Solid Electrolyte Interphase (SEI)

For the SEI, we use the model described in the paper Microstructure-resolved degradation simulation of lithium-ion batteries in space applications from Bolay et al.

The model consider the electron diffusion and migration in the SEI layer given by the flux

$$\begin{array}{r}{N}_{sei}=D^{e^{-1}}\frac{c^{e^{-1}}}{L_{sei}}-zF{\kappa }_{sei}^{e^{-1}}\lambda \varphi \end{array}$$

• $D^{e^{-}}$: Electron diffusion coefficient

• $c^{e^{-}}$: Electron concentration

• $L^{sei}$: SEI length

• ${\kappa }_{sei}^{e^{-}}$: Electron conductivity in SEI

When the electron reaches the SEI interface, it reacts with the electrolyte to create more SEI. This process is modeled by the differential equation

$$\begin{array}{r}\frac{1}{V_{sei}}\frac{d{L}_{sei}}{dt}=N_{sei}\end{array}$$

where

• $V_{sei}$: Mean partial volume of SEI

The SEI layer induces an additional potential drop given by

$$\begin{array}{r}{U}_{sei}=\frac{L_{sei}}{{\kappa }_{L{i}^{+}}^{sei}}{j}_{L{i}^{+}}\end{array}$$

where

• ${\kappa }_{L{i}^{+}}^{sei}$: Conductivity for Lithium ion in SEI

• $j_{L{i}^{+}}$: Lithium ion current density