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Rheological study of a simulated polymeric gel: shear banding

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:. Polymers.

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Rheological study of a simulated polymeric gel: shear banding

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  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 Polymer rheology

  4. Introduction: polymeric gels

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

  6. Polymeric gels • Examples • 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. Attraction beads in chain Repulsion all beads U [e] Distance [s] Bead-spring model [K. Kremer and G. S. Krest. J. Chem. Phys 1990] 1s • Temperature control through coupling with heat bath

  11. Ubond U [e] Unobond Distance [s] Associating polymer [A. Baljon et al., J. Chem. Phys., 044907 2007] • Junctions between end groups : FENE + Association energy • Dynamics …

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

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

  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 T=1.0 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. stress shear rate Shear-Banding in Associating Polymers Plateau in stress-shear curve • PEO in Taylor-Couette system two shear bands velocity distance moving wall fixed wall [J.Sprakel et al., Phys Rev. E 79, 056306 (2009)]

  19. Shear-banding in viscoelastic fluids • Interface instabilities in worm-like micelles time [Lerouge et al.,PRL 96,088301 (2006).]

  20. Stress under constant shear 30 distance from wall [s] All results T=0.35 e (< micelle transition T=0.5 e) 0 stress yield peak plateau

  21. Velocity profiles 30 distance from wall [s] 0 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. Shear direction z y x rij Chain Orientation Qxx=1 Qzz=-0.5

  24. Chain orientation • Effects more outspoken in high shear band

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

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

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

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