On the chemo-thermo-mechanics of constrained reactive mixtures of solids

Abstract

Building upon the classical chemo-mechanical theory of Larch{\'e} and Cahn for equilibrium, numerous studies have investigated the transport of species in solids, with or without trapping phenomena. In most applications -- such as the swelling of hydrogels, hydrogen embrittlement in metals, and the transport of lithium or sodium in battery electrodes -- the formation of a new phase or compound can be directly associated with the concentration of the diffusing species. In the present work, we focus on the formation of solid mixtures made of multiple compounds, each characterized by its own volumetric expansion coefficient. Such a scenario arises, for instance, during the sodiation of tin anodes, among other systems. The classical chemo-mechanical framework is naturally recovered as a particular case of the proposed formulation. The theoretical framework developed herein elucidates and differentiates the concepts of phases and flowing species, while establishing rigorous connections between them. The present note is restricted to the general formulation of the governing equations, whereas application-specific developments will be addressed in forthcoming publications.