Solubility of liquid mixtures

The thermodynamics of polymeric systems have already been described in detail in chapter m,. where it was shown that a basic difference e.tists between a ternary system (a binary liquid mixture and a polymer) and a binary system (polymer and liquid). In the former case not only the amount of liquid inside the polymer (overall sorption) is an important parameter but the composition of the liquid mixture inside the polymer is especially so. This latter value, the preferentiial sorption, represents the sorpdoq selectivity. 

Expressions for the chemical potentials are given by Floiy-Huggins thomodynamics [11] (see chapter HI). When VjA j 2 3 1 2  

This equation, which gives the composition of the liquid mixture inside the membrane, can be solved numerically when the interaction parameters and volume fraction of the polymer are known. 

However, Flory-Huggins interaction parameters for these systems are generally concentration-dependent and this leads to a much more complex expression which also contains the partial derivatives of the interaction parameters relative to concentration. For the sake of simplicity we will foUow the approach given in eq. V -134. When the sorption selectivity a is defined as 

If only entropy effects are considered the component with the smaller molar volume will be sorbed preferentially. Indeed, this factor m es a considerable contribution towards the preferential sorption of water in many systems. The effect increases with increasing polymer concentration and reaches maximum value when 0, = 1. Table V8 lists some 

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The low solubility of gases in po) Tneric materials (at T < Tg) can be described by Henry s law. The much higher solubility of liquids implies that Henry- s law is no longer obeyed, and the Flory-Huggins theory is commonly used to provide an adequate description of the solubility of liquid mixtures and pure liquids into a polymeric material (see also chapter V). 

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