The effects of cross-linking on the equation of state of a polymer solution

Abstract

Measurements of the swelling pressure ω̄ and shear modulus Gs in a set of poly(vinyl acetate) networks swollen to different degrees in toluene and in acetone are reported, using solutions of the uncross-linked polymer to obtain deswelling under known conditions of osmotic pressure. The swelling pressure can be completely described by the difference between two terms, each of which is a simple power law in the polymer volume fraction φ. Identification of the subtractive term with that related to the elastic free energy of the network gives the volume elastic modulus Gv. The shear modulus Gs, obtained from mechanical measurements at constant volume, and Gv are found to coincide for these samples, and neither deviates measurably from a one-third power law dependence on φ, up to values of φ in excess of 0.4. The remaining term in the swelling pressure of the networks behaves like the mixing term in a polymer solution, obeying good solvent scaling predictions as a function of concentration in both diluents. Its magnitude, however, is substantially smaller than the osmotic pressure of an equivalent uncross-linked solution of infinite molecular weight. The difference between the cross-linked and uncross-linked states conflicts with the assumption that the two mixing free energies are identical.