# viscoelasticity of entangled rings with d. vlassopoulos m. kapnistos & m. lang outline...

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• Viscoelasticity of Entangled Ringswith D. VlassopoulosM. Kapnistos & M. LangOutlineIntroduction: Viscoelasticity of Polymers

Dynamics of Entangled Rings

Blends of Rings and Linear Polymers

Conclusions and Open Questions

• Viscoelasticity of PolymersUnentangled polymers self-similar dynamicsG(t) = G0 (t/t0)-a exp(-t/trelax)Rouse a=1/2 Zimm a=1/(3n)Entangled polymers plateau modulus GeLinear chains - reptationEntangled stars arm retraction logarithmic plateauWhat is the viscoelasticity of entangled rings?

• Stress Relaxation Function of Entangled Rings isSimilar to entangled linear chains with a plateau modulus (double-fold)J. Klein 86Similar to entangled branched polymers with a logarithmic plateauSimilar to unentangled polymers with a power law relaxation function4. All of the above G(t) = G0 (t/t0)-a exp(-t/trelax)5. None of the above

• Dynamics of Entangled RingsRelaxation timeEffective friction coefficient of a monomer motion along AB is higher by the factor g/lAB (g/Ne)1/2S. Obukhov, MR, T. Duke, PRL 73, 1263, 1994

• Stress Relaxation Functions of Entangled Rings160KDamelts of PS rings200KDaKapnistos & VlassopoulosTref = 170oC

• Dynamic Moduli of Linear and RingsKapnistos & VlassopoulosTref = 170oCentanglement plateauin linear meltsno plateau in melts of entangled rings

• Mixtures of 200KDa Rings with 200KDa Linear PSplateau appears in mixtures of linear chains with ringsKapnistos & VlassopoulosTref = 170oC

• Relaxation Times of Mixtures of 200KDa Rings with 200KDa Linear PS Melts246810t (s)000.750.80.850.950.91.0volume fraction of ringsmelt of linear chainsmelt of ringsMixtures have longer relaxation times than pure components.

• ConclusionsSelf-similar dynamics of entangled rings leads to a power law stress relaxation function without a plateau.Open Questions2. Entanglement plateau is recovered in mixtures of rings with linear chains.Mixtures of rings with linear chains have longer relaxation times than pure components.At what volume fractions of linear chains does the rubbery plateau disappear?

• Mixtures of 160KDa Rings with 3% of 160KDa Linear PSKapnistos & Vlassopoulos

• Mixtures of 160KDa Rings with 0.8% of 160KDa Linear PSKapnistos & VlassopoulosTref = 170oC

• Mixtures of 200KDa Rings with 0.07% of 200KDa Linear PSKapnistos & Vlassopoulos

• AcknowledgementsFinancial SupportNational Science FoundationNASA URETI Bio-Inspired MaterialsD. VlassopoulosM. KapnistosM. LangCollaborations