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
