Linear Rheology of Entangled Six-Arm and Eight-Arm Polybutadienes

Relaxation dynamics of various model entangled six-arm (A 3 - A -A 3 ) and eight-arm (A 3 - A -A 2 - A -A 3 ) polybutadiene melts are investigated using low-amplitude oscillatory shear and time-dependent step strain measurements. The frequency (time) and temperature range covered in these experiments are sufficiently broad to characterize the entire liquid-state relaxation spectrum of the materials. Several new findings about multiarm polymer dynamics are reported. First, the mean segmental relaxation time of multiarm polymers is a function of crossbar ( A ) molecular weight and polymer architecture. Second, for polymers with fixed arm (A) molecular weight, but variable crossbar molecular weight, terminal relaxation time (λ) and limiting shear viscosity (η 0 ) scale quite strongly with crossbar molecular weight M b (λ ∼ M b ∼6.8-7, η 0 ∼ M b ∼8 ). When the crossbar tube length is renormalized by dilution of relaxed arms and the relaxation time and viscosity are rescaled to remove the inherent M b dependence of segmental scale properties, these scaling exponents become closer to values expected for crossbar reptation in a dilated tube. Finally, relaxation dynamics of eight-arm A 3 - A -A 2 - A -A 3 polybutadienes are found to be quite different from those of six-arm A 3 - A -A 3 polymers with comparable arm molecular weight. Specifically, the slowest relaxation mode in well-entangled eight-arm polymers appears to be dominated by Rouse-like fluctuation effects, which blur the transition from high-frequency arm to terminal backbone relaxation.