In a polymer-electrolyte membrane (PEM) within a fuel cell, water transport can be driven by diffusive, electro-osmotic, and permeative mechanisms. The equilibrium thickness of a PEM is also known to change substantially with respect to both water content and applied pressure. Most physical models treat hydraulic permeation or diffusion/osmosis in isolation; those that account for both phenomena in parallel do not always incorporate the pressure in a way that permits the analysis of all possible boundary conditions. Kusoglu and Weber have recently highlighted the need for models that handle situations involving simultaneous gradients of both pressure and water activity across constrained, swelling membranes [1].

This talk will focus on our recent efforts to reconcile all the transport modes within a rigorous multicomponent transport formalism that incorporates standard diffusive properties such as ionic conductivity, water activity coefficient, water diffusivity, and electro-osmotic drag coefficient alongside elastic properties such as the bulk modulus and Poisson ratio. The key ideas are that a volume-explicit equation of state needs to be incorporated along with the typical governing equations that describe the membrane bulk, and that a momentum balance needs to be included to determine how stress is distributed within the membrane. Information embodied in the stress tensor is, in some sense, independent of the information in the diffusion driving force that accounts for molecular and pressure diffusion. Thus hydraulic and diffusive modes can be handled in parallel without any additional simplifications.

We will present a macroscopic model that describes the volume change of or water redistribution within vapor-equilibrated ionomers in freely swelling or constrained geometries. The model will be used to underpin simulations that show how strain arises (and is distributed) during typical water-flux measurements across vapor-equilibrated membranes [2]. Values of the key parameters will be discussed in light of literature data as well. An experimental program will be suggested through which the most important properties can be probed.

References

[1] A. Kusoglu and A.Z. Weber, “Electrochemical/Mechanical Coupling in Ion-Conducting Soft Matter,” The Journal of Physical Chemistry Letters 6(2015) 4547-4552.

[2] C.W. Monroe, T. Romero, W. Mérida, and M. Eikerling, “A vaporization-exchange model for water sorption and flux in Nafion,” Journal of Membrane Science 324 (2008) 1-6.