Malcolm Mackley "Polymer chain Stretching" presentation. Chamonix (2009). GFR deGennes discussion meeting

1. Chamonix France Feb 2009
Pierre de Gennes Research Meeting
Stretching Polymer Chains
by
Malcolm Mackley
With acknowledgement to
The Late Sir Charles Frank, Sir Michael Berry, The late
Andrew Keller.
Dr Kris Coventry, Dr Tim Lord, Lino Selsci
Department of Chemical Engineering and Biotechnology
University of Cambridge
1

2. Time line
• Pre 1970 Background
“a bit of History” Tom Mcleish
•1970s Stagnation point flows
A slight digression “ Catastrophe”
“Our financial friends” Armand Ajdari
•1980s Real chain stretch
“ we don’t understand entanglements” Ralph Colby
• 2005 Stagnation point flows;
the Cross Slot
2
“use the inventions of others” Armand Ajdari

3. The stretching of liquid droplets G.I.Taylor 1934
Four roll mill Parallel Band
Ca ≥ 1
Summarised by “The Grace diagram”
Simple shear
Capillary
number
η γD
Ca = c 1 pure shear
ν
1
Viscosity ratio of drop to matrix
Capillary number criteria for drop deformation Ca ≥ 1 3

4. The stretching of Polymer; Chains Peterlin and Ziabicki 1960s
Kinetic Theory
Polymer of
Chain extension Kuhn and Kuhn
1940s
β = γτ
 γ = strain rate, τ = chain relaxation time of polymer chain

Β number criteria for polymer chain extension β = γ τ ≥ 1
4

5. Pioneers in Science 1970s
Charles Frank Andrew Keller Pierre de Gennes
Science Science Science
Geometry Crystallisation Scaling
5

6. Albert Pennings; Groningen 1970
6

7. Polyethylene
Diamond
7

8. 1969
Sir Charles Frank Opposed jets
B number criteria for chain extension β = γ τ ≥ 1
8

9. Chain extension with opposed jets
B number criteria for chain extension β = γ τ ≥ 1
9

10. Localized Flow Birefringence of Polyethylene Oxide Solutions in a
Four Roll Mill 1974
Crowley et al. Journal of Polymer Science: Vol 14 1111-1119 (1976)
10

11. B number criteria for chain extension
β = γ τ ≥ 1
Strain criteria for chain extension
γ t ≥ γ 0
11

12. The Two Roll Mill 1974
Confirms localisation in extensional flows
12

13. A short digression.
Christopher Zeeman; University of Warwick 1970s
13

14. Rene Thom; Catastrophe Theory!
(Something our financiers and politicians should have studied !)
14

15. Catastrophe Theory
The teaching of Christopher Zeeman!
“dogs (or birds) ” meeting
Friendly
Control Parameter;
1 / distance apart
Aggressive
15

16. Catastrophe Theory
The economy
Greed
Control Parameter;
Time
Contentment
Margaret Thatcher Tony Blair Gordan Brown
16

17. Catastrophe Theory; The Six Roll Mill 1976
M.V.Berry and M.R. Mackley. Phil. Trans. Roy. Soc. Lond. 287, 1337, 1-16 (1977).
17

18. 18

19. Stream function for Six Roll Mill flow pattern
1 3 2 1
φ (x, y) = γ ( x - x y ) - ω ( x 2 + y 2 ) - Vy x + Vx y
3 2
dφ dφ
Vx = , Vy = -
dy dx
19

20. The elliptic umbilic
Berry and Mackley
20
Bristol 1976

21. Berry and Mackley 1976
21

22. The elliptic umbilic
Berry and Mackley
22
Bristol 1976

23. 1980s Back to stretching chains!
Shish Kebab
Core;
Extended chain
Expect
E=100 GPa
Not usual
E=1 GPa
23

24. Paul Smith. Piet Lemstra
Now ETH Now TU Eindhoven
24

25. UHMWPE gel processing
Piston
1. Low entanglement UHMWPE polymer gel
Solvent recovery
2. Unoriented Gel fibre
4. Hot draw
Quench bath
5. Oriented High Modulus Polyethylene
3. Unoriented Low entanglement semi crystalline fibre
Schematic diagram of High Modulus Polyethylene (HMP) process
P. Smith, and P.J.Lemstra, J. Material. Sci. 1980, 15, 505
25

