Three-dimensional free-energy landscape of hydrogen and oxygen molecules in polymer electrolyte membranes: Insight into diffusion paths

Polymer electrolyte membranes, for example, the Nafion™ membranes, used in the fuel cells are responsible for separating reactive gas molecules as well as for the efficient exchange of protons. Although control of the permeation of the gases is important to enhance the fuel cell performance, the mechanism by which hydrogen and oxygen molecules permeate through the membranes remains unclear. To clarify the mechanism, we investigated the three-dimensional free-energy landscape of hydrogen and oxygen molecules in Nafion membranes with various water contents focusing on relevant diffusion paths. Low-free-energy paths are found mainly in the polymer phase and the interfacial region between the polymer and water phases. Thus, the path of the transportation may be attributed to the polymer phase and interfacial phases. However, the free-energy value in the aqueous phase is only slightly higher (∼1-2 kBT) than that in the other two phases, which indicates that a secondary contribution from the aqueous phase is expected. The free-energy landscape in the polymer and interfacial phases was found rugged, while it is comparatively flat in the water phase. We also found that an increase in water content brings about a smoother free-energy landscape in the polymer and interfacial phases. The decreased ruggedness may facilitate the gas diffusivity. These observations help understand the molecular mechanism of the gas diffusion in the membranes.