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 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, 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 •

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” INDUSTRIAL RESINS THEORY MODEL MATERIALS

Project Idea 2: REPTATE Select view (data representation) Data manipulation Modules Data files Select theory Data and theory plots Theory controls Saved parameters Theory Fitting log parameters window

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: G 0 , τ e (T)

Detailed Chain Formulation (GLAMM model) Graham, Likhtman, Milner, TCBM, J. Rheol, 47, 1171-1200 (2003). s R(s) Reptation +CLF flow CR retraction

Polyisoprene samples Pierre Chambon (Sheffield) Poly(cis-1,4-isoprene) Sample Mw/Mn Mw Z=Mw/ [-] [kg/mol] a 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 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 µ PP2 software tool: RepTate T ref. = 25 °C Lines are predictions from linear theory (Likhtman & McLeish 2002) Model Parameters from linear theory: (Likhtman & McLeish 2002) τ e (25°C) = 0.003 s log G‘, G‘‘ [Pa] G e (25°C) = 0.569 MPa M e = 4.86 kg/mol c v = 0.1 PI-200k PI-90k PI-30k PI-14k PI-4k log ω [s -1 ]

Neutron Spin Echo Wischnewski et al., PRL (2002) - Jülich link Without CLF 0 100 200 ns

Non-linear Rheology (GLAMM + RoliePoly models) Strain-hardening from linear melts when Wi R >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 at greater dilution! Fit data using a multimode “Rolie-Poly” model – allows extraction of effective stretch relaxation time. Phys. Rev. Lett . 103 , 136001 (2009).

Putting it all together: SANS in flow Real World Model World

The Recirculating SANS cell (Bradford/Durham) T. Gough, J. Bent, R. Richards, N. Clarke, E. de Luca, P. Coates,

250k monodisperse PS; We o =13, We s =1 J. Bent et al , Science, 301, 1691-1695 (2003). G F D E B A

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

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

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

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

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

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

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

Decay of R g and Stress Birefringence SANS Different decay times/lengths

13 6 SANS total flow mapping 11 12 4 5 10 9 3 2 8 1

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-like breathing modes Then, the backbone relaxes by “reptation” – but with friction concentrated at the ends of the chain

Check BPW on H-polymers: transient rheology BPW limit for q=2

Check BPW on H-polymers: SANS Synthesis: J. Allgaier, Juelich M a =25k M b =57k (deuterated)

λ =2

FlowSANS: Combs in Linear melt McLeish et al. Soft Matter, 2009, in press Daniel Read and TCBM, PRL, 2007 Flow Linear 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, 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 => τ bi , g i  ‘decorate’ these modes using nonlinear extensional data => q i , τ si

Multi-mode pompom - an example 10 7 10 7 Rates 0.001 s -1 0.003 s -1 Viscosity /Pa · s Extension 0.010 s -1 Viscosity /Pa · s 10 6 10 6 0.030 s -1 Extension 0.100 s -1 0.300 s -1 1.000 s -1 3.000 s -1 10 5 10 5 10.000 s -1 30.000 s -1 10 4 Shear 10 4 Shear 10 3 10 3 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 -1 10 0 10 1 10 2 10 3 10 4 Time /s Strain Rate /s -1 2.5 Rates 10 s -1 Stress /10 5 Pa 2.0 5 s -1 2 s -1 1 s -1 1.5 1.0 0.5 0.0 10 -1 10 0 10 1 10 2 10 3 Time /s Data from Meissner (1972, 1975) and Münstedt and Laun (1979).

Looking at LDPE downstream from a contraction with flowSolve ….

… and with the Cambridge MPR: Characteristic ‘Fangs’ are observed downstream of 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” (tube dilation) z ( t ) http://sourceforge.net/projects/bob-rheology

Linear rheology of arbitrarily branched polymers Two relaxation fronts and a widening tube D.J. Read z ( 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!