Theory of swelling of a crosslinked substance in equilibrium with a solvent in various phases

In this paper the thermodynamic theory of a body in a liquid, crystalline or vaporized solvent is treated. The equilibrium swelling curves are discussed for the different states of the solvent. The slopes of the swelling curves are dependent on the differential enthalpy of dilution of the solvent and, additionally, on the enthalpies of vaporization, crystallization and sublimation of the solvent related to the state of the swelling agent. The slopes of the swelling curves are determined by the differential heat of vaporization, the differential heat of solution of the solvent or the differential heat of fusion according to the state of the swelling agent. Directly below the melting pointT _m,1, or directly above the boiling pointT _b,1 of the solvent the swelling curves change their slopes with a sharp bend. This phenomenon can be used to determine (₁/w ₁) at constant temperature and pressure, which means the change of the chemical potential ₁, with the change of the weight fractionw ₁ of the solvent. Using a simplified statistical thermodynamic relation it is possible to describe the principal courses of the swelling curves in all states of the solvent.