Fall 2014

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.


Date: November 14, 2014

Speaker: Peter Howell
The Mathematical Institute,
University of Oxford

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Title: "Deterministic and Stochastic Modelling of Lithiation/Delithiation in a Lithium-ion Battery Electrode"

Abstract:

Two mathematical models will be presented for the lithiation/delithiation of a single nanoparticle in a Lithium-ion battery electrode.

The first is a deterministic ODE model that describes quasi-equilibrium and out-of-equilibrium lithiation/delithiation under voltage control. The dynamics of a single particle can be reduced to rapid switching between an ‘empty’ state and a ‘full’ state. Using asymptotic analysis, the critical voltage at which the switch occurs is identified under both static and dynamic conditions.

The second model is based on a probabilistic description of the discrete number of Lithium ions in a single particle. Starting from the chemical master equations, a discrete-to-continuum model is derived for the probability distribution during dynamic charging/discharging. Distinct asymptotic regimes are identified in which either discreteness and thermal noise are important or the dynamics is well captured by the continuous deterministic model.