Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Alberto Salvadori, Mattia Serpelloni, Robert M. McMeeking

TL;DR

This work develops a finite‑strain chemo‑thermo‑mechanical theory for constrained reactive solid mixtures, distinguishing phases from migrating species under a single body motion. A multiplicative decomposition ${\bold F} = {\bold F}^{m}{\bold F}^{c}$ introduces a swelling Jacobian $J^{c} = \det{\bold F}^{c}$ that couples concentration changes to volumetric changes, enabling rigorous links between reference, intermediate, and current configurations. The framework derives comprehensive balance laws (mass, momentum, energy) and a Clausius–Duhem–consistent thermodynamic formulation, with constitutive laws for diffusion fluxes, heat conduction, and mass-action kinetics in the reference frame; it also shows how classical Larché–Cahn network models emerge as a special case. A key outcome is the explicit expression for $J^{c}$ as a phase-summing function of composition, providing a robust basis to predict phase formation and swelling in multiphase solids for applications in sodiation of tin, hydrogen embrittlement, hydrogels, and energy-storage materials.

Abstract

Building upon the classical chemo-mechanical theory of Larch{é} 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.

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

TL;DR

This work develops a finite‑strain chemo‑thermo‑mechanical theory for constrained reactive solid mixtures, distinguishing phases from migrating species under a single body motion. A multiplicative decomposition introduces a swelling Jacobian that couples concentration changes to volumetric changes, enabling rigorous links between reference, intermediate, and current configurations. The framework derives comprehensive balance laws (mass, momentum, energy) and a Clausius–Duhem–consistent thermodynamic formulation, with constitutive laws for diffusion fluxes, heat conduction, and mass-action kinetics in the reference frame; it also shows how classical Larché–Cahn network models emerge as a special case. A key outcome is the explicit expression for as a phase-summing function of composition, providing a robust basis to predict phase formation and swelling in multiphase solids for applications in sodiation of tin, hydrogen embrittlement, hydrogels, and energy-storage materials.

Abstract

Building upon the classical chemo-mechanical theory of Larch{é} 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.
Paper Structure (20 sections, 90 equations, 1 figure)

This paper contains 20 sections, 90 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definitions and kinematic assumptions
  3. Phases, species, configurations, volume fractions.
  4. Intermediate configuration
  5. Swelling factor
  6. Transformations of concentrations and volume fractions.
  7. Mechanical deformations
  8. The network model
  9. Balance laws
  10. Reaction kinetics
  11. Mass balance
  12. Referential balance of momentum
  13. Thermodynamics
  14. Energy balance.
  15. Entropy imbalance.
  16. ...and 5 more sections

Figures (1)

  • Figure 1: A schematic of the multiplicative decomposition ${\bold {F}} = {\bold {F}} ^{m} {\bold {F}} ^{c}$ and related configurations.