On Schroeder's paradox

Surface orientation of hydrophilic groups in sulfonated poly(ether ether ketone) membranes

“…It 35 was also found that the bottom surface of a membrane (which was in contact with the glass plate during casting) is more hydrophilic than its top surface (which was in contact with argon during casting). The surface characteristics of SPEEK-HQ membranes were shown to be determined by the sulfonate content as well as by the treatment process.…”

“…In contact with air, Nafion ® exhibits a hydrophobic character, swelling much however during hydration. This phenomenon was initially referred to as 'Schroeder's paradox' [14,15,[33][34][35] indicating that Nafion ® showed differences in water uptake from liquid water compared to saturated water vapor under otherwise identical conditions. This was a consequence of a complex interfacial behavior and this puzzling feature resulted from the microstructural transition of Nafion ® occurring when the environment changed from water vapor to liquid water [15], i.e., Nafion ® micelles at the surface facing a vapor phase tended to align parallel to the surface and formed a thin hydrophobic fluorine layer [14,36].…”

On the Schroeder paradox for nonionogenic polymers

“…The resulting force may, obviously, be represented in the form of Eq. (7); that is, (8) where is the concentration of the segments. Since the resultant force may be written as (9) At B 0 > 0, the stretching forces prevail, and the macromolecule swells relative to the Gaussian coil, while, at B 0 < 0, the macromolecule shrinks.…”

“…Repeated attempts have been made to explain the paradox theoretically. At the present time, diverse (sometimes, exotic) models have been proposed to explain the Schroeder paradox (a long list of works devoted to its experimental and theoretical study may be found in [3][4][5][6][7][8]). …”

Characterization of vapor-induced and liquid-induced moisture migration through fractionated palm kernel (PKO) based multiphase systems

“…The interactions of hydrophilic groups with vapor may be different from the interactions with liquid. Schroeder (1903) reported in a gelatin swelling experiment that when a piece of gelatin was put into contact with saturated water vapor or pure liquid water, a significant difference in terms of the mass gain of the gel phase was observed (Vallieres et al, 2006;Gates and Newman, 2000). Grigoriew and Chmielewski (1997) showed that liquid water penetrates more quickly through cellulosic membranes than vapor and the amount of liquid water uptake is also greater although water activity is the same.…”