The Thiele-Cohen Swelling Equation

For many years, the Flory-Rehner equilibrium swelling equation has served to relate the volume fraction of polymer in the swollen mass, Vu to the number of moles of network chains per cm, i i  

For a homo-IPN, the free energy change, AG, of mixing during swelling may be written as a sum of three contributions, a term for the sum of the contributions of polymer and solvent mixing forces, AGm, and a term for each network s elastic retractive forces  

A key assumption used in this derivation is that networks I and II are assumed to be elastically independent. After Flory  

The first term in equation (4.11) is a mixing term depending only on the relative volumes of polymer and solvent, and on the polymer-solvent interaction parameter, Xs The final form of this term will therefore be analogous to the result derived by Flory, with the volume fraction of 

The second term of equation (4.11) will also be analogous to previous results because of the assumption that the two networks are elastically independent. Thus, the two networks dilute each other. From rubber elasticity 

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