Continuum Theory for Diffusion-Reaction-Deformation in Solids

This research projects aims to develop thermodynamically consistent phase-field continuum theoretical frameworks which couple: i) species diffusion, ii) electrochemical reactions, and iii) mechanical deformation and stress. Particular features of our framework:

  • Allows for both kinetically and thermodynamically driven sharp interface formation. That is sharp interfaces may form either when the reaction kinetics or the diffusion kinetics are limiting.
  • Develops thermodynamically consistent and physically motivated driving force for chemical reactions that distinguishes the role of various chemical and mechanical driving forces. Material parameters for these forces may be readily identified from the literature or experiments.
  • The gradient based phase-field formulation allows one one to capture the application of surface energy boundary conditions which are critical in reproducing experimentally relevant sharp interface reaction front morphologies.

The image below, form Afshar and Di Leo (JMPS, 2021), shows a specialization of the theory towards modeling reaction of FeS2 crystals with Lithium Ions, where we show contours of the reaction coordinate for (a) one-eight of the simulation domain, (b) mirrored about two planes, and (c) the fully-mirrored domain.

As shown in the figure below, the theory is capable of quantitatively reproducing the reaction front morphology of these systems. In particular, we capture the manner in which stress-coupling is responsible for the change in reaction front morphology observed when comparing Lithiation and Sodiation. Experiments shown are by the McDowell group (Boebinger et al., Joule, 2(9), 2018).


Afshar, A., Di Leo, C.V. “A Thermodynamically Consistent Gradient Theory for Diffusion- Reaction-Deformation in Solids: Application to Conversion-Type Electrodes.” Journal of The Mechanics and Physics of Solids, 151, 2021. [html]