The Structural Rheology of Long Chain
Branched Polymers:
Measuring and Modelling
Macromolecules in Flow

Tom McLeish
University of Durham
BASF, Basell, Dow, Ineos,DSM, ICI, Lucite, Mitsubishi
TU Eindhoven, UCL, Reading

The Team•••••••••••

Leeds Oliver Harlen, Daniel Read, David Groves, Alan Duckett, John

Embery, Chinmay Das, Harley Klein, Dietmar Auhl, Ahamadi Malidi,
Michael Kapnistos, Peter Hine, Peter Jimack, Nat Inkson, RosenTenchev, Mark Walkley, David Hoyle, Suneel Kunanameni
Bradford Phil Coates, Tim Gough, Mike Martyn, Rob Spares
Durham Lian Hutchins, Nigel Clarke, Eduardo de Luca, JonathanDodds, Solomon Kumani
Sheffield Tony Ryan, Ellen Heeley, Patrick Fairclough, Ron Young,Christine Fernyhough, Sasha Mykhaylyk
Cambridge Malcolm Mackley, Karen Lee, Ashish Lele, Mark Collis,David Hassell, Tim Lord, Lino Scelsi, Simon Butler
Oxford Paul Buckley, Junjie Wu, David de Foccatis, Huaxuang Li
UCL Helen Wilson, Mehmet Sahin, Tim Reis
Reading Alexei Likhtman, Jorge Ramirez, Bart Vorslaars
Eindhoven Han Meijer, Gerrit Peters, Rudi Steenbakkers
Nottingham Richard Graham
Queensland Tim Nicholson

Polymer Processing in the 21st century?
Reaction Chemistry

Molecular shape

Melt Rheology“Reversing the design arrow”
Erik Wassner, BASF

“Good processing”

What are the Questions?

• Can we understand the physics?
• Can we predict macroscopic flows?
• Can we engineer molecules for PPP?
• Can we do this at the bench-top scale?
• Can we do this at the industrial scale?

Project Idea 1:
Industrial LCB and the “Buffer Zone”
THEORYMODEL MATERIALSINDUSTRIAL RESINSProject Idea 2:REPTATE

Select view
(datarepresentation)Data
manipulation

Modules

Data filesSelect theory

Data andtheory plots

Theorycontrols

Savedparameters

Fitting logwindow

Theoryparameters

Project Idea 3:
Lagrangian viscoelastic CFD tool: flowSolveChain motions in the Tube Model• Linear polymers: • Branched polymers: arm
reptation
fluctuation

Update on Tube Model physics:
Reptation + Contour Length Fluctuation +Constraint Release

Two parameters: G0, τe(T)Detailed Chain Formulation(GLAMM model)
Graham, Likhtman, Milner, TCBM, J. Rheol, 47, 1171-1200 (2003).

R(s)Reptation +CLF

flow

retraction

CRsPolyisoprene samples
Pierre Chambon (Sheffield)Poly(cis-1,4-isoprene)
SampleMw/Mn[-]

Mw[kg/mol]aPI 2k

1.07

2.4

Z=Mw/Me[-]b0.5

PI 4k

1.05

5.2

1.1

PI 8k

1.04

9.2

1.9

PI 14k

1.04

13.6

3.0

PI 20k

1.04

23.5

4.8

PI 30k

1.04

33.6

6.9

PI 40K

1.04

46.2

9.1

PI 90K

1.03

94.4

19.4

PI 200K

1.04

223.2

46.4

a Determined by GPC (triple detector) in THF at

30°C.
b Me = 4.86 kg/mol, determined from linear theory,(Likhtman and McLeish 2002).

3,4 units per chain: 5% - 7%

Linear shear rheology and predictions
D. Auhl et al., Macromolecules, 2009
µPP2 software tool: RepTate
Tref. = 25 °C

Lines are predictions from linear theory(Likhtman & McLeish 2002)

Model Parametersfrom linear theory:(Likhtman & McLeish 2002)

τe (25°C) = 0.003 slog G‘, G‘‘ [Pa]Ge (25°C) = 0.569 MPa
Me = 4.86 kg/mol
cv = 0.1

PI-200k

PI-90k

PI-30klog ω [s-1]PI-14kPI-4k

Neutron Spin Echo

Wischnewski et al., PRL (2002)- Jülich link

Without CLF

0100200 ns

Non-linear Rheology(GLAMM + RoliePoly models)
Strain-hardening from linear melts when WiR>1

Rheology from Dietmar Auhl, PI melts Pierre Chambon

Polydispersity:-Bimodal Blends(GLAMM + RoliePoly models)

Relaxation of fat tube stretch via motion
along thin tube (Daniel Read)•

Effective stretch relaxation time:•

Above argument works provided• It isn’t faster to relax via CR of thin tube along fat tube
• Thin tube has time to equilibrate locally in fat tube•

In either case, expect constant effective stretch relaxation time on
further dilution
Auhl et al. Phys. Rev. Lett. 103, 136001 (2009).

