Models to Couple Mechanics and Electrochemical Transport in Solid Electrolytes
Authors: Goyal Priyamvada , Monroe Charles W 
Published: February 2020

Electrolytic transport models available in the literature primarily deal with liquid media; models for solid electrolytes in polymer-electrolyte-membrane (PEM) fuel cells [1] largely derive from theories originally formulated to describe fluids. Since a solid can sustain a deformation at equilibrium under an applied stress or strain, there is a fundamental difference in the transport physics. Accurately modelling water-induced swelling in ionomer membranes requires that solid mechanics be reconciled with the transport and kinetic behaviour of electrochemical systems [2]. Previous efforts made to consider membrane swelling usually operate on a global basis, accounting only for an overall volume change; it is not clear whether models that include local swelling effects do so in thermodynamically consistent ways. This talk will deal specifically with swollen ionomers, although the principles introduced apply equally well to other solid ion conductors. In the case of Nafion, as Fig. 1 shows, water and ionic transport can produce, and dynamically interact with, non-uniform local volume changes and associated distributions of stress, making electrochemical/mechanical coupling significant.
Our strategy is to return to first principles, identifying and undoing the assumptions made specifically for liquid mixtures, and finding ways to ensure that the simultaneous use of ostensibly independent theories of kinematics, thermodynamics, and transport does not induce internal inconsistencies in the model. The incorporation of additional state variables such as pressure, stress, and strain requires the inclusion of new balance equations and constitutive laws: one must carry along a local balance of momentum, which relates the local pressure within the electrolyte to the distributions of stress and inertia; there must be a stress constitutive law that characterises the mechanical response (viscous, elastic, viscoelastic etc.); and strain must be defined in such a way that it ties deformed coordinates to a reference state while simultaneously abiding by the thermodynamic volume-explicit equation of state. Modifying the system of equations in the manner discussed above and tackling questions of model closure have helped us to produce a more robust and comprehensive set of equations to model Nafion.
The underlying aim is to combine developments in continuum poroelasticity theory with advanced electrochemical transport models. Ultimately, such a model will help us rationalise the physics associated with swollen vapour-equilibrated Nafion-like membranes in fuel cells under isothermal, non-isobaric, and constrained or free-swelling conditions. Such a model could inform better water management schemes and efforts to improve membrane durability. It will also be useful to have a general framework for modelling solid electrolytes that can be applied to materials beyond Nafion where electrochemical/mechanical coupling is important.
[1] Weber, A.Z. and J. Newman, Transport in polymer-electrolyte membranes - II. Mathematical model. Journal of the Electrochemical Society, 2004. 151(2): p. A311-A325.
[2] Kusoglu, A. and A.Z. Weber, Electrochemical/Mechanical Coupling in Ion-Conducting Soft Matter. The Journal of Physical Chemistry Letters, 2015. 6(22): p. 4547-4552.

Figure 1