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

AbstractA 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.

TemperatureSol Gel

Hybrid Molecular dynamics / Monte Carlo simulation*

2

0

2 1ln2

10 R

rkRU ij

FENE

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:

cccijij

LJ rrrrrr

U

,4

612612

= 21/6

*Baljon et al., J. Chem. Phys., 044907 (2007)

• Attempts to form/destroy junctions with probability depending on old and potential new state made frequently:

)/exp(~ TkUP b

Application of constant shear: Fixed wall

v=0.01

h

Fixed wall

h

Moving wall Moving wall

Shear banding

5% chains graftedshear rate: = v/hmeasure: stress

Simulation Results

Plateau in stress vs shear

curve

Velocity profile: within plateau two bands of different

shear co-exist

Shear rate

Ave

rag

e st

ress

Fielding, Soft Matter, 1262, (2007).

Sprakel et al., Phys. Rev. E, 056306, (2007).

Microscopical differences between shear bands

unsheared

low shear bandhigh shear band

Aggregate size

distribution

un-sheared

high shear

low shear

atom concentration

no noticeable difference

lifetime [k] 35 44

aggregate density

[#agg/3]

0.0064 0.0097 0.0056

average aggregate size

19.1 13.0 19.4

end-to-end distance 2 [2]

14.64 22.6 23.4

Orientation tensor:

Shear direction

x

z

y

rij

ij

ji

r

rrQij

3

1

2

32

Single bridge

Double bridge

Link

3 endgroups

NomenclatureAggregate =

•…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

sheared

sheared

unsheared

unsheared

unsheared

Simulations match experiments

average unsheared

average unsheared

Transient stress response: yield

peak

LJnobond

LJFENEassocbond

UU

UUUU

U bond

Unobond

U

Distance Distance

U

UFENE

ULJ

• 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.DMR0517201Funding

Koga et al., Langmuir, 8626 (2009).

stre

ss