Stress relaxation of critically fractionated entangled polybutadiene ring melts

We present linear viscoelastic data with anionically synthesized and critically fractionated polybutadiene (rich in vinyl content) rings having about Z = 22 entanglements. These rings are experimentally as pure as currently possible. They exhibit a power-law stress relaxation G(t) that is well-described by the state-of-the-art fractal loopy globule (FLG) model (power-law exponent of − 3/7). Previously reported data with polystyrene rings, prepared by anionic synthesis in dilute solution and purified by liquid chromatography at the critical condition, having Z = 14 entanglements, showed a power-law G(t) as well. Recent developments with different synthetic methods yielding not so well-characterized rings with a very large number of entanglements (up to 300), suggest that a rubbery plateau emerges in the linear viscoelastic response for Z > 15. Our work confirms the power-law G(t) with the FLG exponent with another chemistry and contributes to the current discussion about different regimes of rheological behavior, indicating that a possible deviation from the power-law FLG type of behavior toward rubbery plateau may occur for Z > 22. To fully capture the experimental G(t) data, the FLG model is complemented by two additional relaxation modes which are attributed to ring-ring (RR) and ring-linear (RL) threading, in accordance with recent reports in the literature. The faster RR mode likely reflects a new mechanism of stress relaxation not described by FLG, and the slower RL mode is attributed to synthetic and material handling imperfections (for example, due to thermal treatment). However, it does not change the punchline of the work: no rubbery plateau for entangled rings with up to 22 entanglements. Stress relaxation modulus for entangled ring polybutadiene (exhibiting power-law decay) and its linear precursor (exhibiting rubbery plateau), along with fits to the data: tube model for linear chains, and fractal loopy globule (FLG) with slow modes (RR and Tsalikis et al.) for the ring.