Semidilute solution theta condition

The first theories that implemented a proper balance of intramolecular interactions and conformational elasticity of the branches were developed by Daoud and Cotton [21] and by Zhulina and Birshtein [22-24]. These theories use scaling concepts (the blob model), originally developed by de Gennes and Alexander to describe the structure of semidilute polymer solutions [64] and planar polymer brushes [65, 66]. Here, the monomer-monomer interactions were incorporated on the level of binary or ternary contacts (corresponding to good and theta-solvent conditions, respectively), and both dilute and semidilute solutions of star polymers were considered. Depending on the solvent quality and the intrinsic stiffness of the arms, the branches of a star could be locally swollen, or exhibit Gaussian statistics [22-24]. 

Theta Condition We can apply all of the relationships that we obtained in the preceding section and the present section to semidilute solutions of a polymer in the theta condition by setting v = 1/2. We list the relationships in Table 4.1 together with the results for the good solvent. 

Problem 4.10 Discuss the partitioning of polymer chains in semidilute solution in the theta condition with a pore of diameter d. Can the partitioning of the semidilute solution be treated as the partitioning of independent blobs ... 

This equation demonstrates that the partitioning of the semidilute solution is equivalent to the partitioning of independent blobs in the theta condition. Compare the last equation with Eq. 2.136. 

Fig. 7.38. Semidilute solutions of polystyrene in cyclohexane. The condition ( ) = Rg Ts)/ 3 may be used to locate the theta temperature. (Reproduced with permission from [235]. Copyright 1997 American Physical Society.)...

Fig. 1 Blob model for nonionic polymer stars a single star under good or theta-solvent conditions (a), semidilute star solution (b), single polymer star partially coUapsed in poor solvent (c). r distance from the center of the star...

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