Transformations at constant chemical potentials preferential adsorption

8 Transformations at constant chemical potentials preferential adsorption 

When a solution contains more than one solvent, these solvents, do not, in general, play the same role. In particular, diluting a solution by adding a small quantity of solvent produces a variation of Gibbs free energy which depends on the nature of the added solvent. 

the polymer chain has the remarkable property that its presence in the solution is able to modify the distribution of the various solvent molecules. 

The study of the osmotic equilibrium between a polymer solution in two solvents and a mixture of these two solvents is quite instructive. In particular, we shall describe a limiting case in which we shall be able to define a coefficient characterizing the action of the polymers on the solvent distribution. First, let us attribute the index 0 to the main solvent, the index 1 to the second solvent, and the index 2 to the polymer. We have / = 1, m = 2. The numbers of molecules are N s, (jit = 0,1,2) in cell I of Fig. 5.1 and (,r/ = 0,1) in cell II. The chemical potentials of the solvents are, respectively, 

A study of the osmotic equilibrium is difficult to make in this case, but the problem simplifies in the following useful3 limit. The pressures P1 and P remaining fixed, the number of molecules in cell II without polymers becomes infinite 

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