The thermodynamics of swollen rubber gels

The elastic Gibbs energy introduced in Chapter 4 must be extended to include the swelling deformation, since the volume of the network will now change. The deformation ratio for isotropic swelling is defined as = V/ Vq, where Vq is the volume of the dry rubber. The elastic Gibbs energy is then  

The swelling ratio is equal to the reciprocal of the volume fraction of the network, since the initial state is a dry rubber = 1 / )2. Because the network is macroscopic, the ratio of the partial volumes of the network and the solvent is effectively infinity. The excess chemical potential is calculated to be  

If the gel is exposed to excess solvent, the network will continue to swell imtil the excess chemical potential vanishes. This is called swelling equilibrium.  

The volume fraction of the network at swelling equilibrium depends on the number density of elastically effective chains in the dry network and the solvent quality as measured by the Flory % parameter. In general, the volume 

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