Morphology of Hydrated Nafion through a Quantitative Cluster Analysis: A Case Study Based on Dissipative Particle Dynamics Simulations

The evolution of the hydrated morphology of Nafion over a range of water contents was quantified through the cluster analysis method. Our findings are in contrast with those solely based on the radial distribution functions (RDFs) where cluster size and separation are approximated by certain characteristics of the RDF. The quantitative cluster analysis along with realistic microscopic images colored by unique IDs leads to a wealth of information on water domain size, shape, and connectivity, which is essential for a mechanistic understanding of proton transport. The percolation threshold of the water domains in hydrated Nafion was found to occur at a hydration level of 5 H2O/SO3H. Below the threshold, isolated individual water clusters cannot contribute to the ion transport. Water clusters grow from small aggregates into larger spheres, elongated rods, and branched and twisted cylinders as the hydration level increases. Beyond the threshold, the percolating water network is conspicuously dominant in the morphology. At the higher hydration levels, a larger percentage of the water beads contribute to the polar network and the size and number of nonparticipating clusters gradually diminish. Our work emphasizes the importance of a proper quantitative tool to understand the nature of ion-conducting domains.