Chain Dimensions in Dilute Polymer Solutions: A Light-Scattering and Viscometric Study of Multiarmed Polyisoprene Stars in Good and θ Solvents

The dilute solution properties of long-arm polyisoprene stars with branch point functionality franging from 3 to 56 have been investigated both in good solvents (cyclohexane and toluene) and under θ conditions (1,4-dioxane). The intrinsic viscosity[η],Huggins coefficient k_H, second virial coefficient A₂, diffusion coefficient D₀, and radius of gyration R_Gwere measured and compared in terms of the equivalent radii. A smooth evolution of properties with increasing fwas found, leading eventually to what we have termed a fuzzy-sphere behavior at high fThus, equilibrium properties such as A₂andrg moveinto a spherelike relationship to one another at large f The dynamical properties, [77] and D₀, do likewise, and approaches k_Hthe hard-sphere value. However, the radii deduced from dynamical properties are consistently smaller than those from equilibrium properties, suggesting the analogy between polymeric stars of larger functionality and spheres with a hydrodynamically penetrable surface layer. The dependence of size on functionality is different in good and θ solvents, but the same fuzzy-sphere relationship emerges when f is large. The literature data for polystyrene stars follow the same pattern, being for the most part in quantitative accord with the polyisoprene data. Some unresolved descrepancies in this simple interpretation are pointed out. Good agreement was found between these results and theoretical predictions based on scaling, Monte Carlo calculations, and simulation. Analytical expressions were less satisfactory, especially at high functionality.