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” THEORYMODEL MATERIALS INDUSTRIAL RESINS

Polymer characterisation Synthesis Scale up Advanced Rheological Characterisation Model Processing Flow Rig Materials testing Solid state Modelling Flow computation Molecular Theory Molecular Configuration Probes 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 Rheological Characterisation Model Processing Flow Rig Materials testing Solid state Modelling Flow computation Molecular Theory Molecular Configuration Probes 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 Rheological Characterisation Model Processing Flow Rig Materials testingSolid state Modelling Flow computation Molecular Theory Molecular Configuration Probes flowSolve Tube models: LCB: Pom-Pom linear: ROLIEPOLY Cambridge MPR4/ Bradford-Durham recirc. Durham SANS Sheffield SAXS hPS+dPS linears +3 blends PB combs PB linears + hPB variants G *, shear transients, step shear Mei  ner extensional Ox ford Model Compression Craze Birefringence Outline

Synthesis Platform Make polybutadiene in controlled fashion –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

Reptation +CLF flow CR retraction Detailed Chain Formulation Graham, Likhtman, Milner, TCBM s R(s)

log  [s -1 ] log G‘, G‘‘ [Pa] Linear shear rheology and predictions µPP2 software tool: RepTate Lines are predictions from linear theory (Likhtman & McLeish 2002) Model Parameters from linear theory: (Likhtman & McLeish 2002)  e (25°C) = s G e (25°C) = MPa M e = 4.86 kg/mol c v = 0.1 T ref. = 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).  b,  s,S, =>  u,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

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 DIFFERENT VIEWS Gnuplot, Origin, Excel, Matlab, Xmgr… THEORIES ReptationCLF DTDCCR SCCRRolie-Poly ….Pom-Pom Set of equations to solve. Program in C, Fortran, C++, Pascal, Maple, Matlab, Mathematica… Need to compare

2PHASE: Mesoscale Simulations Two-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

CRYSTAL Shear-induced crystallization of comb K 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