Hydration of ionomers and Schroeder's paradox in Nafion.

Schroeder's paradox, i.e., different uptake of a liquid solvent and its vapor, is analyzed for ionomers in general and Nafion in particular within a proposed general model of hydrated ionomers. The model considers four types of energy involved in a microphase-separated hydrated ionomer: hydration (solvation) of ionic groups, interfacial energy, and two distinct types of elastic energy associated, respectively, with inflation of the matrix upon hydration and varying stretching of the corona regions adjacent to the microscopic interface. By analyzing equilibrium in the bulk and surface regions of the polymer using approximate phenomenological relations for each contribution, it is shown that Schroeder's paradox is a consequence of a composite interfacial-elastic "Laplace" pressure that is exerted on the aqueous microphase in equilibrium with a solvent vapor but exactly cancels out in equilibrium with a liquid as a result of structural rearrangements starting from the surface. The crucial difference with the previous models is association of this pressure with the microscopic polymer-liquid interface. The model conforms to the general picture of structural evolution of Nafion in the full range of hydrations and to the available scattering data, indicating a 2D morphology in a wide hydration range. It also allows for analysis of realistic nonequilibrium hydrated states stabilized by a transient rigidity of the matrix, apparently characteristic of Nafion at ambient conditions. Available data on hydrated Nafion strongly suggests that transient rigidity may be responsible for many of its unusual properties, such as unique morphologies, high conductivity, and its loss at high temperatures. Slow relaxation in the bulk and at the surface may also explain the controversies regarding observation of Schroeder's paradox and the importance of thermal and hydration history.