Gibbs free energy chains

The structure of hydrogels that do not contain ionic moieties can be analyzed by the Flory Rehner theory (Flory and Rehner 1943a). This combination of thermodynamic and elasticity theories states that a cross-linked polymer gel which is immersed in a fluid and allowed to reach equilibrium with its surroundings is subject only to two opposing forces, the thermodynamic force of mixing and the retractive force of the polymer chains. At equilibrium, these two forces are equal. Equation (1) describes the physical situation in terms of the Gibbs free energy. 

The standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

As the Gibbs free energy in general is influenced by the length of the polymer chain and its chemical structure, contributions AG for the polymer chain and AGj for the heterogeneity may be introduced. 

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