In this work we describe the application of thermodynamic approaches to evaluate the uptake of acids into ion exchange membranes under conditions of equilibration of the membranes with concentrated solutions. This situation is encountered in practical electrochemical reactor systems such as redox flow batteries (RFBs). First, we collect data describing that uptake for a series of acids in contact with perfluorosulfonic acid membranes. We then develop a treatment of the activity coefficients in such systems with a standard thermodynamic analysis of equilibrium between the solution and membrane phases. This is augmented by the Freeman-Manning counterion condensation approach. The latter fails to capture the behavior. As an alternative, based on the first part of the Freeman-Manning analysis we estimate the Donnan potential difference at the membrane surface. This parameter reliably captures the membrane behavior, with the potential tending toward the same constant value for the membrane exposed to different acids. The counterion condensation theory may provide insight into the evolution of the Donnan potential as a function of concentration in the low concentration regime. Finally, we comment on the possible development of this approach as a useful predictive parameter for membrane behavior in RFBs.
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