Absence of Schroeder's paradox in a nanostructured block copolymer electrolyte membrane

This is a study of morphology, water uptake, and proton conductivity of a sulfonated polystyrene-block-polyethylene (PSS-PE) copolymer equilibrated in humid air with controlled relative humidity (RH), and in liquid water. Extrapolation of the domain size, water uptake, and conductivity obtained in humid air to RH = 100% allowed for an accurate comparison between the properties of PSS-PE hydrated in saturated vapor and in liquid water. We demonstrate that extrapolations of domain size and water uptake on samples equilibrated in humid air are consistent with measurements on samples equilibrated in liquid water. Small (5%) differences in proton conductivity were found in samples equilibrated in humid air and liquid water. We argue that differences in transport coefficients in disordered heterogeneous systems, particularly small differences, present no paradox whatsoever. Schroeder's Paradox, wherein properties of polymers measured in saturated water vapor are different from those obtained in liquid water, is thus not observed in the PSS-PE sample.