parameters used in this model are still questionable or undetermined. For example, the charge transfer number is not the unity and the diffusion coefficient of anion cannot be determined. Fabre et al.2proposed a simpler model with good accuracy, which however ignored the variation of cation’s concentration in electrolyte, which then fails to show what is actually happening in the electrolyte and results in inaccuracy of discharge curves at high C-rate. Although the two models provide a description of several physical mechanisms of ASSLB, its stress analysis is lacking.

In this work, we establish a comprehensive physical model for ASSLB and discuss the behavior of the battery when it is under bending. Similar to the work in [3], we derive the concentration and potential distribution in electrolyte by Nernst-Plank equation(1) and Poisson equation(2).

In addition, we obtain the boundary conditions of the electrolyte potential, which are derived from Butler-Volmer equation rather from the theory of Stern layer. In this way, the diffusion coefficient of anion is not needed and the dielectric constant can be easily yielded.

Figure 1 demonstrates a good match between our electrochemical model and the experiment data for different C-rates. Regarding the bending stress analysis, it is noted in [4] that external force may influence the diffusion process in the electrode. This motivates us to empirically set the diffusion coefficient in positive electrode as a function of deformation angle. The simulation of the performance of flexible battery under different bending conditions is shown in Fig. 2. The relationship between the bending stress and the battery performance can be of help in finding a more appropriate design and range of use for flexible thin film battery. Further development of related analyses and experiments is now under way.

REFERENCES

[1] D. Danilov, R. Niessen, and P. Notten, J. Electrochem. Soc.
158, 215 (2011).

[2] S. D. Fabre, D. Guy-Bouyssou, P. Bouillon, F. Le Cras, and C. Delacourt, J. Electrochem. Soc.
159,104 (2012)

[3] K. Becker-Steinberger, S. Funken, M. Landstorfer, and K. Urban, ECS Trans.
25(36), 285 (2010).

[4] Han JN, Pyun SI J Korean Electrochem Soc.4, 70 (2001).

[5] Koo, M. Park, K.I. Lee, S.H. Suh, M. Jeon, D.Y. Choi, J.W. Kang, K. Lee, K.J. Nano Lett. 12, 4810 (2012).

Figure 1