J. Stegen + , J. Billen ° , M. Wilson ° , A.R.C. Baljon ° . A.V. Lyulin +
-
Upload
wade-carson -
Category
Documents
-
view
20 -
download
2
description
Transcript of J. Stegen + , J. Billen ° , M. Wilson ° , A.R.C. Baljon ° . A.V. Lyulin +
Structural origin of non-Newtonian rheologyComputer simulations on a solution of telechelic associating polymers
J. Stegen+, J. Billen°, M. Wilson °, A.R.C. Baljon °. A.V. Lyulin+
+ Eindhoven University of Technology (The Netherlands)
° San Diego State University (USA)
Introduction
Polymeric gels
Reversible junctions between end groups (telechelic associating polymers)
Temperature
Sol Gel
Concentration
Constitutive relation for gel
Stress Shear rateViscosity
Constitutive relation for gelRegime where stress decreases with increasing shear due to shear induced structure:•decrease in number of elastic junctions•increased orientation in shear direction
/ /
/ , /x
F A F xy
x z v z
shear ratest
ress
Hybrid MD/MC simulation of a polymeric gel
Molecular dynamics simulation
Molecular dynamics:
Grest-Kremer bead-spring model
Equations of motion:
(Langevin equation, coupling to heat bath through fluctuation dissipation theorem)
i i i ir U rm r R t ��������������
Bead-spring model [K. Kremer and G. S. Krest.J. Chem. Phys 1990]
1
Distance
U
2
0
2 1ln2
10 R
rkRU ij
FENE
Repulsion all beads
Attraction beads in chain
12 6 12 6
4 ,
1.12
LJij ij c c
c
Ur r r r
r r
Associating polymer
Junction between end groups : LJ + FENE + Association energy
[A. Baljon et al., J. Chem. Phys., 044907 2007]
LJnobond
LJFENEassocbond
UU
UUUU
U bo
nd
Unobond
U
Distance
22assocU ò
Dynamics of associating polymer
Monte Carlo: attempt to form or destroy junction
~ exp( )B
UP
k T
new old
assoc FENE
U U U
U U
P<1possibleform
P=1form
Distance
Uassoc=-22
U
Simulation details
• 1000 polymeric chains, 8 beads/chain
• Units: (length), (energy & temperature), m (mass), (m/ (time);
• Box size: (23.5 x 20.5 x 27.4) with: • periodic boundary conditions in x,y
direction.• Fixed walls in z-direction
• Average volume density in system: 0.32
• NVT simulation
Shearing the system
Move wall with constant shear rate.
Some chains grafted to wall to minimise wall slip (50 per wall)
fixed wall
moving wall
Nomenclature
Bead (8 per chain) • Chain bead (6 per chain, white/gray)• End group (2 per chain)
• Dangler (blue)• Loop (orange)• Aggregate (red & orange)
Single chain
Network structure of 4 chains
Structural properties in equilibrium
Structural properties in mechanical equilibrium I
phase # aggregates # loops # danglers
T=1.0 Solution 390 ± 11 67 ± 8 593 ± 23
T=0.55 Gel transition
198 ± 7 184 ± 12 151 ± 11
T=0.35 Gel 107 ± 4 257 ± 4 62 ± 4
Structural properties in mechanical equilibrium II
Structural properties in mechanical equilibrium II
Structural properties in mechanical equilibrium III
T=1.0
Structural properties in mechanical equilibrium III
T=0.55
Structural properties in mechanical equilibrium III
T=0.35
Structural properties in mechanical equilibrium IV: Conclusions
• Aggregates increase in size with decreasing temperature
• Gel network immobile, macroscopic lifetime
• Spatial ordering of aggregates observed in gel phase
• Boundary effects visible at all temperatures, induces structure and ordering at lower temperature
Shear Banding
Shear banding: theory
Instable region in constitutiverelation (striped)
Stable configuration throughtwo shear bands coexisting ata stress σ
Lever rule: 3 1 1 2 2
1 2
· · · ,d
d
d d
d d
Plateau in shear-stress curve
Difference in mesoscopicstructure between bands
Shear banding: force and velocity profile
Simulation details: T=0.35εwall velocity 0.01 σ/τshear rate 3.6*10-4 τ -1
total wall displacement ~700 σ
Shear banding: aggregate size distribution
• More small and large aggregates in shear banding state• Large aggregates strong influence on velocity profile?
Shear banding: orientation function
ij
ji
r
rrQij
3
1
2
32
Orientation in xx-direction, xz-direction and perpendicular to zz-direction: effects of applied shear on chains decrease
No significant differences between shear bands
xx
zzxz
Shear banding: spatial distribution
High shear band very small (~5σ), too small to contain mesoscopic structure?
Fluctuations in density of ~10% at bottom of high shear band. No stationary flow but hopping like behaviour of end groups at interface?
Shear direction
Conclusion
• Shear bands in velocity profile observed.
• High shear band too small to accommodate a mesoscopic structure different from the low shear band.No significant differences in structure observed between bands.
• More large aggregates in a sheared system, these could be responsible for the observed shear banding.
• Fluctuations in end-group density at interface, no steady flow.
• Validity of lever rule has not been checked. Uncertain if observed shear banding corresponds to the shear banding observed in experiment.
Other work…
Jammed system at constant stress & fluctuation relation• Elastic behaviour visible • Two types of behaviour observed in time• Deviations from fluctuation relation observed
Questions?