# Viscosity of ring polymer melts

We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts ?0,linear to their ring counterparts ?0,ring at isofrictional conditions is discussed as a function of the number of entanglements Z. In the unentangled regime ?0,linear/?0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation ?0,linear/?0,ring = 2. In the entanglement regime, the Z-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 \textless Z \textless 20, ?0,linear/?0,ring ? Z1.2±0.3, is weaker than the scaling prediction (?0,linear/?0,ring ? Z1.6±0.3) and the simulations (?0,linear/?0,ring ? Z2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem.\$\$nWe have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts ?0,linear to their ring counterparts ?0,ring at isofrictional conditions is discussed as a function of the number of entanglements Z. In the unentangled regime ?0,linear/?0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation ?0,linear/?0,ring = 2. In the entanglement regime, the Z-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 \textless Z \textless 20, ?0,linear/?0,ring ? Z1.2±0.3, is weaker than the scaling prediction (?0,linear/?0,ring ? Z1.6±0.3) and the simulations (?0,linear/?0,ring ? Z2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem.

### Cited Authors

• Pasquino, R; Vasilakopoulos, TC; Jeong, YC; Lee, H; Rogers, S; Sakellariou, G; Allgaier, J; Takano, A; Brás, AR; Chang, T; Gooßen, S; Pyckhout-Hintzen, W; Wischnewski, A; Hadjichristidis, N; Richter, D; Rubinstein, M; Vlassopoulos, D

• 2013

• 2161-1653

### Digital Object Identifier (DOI)

• 10.1021/mz400344e