(609c) Nano- and Mesoscale Transport and Mechanics in Ionomers

The quintessential fuel-cell membrane is a perfluorinated sulfonic-acid (PFSA) ionomer. These copolymers phase separates into bicontinuous morphology with a hydrophobic phase that provides structural integrity and a water-filled hydrophilic phase that forms a network of domains, which facilitates solvent and ion transport. The mesoscale properties of the hydrophilic transport network (e.g. domain size, distribution, and connectivity) determine the effective macroscale transport properties of these membranes. Similarly, the mesoscale topology of the hydrophobic network determines the mechanical properties. These two networks communicate through hydrophilic domain swelling and propagation of stress to neighboring domains through the membrane. Consequently, the relationship between properties of these two network and macroscopic transport determines fuel-cell membrane efficacy. In this work, we instantiate this relationship by simulating solvent and ion transport along with local stress distribution throughout the hydrophilic and hydrophobic phases.

In this work, resistor and spring networks coarse-grains the interconnected hydrophilic and hydrophobic domains, respectively, as segments connecting nodes. Conservation of species flux and stress at each node in the hydrophilic and hydrophobic networks dictates electrochemical potential and strain in segments, respectively. A mean-field nanoscale model of the domains parametrizes resistances of the segments as a function of size (thickness and length) and water content. The average and distribution of domain sizes and connectivity are consistent with experiments. Accordingly, there is a distribution of segment resistances and modulus in the networks. Congruent with Onsager-Stefan-Maxwell concentrated solution theory, we treat chemical and electrostatic gradients as driving water and ion transport and their corresponding coupling (electroosmotic effect). We validate the predicted modulus, diffusion and electroosmotic coefficients, and conductivity against experiments.

We find macroscopic transport and mechanics behavior emerges out of the mesoscale. For example, how nanoscale resistance depends on domain size dictates which pathways a species will take across the network. Accordingly, different modes of transport utilize different network pathways and have different effective tortuosities. Moreover, water gradients at the macroscale induce mesoscale electrostatic potential gradients (and visa-versa). These results show how design of emergent behavior improves membrane performance.