On Schroederʹs paradox

In 1903, von Schroeder reported a difference in solvent uptake (i.e. swelling) by a solid polymer sample (i.e., gel or membrane) when the sample was exposed to a saturated vapor versus a pure liquid. While “Schroederʹs paradox” has been disregarded for a long time, it has been recently reported for several systems, which involve either glassy or ion exchange polymers and small polar molecules. In this work, we report the apparent occurrence of the paradox for a simple system based on an elastomer (crosslinked polydimethylsiloxane) swollen in 2-propanol. The phenomenon is not general (i.e. it depends on the type of system) and is shown to be reversible when it does occur. Contrary to previous explanations based on non-equilibrium or permanent pores in the polymeric matrix, an interpretation based on the classical phase equilibrium equation for gels is proposed. The implications in terms of mass transfer in dense membranes and the numerous lingering questions related to this paradox are discussed.