26. Continuous processing of UHMWPE Dyneema
Solvent
r
UHM WPE Polymer powde
Low entanglement polymer gel
Screw extrude r
Spinneret
Solvent recovery
Gel fibres
Hot draw
Quench bath
Low entanglement semi crystalline fibre
Schematic diagram of continuous High M odulus Polyethylene (HM P) process
26

27. 2000
Whitstable
UK
27

28. 2005
Back to stagnation point flows
The Cross-Slot
• Generate a hyperbolic
pure shear flow pattern
as shown.
• Near the walls the flow
deviates from ideal.
• Along the symmetry axes
rotation free pure extensional flow.
28

29. The MultiPass Rheometer, (MPR) 1995
MPR for Cross-Slot Flow 2005
• The MPR action modified
for cross-slot flow
• Pistons force polymer melt
through a cross-slot
geometry
Kris Coventry and Collaborative project with Leeds University; Tom Mcleish et al
29

30. Apparatus
Servo-hydraulically
• Molten polymer is driven piston
driven through test
section by two servo-
hydraulic pistons.
0.75 mm
1.5 mm radius
• Air pressure is used to Slave piston
driven by air Slave piston
return polymer so that pressure driven by air
pressure
multiple experiments 1.5 mm
can be carried out.
Servo-hydraulically
driven piston
30

31. Apparatus
31

32. Centre Section
3 cm
32

33. Cross Section of Apparatus
Hot oil supply Camera lens
Beam Focus
Analyser
Light Source and Polariser
monochromatic
P, T Transducers
Nitrogen supply (for cross-slot
flow only)
33

34. Typical Result
-Dow PS680E
-Piston velocity of 0.5
mm/s (maximum
extension rate =4.3/s).
-Inlet slit
width=1.5mm
-Section depth=10mm
- T=180°C.
34

35. Newtonian Simulation
Polyflow
Newtonian
Constitutive
Equation:
Viscosity =
7000 Pa.s
35

36. Power Law Simulation
Polyflow
Power Law
Constitutive
Equation:
Effective
Viscosity =
7000*(0.3*γ)
^ 0.75 Pa.s
36

37. Integral Wagner Simulation
Polyflow
- Integral Wagner
Constitutive
Equation
- 8 mode
relaxation
spectrum.
- Single damping
coefficient
37

38. Reptation based Pom-Pom Simulation
Flowsolve (Leeds)
8 mode
Pom-Pom
Constitutive
Equation.
38

39. Pom-Pom Simulation
from Software by Rudy Valette
-8 mode
Pom-Pom
model.
-Acknowledge
R. Valette
(CEMEF)
39

40. Tim Lord, David Hassell and Dietmar Auhl 2008
EPSRC Microscale Polymer Processing project
40

41. Newtonian Mildly
viscoelastic
Viscoelastic
Viscoelastic
solution
melt
41

42. Stagnation Point flows as rheometers
Dr Dietmar Auhl et al,
Leeds University 2008
6
elongational viscosityµ(t), Pas 10
0.3
. -1 1 0.1 0.03 0.01
ε0 [s ]
shear viscosity η(t), Pas
3 0.003
10 0.001
5
10 . -1
γ0 [s ]
0.001
0.01
0.1
4 0.5
10 1
2
5
LDPE
T = 150°C 10
3
10
-1 0 1 2 3
10 10 10 10 10
time t, s
42

43. η E ,st (ε) = (σ xx − σ yy ) st / εst steady-state elongational viscosity
at the stagnation point
0
ε
 =
principle
ε

0
∆ n = SOC (σX xx − σ yy ) + 4σ xy
• 2 2
ε st = A x V piston -4 -2 0 2 4
43

44. Dr Dietmar Auhl et al , Leeds University
44

45. So;
Is the Frank, Keller, de Gennes era
over ?
45

46. Yes.
but,
I hope others will follow
their inspirational example.
46