Shear banding in a simulated telechelic polymeric gel J. Billen, J. Stegen +, M. Wilson, A. Rabinovitch°, A.R.C. Baljon San Diego State University + Eindhoven University of Technology (The Netherlands) ° Ben Gurion University of the Negev (Be’er Sheva, Israel) Funded by:

Temperature Sol Gel Associating polymers Reversible junctions between endgroups Concentration

Shear-Banding in Associating Polymers Plateau in stress-shear curve two shear bands fixed wall moving wall distance shear rate stress velocity Polyethylene Oxide (with hydrophobic groups at chain ends) under shear [J.Sprakel et al., Phys Rev. E 79, (2009)] distance from wall PEO

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

Hybrid MD / MC simulation (I) Molecular dynamics simulation: Bead-spring model 1000 polymeric chains, 8 beads/chain Junctions between end groups possible Lennard-Jones interaction between beads FENE: between beads in chain and junctions Temperature control (coupled to heat bath) [A. Baljon et al., J. Chem. Phys., ]

Hybrid MD / MC simulation (II) Monte Carlo: junctions formed / destroyed with probability: Some chains grafted to wall; move wall with constant shear rate fixed wall moving wall

Stress under constant shear All results T=0.35 (< micelle transition T=0.5 ) stress yield peak plateau

Before yield peak: homogeneous After yield peak: 2 shear bands Velocity profiles distance from wall  0 30

Velocity profile over time Fluctuations of interface fixed wall moving wall velocity  time  distance from wall 

Chain Orientation Shear direction x z y r ij Q xx =1 Q zz =-0.5

Chain orientation Effects more outspoken in high shear band

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

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 Conclusions

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, Interaction energy Friction constant Heat bath coupling – all complicated interactions Gaussian white noise