chen-yang liu, roland keunings, christian bailly ucl, louvain la neuve, belgium
DESCRIPTION
Ideas Questions. Old New. . . …about viscosity, plateau modulus and Rouse chains. Chen-Yang Liu, Roland Keunings, Christian Bailly UCL, Louvain la Neuve, Belgium. Dynamics of complex fluids: 10 years on, Cambridge, October 2-5 2006. Objectives - outline. - PowerPoint PPT PresentationTRANSCRIPT
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Chen-Yang Liu, Roland Keunings, Christian Bailly
UCL, Louvain la Neuve, Belgium
Dynamics of complex fluids: 10 years on, Cambridge, October 2-5 2006
OldNew
IdeasQuestions
…about viscosity, plateau modulus and Rouse chains
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Objectives - outline
• Some old and recent results suggest there are still significant inconsistencies/questions about the LVE predictions of tube models
• Three examples :
– Why is Z-dependence of the plateau modulus is less than predicted ?
– Is the 3.4 power law fully understood after all ?
– Is Rouse really Rouse ?
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Plateau modulus and zero shear viscosity :
questions about constraint release and fluctuations
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1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 101E-3
0.01
0.1
1
10
τd τR
τeG', G"/Ge
ωτe
G' G"
Ze = 100
Gexpl determination
Gapp = G '(wmin G '' )
limZÆ •
(Gapp ) = GN0
Ferry (1980)
t (Gmin" ) ª t e.t R w(Gmin
" )
Minimum G’ method
Gexp l
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Low polydispersity model polymers (anionic polymerization)-Polybutadiene-Polyisoprene-Polystyrene
Systems analysed
Raju VR; Menezes EV; Marin G; Graessley WW; Fetters LJ. Macromolecules 1981 1668 Struglinski MJ; Graessley WW. Macromolecules 1985 2630 Colby RH; Fetters LJ; Graessley WW. Macromolecules 1987 2226 Rubinstein M; Colby RH. J. Chem. Phys. 1988 5291 Baumgaertel M; Derosa ME; Machado J; Masse M; Winter HH. Rheol. Acta 1992 75 Wang SF; Wang SQ; Halasa A; Hsu WL. Macromolecules 2003 5355
Getro JT; Graessley WW. Macromolecules 1984 2767 Santangelo PG; Roland CM. Macromolecules 1998 3715 Watanabe et al. Macromolecules 2004 1937; and 2000 499Abdel-Goad M; Pyckhout-Hintzen W; Kahle S; Allgaier J; Richter D; Fetters LJ. Macromolecules 2004 8135
Onogi S; Masuda T; Kitagawa K. Macromolecules 1970 109 Graessley WW; Roovers J Macromolecules 1979 959 Schausberger A; Schindlauer G; Janeschitz-Kriegl H. Rheol. Acta 1985 220 Lomellini P. Polymer 1992 1255
Liu, He, Keunings, Bailly
Polymer (2006)
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2.1 Dependence of GN0 on ZeDependence of Gexpl on Z
Red
uced
Gex
p
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LM Theory : Exact CLF treatment + CR
Likhtman and McLeish Macromolecules (2002)
MW dependence of plateau modulus less than predicted by advanced tube models:
Liu et al. Macromolecules (2006)
Dependence of Gexpl on Z
10 100 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
G'min G'' integral 3.56 G''max G'min 3.56 G''max
Z
Normalized
G0 app
G'min of L-M model K-N model
100k 1M20k Mw (g/mol)
Nor
mal
ized
Gep
xtl
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2.2 Comparison experimental data with predictions
Excellent accuracy for the terminal relaxation time
Significant stress deviations for low Mw samples
Relaxation time-modulus contradiction
Experimental data vs. predictions of LM theory
Inconsistency for the value of
G0F ; G0
NF 1- m.Z - 1/2ÈÎ
˘˚
t 0F ; t 0
NF 1- m.Z - 1/2ÈÎ
˘˚2
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Non-permanententanglements
Fluctuations
3.4
0 MW3.4
D MW-2.3
Experimental scaling:
0
MW
Zero shear viscosity
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CLF of Probe chainsUnaffected (?)
Tube Motion suppressed
Separate contributions of tube motion from CLF
Idea goes back to Ferry and coworkers (1974-81)
Put a small amount of short chains in a very high MW matrix
Probe rheology
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CLF of Probe chainsunaffected
Tube Motion suppressed
Separate contributions of tube motion from CLF
Key question : is there a MW dependence of the retardation factor ?
RF =
τ d of probe in Maτrixτ d of probe Self−elτ
Probe rheology
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CLF of Probe chainsunaffected
Tube Motion suppressed
Separate contributions of tube motion from CLF
If yes, there should be a contribution of tube motions to the non reptation scaling of viscosity !
