M.A.P.L.E. Lab

Lithium Intercalation in Core-Shell Materials–Theoretical Analysis

This page provides maple code for isotropic 1-dimensional diffusion with galvanostatic boundary condition in composite slab, cylinder and sphere using separation of variables method and the intercalation-induced stress (radial and tangential) in spherical core shell composite particle.

Core-shell composite structures are potential candidates for Li-ion battery electrodes as they can take advantage of materials with higher energy density and materials with higher cyclability. Sophisticated manufacturing and material design approaches have enabled the production of particle with graded composition and core shell structure. While materials such as silicon and tin have high energy density compared to graphite, they suffer from high volumetric expansion (∼400%) during intercalation/deintercalation which results into pulverization and electrical isolation of the electrode materials. A change in volume of such magnitude causes delamination of the solid electrolyte interface (SEI) from the active material. Delamination and formation of new SEI layer at the exposed surface continuously consumes active materials resulting in faster capacity fade. One way to take advantage of higher energy density materials is to develop core –shell composite materials where the shell materials have more favorable mechanical properties than the core.

Figure: Core shell composite geometries

Analytical solution for isotropic 1-dimensional diffusion with galvanostatic boundary condition in composite slab, cylinder and sphere using separation of variables method are given here: (Planner geometry, Cylindrical geometry and Spherical geometry).

The codes given have following sections:

1. User defined parameters: (ratios of diffusivities, thicknesses, equilibrium concentration, intercalation flux etc.)
2. Separation of variable solution (in the form of infinite series)
3. Calculation of concentration profiles in both phases using numerical eigenvalues
4. Plots of the concentration profiles
5. Mass conservation check

The intercalation-induced stress (radial and tangential) in spherical core shell composite particle at fixed intercalation flux is given here:

(Spherical geometry with stresses).

Please feel free to contact Dr. Venkat Subramanian for any comments.