Cloud-point curves by DSC measurements at different scanning rates on solutions of two samples of poly(vinyl methyl ether) in water show two minima in a temperature−composition plot. The significance of the data was confirmed by static measurements of the coexisting-phase compositions and phase-volume ratios. A thermodynamic analysis in terms of a strongly concentration-dependent interaction parameter leads to the conclusion that the system H2O/PVME exhibits so-called type III behavior. For polymers of infinite molar mass, such behavior is characterized by the occurrence of two off-zero critical concentrations, in addition to the usual zero critical concentration marking the ϑ state.

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An analysis is made of the distribution function and its moments for a linear combination of three randomly chosen orthogonal components of the so-called radius of gyration of an unrestricted random-flight chain, and certain averages of moments are obtained of the three-dimensional distribution W (L12L22L32), where L1 ≤ L2 ≤ L3 are the orthogonal components of the radius of gyration along the principal axes of inertia of the chain. The strong departures of the chain shape from spherical symmetry indicated by these results are confirmed and complemented by Monte Carlo studies of unrestricted random walks on a simple cubic lattice. A surprisingly high ratio of principal components is found for chains with 50 and 100 bonds, 〈L32〉: 〈L22〉: 〈L12〉 ≃ 11.7:2.7:1.

Equilibrium swelling of networks capable of separating into a highly swollen and a collapsed phase is discussed on the basis of a concentration-dependent pair interaction parameter. Classic rules, to be obeyed by the various binodals and their metastable and unstable extensions, rationalize the experimentally accessible portions of the phase diagram and are covered by a simple model yielding acceptable parameter values when fitted to swelling data on the system water/polyW-isopropylacrylamide). The description of the solvent/network binodal is good, but the predicted location of the LCST miscibility gap for linear chains deviates considerably from the measured cloud points. It is probable that linear and branched chains do not differ much in enthalpic contributions to the interaction parameter but deviate appreciably in the entropic terms. This feature offers an acceptable explanation for the discrepancy.

It is demonstrated that the collapse of gels of radiation cross-linked poly(vinyl methyl ether) swollen in water is a truly discontinuous process obeying classic thermodynamic principles. The phenomenon can further be shown to be related to the relevant type of limiting critical demixing of solutions of the corresponding non-cross-linked polymer. There are three such types, including “classic” ϑ behavior, and they can also be recognized in the swelling behavior of the cross-linked analogue.