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Micro-scale Polymer Processing:Multiscale Modelling of Entangled Polymers
Polymer Processing in the 21st century?
Reaction Chemistry
Molecular shape
“Good processing”
Melt Rheology
Industrial LCB and the “Buffer Zone”
THEORY MODEL MATERIALS INDUSTRIAL RESINS
18 20 22 24 26
0.0
0.2
0.4
0.6
0.8
1.0
RI
(rel
ativ
e in
ten
sity
)
Retention time (minutes)
DOW680E 200k before 200k after
103
104
105
106
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Model distribution for CM3
MW
Fre
quen
cy
102
104
106
108
10-4
10-1
102
105
108
G'(
), G
''()
0
2
4
6
-5 0 5 10
log
log
G'(
), G
''()
Polymer characterisation
Synthesis Scale up
Advanced RheologicalCharacterisation
Model ProcessingFlow Rig
Materials testingSolid stateModelling
Flow computation
Molecular Theory
Molecular ConfigurationProbes
Synthesis
Rheology
Processing
Properties
INDUSTRY
The Scaffold Concept
• “Follow the processing path of well characterised polymers from synthesis through processing and property evaluation combined with the parallel development of a mathematical and computational protocol.”
Polymer characterisation
Synthesis Scale up
Advanced RheologicalCharacterisation
Model ProcessingFlow Rig
Materials testingSolid stateModelling
Flow computation
Molecular Theory
Molecular ConfigurationProbes
The Principle
The Team• Leeds
– Tom McLeish, Oliver Harlen, David Groves, Alexei Likhtman, Tim Nicholson, Alan Duckett, John Embery, Jorge Ramirez, Chinmay Das, Harley Klein, Dietmar Auhl
• Bradford– Phil Coates, Tim Gough, Mike Martyn, Rob Spares
• Durham– Lian Hutchins, Nigel Clarke, Eduardo de Luca
• Sheffield– Tony Ryan, Ellen Heeley, Patrick Fairclough, Ron Young,
Christine Fernyhough
• Cambridge– Malcolm Mackley, Karen Lee, Ashish Lele, Mark Collis, David
Hassell
• Oxford– Paul Buckley, Junjie Wu, David de Foccatis
Polymer characterisation
Synthesis Scale up
Advanced RheologicalCharacterisation
Model ProcessingFlow Rig
Materials testingSolid stateModelling
Flow computation
Molecular Theory
Molecular ConfigurationProbes
flowSolve
Tube models:LCB: Pom-Pomlinear: ROLIEPOLY
Cambridge MPR4/Bradford-Durham recirc.
Durham SANSSheffield SAXS
hPS+dPS linears +3 blendsPB combs PB linears + hPB variants
G*, shear transients, step shearMeiner extensional
Ox ford ModelCompressionCrazeBirefringence
Outline
Synthesis Platform
• Make polybutadiene in controlled fashion
sec-Bu-Li+ +
1,4-polybutadiene (cis- and trans-)
1,2-polybutadiene
93%
7%
n
m
-
Li+
– Polydispersity < 1.05– Molecular weight determined by reagent quantities– Micro-structure affected by temperature, solvent
• Then hydrogenate to make polyethylene
Update on tube model physics:Reptation + Contour Length Fluctuation + Constraint Release
Molecular Theory Platform
)','(ln'
)',('
),(ln)',(2
1
)('2
3)(
')',(
'
2
2
2
2
2
ssftrs
ssfs
ssftrs
ssfs
ffss
ffffss
ssDsst
f
e
eqT
eq
)','(ln'
)',('
),(ln)',(2
1
)('2
3)(
')',(
'
2
2
2
2
2
ssftrs
ssfs
ssftrs
ssfs
ffss
ffffss
ssDsst
f
e
eqT
eq
Reptation +CLF flow CR
retraction
Detailed Chain FormulationGraham, Likhtman, Milner, TCBM
zdsssf
s
tsR
s
tsRtssf
0),(;
'
),'(),(),',(
z
dsssfs
tsR
s
tsRtssf
0),(;
'
),'(),(),',(
s
R(s)
Log(w)43210-1-2-3-4
Lo
g(G
'(w
),G
''(w
))
7e0
6e0
5e0
4e0
3e0
2e02
taue=0.0030221
5.756 Ge=5.6985E5
log [s-1]
lo
g G
‘, G
‘‘ [
Pa
]Linear shear rheology andpredictions
µPP2 software tool: RepTate
Lines are predictions from linear theory (Likhtman & McLeish 2002)
Model Parameters from linear theory:(Likhtman & McLeish 2002)
e (25°C) = 0.003 s
Ge (25°C) = 0.569 MPa
Me = 4.86 kg/mol
cv = 0.1
Tref. = 25 °C
PI-4kPI-14kPI-30kPI-90kPI-200k
• Solve momentum and mass conservation equations:
where is the polymeric stress
Flow solving Platform
• Constitutive equation can be used to calculate polymer stress.
• Develop a Lagrangian finite element flow solver whose
moving triangular grid elements can hold the constitutive parameters (orientation and stretch for each mode).
2u p
u 0
b,s,S,=>
u,p
u,pu,p
Nicholson, Bishko, Harlen
flowSolve output – planar flow
• The recirculating vortex in the corner grows considerably as the simulation proceeds.
• The maximum stretch is not along the centre line, but lies between the centre line and the recirculating region where the material is sheared prior to extension.
MuPP2 Structure
A Matrix approach to Industrial demand and technical opportunity
Platform I: Synthesis and Characterisation
Platform II: Theoretical Molecular Modelling
Platform III: Experimental Probes
Platform IV: Flow Visualisation
Platform V: Solid State Properties
Stm1: CRYSTAL Stm2: TOOLBOX Stm3: 2-PHASE
MuPP2 Management
+ Special task groups:• Rheology team• Synthesis team• Solid State team• Flow solving software team• PDRA conference
EXPERIMENTAL DATA
Text, binary file*.txt, *.dat, *.out…
ToolBox
Need to visualize
w0.001 0.01 0.1 1 10 100 1,000
G'(
w),
G''(w
)
1e2
1e3
1e4
1e5
1e6DIFFERENT
VIEWS
Gnuplot, Origin, Excel, Matlab, Xmgr…
THEORIES
Reptation CLFDTD CCRSCCR Rolie-Poly…. Pom-Pom
Set of equations to solve.Program in C, Fortran, C++, Pascal, Maple, Matlab, Mathematica…
Need to compare
2PHASE: Mesoscale SimulationsTwo-dimensional simulations of freely suspended particles in a polymeric fluid under shear flow.
Biperiodic lattice to extend a unit cell containing N particles to an infinte domain.
•Under shear these cells slide
• relative to one another.
O. Harlen and A. Malidi
CRYSTALShear-induced crystallization of comb 10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
0 200 400 600 800 1000 1200 1400
Time /sec
No
rmal
ised
inte
nsi
ty /A
rb
363K iso
368K iso
363K shear
368K shear
370K shear
363K 1020 s
sheared at 100 s-1 for 5 s prior to crystallisation
• Massively increased rates after shear
• Well oriented crystals (no shearing during crystallisation)
54 kg mol-1 backbone with 8 arms of 15 kg mol-1
No shear
• Model materials refine new entanglement physics
• Molecular structure has flow-field consequences
• Chain orientation is a family of numbers
• Routes to Polydisperse architectures
• Methodology extends to product structure in phase
and crystallinity.
Conclusions