Experimental and theoretical studies of scaling of sizes and intrinsic viscosity of hyperbranched chains in good solvents

Using a set of hyperbranched polystyrenes with different overall molar masses but a uniform subchain length or a similar overall molar mass but different subchain lengths, we studied their sizes and hydrodynamic behaviors in toluene (a good solvent) at T = 25 °C by combining experimental (laser light scattering (LLS) and viscometry) and theoretical methods based on a partially permeable sphere model. Our results show that both the average radii of gyration ( ) and hydrodynamic radius ( ) are scaled to the weight-average molar mass (M(w)) as ~ ~ M(w)(γ)M(w,s) (φ), with γ = 0.47 ± 0.01 and φ = 0.10 ± 0.01; and their intrinsic viscosity ([η]) quantitatively follow the Mark-Houwink-Sakurada (MHS) equation as [η] = K(η)M(w)(ν)M(w,s)(μ) with K(η) = 2.26 × 10(-5), ν = 0.39 ± 0.01, and μ = 0.31 ± 0.01, revealing that these model chains with long subchains are indeed fractal objects. Further, our theoretical and experimental results broadly agree with each other besides a slight deviation from the MHS equation for short subchains, similar to dendrimers, presumably due to the multi-body hydrodynamic interaction. Moreover, we also find that the average viscometric radius ( ) determined from intrinsic viscosity is slightly smaller than measured in dynamic LLS and their ratio ( / ) roughly remains 0.95 ± 0.05, reflecting that linear polymer chains are more draining with a smaller than their hyperbranched counterparts for a given intrinsic viscosity. Our current study of the "defect-free" hyperbranched polymer chains offers a standard model for further theoretical investigation of hydrodynamic behaviors of hyperbranched polymers and other complicated architectures, in a remaining unexploited research field of polymer science.