Battery knowledge · Transport and modelling
Solid-state diffusion
Lithium moving through the crystal lattice of an active-material particle, with diffusion coefficients of about 10⁻¹⁶ to 10⁻¹³ m²/s — three or more orders of magnitude slower than the 10⁻¹⁰ m²/s of the liquid. It is usually the rate-limiting step for thick electrodes and large particles. [1]
- Unit
- m²/s
Example
Flux follows the concentration slope
Flux J = 500 μmol/(m²·s), toward increasing position.
The profile is imposed and static. Time evolution requires Fick’s second law and boundary conditions.
Explore the graph
The minus sign in Fick’s law sends material down its concentration gradient.
Flux J = 500 μmol/(m²·s), toward increasing position.
J = −D dc/dx
Illustrative model. The profile is imposed and static. Time evolution requires Fick’s second law and boundary conditions.
Use in Lemonergy
Specify phase, direction and boundaries.
This is a reference concept. No executable Lemonergy block has been verified for this term.
References & further reading
Technical references
- Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell
Marc Doyle, Thomas F. Fuller, John Newman · Journal of The Electrochemical Society · 1993
Technical reference · Porous-electrode transport and insertion-cell modeling; foundational work rather than a specification for a particular commercial cell.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing
IUPAC · 2011
Topic background · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.