Osmotic pressure and structure of the solution with overlap

3 Osmotic pressure and structure of the solution with overlap 

For long polymer chains in dilute solutions, the osmotic pressure is always very weak, and the reasons for this are as follows. In order to keep the solution dilute when M increases, one must diminish the mass concentration p when p decreases at fixed molecular mass, the pressure decreases finally, when M increases at fixed p, the pressure decreases again. In conclusion, measurements of osmotic pressure are not adapted to the study of the asymptotic state of polymers in dilute solutions. 

On the contrary, the measurement of the osmotic pressure for different overlap ratios provides essential information on the structure of semi-dilute solutions. Data have been available since the time when this technique was first used. However, this approach required a theoretical basis and we have a good theory only since 1975. 

The essential difference between naive theories and theories which account for the critical aspects of the polymer solutions is clearly in the expression of the 

In good solvents, the quantity zCS3/2 oc S2 is much greater than g CXi oc S3v. Hence, for d = 3, the theory which accounts for the chain swelling predicts for given p and S, a much lower pressure than the simple-tree approximation. 

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