Semidilute solution osmotic compressibility

This equation holds for theta, good, and athermal solvents. Hence, osmotic pressure or osmotic compressibility measurements provide a con-venient means ot measuring the correlation length in semidilute solutions. 

It is well known that the osmotic pressure of a solution of one polymer can be scaled with a single dimensionless variable "S" which is proportional to polymer concentration at least for the case of mixtures with good solvents in the dilute to semidilute regime (12, 17). This implies that the osmotic compressibility factor (ti/cRT) can be expressed as some function of "S" only as shown in Equation 11. 

The conformational stmcture of stars in regimes II, IVg of a semidilute solution is mirrored hy the corresponding thermodynamic consequences. There is a discontinuity in the osmotic compressibility c" (dc/dn)7-near Indeed, in dilute-solution... 

Concentration effects in solutions of randomly branched polymers are similar to those in solutions of other types of branched macromolecules but exhibit some specific features. Similar to the case of star-branched polymers, in semidilute solutions of fairly monodisperse branched polymers beyond the overlap concentration cj ja,jched- / branched, individual macromolecules contract without significant interpenetration. Appearance of a sharp corrdation peak in the stmrture fartor and vanishing osmotic compressibility in the concentration range dose to are the concomitant effects. 

Finally, analytic predictions for the osmotic pressure of polymers in good and theta solvents can be derived based on the Gaussian thread model, PRISM theory, and the compressibility route. The qualitative form of the prediction for large N is " pP °c (po- ), which scales as p for theta solvents and p " for good solvents. Remarkably, these power laws are in complete agreement with the predictions of scaling and field-theoretic approaches and also agree with experimental measurements in semidilute polymer solutions. ""... 

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