We present a statistical mechanical approach for predicting the self-assembled morphologies of amphiphilic copolymers-sulfonated poly (ether ether ketone) (sPEEK) and Nafion-which combine, in one macromolecule, both hydrophobic and hydrophilic segments, giving rise to a constrained hydrophobic/hydrophilic nano-separation. We have developed a coarse-grained model of sPEEK that constitutes an important class of the promising membrane materials for fuel cell applications. Using a mesoscale dynamic density functional theory (DDFT) framework, we explore the phase behavior of sPEEK and Nafion in the presence of physisorbed water. To determine the impact of polymer chemistry on the morphology of sPEEK membranes, multiblock copolymers with a variation in both molecular architecture (block size) and chemical composition (degree of sulfonation) are studied in a large window of water contents. At sufficiently high hydration levels, the simulations predict a tricontinuous morphology, where all the microphase-separated subphases-hydrophilic and hydrophobic blocks and water-percolate, resulting in the formation of three co-continuous phases. Above the percolation threshold, the distribution of water in the sPEEK membrane can be represented as a topologically complex sponge-like network consisting of narrow channels, while the main structural motif of Nafion is characterized by the presence of long but randomly packed water-filled tubes, in agreement with the fibrillar model recently proposed by Schmidt-Rohr and Chen. Although the polymer matrix of sPEEK tends to confine water to narrower channels compared to those in Nafion, the average cross-sectional area of the channels is comparable for the two systems with the same hydration level.
