The Structural Rheology of Long Chain Branched Polymers: Measuring - - PowerPoint PPT Presentation

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

BASF, Basell, Dow, Ineos, DSM, ICI, Lucite, Mitsubishi TU Eindhoven, UCL, Reading

Tom McLeish University of Durham

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, Rosen Tenchev, Mark Walkley, David Hoyle, Suneel Kunanameni

• Bradford Phil Coates, Tim Gough, Mike Martyn, Rob Spares
• Durham Lian Hutchins, Nigel Clarke, Eduardo de Luca, Jonathan

Dodds, 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

“Reversing the design arrow” Erik Wassner, BASF

Polymer Processing in the 21st century?

Reaction Chemistry Molecular shape “Good processing” Melt Rheology

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”

THEORY MODEL MATERIALS INDUSTRIAL RESINS

Data and theory plots Select view (data representation) Modules Data manipulation Data files Fitting log window Theory parameters Select theory Theory controls Saved parameters

Project Idea 2:REPTATE

Project Idea 3: Lagrangian viscoelastic CFD tool: flowSolve

Chain motions in the Tube Model

• Linear polymers:

reptation

• Branched polymers: arm

fluctuation

Update on Tube Model physics:

Reptation + Contour Length Fluctuation + Constraint Release Two parameters: G0, τe(T)

Reptation +CLF flow CR retraction

Detailed Chain Formulation (GLAMM model)

Graham, Likhtman, Milner, TCBM, J. Rheol, 47, 1171-1200 (2003).

s R(s)

Polyisoprene samples

Pierre Chambon (Sheffield)

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).

Sample Mw/Mn [-] Mw [kg/mol]a Z=Mw/ Me [-]b PI 2k 1.07 2.4 0.5 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

Poly(cis-1,4-isoprene)

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

log ω [s-1] log G‘, G‘‘ [Pa]

Linear shear rheology and predictions

• D. Auhl et al., Macromolecules, 2009

µPP2 software tool: RepTate

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

Model Parameters from linear theory:

(Likhtman & McLeish 2002)

τe (25°C) = 0.003 s

Ge (25°C) = 0.569 MPa Me = 4.86 kg/mol cv = 0.1

• Tref. = 25 °C

PI-4k PI-14k PI-30k PI-90k PI-200k

Neutron Spin Echo

100 200 ns

Wischnewski et al., PRL (2002)

• Jülich link

Without CLF

Non-linear Rheology

(GLAMM + RoliePoly models)

Rheology from Dietmar Auhl, PI melts Pierre Chambon Strain-hardening from linear melts when WiR>1

Polydispersity:-Bimodal Blends

(GLAMM + RoliePoly models)

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

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 at greater dilution! Fit data using a multimode “Rolie-Poly” model – allows extraction of effective stretch relaxation time.

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

Real World Model World

Putting it all together: SANS in flow

The Recirculating SANS cell

(Bradford/Durham)

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

G D F E A B

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).

250k monodisperse PS; Weo=13, Wes=1

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

Decay of Rg and Stress

Different decay times/lengths

SANS Birefringence

5 6 3 4 2 1 13 11 12 8 9 10

SANS total flow mapping

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

SANS near corner flow 250K PS linear

Macromolecules, 43, 1539-1542 (2010) Soft Matter, 5, 4426-4432 (2009).

Branched polymers relax from outside in – e.g. H-polymer First, the arms relax by star-like breathing modes Then, the backbone relaxes by “reptation” – but with friction concentrated at the ends of the chain

Higher-Order Branched Polymers

Check BPW on H-polymers: transient rheology

BPW limit for q=2

Mb=57k (deuterated) Ma=25k

Synthesis: J. Allgaier, Juelich

Check BPW on H-polymers: SANS

λ=2

FlowSANS: Combs in Linear melt

Flow

Linear Melt

Daniel Read and TCBM, PRL, 2007 McLeish et al. Soft Matter, 2009, in press

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, with side-arms providing the friction. c.f. H-polymer terminal relaxation

