Modeling of Water Sorption and Swelling in Polymer Electrolyte Membranes: Diagnostic Applications

The polymer electrolyte membrane (PEM) fulfills vital functions as separator, proton conductor, and electronic insulator in a polymer electrolyte fuel cell (PEFC). The well-studied and practically used solid polymer electrolyte membranes are perfluorosulfonic acid (PFSA) polymer membranes such as Nafion. These membranes offer high proton conductivity, high mechanical strength and good chemical stability. The efficiency of the chemical-to-electrical energy conversion in a PEFC critically depends on the ability of the PEM to transport protons from the anode to the cathode. Proton conductivity of the PEM is a key parameter to achieve high power density and performance. The main variable to characterize the state of a PEM and determine its transport properties is its water content. In particular, the proton conductivity is highly sensitive to the level of hydration. Membranes experience continuous stresses and consequently continuous loss of performance throughout their operational life. Chemical degradation alters the chemical structure of the PEM, which affects the water distribution in it. A consistent description of water sorption and swelling under conditions relevant for the PEFC operation lies at the heart of understanding transport properties, performance and degradation phenomena. This work expands on a previously developed poroelectroelastic model of water sorption in PEMs [Soft Matter 7, 5976 (2011)]. The theory relates the charge density at the pore walls to a microscopic swelling parameter. Extended to the water sorption equilibrium in a pore ensemble, the model reconciles microscopic swelling in a single pore with macroscopic swelling of the membrane. This work provides a generalized treatment of elastic effects in PEMs. Different deformation modes of polymeric pore walls are used to derive stress-strain relationships that determine the law of swelling. Moreover, this work enhances the diagnostic capabilities of the model; it provides the statistical pore size distribution as well as a statistical distribution of microscopic fluid and elastic pressures inside the PEM. Thereafter, the model is applied to different sets of water sorption data for PEMs that had undergone either hygrothermal aging or chemical degradation. The model-based analysis provides mechanistic explanations of structural changes and their impact on microscopic distributions of charge density and elastic properties in PEMs.