In Situ Measurements of Strains in Composite Battery Electrodes during Electrochemical Cycling

Abstract

The cyclic stress in lithium-ion battery electrodes induced by repeated charge and discharge cycles causes electrode degradation and fracture, resulting in reduced battery performance and lifetime. To investigate electrode mechanics as a function of electrochemical cycling, we utilize digital image correlation (DIC) to measure the strains that develop in lithium-ion battery electrodes during lithiation and delithiation processes. A composite graphite electrode is cycled galvanostatically (with constant current) in a custom battery cell while optical images of the electrode surface are captured in situ. The strain in the electrode is computed using an in-house DIC code. On average, an unconstrained composite graphite electrode expands 1.41 % during lithiation and contracts 1.33 % during delithiation. These strain values compare favorably with predictions based on the elastic properties of the composite electrode and the expansion of graphite-lithium intercalation compounds (G-LICs). The establishment of this experimental protocol will enable future studies of the relationship between electrode mechanics and battery performance.

Appendix

Continuing the model in section “Analytical Prediction of Composite Electrode Expansion”, the shear modulus of a complete composite electrode, G _e , is estimated by applying the “S-Combining Rule” [28] for graphite particulates in a porous matrix according to:

$$G_{e} = \frac{G_{pm} \left(1 + \phi_{g} \xi_{Gl}\chi_{G}\right)}{1- \phi_{g} \Psi_{G} \chi_{G}}$$

(18)

with

$$\begin{array}{@{}rcl@{}}\chi_G = \frac{G_{g}-G_{pm}}{G_{g} + \xi_{Gl} G_{pm}}\end{array} $$

(19a)

$$\begin{array}{@{}rcl@{}}\Psi_G \!=\! 1 \!+\! \frac{\phi_{g} \phi_{pm} \left(1{\kern-1.5pt}-{\kern-1.5pt}\gamma \phi_{pm}\right) \left(G_{g}{\kern-1.5pt}-{\kern-1.5pt}G_{pm}\right)\left(\xi_{Gu}{\kern-1pt}-{\kern-1pt}\xi_{Gl}\right)} {G_{g}{\kern-1pt}+{\kern-1pt}\xi_{Gu} \left(\phi_{g} G_{g}{\kern-1pt}+{\kern-1pt}\phi_{pm} G_{pm} \right)}\end{array} $$

(19b)

$$\begin{array}{@{}rcl@{}} \xi_{Gu} = \frac{\left(7-5\nu_{g} \right) G_{g}}{\left(8-10\nu_{g} \right) G_{pm}} \end{array} $$

(19c)

$$\begin{array}{@{}rcl@{}} \xi_{Gl} = \frac{7-5\nu_{pm}}{8-10\nu_{pm}} \end{array} $$

(19d)

$$\begin{array}{@{}rcl@{}} \gamma = \frac{2 \lambda^{*} - 1}{\lambda^{*}} \end{array} $$

(19e)

where G _pm is the shear modulus of the CB/CMC porous matrix, calculated from the bulk modulus, K _pm (equation (11)), and the Poisson’s ratio, ν _pm = 1/3, of the porous matrix assuming isotropy, and G _g is the shear modulus of G-LICs, calculated from the bulk modulus, K _g , and the Poisson’s ratio, ν _g , of the G-LICs assuming isotropy. All other variables are defined in section “Analytical Prediction of Composite Electrode Expansion”.

The Young’s modulus of the porous composite electrode is calculated from the predicted shear modulus, G _e , and bulk modulus, K _e , assuming isotropy. It was found to range between 0.46 GPa and 0.48 GPa depending on the lithium content of the G-LICs, which is two orders of magnitude smaller than the modulus of G-LICs. Moreover, the Young’s modulus of the electrode is predicted to remain nearly constant for all lithium contents, despite a three-fold increase in the modulus of G-LICs.

Zheng et al. experimentally measured the Young’s modulus of unlithiated electrodes comprised of 88.8 wt.% graphite, 8 wt.% polyvinylidene difluoride (PVDF) binder, and 3.2 wt.% carbon black with 35 vol.% porosity [32]. They found that the Young’s modulus lies in the range of 0.26 GPa to 0.69 GPa. This is in good agreement with the predicted modulus.