Published: November 11, 2011 r2011 American Chemical Society 15188 dx.doi.org/10.1021/jp208209c | J. Phys. Chem. B 2011, 115, 15188–15195 ARTICLE pubs.acs.org/JPCB Paradoxes of Thermodynamics of Swelling Equilibria of Polymers in Liquids and Vapors Vadim A. Davankov* and Alexander V. Pastukhov Nesmeyanov-Institute of Organo-Element Compounds, Russian Academy of Sciences, Vavilov st. 28, 119991 Moscow, Russia ’ INTRODUCTION When developing basic notions of modern thermodynamics by the end of 19th century, Gibbs introduced the chemical poten- tial of a compound as a new entity that characterizes the contri- bution of the compound to the total free energy of a system and its ability to participate in interphase equilibria. The chemical potential of any component that is common for two phases stand- ing at equilibrium was postulated to be equal. Thus, chemical potentials of water molecules in liquid water and in saturated vapor at any temperature were said to be equal, in spite of the fact that all physical properties of the liquid and vapor strongly differ from each other. The notion of chemical potential proved to be applicable in the thermodynamic description of equilibria be- tween two phases. The first problem arose in the interpretation of situation with a three-phase system, when in addition to the liquid and vapor, a gel emerged in contact with these phases. The term gel is generally used to describe an insoluble (polymeric) solid that is capable of incorporating a low-molecular weight component which exists in the system in the form of a liquid or vapor. As early as 1903, Schroeder published 1 results of a simple but very convincing and vivid experiment where a plate of gelatin was partially immersed into water in a sealed vessel. After the system equilibrated, the swelling of the water-wetted part of the sample was observed to be substantially stronger (1139%) than that of the part contacting the saturated water vapor (41%). The author corroborated this observation with several thorough weighing experiments. From the viewpoint of common sense, this difference in the swelling extents appears to be rather logical, considering the fact that the concentration of water molecules in liquid water is over 10 000 times higher than that in the saturated vapor. But, in view of the generally accepted framework of phase equilibrium thermodynamics, 2,3 the solvent uptake by cross-linked polymers is solely linked to solvent chemical potential in the fluid phase, irrespective of the state of the fluid phase. The chemical poten- tials of water in the pure liquid and saturated vapor phases are assumed to be equal (sometimes even the activity of water both in pure liquid and saturated vapor is said to be equal, namely, unity). For this reason, the difference in solvent uptake by a solid polymer sample, when exposed to a saturated vapor versus a pure liquid, was termed Scroeder's paradox. Schroeder's data have been re-examined and basically confirmed. 46 It was found that the swelling difference in water and its vapors is really large, though the exact numbers are diffi- cult to reproduce because properties of gelatin samples depend on the source of the material and, moreover, the gel is prone to slow hydrolysis and fouling. It was also noted that a water- swollen gelatin sample, when placed in the atmosphere of satura- ted vapor, slowly loses water, so that its water content in two weeks drops from 1076 to 343%, 1,6 thus creating an impression that it tends to reach the above value of 41% characteristic of the gelatin/vapor system. (At that time it was not yet known that Received: August 25, 2011 Revised: October 31, 2011 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, hypercros- slinked, 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.