Equilibrium swelling is one of the common methods to determine the average network arc length. During the swelling of a network in a solvent, the solvents entry into the polymer matrix leads to an increase of volume (attractive interactions between solvent and polymer matrix) and the Gibbs enthalpy of mixing ΔGm. The entropy driven resetting force ΔGel takes an adverse effect on this process. As soon as the equilibrium is reached, the Gibbs free energy is ΔG is zero. ΔGm can be determined with the help of the Flory-Huggins equation and the Gaussian network theory. From the condition ΔG=0 for the equilibrium state of the swelling process, follows the Flory-Rehner equation:
If the density of the polymer and the Huggins interaction parameter are known, the swelling experiments to determine the volume share of the polymer allow the determination of the average network arc length MC .
With the described process it is possible, for example, to monitor the development of the network arc length or the cross-linkage density of an elastomeric part during aging.