Probe rheology
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10% Probe in Matrix
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Probe Rheology
▪ G’ ω2 and G’’ ω
▪ G’ and G’’ cross-point close to G’’max
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5 10 50 100 500
2.5
5
7.5
10
CR model: RF ~ 2.5
slope = - 0.3Retardation factors
Z
PBD PI PS Ref 45 Ref 46
Retardation Factors as a function of Z
meltSelfprobeofMatrixinprobeofRF
d
d
−=ττ
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10 10010-5
10-4
10-3
10-2
10-1
100
3.4
3.1
τd
Z
in Maτrix in Self- elτ
τ d
τ d/Z
3
Probe rheology
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CR parameter:
Cv = 1 or 0: with or without CRDoi (1981, 1983)Milner and McLeish (1998)Likhtman and McLeish (2002)
τ d/Z
3
Probe rheology
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Probe Rheology vs Tracer Diffusion
Lodge (1999)Wang (2003)
Two entangled environments:in Self-melt or in High Mw Matrix
DM
2
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Rouse region :
Longitudinal modes and « is it Rouse ? »
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PBD 1.2M Master Curve
10-3 10-1 101 103 105 107104
105
106
G' G'' Slope 0.71 CutRouse
G', G'' (Pa)
ω (rad/s)
τpeak ~ a few multiples of τe
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10-1 100 101 102104
105
106
107
Slope = 0.71
G' G''
G', G'' (Pa)
ω (rad/s)
PBD 1.2M –80 oC
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G’’ - (A.ω0.71)
10-1 100 101 1020
1x105
2x105
G'' - (A.ω0.71)
G'' (Pa)
ω (rad/s)
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10-3 10-1 101 103 105 1070.0
2.0x105
4.0x105
1.15E62.44E5
G'' CutRouse
G'' (Pa)
ω (rad/s)
Relaxation strength ~ 1/4 GN0
PBD 1.2M Master Curve Linear-Log
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Longitudinal Modes
Shape of relaxation peak ~ Maxwell
105 106 107 1080
1x105
2x105
3x105
G', G'' (Pa)
ω/ω ax
Maxωell G' Maxωell G'' G' G''
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102 104 106 108
0.0
0.2
0.4
0.6
0.8
1.0
1/τe = 106
1/τR = 100
G', G''
ω (rad/s)
G' of longiτudinal odes G'' of longiτudinal odes G' of Maxωell τx = 3 τe G'' of Maxωell τx = 3 τe
Slippage of a polymer chain through entanglement links.
Likhtman-McLeish Macromolecules 2002 Lin Macromolecules 1984
τpeak = 3τe
LM prediction vs Maxwell
Redistribution of monomers along the tube
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Conclusions - Questions
▪ There seem to be inconsistencies of tube model predictions for time/stress and CR/CLF balance
▪ Probably some of the inconsistencies come from the non-universality of real chains.
▪ Several possible reasons :
a chain hits entangled constraint before reaching Rouse behavior
local stiffness effects
interchain correlations
▪ Moreover: the assumption that fluctuations are unaffected in bimodal blends can be wrong if fluctuations depend on the environment
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Gexp l = 2
pG"(w)d ln
- •
+ •
Ú w
Ferry (1980)
Published methods for Gexpl determination
G” Integral method
-3 -2 -1 0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
G"/G"
max
ω/ωax
in the terminal region
(Kramer-Kronig principle)
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Gexp l
G ''max
= 2.303 2p
G"(w / wmax )G ''max
d log w / wmax( )- •
+ •
ÚÈ
ÎÍÍ
˘
˚˙˙= 3.56
Raju et al. Macromolecules (1981)
If the shape is universal, Gapp must be proportional to the maximum of the terminal G” peak
Maximum G” method
Published methods for Gexpl determination
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G’’max vs. Z : data vs. predictions
Too strong Z dependence
G” m
ax /
Gex
pl
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PBD 99K in 1.2M Matrix
τe▪ Probe in Matrix vs. Probe Self-melt
▪ Probe in Matrix vs. Matrix
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10-1 100 101 102 103 104 105 106 107
104
105
G', G'' (Pa)
ω (rad/s)
Probe-99k G' Probe-99k G'' Probe-39k G' Probe-39k G'' Probe-14k G' Probe-14k G''
10-1 100 101 102 103 104 105 106 107
104
105
G', G'' (Pa)
ω (rad/s)
Probe-99k G' Probe-99k G'' Probe-39k G' Probe-39k G'' Probe-13k G' Probe-13k G''
Probe Rheology vs. LM Model without CR
▪ Same horizontal shift factors for ALL: 5.2 106
Vertical shift factor: (1 – fmatrix2) GN
0
▪ Horizontal shift factors: 5.2 106; 4 106; 2 106
Data from: Likhtman and McLeish (2002)
Z = 63, 24, 9; Constraint release parameter cv = 0
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Graessley (1980)
Evaluation of the τd
▪ Narrow G’’ peak
▪ Retardation of the τd
Suppression of tube motions
Two Key Results for Probe Chain
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100 101 102 103 104 105
104
105
-1/4
-1/2
G', G'' (Pa)
ω (rad/s)
PBD-99K probe Ze-63 LM odel ωiτ Cv = 0
CLF for Well-entangled case
▪ Excellent agreement with model w/o CR
Likhtman and McLeish (2002)Vertical shift: (1 – fmatrix2) GN
0
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102 103 104 105 106104
105
PBD-14K Subtraction of Rouse modes 10% PBD-14K in Matrix Subtraction of diluted Matrix
5.1G'' (Pa)
ω (rad/s)