Classic Theory for Gels

Similarly to the van der Waals fluid, polymer gels were found to have a volume-phase transition. In the case of gels, the gas and liquid phases correspond to the swollen and collapsed (shrunken) phases, respectively. The prototype of the free energy expression was given by [9, 10, 18]. 

If the gel has ionic groups, a Donnan-type potential due to the presence of the translational entropy of the counter ions also contributes to the osmotic pressure, which is given by 

For small j , the logarithmic term in Eq. (2.12) can be expanded into a power series and then n is written in the following form 

This is a virial expansion form of the osmotic pressure analogous to the van der Waals fluid. Dusek and Patterson examined this equation and predicted the presence of two phases, i.e. collapsed and swollen phases. % is temperature dependent and is given by, 

---

When A/x/kfiT 1, there will be few free stickers. According to the classical theory for gels, the modulus of a telechelic gel should be simply given by Eq. (5-2), Go = vksT,... 

---