Swelling of rubbers in solvents

Rubbers may swell considerably in good solvents. The swelling leads to isotropic extension of the network (Fig. 3.13). 

The volume expansion factor A = 1/ 2 where Vi is the volume fraction of polymer component in the swollen gel, is inserted into eq. (3.41)  

A detailed presentation of the thermodynamics of polymer solutions is given in Chapter 4 here only the final Flory-Huggins equation (eq. (3.45)) is presented. The decrease in free energy comes from the mixing enthalpy and entropy and the molar free energy of mixing (AGj J becomes  

The free energy for the network expansion (eq. (3.43)) can be converted to the molar free energy (AGj el) of dilution by substituting I/V2 = 1 + where rii is the mole fraction of the solvent and Vi is the molar volume of the solvent, and by taking the partial derivative with respect to n  

The equilibrium degree of swelling, represented by up is described by eq. (3.46) and the type of relationship between v and is shown in Fig. 3.14. 

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