Criteria for Polymer Solubility

A polymer dissolves in a solvent if, at eonstant temperature and pressure, the total Gibbs free energy ean be deereased by the polymer going into solution. Therefore, it is neeessary that the following hold  

A partial molar quantity is the derivative of an extensive quantity M with respect to the number of moles n, of one of the components, keeping the temperature, the pressure, and the number of moles of all the other components fixed. Thus, 

It is easy to show [2] that the mixture property M can be represented in terms of the partial molar quantities as follows  

For an open system at constant temperature and pressure, however, dM = Mi drii 

Let us identify M with the Gibbs free energy G and eonsider the mixing of i moles of pure component 1 with 2 moles of pure component 2. Before mixing, the free energy of both components taken together, Gcomp, is 

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