Semidilute theta solutions

The correlation length is determined by recognizing that only g monomers from a single chain are inside the correlation volume and that these correlation volumes are space-filling. The volume fraction of polymer in 

Concentration dependence of osmotic pressure data for five poly(a methyl styrene)s in the good solvent toluene at 25 °C. (a) Raw data—the data below c for the lowest three molar masses are 

The concentration dependence of the correlation length in semidilute 6 -solutions is stronger than that in good solvent  

This concentration dependence can also be determined by a scaling argument similar to the one used in semidilute good solvent. The correlation length is equal to the ideal chain size Rq at the overlap concentration 

In the semidilute regime, the scaling assumption is that the correlation length decreases as a power law in concentration  

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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...

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]. 

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. ""... 

Dynamical Properties of Semidilute Polymer Solutions at the Theta... 

DYNAMICAL PROPERTIES OF SEMIDILUTE POLYMER SOLUTIONS AT THE THETA TEMPERATURE... 

All the experimental results obtained in the semidilute 0-solutions are consistent with the idea of de Gennes and Brochardthat at the theta temperature, where the second virial coefficient of the osmotic pressure vanishes, the mesh size of the transient gel is not proportional to the correlation length of concentration fluctuations as it is in the case of a good solvent. ... 

The sample was a solution of polystyrene (PS) dissolved in dioctyl phthalate (DOP). This system has a theta temperature of approximately 22°C [183] and has been the subject of most of the studies investigating flow-induced phase transitions in polymer solutions. The particular sample used here had a molecular weight for PS of 2 million, a poly-dispersity of MW/MN = 1.06, and a concentration of 6%. This results in a semidilute... 

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. 

Fig. 2. (a) Schematic phase diagram of a polymer solution, at constant pressure, using temperature T and volume fraction 0 of the polymer as variables. Phase separation into a dilute or semidilute solution (with volume fraction 0e ex) a more concentrated solution (with volume fraction 0 x)occurs for states (T, 0) that fall in the two-phase region underneath the coexistence curve (binodal). The binodal ends in the critical point 0c(AO, TdN), where N is the degree of polymerization of the polymer. For iV - oo the critical point merges with the theta point of the dilute solution, ie, T = 0,0c(iV oo) = 0. For further explanations cf text,... 

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.)...

One of the recent topics in studies of dynamic light scattering is finding the slow mode for polymeric systems. First observation of the slow mode was reported on the semidilute solutions of polystyrene in theta solvent by Adam and Delsanti [1]. Since then, the slow mode has been observed in several solutions in theta or poor solvents where polymer chains tend to associate with each other weakly [2-5]. Besides them, in recent years, the slow relaxation mode was also observed in the thread-like micellar system formed by the cationic surfactant in aqueous solutions [6]. If weak interaction between chains... 

Hre butterfly patterns were observed at various tempera-mres and concentrations and for various solvents such as DOP, tydohexane, and diethyl malonate, which are theta solvents for PS at 35°C, as wdl as dibutyl phthalate and tricresyl phosphate, which are good solvents for PS. The patterns were also observed for semidilute solutions of polyethylene with paraflin as the solvent (athermal solution) and for sheared colloidal srrspensions. They are thus quite general for sheared dynamically asymmetric systems. The butterfly pattern was also formd for PS/PVME mixtures by Mani et and Gerard et and for other polymer mixtures. ... 

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