Viscoelasticity of Entangled Rings with D. Vlassopoulos M. Kapnistos & M. Lang Outline Introduction: Viscoelasticity of Polymers Dynamics of Entangled Rings Blends of Rings and Linear Polymers Conclusions and Open Questions

Viscoelasticity of Polymers Unentangled polymers – self-similar dynamics G(t) = G0 (t/t0)-a exp(-t/trelax) Rouse a=1/2 Zimm a=1/(3n) Entangled polymers – plateau modulus Ge Linear chains - reptation Entangled stars – arm retraction “logarithmic” plateau What is the viscoelasticity of entangled rings?

Stress Relaxation Function of Entangled Rings is Similar to entangled linear chains with a plateau modulus (double-fold) J. Klein ‘86 Similar to entangled branched polymers with a logarithmic plateau Similar to unentangled polymers with a power law relaxation function G(t) = G0 (t/t0)-a exp(-t/trelax) 4. All of the above 5. None of the above

Dynamics of Entangled Rings B B A A B Effective friction coefficient of a monomer motion along AB is higher by the factor g/lAB ≈ (g/Ne)1/2 Relaxation time Self-similar stress relaxation S. Obukhov, MR, T. Duke, PRL 73, 1263, 1994

Stress Relaxation Functions of Entangled Rings melts of PS rings 160KDa 200KDa Tref = 170oC Kapnistos & Vlassopoulos

Dynamic Moduli of Linear and Rings 160kg/mol – PS rings 200kg/mol – PS rings 160kg/mol – PS linear 200kg/mol – PS linear entanglement plateau in linear melts no plateau in melts of entangled rings Kapnistos & Vlassopoulos Tref = 170oC

Mixtures of 200KDa Rings with 200KDa Linear PS plateau appears in mixtures of linear chains with rings Kapnistos & Vlassopoulos Tref = 170oC

Relaxation Times of Mixtures of 200KDa Rings with 200KDa Linear PS Melts 10 8 t (s) 6 4 melt of linear chains 2 melt of rings 0.75 0.8 0.85 0.9 0.95 1.0 volume fraction of rings Mixtures have longer relaxation times than pure components.

Conclusions Open Questions Self-similar dynamics of entangled rings leads to a power law stress relaxation function without a plateau. 2. Entanglement plateau is recovered in mixtures of rings with linear chains. Mixtures of rings with linear chains have longer relaxation times than pure components. Open Questions At what volume fractions of linear chains does the rubbery plateau disappear?

Mixtures of 160KDa Rings with 3% of 160KDa Linear PS Tref = 170oC Kapnistos & Vlassopoulos

Mixtures of 160KDa Rings with 0.8% of 160KDa Linear PS Tref = 170oC Kapnistos & Vlassopoulos

Mixtures of 200KDa Rings with 0.07% of 200KDa Linear PS Tref = 170oC Kapnistos & Vlassopoulos

Acknowledgements Collaborations D. Vlassopoulos M. Kapnistos M. Lang Financial Support National Science Foundation NASA URETI Bio-Inspired Materials