A computational study of shear banding in reversible associating polymers J. Billen +, J. Stegen *, A.R.C. Baljon + + Department of Physics, San Diego State University, San Diego, CA 92128, USA * Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands Associating polymers (AP) Topological differences due to shearing Polymer chains dissolved in a solution Endgroups have different chemical composition and can aggregate together E.g. water-soluble PEO with hydrophobic sticker at chain ends Reversible network is formed where junctions break and form over time Depending on T sol / gel state Use: wide range of consumer products (skin creams, laxatives, eye drops, print heads, spandex,etc.), representative for biopolymer networks (actin, fibrin, …) Theory / Experiment Abstract A novel hybrid MD/MC simulation technique is employed to study the rheological properties of telechelic polymers. When enough polymer end-groups aggregate together, a reversible network is formed. The polymer chains act as bridges between the aggregates. We study the system in its low temperature gel state where there is a long relaxation time . When the typical time of the applied shear is larger than the relaxation time, the network yields and subsequently flows. Two shear bands are observed in the flow profile, a phenomenon also observed in recent experimental studies. The stress fluctuates erratically over time. These macroscopic observations are correlated with the microstructure. The simulation allows us to investigate differences between the two shear bands, and between the sheared and the unsheared system. Temperature SolGel Hybrid Molecular dynamics / Monte Carlo simulation* Bead-spring model (Kremer-Grest) interactions within chain Junctions between end groups Lennard-Jones interaction between all beads: FENE between all beads in chain and junctions: = 2 1/6 * Baljon et al., J. Chem. Phys., (2007) Attempts to form/destroy junctions with probability depending on old and potential new state made frequently: Application of constant shear: Fixed wall v=0.01  h Fixed wall h Moving wall Shear banding 5% chains grafted shear rate: = v/h measure: stress Simulation Results Plateau in stress vs shear curve Velocity profile: within plateau two bands of different shear co-exist Shear rate  Average stress Fielding, Soft Matter, 1262, (2007). Sprakel et al., Phys. Rev. E, , (2007). Microscopical differences between shear bands unsheared low shear band high shear band Aggregate size distribution un- sheared high shear low shear atom concentration no noticeable difference lifetime [k  ]  3544 aggregate density [#agg/  3 ] average aggregate size end-to-end distance 2 [  2 ] Orientation tensor: Shear direction x z y r ij Single bridge Double bridge Link 3 endgroups Nomenclature Aggregate = …No (ratio links/loops same) but fewer bridges # single/double/triple bridges drops # of strong (>4) bridges increases, these strong bridges link large aggregates sheared unsheared Simulations match experiments average unsheared Transient stress response: yield peak U bond U nobond U  Distance  U  U FENE U LJ Units:  (length),  (energy),  =  (m/  ) 1/2 (time) all results at T=0.35 (below gel transition) Loop Does shear change the ratio loops/links? … Goal: study shear-induced changes in associating polymer through simulations Grant No. DMR Funding Koga et al., Langmuir, 8626 (2009). stress