Swelling of Neutral and Electrolytic Gels

The take-up of solvent molecules from the surroundings transfers a network from its initial dry state with volume Vgo to a swollen state with a larger value Vg. The equilibrium is associated with a certain swelling ratio 

How is this equilibrium state of the gel determined solvent filled networks are generally addressed as gels, water filled networks often also more specifically as hydrogels Equilibrium conditions have to be established for the solvent molecules, because they can move freely from one part of the system, the gel, to the other part, the surroundings with the pure solvent. The requirement is the equality of the (molar) chemical potential of the solvent (subscript s) in the two phases (superscripts g and 0) 

Since the solvent concentration is reduced in the gel and thus the chemical potential under normal pressure, an equal chemical potential can only be achieved for an enhanced pressure in the gel, i.e., Pg Pg- The pressure difference is the osmotic pressure 

In order to determine the equilibrium we need expressions for the dependence of both n and a on the swelling ratio Q. 

An expression for the isotropic network stress is obtained using Eq. (9.22) in the case of an isotropic dilatation 

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