(553g) A Molecular Dynamics Study of Nafion Polyelectrolyte Membrane and the Aqueous Phase Structure for Proton Transport

Proton transport through a proton exchange membrane is an important fundamental and practical problem in fuel cell design. Despite its importance, the molecular level understanding of the problem appears to be limited. Only a few molecular simulation works have been published on the subject. For bulk aqueous solution, there has been significant progress toward understanding the proton transport process. It is believed that the Zundel ion and Eigen ion complex structures induced by proton sharing in aqueous solution significantly enhance the proton transport process [1]. In Nafion membranes, proton transport strongly depends on water content, as a result of water cluster formation and the mobility of Zundel and Eigen ions. In this work, we aim to understand the molecular mechanism of the proton transport by studying the structure of water, the Zundel and Eigen ion complex, the structure of the polyelectrolyte, and their interactions with the aqueous phase in facilitating the transport of protons. The ultimate objective of this research is to use molecular dynamics simulation to understand proton transport across the electrode/electrolyte interface of a PEM fuel cell.

II. Molecular Models and Method

We use the united atom model for the Nafion polyelectrolyte. The potential model for Nafion is taken from [2-5]. Partial charges are given in ref. [2]. It includes bond stretching, bond bending, bond torsion, intramolecular non-bonded interactions between molecules separated by at least three bonds, and intermolecular non-bonded interactions. The non-bonded interactions contain the Lennard-Jones interaction and the electrostatic interaction. The Lennard-Jones interaction is treated using a cut-off and the electrostatic interaction is treated with a site-site reaction field that has been proven to be accurate [7]. The water is modeled with the TIP3P model [8] with a flexible OH bond [6]. The model for hydronium ions, H₃O⁺, is that of Urata et al. [4]. Notably, this potential does not allow for structural diffusion of protons

III. Results

In the simulation of the bulk hydrated Nafion, we included 64 polymers (192 monomers), and 192 H₃O⁺, required to balance the charges. We varied the water content and characterized it as the λ ratio of water molecules to SO₃^- groups, exploring λ = 3.44, 7.25 8.63, and 11.83. This resulted in simulations with 660, 1392, 1656, and 2272 water molecules, corresponding to 7932, 10128, 10920, and 12768 total interactions sites in the simulations. The thermodynamic state of the system was chosen to match literature data [9]. The temperature was 300 K and the densities for the four levels of hydration were 1.95, 1.87, 1.80, and 1.74 g/cm³. We characterized the bulk structure of the hydrated Nafion membrane by three methods: pair correlation functions, cluster size histograms, and visual snapshots. The configuration shows the effect of the polymers on the segregation into hydrophobic and hydrophilic regions within the system. This is because the backbone of the polymer is hydrophobic and the side chains are hydrophillic. The water and the hydronium ions are mostly clustered around the hydrophilic sites of the side chains which are themselves tended to cluster together. With increasing water content, most water molecules are contained in a large cluster, which suggests that it may increase the ability for proton transport through the Zundel ion mechanism. Pair correlation functions provide important structural properties, in particular the pair correlation function involving the hydronium ion will aid in the characterization of the Zundel and Eigen ions. To characterize quantitatively the structure, we have calculated pair correlation functions between many different pairs of atoms of the multicomponent system, including O_H2O-O_H2O, O_H2O-H_H2O, H_H2O-H_H2O, O_H2O-O_H3O+, O-H_H3O+, H_H2O-O_H3O+, H_H2O-H_H3O+, S-O_H2O, S-H_H2O, S-O_H3O+, and S-H_H3O+. The sulfur-water oxygen peak decreases with water content, suggesting tighter binding at low water concentration due to low solvation power by the aqueous phase. We also examined water cluster size distribution. In general, water cluster distribution depends on the chosen critical size. We have varied the critical size from 3.5 Å to 5.5 Å to determine this effect. We find a large number of small clusters with relatively high probability, and a small number of large clusters with relatively low probability. The probability of large cluster formation increases with water content. However, the vast majority of the water molecules are in the large cluster. The cluster sizes are dynamically changing, corresponding to the migration of water and hydronium ions. We believe that dynamic exchange of water and hydronium ions may play an important role in the proton transport in the hydrated polyelectrolyte membranes.

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