Swelling of Crosslinked Polymers in Liquids and Vapors. Rational Explanation of Thermodynamic Paradoxes

Abstract

Schroeder's paradox, stronger swelling of gelatin in liquid water compared to swelling in saturated water vapor, did not receive any acceptable thermodynamic explanation for more than 100 years. By an automatic registration of the growing size of a single polymeric sphere (of less than 1 mm in diameter) placed first into saturated vapor atmosphere and then into corresponding liquid, we showed that the above effect is a general phenomenon characteristic of all crosslinked polymers and all types of aqueous or organic media. Explanation of the paradox is presented in terms of higher activity and chemical potential of the bulk liquid compared to saturated vapor over it, due to the unidirectional attraction of the surface molecules toward the condensed liquid phase. Also, it was found that saturated vapor can exist in a prolonged equilibrium with polymer samples which incorporate any amount of the sorbate within the broad range from the vapor-equilibrated to liquid-equilibrated extremes. This paradox is explained by the dependence of the system of inter-chain interactions within the network on the pre-history of the sample.

Fundamentals and Applications of Polymer Brushes in Air

“…This result, known as Schroeder’s paradox, was found for gelatin by Schroeder in 1903, and it has recently attracted renewed attention for its relevance to polymeric membrane materials. 63 , 64 However, as no conclusive thermodynamic explanation for this effect exists as of yet, this cannot be accounted for theoretically.…”

Kerogen Swelling in Light Hydrocarbon Gases and Liquids and Validity of Schroeder’s Paradox

“…The difference in swelling at saturation pressure is known as Schroeder’s paradox . Schroeder’s paradox has been confirmed in various experiments by different authors. − A number of authors have questioned the validity of the data and have related the difference to experimental artifacts. , In the last several years, there has been renewed interest in Schroeder’s paradox in the polymer membrane fuel cells where water in contact with the membrane may be either in a liquid or gas state . Water uptake and membrane swelling influence the membrane conductivity, which affect the fuel cell performance. ,− The same topic in relation to sorption and swelling in gases and liquids is very relevant in hydrocarbon extraction from shale formations.…”

Macro- and Nanoscopic Studies of Porous Polymer Swelling

“…There is also a great difference in the swelling mechanism with regard to whether swelling occurs in a liquid solvent or a vapor. 16 The initial uptake of the liquid solvent is almost instant. In this case, the swelling of a particle is proportional to the amount of the swelling polymer specimen.…”

“…In the case of adsorption, the porosity of polymeric material is the dominant factor controlling the swelling kinetics. There is also a great difference in the swelling mechanism with regard to whether swelling occurs in a liquid solvent or a vapor . The initial uptake of the liquid solvent is almost instant.…”