Effect of Water Cluster Structure on Proton Transport in Proton-Exchange Membranes Using Reactive Molecular Dynamics Simulations
Authors: Mabuchi Takuya , Tokumasu Takashi 
Published: February 2020

The proton-exchange membrane (PEM) is one of the principal components for polymer electrolyte fuel cells. In the nanoscopic structure of the membrane, proton transport is one of the dominant factors that governs power generation efficiency, which are largely attributed to the nanoscopic structure of PEMs and water aggregations. Therefore, it is critical to understand the proton transport mechanisms through PEM and clarify an important link between the membrane nanostructure and the proton transport properties. As the phase separation is considered one of the primary factors affecting its performance, the morphological properties of PEM have been studied experimentally and been characterized by proposing the cluster models (e.g., the cylinder model and the lamellar model) which reasonably fit the experimental scattering spectra. However, a detailed relationship between the morphological features and proton transport properties is still under debate. Therefore, in this study, reactive molecular dynamics simulations have been performed to study the effects of water cluster structure on proton transport properties by constructing the cluster models in the simulations. The anharmonic two-state empirical valence bond (aTS-EVB) model has been used to incorporate excess proton transport efficiently through the Grotthuss hopping mechanism, providing an accurate estimation of proton transport properties in multiproton environments within the simplicity of the theoretical framework. The proton transport properties have been estimated in terms of diffusion coefficient and proton distributions in the two hydrophilic cluster structures (i.e., the cylinder model and the lamellar model) that are the most typical proposed morphological models in PEMs. The cylindrical systems with radii from 0.5 nm to 1.7 nm and the lamellar systems with the thicknesses from 0.6 nm to 1.6 nm were constructed for the purpose of comparison. The water contents for all of the models were kept at λ = 7, where the parameter λ indicates the ratio of the number of water molecules to that of SO3
-, which is equivalent to ~10 wt %, typical operating conditions in real PEM fuel cells. To construct the desired water cluster models in the PEM system, water domains with the desired geometric shapes were obtained from equilibrated simulations of bulk water. The systems were built by first placing the water domains into an empty box and then growing polymers around the water. The sulfonate groups were arranged so that they were in close contact with the surfaces of the water domains. The simulation cell for each model was then equilibrated while the positions of water molecules and hydronium ions were constrained. In the production run, a carbon atom in the backbone of each monomer was fixed to maintain the proper geometric shape of the water domain, while still allowing reasonable fluctuations of the sulfonate groups. All other atoms in the system were allowed to relax. The diffusion coefficients in each dimension are calculated and correlated with the cluster size and the type of cluster models. It is found that the proton diffusion shows the peaks in the 0.8 nm radius of the cylinder model and in the 0.9 nm thickness of the lamellar model, and decreases with increasing the cluster size. Nevertheless, the proton diffusions at any cluster size calculated in this study show the higher value than that in the random PEM model using the aTS-EVB method (~0.23×10-5
cm2/s), suggesting that the proton can be transferred effectively in the non-random cluster models. In the cylinder model with 0.8 nm radius, where the proton shows the higher diffusion, a comparatively large number of protons that are farther than the radius of the solvation shell are found in the center of cylinder, and thus the protons are freer to explore the free water region. Similarly, the more protons distribute in the surface of the lamellar model at larger thickness because the surface density of the sulfonate groups increases at larger thickness of the lamellar model. In the lamellar model with 0.9 nm thickness protons show the higher distributions in the center of the lamellar model, suggesting that protons are able to cross from interface to interface and are less hindered by the sulfonate groups, resulting in the faster proton diffusion. In the larger size of clusters, the protons are trapped in the interface of the water domains because the surface density of the sulfonate groups becomes higher at larger cluster sizes, resulting in the slower proton diffusion. Our simulation results provide insight into quantitative information about the water cluster structure dependence of the proton transport properties at an atomic level.