1. Entanglements and stress correlations in coarsegrained molecular dynamics
Alexei E. Likhtman,
Sathish K. Sukumuran,
Jorge Ramirez
Department of Applied Mathematics,
University of Leeds, Leeds LS2 9JT, UK

2. Hierarchical modelling in polymer dynamics
Constitutive equations
Tube theories
Single chain models
Coarse-grained many-chains models
Atomistic simulations
> Quantum mechanics simulations
Traditional rheology CR
Tube
Model?
Traditional physics
The weakest
link
Kremer-Grest MD,
Padding-Briels Twentanglemets,
NAPLES
Well established coarse-
graining procedures,
force-fields,
commercial packages

3. The missing link Many chains system One chain model The ultimate goal:
Stochastic equation of motion
for the chain in
self-consistent entanglement field
Many chains system
+ self-consistent field
One chain model

4. Is there a tube model?
Best definition of the tube model: one-dimensional Rouse chain projected onto three-dimensional random walk tube.
Open questions:
Can I have expression for the tube field, please?
How to “measure” tube in MD?
Is the tube semiflexible?
Diameter = persistence length?
Branch point motion
How does the contour length changes with deformation?
Tube parameters for different polymers?
Tube parameters for different concentrations?

5. Rubinstein-Panyukov network model
Rubinstein and Panyukov, Macromolecules 2002, 6670

6. Construction of the model

7. Shanbhag, Larson, Takimoto, Doi 2001
Constraint release
Hua and Schieber 1998
Shanbhag, Larson, Takimoto, Doi 2001

8. A.E.Likhtman, Macromolecules 2005

9. Relaxation of dilute long chains (36K) in a short matrix: constraint release
Mwmat
labeled
Rouse
M.Zamponi et al, PRL 2006

10. Molecular Dynamics -- Kremer-Grest
Polymers – Bead-FENE spring chains
k = 30/2
R0=1.5
With excluded volume – Purely repulsive Lennard-Jones interaction between beads
Density,  = 0.85
Friction coefficent,  = 0.5
Time step, dt = 0.012
Temperature, T = /k
K.Kremer, G. S. Grest
JCP (1990)

11. g1(t) from MD for N=100,350 1 d
0.5
1/4
0.5 R e

12. g1(i,t)/t0.5 from MD for N=350
ends
g1(i,t)/t0.5
middle t

13. G(t) from MD for N=50,100,200,350 (Ne~50)

14. G(t) from MD for N=50,100,200,350 (Ne~70)

15. g1(i,t) -- MD vs sliplinks mapping 1:1 (N=200)
Lines - MD
Points - slip-links d 1 1 0
g1(i,t)/t0.5 e t

16. G(t) -- MD vs sliplinks mapping 1:1 (N=200)0 1 5
G(t)*t1/2
Lines - MD
Points - slip-links e t

17. Questions for discussion
Binary nature of entanglements?
Can one propose an experiment which contradicts this?
Non-linear flows:
do entanglements appear in the middle of the chain?
Is there an instability in monodisperse linear polymers?