ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
Renormalization group methods are developed for describing the osmotic pressure of semidilute polymers in the theta region, where large binary polymer interactions may become screened. The analysis requires a combination of renormalization group methods as they are applied, on the one hand, to semidilute polymer solutions in marginal-to-good solvents, and, on the other hand, to single polymers in theta solutions. Ternary interactions are shown to contribute to the screening of binary interactions in these semidilute theta solutions, and an effective binary interaction is introduced that is defined to vanish at the theta point along with the second virial coefficient, leaving residual ternary interactions. Screening of the effective binary interactions is described through an Edwards decoupling scheme, and perturbation expansions are developed in the presumed small screened effective binary and the residual ternary interactions. Formal divergences in the osmotic pressure are absorbed into phenomenologically defined second and third virial coefficients. The renormalized osmotic pressure, which is written solely in terms of direct observables, is found to be a simple generalization of the results obtained for semidilute polymer solutions in good-to-marginal solvents. It is also found to agree with experimental results on semidilute polymer solutions that cover the temperature domain between theta and good solvents. The present work is carried to lowest order in both the effective binary interaction and the residual ternary interaction, but the general method of treating higher order corrections is outlined. A recent result for the special limit of semidilute solutions at the theta point with three-body fixed point interactions is recovered as a limit of our more general formulation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.452322
