The relationship between relative humidity of gas phase and proton conductivity in proton exchange membranes has been subject of extensive investigations [1],[2]. Herein, a theoretical framework is presented which describes proton transport in relation to stepwise equilibria that reflect the water uptake. In the proposed model, at first, the hydration process is treated as a stepwise equilibrium process, in agreement with experimental observations. Several hierarchical levels of structure evolve with increasing hydration. These levels are easily confirmed by the analysis of the electric response of perfluorinated based membranes by complex dielectric and conductivity spectra. Thus, a wide range of literature data on hydration of Nafion as a function of activity and temperature has been analyzed by means of the proposed model to extract chemical parameters diagnostic of the type of interactions characterizing the hydrophilic domains of membranes.

These parameters, which are crucial in order to modulate the ion transport phenomena in ionomers, are then introduced into the model to describe the functional dependence of conductivity on water activity in gas phase. The treatment of proton conductivity is built on the approaches commonly adopted to describe transport in solids [3]. Key proton migration phenomena appropriate to the levels of the structural hierarchy are considered. The conductivity model is used to describe a set of conductivity vs. water uptake data as a function of temperature, with data taken to exceptionally low water contents. The formalism is then used to analyze a set of data for a perfluorosulfonic acid (PFSA) membrane as a function of hydration, temperature and polymer equivalent weight. The main advantage of the proposed framework is the possibility of a straightforward application to multiple membrane types based on the energetics of water uptake. Actually, the focus on chemical interactions allows to better correlate the effects of the morphology and relaxation events of the matrix to the proton migration phenomena of the membrane.

Acknowledgements

This work has received funding from: (a) the European Union’s Horizon 2020 research and innovation program under grant agreement 881603; (b) the project ‘Advanced Low-Platinum hierarchical Electrocatalysts for low-T fuel cells’ funded by EIT Raw Materials.

References

[1] Kreuer K.D., Schuster M., Obliers B., Diat O., Traub U., Fuchs A., Klock U., Paddison S.J., Maier J. 2008 J. Power Sources 178 499-509.

[2] Maalouf M., Pyle B., Sun C.N., Wu D., Paddison S.J., Schaberg M., Emery M., Lochhaas K.H., Hamrock S.J., Ghassemi H., Zawodzinski, T.A. 2009 ECS Trans. 25 1473.

[3] A.D. LeClaire and A. Rabinovitch, 1981, J. Phys. C, 14 3863.