1. Simulations of associating polymers under shear J. Billen, M. Wilson, A.R.C. Baljon San Diego State University Funded by:

2. Outline Motivation: Shear banding Molecular dynamics/Monte Carlo simulation Sheared associating polymer networks Shear banding Topological changes Temperature SolGel

3. Shear Banding in Experiments on Associating Polymers Plateau in stress-shear curvetwo shear bands fixed wall moving wall distance shear rate stress velocity Material used: Polyethylene Oxide (with octadecyl alkane (hydrophobic) groups at chain ends) [J.Sprakel et al., Phys Rev. E 79, 056306 (2009)]

4. Molecular Dynamics / Monte Carlo Simulation

5. Hybrid MD / MC simulation (I) [A. Baljon et al., J. Chem. Phys., 044907 2007] Molecular dynamics simulation: Bead-spring model (Kremer-Grest) interactions within chain Monte Carlo: Junctions between end groups Lennard-Jones interaction between all beads FENE: between beads in chain and junctions Temperature control (coupled to heat bath) Units:  (length),  (energy),  =  (m/  ) 1/2 (time) = 2 1/6

6. Hybrid MD / MC simulation (II) Monte Carlo: junctions formed / destroyed with probability: U assoc = -22 

7. Simulation details 1000 polymeric chains, 8 beads/chain Box size: (23.5 x 20.5 x 27.9)   with periodic boundary conditions in x/y direction Concentration = 0.6 beads /   ( in overlap regime ) Radius of gyration:

8. Previous results: unsheared system

9. Micelle transition: T=0.5 Percolation transition T=1.5 Numerical study of associating polymers d 2  dT 2 =0 Order parameter: Number of junctions  Baljon et al.; J Chem. Phys. 126, 044907 2007 Temperature # of junctions 

10. Topological changes at the gel transition Billen et al. Europhys. Lett. 87 (2009) 68003. T=0.5 Micelle transition Node Link T=1.5 Percolation transition Temperature

11. Fresh Results

12. Simulation under constant shear Fixed wall shear rate: = v/h measure: stress  temperature below micelle transition Shear velocity: v h Fixed wall h Moving wall 5% chains grafted to wall

13. Shear stress Stress peak

14. Stress – shear plateau plateau

15. Velocity profile 2 bands = 3.6 x10 -4  

16. unshearedlow shear rate band high shear rate band end-to-end distance 2 [  2 ] 14.6423.422.6 lifetime [k  ]  4435 atom concentration [atoms/  3 ] 0.6170.6210.609 aggregate density [#agg/  3 ] 0.00860.00790.0089 average aggregate size17.919.617.8 Microstructural differences

17. Size distribution

18. Fixed wall Moving wall = 2.15 x10 -2  

19. Topological changes under shear Single bridge Double bridge Link Loop

20. Ratio loops / links / bridges drop # links

21. Distribution of multiple bridges Stronger links

22. Average size of bridged aggregates

23. Probability that a chain is part of a strong (m>6) link stronger links close to moving wall = 2.15 x10 -2  

24. MD / MC simulation associating polymers Simulation under shear –Plateau in stress-shear curve –Shear banding observed within plateau –Shear-induced aggregation –Gradual differences between both bands Topological changes under shear –No change in loop/bridge ratio –Fewer but stronger links, especially close to moving wall Conclusions

25. Bead-spring model Temperature control through coupling with heat bath [K. Kremer and G. S. Krest. J. Chem. Phys 1990] 11 Distance  U  Attraction beads in chain Repulsion all beads

26. Associating polymer Junctions between end groups : FENE + Association energy Dynamics … [A. Baljon et al., J. Chem. Phys., 044907 2007] U bond U nobond U  Distance 

27. Dynamics of associating polymer (I) Monte Carlo: attempt to form junction Distance   U  P<1 possible form P=1 form U assoc

28. Dynamics of associating polymer (II) Monte Carlo: attempt to break junction Distance   U  P=1 break P<1 possible break U assoc