Modelling stress-affected chemical reactions in non-linear viscoelastic solids

Application to lithiation reaction in spherical Si particles


In past decades, Li-ion batteries became relatively widespread due to a number of advantages over conventional energy technologies. Currently, one of the major problems for battery technology is limited energy storage capacity, which can be partially addressed by the use of novel active materials.

Si is one of the most promising active materials, due to its ability to accommodate a larger number of Li ions than currently used graphite. However, Si undergoes large volumetric expansion and shrinking during battery cycling, which leads to the emergence of mechanical stresses. The role of the stresses is twofold – first, they can lead to material damage, second, they can affect the charging/discharging rate by inhibiting the diffusion of Li ions and the chemical reaction between Li ions and Si. Therefore, understanding of the interaction between the chemically-induced mechanical stresses and the kinetics of the lithiation process of Si particles is important for exploiting the possibility of using Si as anode active material.

The chemical reaction between Li ions and Si is localized and is often referred to as the two-phase lithiation process. This implies the existence of Li-ion concentration-rich and concentration-poor phases with chemical reaction taking place at the interphase boundary. Furthermore, as Li ions are consumed by the chemical reaction and form an alloy with Si, there is a diffusion of Li ions through the Li-ion concentration-rich phase.

There are two distinct ways of accounting for the mechanical stresses – via the dependence of the diffusion rate on the stresses and via the dependence of the kinetic parameter of the chemical reaction on the stresses. Most established models of stress-affected chemical reaction kinetics take the former route. There are models that opt for the latter choice; however, such models include stresses heuristically, usually by assuming a dependence only on one part of the stresses – pressure.

In a recent research paper published in the International Journal of Engineering Science, Dr. Michael Poluektov and Dr. Łukasz Figiel from the University of Warwick in collaboration with Prof. Alexander Freidin from the Institute for Problems in Mechanical Engineering of Russian Academy of Sciences developed a model that allows investigating the stress-affected two-phase lithiation kinetics in Si particles and following the second pathway includes stresses into the chemical reaction rate. The novelty consists in utilizing the so-called chemical affinity tensor framework, which has been developed by Prof. Freidin in earlier publications. In this approach, the reaction rate becomes dependent on the orientation of the surface, where the localized reaction takes place, with respect to the local stress fields. This follows naturally from the thermodynamic balance laws and, therefore, accounts for the mechanical stresses in a thermodynamically-consistent way.

In the paper, the chemical affinity tensor framework has been combined for the first time with finite strains and complex rheological behavior of solid materials, more specifically, non-linear elasto-viscoplastic deformation of Si. The major achievement of the paper consists in analysis of the interconnection between mechanics and the chemical reaction kinetics. The model predicts the retardation and blocking of the chemical reaction front, which have been observed experimentally within a Si particle. The paper also explores the influence of external conditions, to which Si particles are subjected, as well as other factors on the reaction kinetics and the front blocking. The second major highlight of the paper is simultaneous focus on an industrially relevant application – Si-particle-based anodes in future Li-ion batteries. Thus, the results of the paper may be interesting for researchers working in solid mechanics, chemo-mechanics and materials modelling, as well as researches focusing on a specific application of Si lithiation and Si anode design.


Poluektov, M., Freidin, A., & Figiel, Ł. (2018). Modelling stress-affected chemical reactions in non-linear viscoelastic solids with application to lithiation reaction in spherical Si particles. International Journal of Engineering Science, 128, 44-62.

Go To International Journal of Engineering Science

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