Transport in Polymer-Electrolyte Membranes

Abstract

In this paper, a physical model is developed that is semiphenomenological and takes into account Schroeder's paradox. Using the wealth of knowledge contained in the literature regarding polymer-electrolyte membranes as a basis, a novel approach is taken in tying together all of the data into a single coherent theory. This approach involves describing the structural changes of the membrane due to water content, and casting this in terms of capillary phenomena. By treating the membrane in this fashion, Schroeder's paradox can be elucidated. Along with the structural changes, two different transport mechanisms are presented and discussed. These mechanisms, along with the membrane's structural changes, comprise the complete physical model of the membrane. The model is shown to agree qualitatively with different membranes and different membrane forms, and is applicable to modeling perfluorinated sulfonic acid and similar membranes. It is also the first physically based comprehensive model of transport in a membrane that includes a physical description of Schroeder's paradox, and it bridges the gap between the two types of macroscopic models currently in the literature.

Modeling Water Management in Polymer-Electrolyte Fuel Cells

“…With the corresponding differences in water content, the membrane microstructure and hence its transport parameters and maybe even transport phenomena may change. 54 For more detailed discussions please see the relevant literature including very good reviews on Nafion ® (the current polymer of choice) 55 and alternative hydrocarbon membranes. 56 Due to its importance and complexity, the membrane's behavior has been simulated with a whole range of models, from the atomistic and molecular through to the macroscopic.…”

Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes

“…Upon water uptake, 3 water molecules initially ionize the SO 3 groups and remain bound to them. Additional water molecules are then free to move through the ionomer, causing growth of the clusters and consequently the macroscopic swelling of the membrane [8,9,11,24,34,[38][39][40][41].…”

“…This relationship is referred to as non-affine deformation and has been shown to occur for PFSA membranes by a number of studies in literature [11,[18][19][20][21][22]29,[33][34][35]. Despite the growing body of literature on the sorption behavior [7,8,10,24,34,35,38,40,[44][45][46][47][48][49][50] and nano-structural modeling and characterization [11,13,[17][18][19][20][21][22]28,29,31,[33][34][35][36]39,49,51,52] of PFSA ionomers, the relationship between the water uptake and nanostructure, temperature, mechanical properties and membrane pretreatment is not well established. Understanding of these issues requires a general, yet fundamental model, which is the subject of this study.…”

Macroscopic Modeling of Polymer-Electrolyte Membranes

“…Such models aim to explain transport across the whole range of possible membrane water contents and bridge the gap between the two categories above. Essentially, the two approaches above operate at one limit of water concentration, and are then somehow averaged between those limits [13,14]. The three main model categories are examined in more detail and in terms of equations in section 3.2…”

“…Doing the above substitution into equation (14) where the m denotes the interaction with the membrane and e denotes an effective property of the membrane. As discussed by Fimrite et al [3,86], this treatment is similar to that of the dusty-fluid model applied to the membrane [87][88][89], but accounts for the bulk movement of water in a more consistent manner using a different reference frame.…”