A computational study of shear banding in reversible associating polymers J. Billen, J. Stegen +, A.R.C. Baljon San Diego State University + Eindhoven University of Technology (The Netherlands) Funded by:

Associating polymers: reversible networks: Outline Molecular dynamics/Monte Carlo simulation Shear banding Shear-induced differences –Shear vs Unshear –High vs Low shear band Temperature SolGel

Hybrid MD / MC simulation (I) [A. Baljon et al., J. Chem. Phys., ] 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

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

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: = 2.69  2

Gel 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, ] Temperature 

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

Experiment: 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 octadecyl alkane (hydrophobic) groups at chain ends) under shear [J.Sprakel et al., Phys Rev. E 79, (2009)]

Theory: Visco-elastic fluid [S. Fielding, Soft Matter 3,1262 (2007)]  Shear banding  relaxation time

Simulation: Constant shear Fixed wall shear rate: = v/h measure: stress  Shear velocity: v h Fixed wall h Moving wall 5% chains grafted to wall

Stress under constant shear All results T=0.35 below gel transition; stress yield peak plateau -4  0 = 

Before yield peak: homogeneous After yield peak: 2 shear bands Velocity profiles -4

Microscopic differences

Endgroup concentration 2.5% larger in high shear band Average # aggregates larger in high shear band than in low shear band Junctions live longer in low shear band Radius of gyration: unsheared High shear band low shear band

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

Aggregate sizes Sheared/Unsheared –Increase of smaller and larger aggregates during shear –Lower preference for average size under shear High / low shear band –Average aggregate size lower in high shear band low shear band high shear band unsheared unsheared19.1 high shear13.0 low shear19.4

Topological differences

Node = 3 endgroups Double bridge Single bridge Link Loop Nomenclature Links can consist of more than 1 bridging molecule

Influence of shear on network structure unsheared sheared unsheared sheared no change # loops/ bridging molecules drop # links unsheared sheared

average unsheared average unsheared Influence of shear on network structure average unsheared

Spatial distribution of bridges High/low shear band: –Dip # links near interface –More multiple bridges in high shear band sheared unsheared

MD / MC simulation associating polymers Shear banding observed in simulations Study of differences –Sheared vs Unsheared Chains orient and R g increases No change in # loops / # bridging molecules Number of links decreases Formation of links with high # bridging molecules –High vs Low shear band More aggregates in high shear band Larger endgroup concentration in high shear band Smaller aggregate size in high shear band More links with high # bridging molecules Conclusions Poster 49 on Wednesday

Spatial distribution of bridges (II)

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

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

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

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

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

Endgroup distributions unshearedsheared