Thermodynamics of Swelling. I. Thermodynamic Properties of Crosslinked Binary Systems

Abstract

Abstract Part I of this article was devoted to the thermodynamic properties of binary-mixed phases, in which one component was a low-molecular-weight liquid and the other a polymer crosslinked by primary-valence bonds. Special attention was paid to the case where the macromolecular material is in a glassy state at the measurement temperature. When solvent concentrations are low, the mixed phases are also in the glassy state. If the freezing concentration is exceeded during isothermal absorption of liquid, elastic materials appear, stable as to form when swelled, which are designated gels. Like liquids, gels are in a state of internal equilibrium. When polymer components have primary-valence crosslinks, liquid take-up always leads to an equilibrium state (swelling maximum, saturated gel). The enthalpy-concentration diagram was investigated rather thoroughly. If the polymer is in internal equilibrium at the measurement temperature, then the heat of mixing (heat of swelling) arises only from interaction between molecules. On the other hand, if the pure polymer component is frozen, the negative heat of freezing is superposed upon the “genuine” heat of swelling, resulting from interaction. Even when the enthalpy of the mixed phase is an additive function of the values for the pure components, a heat of mixing appears which originates only from liberation of the heat of freezing. The sign of the limiting heat of dilution, i.e., the differential heat of dilution at the swelling maximum, determines the temperature dependence of the swelling equilibrium. In athermic systems, maximum swelling is independent of temperature. The osmotic swelling equilibrium was investigated thermodynamically. It was shown that swelling pressure in crosslinked systems corresponds to osmotic pressure in solutions. A survey of results from the statistical theory of crosslinked systems is presented using, as a basis, Flory's theory for an ideal-athermal gel. As with the thermodynamic treatment of low-molecular-weight systems, excess functions were also introduced here. For low-molecular-weight, liquid mixtures, the excess functions have reference to formulas for an ideal solution. For polymeric, crosslinked systems, however, the reference values suggested are the statistical equations for an ideal-athermal gel. Finally, limiting laws for infinite dilution are derived for a crosslinked, mixed phase.