Phenomenological Theory of Electro‐osmotic Effect and Water Management in Polymer Electrolyte Proton‐Conducting Membranes

Abstract

Partial dehydration of the proton-conducting membrane under working conditions is one of the major problems in low-temperature fuel cell technology In this paper a model, which accounts for the electro-osmotically induced drag of water from anode to cathode and the counterfiow in a hydraulic pressure gradient is proposed. A balance of these flows determines a gradient of water content across the membrane, which causes a decline of the current-voltage performance. Phenomenological transport equations coupled with the capillary pressure isotherm are used, involving the conductivity permeability and electro-osmotic drag coefficients dependent on the local water content. The effects of membrane parameters on current-voltage performance are investigated. A universal feature of the obtained current-voltage plots is the existence of a critical current at which the potential drop across the membrane increases dramatically due to the dehydration of membrane layers close to the anode. For a membrane with zero residual conductivity in its dry parts, the critical current is a limiting current. Well below the critical current the effect of dehydration is negligible and the currentvoltage plot obeys Ohm's law. The shape of the capillary pressure isotherm determines the nonohmic corrections. A comparison of the results of this study to those of the pertinent diffusion-type models reveals qualitatively different features, the convection model is found to be closer to experimental observations.

Modelling of morphology and proton transport in PFSA membranes

“…[23][24][25][26] In this article, we review the existing atomistic modelling studies of PFSA membrane morphology and proton transport, in particular to what extent the results of these investigations are consistent with experimental studies, and present a synthesis with some of our own recent multiscale simulations. The current state of understanding of Nafion morphology from various perspectives, was recently reviewed by Mauritz and Moore, 27 and the reader is referred to their article, along with a number of other sources, [28][29][30][31][32] for a fuller discussion of structural models for Nafion and related polymers proposed on the basis of scattering experiments or phenomenological considerations.…”

Macroscopic Modeling of Polymer-Electrolyte Membranes

“…While almost all models are solved in the above fashion, analytic solutions are obtainable in certain instances [34,68,104,116,121,135,[142][143][144]. The problem is that such models typically make assumptions like uniform properties, which make the solution of limited significance.…”

“…The use of such a simple relation can be justified since the gases in the membrane are in low concentration and do not interact significantly with each other; a dilute-solution approach is valid. The models that follow the Bernardi and Verbrugge framework treat gas crossover more-or-less the same [102-109, 111, 114, 134], although some allow for a changing gas-phase volume fraction [135,136].…”

“…For the hydraulic models, the water content is not as important since the membranes are assumed to be fully liquidequilibrated. An exception to this is the model of Eikerling et al [135,136] as mentioned in section 3.2.4. This model allows for the existence of swollen and nonswollen pores, much like the expanded and collapsed channels of Weber and Newman [91].…”

“…A more straightforward and rigorous, albeit more numerically intensive, approach is to account for swelling explicitly [88,91,117,135,149,161,172]. Essentially, this is done by doing a mass balance on the membrane and using the above wet-volume expression (equation 48) with the average membrane water content.…”