Generalized free-volume theory GFVT

We treat the extension of FVT and incorporate correct expressions for the (polymer concentration-dependent) depletion thickness and osmotic pressure, resulting in generalized free volume theory (GFVT). Expression (4.4) for the semigrand potential is still valid in GFVT it does not contain any assumption as yet on the physical properties of the depletants or the colloids. But now we need to... 

Expression (6.46) may be regarded as a generalized free volume theory (GFVT) semi-grand potential for rods plus interacting polymers. Subsequently, we can specify the quantities a and P for interacting polymers. 

For q = 0.57 the composition of the colloidal liquid that coexists with a colloidal gas and crystal was determined by Moussaid et al. [26]. In Table 4.1 we compare these data with FVT and GFVT predictions. The experimental colloid volume fraction and polymer concentration clearly deviate significantly from FVT. Especially the polymer concentration of the coexisting colloidal liquid phase is about 30 times larger than the FVT prediction. Generalized free volume theory gives a much better prediction of the composition, especially if the polymers are assumed to be in a good solvent. 

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