Semidilute solutions osmotic modulus

At swelling equilibrium, the elasticity is balanced by the osmotic pressure n of a semidilute solution of uncrosslinked chains at the same con-centration. Since the modulus is proportional to the elastic free energy per unit volume, any gel swells until the modulus and osmotic pressure are balanced. The equilibrium swelling ratio Q is the ratio of the volume in the fully swollen state and the volume in the dry state ... 

What is the physical significance of the fact that the value of the stress relaxation modulus at the relaxation time of a correlation blob G(r ) is proportional to the osmotic pressure in semidilute solutions ... 

Tnteractions are not important. The dynamics on these intermediate scales (for r < t< Te) are described by the Rouse model with stress relaxation modulus similar to the Rouse result for unentangled solutions [Eq. (8.90) with the long time limit the Rouse time of an entanglement strand Tg]. At Te, the stress relaxation modulus has decayed to the plateau modulus Gg[kT per entanglement strand, Eq. [(9.37), see Fig. 9.9)]. The ratio of osmotic pressure and plateau modulus at any concentration in semidilute solution -in athermal solvents is proportional to the number of Kuhn monomers in ... 

In dilute (C 0) and semidilute solutions, the osmotic bulk modulus (or osmotic pressure) is proportional to the number of non-interacting... 

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