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.