Limitations of the Water Sorption Model

Upon increasing the external relative humidity (P /P% capillary equilibrium advances from pores with small ao to those with large cro- Weakly charged pores fill first and they attain smaller equilibrium radii because they have the smaller osmotic pressure to push pore walls apart against the elastic pressure. 

The transition from equilibrium under saturated vapor conditions to liquid water conditions, implies a discontinuity in the liquid pressure in the pore, which debunks Schroder s paradox as a first-order phase transition at the pore level. At the PEM level, the jump in water uptake is tied to the maximal wall charge density a that is physically possible. 

The model predicts huge internal liquid and osmotic pressures, with absolute values in the range of 10 bar. These pressures depend strongly on P /P and T, as well 

Quantitative predictions of the model are sensitive to the shape of pores, the distribution of fixed-charged groups at pore walls, the reorganization of charged groups at pore walls upon swelling, proton distribution effects in pores, and microscopic elastic properties of the polymer matrix. A consistent model must account for, and properly validate, all of these details. However, there is significant experimental uncertainty related to all of these properties and there are statistical spatial fluctuations in all of them. 

Future work should scrutinize these structural aspects and refine corresponding approaches. The effective permittivity of water in pores increases with pore size, resulting in lower osmotic pressures, compared to the constant permittivity case due to a modified proton distribution. Consequently, the water uptake should be less steep at large RH. The inclusion of a Stern layer would further affect the proton distribution and, hence, water sorption. In fact, a modified Poisson-Boltzmann approach might be better suited to describe the electrostatic phenomena in such PEM pores. 

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