Ten Years of PomPoms: The Branched Polymer Challenge

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Ten Years of Pom-PomsThe Branched Polymer
Challenge
Tom McLeish School of Physics and Astronomy,
University of Leeds INIMS, October 2006
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With immense gratitude to Ron Larson Oliver
Harlen Graeme Bishko David Bick Nat
Inkson Richard Blackwell Richard Graham Tim
Nicholson Nigel Clarke Harley Klein Alexei
Likhtman Daniel Read
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The Puzzles in 1996

• Star Polymers did not reptate, but
• LDPE processes well
• Shear-thinning but extension-hardening
• Hardening in both elongation and planar
• No strain-measure did this.
• Star polymers did not extension-harden.

Laun and Schuch 1989
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What we knew Star Polymers relax by Retraction
in a tube
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End-retraction is an activated process over a
thermal barrier M
M
Milner and McLeish, Macromolecules, (1998)
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Linear rheology of arbitrarily branched
polymers Relaxation of a branched polymer
Occurs from the outside of the polymer towards
the inside
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Linear rheology of arbitrarily branched
polymers Relaxation of a branched polymer
Occurs from the outside of the polymer towards
the inside
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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
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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
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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
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Need to think about 2-branch point objects
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The Picture
High Frequency
Mid-Frequency (star-arms)
Low Frequency (reptation)
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The Physics

• Separate orientation (traceless ?) from stretch
  (trace ?)
• Endow each with its own relaxation time (?bgt?s)
• Let branch point withdrawal limit stretch ? at
  q

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Prior art?
Pearson, Herbolzheimer, Grizzuti, Marrucci, J.
Poly. Sci. B, 29, 1589 (1991)
with ?(t) ?(t)2S(t)
For linear polymers
But from 1988I noticed
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What you tell the boss..
186 citations to 2006
1998
2002
2006
McLeish and Larson, Journal of Rheology, 42, 1,
81-110, (1998).
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Corrolary1 Flow-Solving (Bishko, Harlen et al.)
Phys Rev Lett, 79(12), 2352-2355, (1997)
Stress is greatest here..not here
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Corrolary2 Polydisperse LCB Polymers
Represent as a spectrum of pom-poms..

• Linear relaxation spectrum gt tbi, gi
• decorate these modes using nonlinear
  extensional data gt qi, tsi

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Multi-Mode Pom-Poms
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The q-spectrum
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• Gradient discontinuities
• 2nd normal stress
• Unbounded A(r,t)

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..they mean XPP! (Dutch version)

• Shear-stress divergence
• Multivaluedness
• (Clemur et. al. R. Acta 2003)

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• Agreement in shear and planar much better for
  differential model
• Multi-mode P-P not strain-time separable.

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?
t
t1

• P-P differential model does about as well in DSS
  as KBKZ

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New Metallocene Melts q-spectra
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New Flow Phenomena Fangs in LCB melt outflows
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Exact Architecture Studies H-Polymers
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Linear Rheology
Polydispersity correction
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Increasing the arm length.
Polydispersity correction
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Check BPW on H-polymers transient rheology
BPW limit for q2
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Check BPW on H-polymers SANS
Synthesis J. Allgaier, Juelich
Ma25k
Mb57k (deuterated)
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?2
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BPW on H-polymers SANS theory
Daniel Read, Leeds

• Arm retraction
• BPW
• Cross-bar stretch
• Elastic inhomogeneities
• Polydispersity of blocks
• Tube deformation with ?0.5

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Exact Architecture Studies Pom-Poms
q3
They really arent time-strain separable!
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Polydisperse LCB Really separable? A new
rheological technique (M. Willhelm, Mainz)
Nyquist plot
Separable integral equations cannot capture
richness of I3/I1(?,?)
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Detailed Chain Formulations for linear chains
Graham, Likhtman, Milner, TCBM J. Rheol, 47, 1171
(2003)
Reptation CLF
flow
CR
retraction
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Enter the ROLIE POLY equation!!
A. Likhtman, R. Graham, JNNFM (2003)
Reptation time
Plateau modulus
Stretch relaxation or Rouse time
CCR parameter
CCR power
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MP/FlowSolve Comparison Monodisperse linears
PS 262 We1
PS 262 We100 WeR12
PS 485 We300 WeR12
Monodispersity separates orientation and stretch
effects in flow
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Monodisperse linears time development of flow
t(s) 0.25, 0.5, 0.75, 1.0, 1.25,
1.75 We (rept) 100 We (Rouse) 4
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Neutron and Optical Flow Mapping
J. Bent et al, Science, 301,1691-1695 (2003).
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But what are the real molecular models for LCB
melts?
At a given timescale, what is the effective
spring-constant for further retraction? Given by
that part of the arm which moves coherently with
the arm end at that timescale.
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• Gelation class polymers (Lusignan et al, PRE
  1999, 60, 5657)
• Revisit an old prediction for (approximate)
  dynamic exponent u

G(t) t-u
Zurek et al.
These calculations
Lusignan et al,
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Classes of LCB and q-Spectra
LDPE
Metallocene
Comb 9
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Flow-Solving with LCB metallocenes(D. Hassell,
H. Klein, O. Harlen)
Leeds flowSolve
Cambridge MPR
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Where to now?

• Fully disperse architectures in strong flows
• Information flow in connected molecules
• Convective Constraint Release in LCB
• Separability and FT-Rheol
• SANS and other molecular probes
• Flow fields for different topologies
• Instabilities and control