Measure stretch relaxation times using extensional rheology•Series of 480k / 33k polyisoprene blends, measured in extension
at range of rates (SER rheometer)
Qualitatively,
hardening at
lower rates atgreater dilution!
Fit data using a
multimode“Rolie-Poly”
model – allows
extraction ofeffective stretch
relaxation time.

Phys. Rev. Lett. 103, 136001 (2009).

Putting it all together: SANS in flow
Model World

Real WorldThe Recirculating SANS cell(Bradford/Durham)

T. Gough, J. Bent, R. Richards, N. Clarke, E. de Luca, P. Coates,

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

GFDEBA250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

250k monodisperse PS; Weo=13, Wes=1
J. Bent et al, Science, 301, 1691-1695 (2003).

Decay of Rg and Stress
SANS

Birefringence

Different decay times/lengths

SANS total flow
mapping

136

124

115

102

9381

Macromolecules, 43, 1539-1542 (2010)

SANS near corner flow
Soft Matter, 5, 4426-4432 (2009).
250K PS linear

Eduardo de Luca, Kamakshi Jagannathan, Richard Graham, Harley Klein, Nigel Clarke

Higher-Order Branched Polymers

Branched polymers relax
from outside in – e.g. H-polymer

First, the arms relax by star-likebreathing modes

Then, the backbone relaxes by“reptation” – but with friction
concentrated at the ends ofthe chainCheck BPW on H-polymers: transient rheology

BPW limit for q=2

Check BPW on H-polymers: SANS
Synthesis: J. Allgaier, Juelich

Ma=25kMb=57k (deuterated)

λ=2

FlowSANS: Combs in Linear melt
McLeish et al. Soft Matter, 2009, in press
Daniel Read and TCBM, PRL, 2007
FlowLinear MeltLinear rheology of arbitrarily branched polymers
Relaxation of a branched polymer
Occurs from the outside of the polymer
towards the insideLinear rheology of arbitrarily branched polymers
Relaxation of a branched polymer
Occurs from the outside of the polymer
towards the insideLinear rheology of arbitrarily branched polymers
Relaxation of a branched polymer
Sometimes side arms relax – relaxation
cannot proceed further until the main arm“catches up”.

Side arms give extra “friction”

Linear rheology of arbitrarily branched polymers
Relaxation of a branched polymer
Sometimes side arms relax – relaxation
cannot proceed further until the main arm“catches up”.

Side arms give extra “friction”

Linear rheology of arbitrarily branched polymers
Relaxation of a branched polymer
Eventually there is an effectively linear
section which relaxes via reptation, withside-arms providing the friction.

c.f. H-polymer terminal relaxation

Let’s try to be useful: LCB melts as aspectrum of pom-poms

Linear relaxation spectrum=> τbi, gi ‘decorate’ these modes
using nonlinear extensional
data => qi, τsiMulti-mode pompom - an example
107

Viscosity /Pa·s

107

Viscosity /Pa·s

Extension

106

106

105

0.001 s-1
0.003 s-1
0.010 s-1
0.030 s-10.100 s-1
0.300 s-1
1.000 s-1
3.000 s-1
10.000 s-1
30.000 s-1

Extension

105

Shear

104
103

Rates

10-3

10-2

10-1

104

100

Strain Rate /s-1

101

102

Shear

103

10-1

100

101

102

Time /s

103

104

Stress /105 Pa

2.5Rates
10 s-1
5 s-1
2 s-1
1 s-1

2.0
1.5
1.0
0.5
0.0

Data from Meissner (1972, 1975) and Münstedt and Laun (1979).

10-1

100

101

Time /s102

103

Looking at LDPE downstream froma contraction with flowSolve….

… and with the Cambridge MPR:

Characteristic‘Fangs’ areobserved
downstreamof contraction

But in MuPP2 it was a different story…
D. Hassell, M. Mackley

D. Hoyle, O. Harlen, TCBM

Linear rheology of arbitrarily branched polymers
Relaxation of a branched polymer•

Suggests an algorithm which monitors amount of polymer
relaxation as a function of (logarithmic) time•

Requires a time-integration along chain-contour variables•

Chains communicate via “constraint release” (tubedilation)z(t)http://sourceforge.net/projects/bob-rheology

Linear rheology of arbitrarily branched polymers
Two relaxation fronts and a widening tube
D.J. Readz(t)Inner front determines depth of coherent length
fluctuations: effective potential strengthLinear rheology of arbitrarily branched polymers
Fix parameters by comparison with data from “monodisperse”
polymers
asymmetric stars

H-polymers

Can put in (properly) the polydispersity (i.e. range of polymer sizes)
present in even these polymers.
In polymers, “monodisperse” means same size on a logarithmic scale!

