Shear and extensional properties of three-arm polystyrene solutions

Following the impressive advances in understanding the rheology of linear p olymers using the basic Doi-Edwards model of reptation and its variants, rh eologists are turning their attention to branched polymers. This is primari ly motivated by a desire to understand the connection between chain topolog y and rheology. We examine the behavior of star polymers in shear and exten sional flows. We use this study to illustrate the dramatic effect that the branch point has on both shear and extension. Data on steady and oscillator y shear and step strain shear are presented and analyzed using the Milner-M cLeish model. Excellent agreement, using a consistent parameter set, is obt ained between this theory and experiments. The filament-stretching rheomete r is used to obtain the extensional viscosity of these solutions, The stead y-state extensional viscosity shows strain rate softening at moderate strai n rates and strain rate hardening at high strain rates. At low Weissenberg numbers (based on the longest relaxation time), the steady extensional stre ss depends on the number of chain entanglements. At the other extreme, at h igh Weissenberg number (based on the Rouse time), the steady-state stress d epends only on the Weissenberg number. Qualitative similarities and some di fferences with linear polymers are noticed. The differences appear to be re lated to the different time constants for the longest relaxation times in t hese systems.