Viscoelasticity of Entangled Ringswith D. VlassopoulosM. Kapnistos & M. Lang

OutlineOutline

1. Introduction: Viscoelasticity of Polymers

2. Dynamics of Entangled Rings

3. Blends of Rings and Linear Polymers

4. Conclusions and Open Questions

Viscoelasticity of Polymers

10-2 10-1 100 101 102 103

G'M

/(cR

T)

(

G''

- s)

M/(

cRT

)

10-3

10-2

10-1

100

101

102

Unentangled polymers – self-similar dynamics

G(t) = G0 (t/0)- exp(-t/relax)

Rouse =1/2 Zimm =1/(3)

Entangled polymers – plateau modulus Ge

Linear chains - reptation

repe

tGtG

exp)(

Entangled stars – arm retraction “logarithmic” plateau

What is the viscoelasticity of entangled rings?

Stress Relaxation Function of Entangled Rings is

1. Similar to entangled linear chains with a plateau modulus (double-fold)

J. Klein ‘86

2. Similar to entangled branched polymers with a logarithmic plateau

3. Similar to unentangled polymers with a power law relaxation function

4. All of the above

G(t) = G0 (t/0)- exp(-t/relax)

5. None of the above

A

BA B

Dynamics of Entangled Rings

B

A eAB gNl

Relaxation time

2/5

22/10 /

eee N

ggNgg

2/5

eering N

N

Self-similar stress relaxation ringe

e tt

GtG

/exp5/2

Effective friction coefficient of a monomer motion along AB is higher by the factor g/lAB ≈ (g/Ne)1/2

S. Obukhov, MR, T. Duke, PRL 73, 1263, 1994

Stress Relaxation Functions of Entangled Rings

ringe

e tt

GtG

/exp5/2

160KDamelts of PS rings

200KDa

Kapnistos & Vlassopoulos

Tref = 170oC

Dynamic Moduli of Linear and Rings

160kg/mol – PS rings

200kg/mol – PS rings

160kg/mol – PS linear

200kg/mol – PS linear

Kapnistos & VlassopoulosTref = 170oC

entanglement plateauin linear melts

no plateau in melts of entangled rings

Mixtures of 200KDa Rings with 200KDa Linear PS

plateau appears in mixtures of linear chains with rings

Kapnistos & VlassopoulosTref = 170oC

Relaxation Times of Mixtures of 200KDa Rings with 200KDa Linear PS Melts

2

4

6

8

10

(s)

00 0.75 0.8 0.85 0.950.9 1.0

volume fraction of rings

melt of linear chains melt of rings

Mixtures have longer relaxation times than pure components.

Conclusions1. Self-similar dynamics of entangled rings

leads to a power law stress relaxation function without a plateau.

Open Questions

2. Entanglement plateau is recovered in mixtures of rings with linear chains.

3. 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 PS

Tref = 170oC

Kapnistos & Vlassopoulos

Mixtures of 160KDa Rings with 0.8% of 160KDa Linear PS

Kapnistos & Vlassopoulos

Tref = 170oC

Mixtures of 200KDa Rings with 0.07% of 200KDa Linear PS

Tref = 170oC

Kapnistos & Vlassopoulos

Acknowledgements

Financial SupportNational Science Foundation

NASA URETI Bio-Inspired Materials

D. VlassopoulosM. Kapnistos

M. Lang

Collaborations