1. Rheological study of a simulated polymeric gel: shear banding
J. Billen, J. Stegen+, M. Wilson, A. Rabinovitch°, A.R.C. Baljon
+ Eindhoven University of Technology (The Netherlands)
° Ben Gurion University of the Negev (Be’er Sheva, Israel)
Funded by:

2. Polymers Long-chain molecules of high molecular weight polyethylene
[Introduction to Physical
Polymer Science,
L. Sperling (2006)]

3. Motivation of research
Polymer science
Polymer chemistry
(synthesis)
Polymer physics
*natural: starch, cotton, wool, proteins
*Nylon, bakelite
*length of chain: polyethylene: gas-liquid-medium viscosity-crystalline-plastic-fibers
*focus on materials and their properties, only later academic
Polymer rheology

4. Introduction: polymeric gels

5. Polymeric gels
Reversible junctions between endgroups (telechelic polymers)
Concentration
Differnet chemistry endgroups
Micelle transition
Temperature
Sol
Gel

6. Polymeric gels Examples Importance:
PEO (polyethylene glycol) chains terminated by
hydrophobic moieties
Poly-(N-isopropylacrylamide) (PNIPAM)
Importance:
laxatives, skin creams, tooth paste, paintball fill, preservative for objects salvaged from underwater, eye drops, print heads, spandex, foam cushions,…
cytoskeleton

7. Visco-elastic properties
Viscosity
Shear rate
[J.Sprakel et al.,
Soft Matter (2009)]

8. Hybrid MD/MC simulation of a polymeric gel

9. Molecular dynamics simulation
ITERATE
Give initial positions, choose short time Dt
Get forces and acceleration a=F/m
Move atoms
Move time t = t + Dt

10. Bead-spring model U [e] Distance [s]
[K. Kremer and G. S. Krest.
J. Chem. Phys 1990]
Distance [s]
U [e]
Attraction beads in chain
Repulsion all beads
LJ pure repulsive
Temperature control through coupling with heat bath 1s

11. Associating polymer Ubond Unobond U [e] Distance [s]
[A. Baljon et al., J. Chem.
Phys., ]
Junctions between end groups : FENE + Association energy
Dynamics …
Ubond
Unobond
U [e]
Distance [s]
Uassoc negative

12. Dynamics of associating polymer (I)
Monte Carlo: attempt to form junction
Distance [s]
Uassoc
D U [e]
P<1
possible
form
P=1 ?

13. Dynamics of associating polymer (II)
Monte Carlo: attempt to break junction
Distance [s]
-D U [e]
Uassoc
P=1
break
P<1
possible break ?

14. Simulation details 1000 polymeric chains, 8 beads/chain
Units: s (length), e (energy&temperature), m (mass), t=s(m/e)1/2 (time);
Box size: (23.5 x 20.5 x 27.4) s3 with periodic boundary conditions

15. Simulated polymeric gel
only
endgroups
shown

16. Shearing the system Some chains grafted to wall;
move wall with constant shear rate
moving wall
fixed wall

17. Shear banding in polymeric gel

18. Shear-Banding in Associating Polymers
PEO in Taylor-Couette system
Plateau in stress-shear curve
two shear bands
shear rate
stress
velocity
distance
fixed wall
moving wall
[J.Sprakel et al.,
Phys Rev. E 79, (2009)]

19. Shear-banding in viscoelastic fluids
Interface instabilities in worm-like micelles
time
[Lerouge et al.,PRL 96, (2006).]

20. Stress under constant shear30
distance from wall [s]
All results T=0.35 e (< micelle transition T=0.5 e)
stress yield peak
plateau

21. Velocity profiles After yield peak: 2 shear bands Before yield peak:30
distance from wall [s]
After yield peak:
2 shear bands
Before yield peak:
homogeneous

22. Velocity profile over time
Fluctuations of interface
moving
wall
distance from wall [s]
velocity [s/t]
fixed
wall
time [t]

23. Chain Orientation
Qxx=1 Qzz=-0.5
Shear direction x z y
rij

24. Chain orientation
Effects more outspoken in high shear band

25. Aggregate sizes Sheared: more smaller and larger aggregates
High shear band: largest aggregates as likely
size=4

26. Conclusions MD/MC simulation reproduces experiments
Plateau in shear-stress curve
Shear banding observed
Temporal fluctuations in velocity profile
Microscopic differences between sheared/ unsheared system
Chain orientation
Aggregate size distribution
Small differences between shear bands
Current work: local stresses, positional order, secondary flow, network structure

27. Equation of Motion
K. Kremer and G. S. Grest. Dynamics of entangled linear polymer melts: A
molecular-dynamics simulation. Journal of Chemical Physics, 92:5057, 1990.
Interaction energy
Friction constant;
Heat bath coupling – all complicated interactions
Gaussian white noise
<Wi2>=6 kB T (fluctuation dissipation theorem)

28. Predictor-corrector algorithm
1)Predictor: Taylor: estimate at t+dt
4) Corrector step:
2) From calculate forces and
acceleration at t+dt
3) Estimate size of error in prediction step:
Dt=0.005 t

29. Polymeric gels Associating: reversible junctions between endgroups Gel
Concentration
Sol
Gel
Temperature

30. Simulation details 1000 polymeric chains, 8 beads/chain
Units: s (length), e (energy&temperature), m (mass), t=s(m/e)1/2 (time);
Box size: (23.5 x 20.5 x 27.4) s3 with periodic boundary conditions
Concentration = 0.6/s3 (in overlap regime)
Radius of gyration:
Bond life time > 1 / shear rate