Charge transport modelling of Lithium-ion batteries

Abstract

This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries (LIBs) as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of dilute and moderately concentrated electrolytes and indicates the modelling assumptions required for their development. Particular attention is paid to the interface conditions imposed between the electrolyte and the active electrode material; necessary conditions are derived for one of these, the Butler–Volmer relation, in order to ensure physically realistic solutions. Insight into the origin of the differences between various models found in the literature is revealed by considering formulations obtained by using different measures of the electric potential. Materials commonly used for electrodes in LIBs are considered and the various mathematical models used to describe lithium transport in them discussed. The problem of upscaling from models of behaviour at the single electrode particle scale to the cell scale is addressed using homogenisation techniques resulting in the pseudo-2D model commonly used to describe charge transport and discharge behaviour in lithium-ion cells. Numerical solution to this model is discussed and illustrative results for a common device are computed.

Potentiometric MRI of a Superconcentrated Lithium Electrolyte: Testing the Irreversible Thermodynamics Approach

“…Newman’s concentrated-solution theory derives from the Onsager–Stefan–Maxwell (OSM) model of multicomponent diffusionan implementation of irreversible thermodynamics that takes electrochemical-potential gradients, rather than concentration gradients, to be the fundamental forces that drive diffusion . Unlike Nernst–Planck dilute-solution theory, OSM theory also accounts explicitly for ion/ion diffusional drag interactions, which generally cannot be neglected in battery electrolytes. , The thermodynamic principles that underpin OSM theory also support the consistent inclusion of standard equilibrium properties, such as component partial molar volumes and Darken thermodynamic factors. , …”

“…28 Unlike Nernst−Planck dilute-solution theory, OSM theory also accounts explicitly for ion/ion diffusional drag interactions, which generally cannot be neglected in battery electrolytes. 29,30 The thermodynamic principles that underpin OSM theory also support the consistent inclusion of standard equilibrium properties, such as component partial molar volumes and Darken thermodynamic factors. 31,32 For binary electrolytic solutions wherein speciation kinetics is very fast, a single (Darken) thermodynamic factor χ accounts for deviation from the ideal Nernstian relationship between concentration polarization and concentration overpotential.…”

Porous Electrode Modeling and its Applications to Li‐Ion Batteries

“…[ 50,53 ] When adopting absolute potentials in a porous electrode model, the 2( RT / F )(1 − t + ) multiplier in Equation (8) and (13) should be replaced by ( RT / F )(1 − 2 t + ). [ 48,54 ]…”

“…[50,53] When adopting absolute potentials in a porous electrode model, the 2(RT/F)(1 − t + ) multiplier in Equation ( 8) and ( 13) should be replaced by (RT/F)(1 − 2t + ). [48,54] Due to the complex coupled relations among the equations listed in Table 1, analytical solutions to the system are not available. Numerical solutions are therefore commonly applied.…”

“…[263] Two approaches have been used to simulate the influence of mechanical fatigue on the electrochemical performance of batteries using a P2D model. The first approach is to express the degradation using a decreased Li diffusion coefficient and mechanical properties, as shown in Equations (54)(55)(56). A socalled damage factor [259,260] has been proposed to modify the Li [261] b) Interfacial debonding of active particles from the conductive network.…”