Linear rheology of arbitrarily branched polymersThen we can make more predictions for “model” polymers
PB “Dendrimac”(two-level Cayley tree)

Made by Lian Hutchings, Durham

Can put in (properly) the polydispersity (i.e. range of polymer sizes)
present in even these polymers.
In polymers, “monodisperse” means same size on a logarithmic
scale!

Linear rheology of arbitrarily branched polymers
Then we can make more predictions for “model” polymers
PS Combs
Made by Pierre
Chambon +Christine
Fernyhough(Sheffield)
TGIC byTaihyun Chang(Pohang, SouthKorea)

Statistical modelling of molecular architectures
Single-site metallocenes, CSTR
UPMolecules are self-similar anddirectional!
CatDAllows:• analytical calculations to calculate MWD,branching distribution,(D.J. Read, TCBM, Macromolecules 2001)• Monte-Carlo generation of representative setof molecular architectures(various algorithms in literature, but easiest isin Das et al, Journal of Rheology 2006).

DOWN

Linear rheology of arbitrarily branched polymers
Can then make predictions for truly polydisperse polymers
Set of metallocene
polyethylenes (Dow).
Branching probability andmolecular weight byscattering.
Only two remaining
adjustable parameters –matches entire dataset.
Das et alJ. Rheology, 2006, 50, 207

UPCatDDOWN

From chemistry to Processing: LDPE
Statistical modelling of molecular architectures (2)Monte-carlo simulation of free-radical polymerisation;fundamental processes of:•initiation• chain propagation• branch formation• scission• termination by combination(H. Tobita, J. Polym. Sci. B, 2001)

Ri
Rp=kp[R][m]Assumptions:• “batch reaction” and “tubular reactor” are equivalent (i.e. plug flow approximation).
• continuous initiation• Rp>> reaction timescale (“instantaneous chain propagation”)
4. Did the first segment initiate from a branch point?
2. Did it branch?
5. Did any termination combine?

0

3. Did the daughters branch?

xf

1. Form a segment
6. Apply the branching algorithm recursively

Generates a 5-parameter representative set of molecular architectures
Termination
Combination
Branching
Scission

xfConversion

Statistical modelling of molecular architectures (2)6 well-characterised tubular LDPEs from Basell and Dow

Fitting MWD + g-factor gives indicative predictionof linear rheology (all with same τe, Me)
Some small tweaks of reaction parameters thenused to fit linear rheology

Approximate non-linear rheology: mapping to multimode pom-pom
The “top-level” division for a Maxwell mode

Stress relaxation due toescape of polymer
chains from the confining
tube at this timescaleStress relaxation due toconstraint release on remaining
polymer chains trapped within
confining tube at this timescale….then subdivide further into modes with different priority and stretch time
BUT NOTE constraint release physics is not embedded in the pom-pom model.

Approximate non-linear rheology: mapping to multimode pom-pom
Priorities
11• The maximum stretch ratio of achain strand in its tube

1

• Obtained from a “force balance” atbranch points

2235151

14121221111• Some chain ends might notcontribute – either too short, or
relaxing too fast (idea of “snipping”)… we should use some “timedependent” priority.

Approximate non-linear rheology: mapping to multimode pom-pom
One of the tubular LDPEs (1840H).....
• Transient viscosity during start-up extension / shear• Dashed curves – no snipping. Stress levels too high.
• Dashed –dot – full snipping. Stress levels too low.
• Full curves – renormalised snipping.

Approximate non-linear rheology: mapping to multimode pom-pom
Tubular LDPE family: analysing how LDPE works

Segments
relaxing at short,medium and longtimes

From reaction chemistry…….
Reaction Chemistry

Statistical methods forpolymerisation reactions, e.g. Tobita
algorithm (Monte Carlo) for LDPE

Molecular shape

Melt Rheology

Linear rheology: “BoB”(predicts linear rheology ofarbitrary branch-on-branchpolymer distributions)Non-linear rheology
Approximate parameter
mapping from BoB onto a
multimode pom-pom ensemble

Linear rheology: looking in reasonable shapeNon-linear rheology: not bad, given many of the approximations

X-Slot rheometry for extensional steady-state
can give true q-value spectra

D. Hoyle, T. Lord and D. Auhl (2010)

But both X-slot rheometry (compared toextensional) and controlled-strain filament
stretching suggest overshoots in LCB flows

D. Hoyle, T. Lord and D. Auhl (2010)

Rasmussen et al. (2005)

Multi-mode pom-pom with overshootD. Hoyle, T. Lord and D. Auhl (2010)

LDPE flows calculated in full 3D

O. Harlen, R. Tenchev, P. Jimack, D. Hoyle

From chemistry to Processing: LDPE flows

H. Klein, D. Hassell, O. Harlen, TCBM (2009)

Conclusions• Model materials give insight into entanglement physics• Molecular structure has flow-field consequences• LCB tailors rates for melt strength• Chemistry→Rheology→Flow is possible• Teamwork is essential!
• See more at www.mupp2.com• And REPTATE.com !!!