Flory-Rehner approximation

The swelling pressure k depends on gel and solution properties in a non-trivial manner. The commonly used Flory-Rehner approximation [1] assumes that k consists of three independent contributions ... 

Since vr0jvT varies only slowly with vr0, while v is a rather sensitive function of the inverse swelling ratio, the result of substituting vr into the Flory-Rehner equation is a vapp which is too large, but which still reflects rather faithfully any changes in vr0 brought about by varying the network chain density. Thus we may write as an approximation... 

The Flory-Rehner equilibrium swelling method (see Section 4.2.2) was used to evaluate the change in crosslink density of the IPNs, using dioxane as the swelling agent. The Flory interaction parameter was found to be approximately 0.30 for dioxane and either polymer, simplifying the analysis. Table 6.4 gives the results for the effective crosslink densities, vj K where V is the polymer volume in cm. Table 6.4 also shows the theoretical values of vj K calculated in accordance with the law of additivity. 

Other network models based on the inverse Langevin function are the tetrahedral model of Flory and Rehner (1943) subsequently modified by Treloar (1946) and the inverse Langevin approximation (Treloar, 1954). The relative merits of these approaches, which yield similar results have been discussed by Treloar (1975) who points out the overwhelming advantages of the three-chain model in ease of computation. 

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