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

 Linear relaxation spectrum

=> τbi, gi

 ‘decorate’ these modes

using nonlinear extensional data => qi, τsi

Multi-mode pompom - an example

10-3 10-2 10-1 100 101 102

Strain Rate /s-1

103 104 105 106 107

Viscosity /Pa·s Extension Shear

0.001 s-1 0.003 s-1 0.010 s-1 0.030 s-1 0.100 s-1 0.300 s-1 1.000 s-1 3.000 s-1 10.000 s-1 30.000 s-1

Rates

10-1 100 101 102 103 104

Time /s

103 104 105 106 107

Viscosity /Pa·s Extension Shear

10-1 100 101 102 103

Time /s

0.0 0.5 1.0 1.5 2.0 2.5

Stress /105 Pa

10 s-1 5 s-1 2 s-1 1 s-1

Rates

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

Looking at LDPE downstream from a contraction with flowSolve….

Characteristic ‘Fangs’ are

• bserved

downstream

• f contraction

… and with the Cambridge MPR:

But in MuPP2 it was a different story…

• D. Hassell, M. Mackley
• D. Hoyle, O. Harlen, TCBM

• 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” (tube

dilation)

z(t)

http://sourceforge.net/projects/bob-rheology

Linear rheology of arbitrarily branched polymers Relaxation of a branched polymer

z(t)

Linear rheology of arbitrarily branched polymers Two relaxation fronts and a widening tube Inner front determines depth of coherent length fluctuations: effective potential strength

D.J. Read

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 polymers Then we can make more predictions for “model” 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! PB “Dendrimac” (two-level Cayley tree)

Made by Lian Hutchings, Durham

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 by Taihyun Chang (Pohang, South Korea)

Statistical modelling of molecular architectures Single-site metallocenes, CSTR

Cat

D

UP DOWN

Molecules are self-similar and directional! Allows:

• analytical calculations to calculate MWD,

branching distribution, (D.J. Read, TCBM, Macromolecules 2001)

• Monte-Carlo generation of representative set
• f molecular architectures

(various algorithms in literature, but easiest is in Das et al, Journal of Rheology 2006).

Linear rheology of arbitrarily branched polymers Can then make predictions for truly polydisperse polymers Set of metallocene polyethylenes (Dow). Branching probability and molecular weight by scattering. Only two remaining adjustable parameters – matches entire dataset.

Das et al

• J. Rheology, 2006, 50, 207

Cat D UP DOWN

Monte-carlo simulation of free-radical polymerisation;fundamental processes of:

• initiation
• chain propagation
• branch formation
• scission
• termination by combination

From chemistry to Processing: LDPE

Rp=kp[R][m] Ri

Statistical modelling of molecular architectures (2)

(H. Tobita, J. Polym. Sci. B, 2001)

Assumptions:

• “batch reaction” and “tubular reactor” are equivalent (i.e. plug flow approximation).
• continuous initiation
• Rp>> reaction timescale (“instantaneous chain propagation”)

xf

• 1. Form a segment
• 2. Did it branch?
• 3. Did the daughters branch?
• 4. Did the first segment initiate from a branch point?
• 5. Did any termination combine?
• 6. Apply the branching algorithm recursively

Generates a 5-parameter representative set of molecular architectures

xf

Termination Combination Branching Scission Conversion

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

Fitting MWD + g-factor gives indicative prediction

• f linear rheology (all with same τe, Me)

Some small tweaks of reaction parameters then used to fit linear rheology

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

Stress relaxation due to escape of polymer chains from the confining tube at this timescale Stress relaxation due to constraint 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 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 5 5 4

• The maximum stretch ratio of a

chain strand in its tube

• Obtained from a “force balance” at

branch points

• Some chain ends might not

contribute – either too short, or relaxing too fast (idea of “snipping”) … we should use some “time- dependent” 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 long times

Reaction Chemistry Molecular shape Melt Rheology

From reaction chemistry…….

Statistical methods for polymerisation reactions, e.g. Tobita algorithm (Monte Carlo) for LDPE Linear rheology: “BoB” (predicts linear rheology of arbitrary branch-on-branch polymer distributions) Non-linear rheology Approximate parameter mapping from BoB onto a multimode pom-pom ensemble Linear rheology: looking in reasonable shape Non-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)

Rasmussen et al. (2005)

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

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

Multi-mode pom-pom with overshoot

• D. 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 !!!