Paradoxes of Thermodynamics of Swelling Equilibria of Polymers in Liquids and Vapors

Abstract

An automatic registration of the changing size of a single spherical microbead of a cross-linked polymer was applied for studying the swelling process of the bead by the sorption of vapors and/or liquids. Many representatives of all three basic types of polymeric networks, gel-type, hypercrosslinked, and macroporous, were examined. Only the first two display large volume changes and prove suitable for following the kinetics and extent of swelling by the above dilatometric technique. The results unambiguously prove that swelling of all polymeric networks in liquids is always higher than in corresponding saturated vapors (Schroeder's paradox). The general nature of this phenomenon implies that the absolute activity of any sorbate in its liquid form is always larger than in the form of its saturated vapor. Surprisingly, gels with any solvent contents, which fall into the broad range between the vapor-equilibrated and liquid-equilibrated extreme contents, retain their volumes constant in the saturated vapor atmosphere. This paradox of a wide range of gels swollen to a different extent and, nevertheless, standing in equilibrium with saturated vapor is explained by the specificity of the network polymers, namely, that the energy of the solvent-polymer interactions is easily compensated by the energy of remaining between-chain interactions at any solvent content in the above range. Therefore, the strain-free swollen gels do not generate enhanced vapor pressure, but neither display the ability to take up more sorbate from its vapor.

Synergic Swelling of Interactive Network Support and Block Copolymer Films during Solvent Vapor Annealing

“…The general nature of this phenomenon is explained by the fact that the absolute activity of any sorbate in its liquid form is always larger than in the form of its saturated vapor. Earlier study on the swelling of cross-linked polymeric beads led to another possible explanation of Schroeder’s paradox . The authors found that strain-relaxed gels with any solvent contents retain their volumes constant in the saturated vapor atmosphere, and they attributed this effect to the specificity of the polymer–solvent interactions in network polymers.…”

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

“…Of course, the above consideration must be valid, to a more or less evident extent, for borders between any liquid and gaseous or solid phases, rather than just for borders between water (or aqueous solutions) and their vapors or immersed polymers. Indeed, Schroeder's effect was also shown to be characteristic of all organic solvents in combination with corresponding swelling polymers, without any exception [12].…”

“…A rather complete list of relevant references can be found in publications by Davankov and Pastukhov [12] and, in particular, by Jeck et al [13].…”

“…More recently, we undertook an extensive experimental work aimed at the validation or disproof of Schroeder's paradox [12,29]. We applied new and extremely productive technique where only a single spherical polymer bead of less than 1 mm in diameter was exposed to saturated vapor of an appropriate sorbate and then wetted with the corresponding liquid [30].…”

“…Very small size of the sample (about 0.5 mg) and small volume of the surrounding vapor chamber provide for a rapid establishing of the sorption equilibria, so that the whole experiment takes no more than a couple of hours. Some 30 various polymer samples have been examined representing all basic types of chemically crosslinked polymeric networks [12,29]. They included following classes of networks:…”