Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 1
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ITP 27 March 2002ITP 27 March 2002
Rheology of Wormlike M icelles
Université de Montpellier II
GrégoirePor teDenis RouxJean-FrançoisBerret*
Sandra LerougeJean-Paul Decruppe Université de Metz
Peter LindnerLaurenceNoirez
Institute L aue-LangevinLaboratoire Léon Br ill ouin
*present addressComplex Fluids laboratory, CNRS-Rhodia259 Prospect Plains Road Cranbury NJ 08512 USA
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ITP 27 March 2002
Phase Behavior Cylindrical aggregates are intermediate in terms of curvature of the surfactant film between spheres and bilayers
watercosurfactant
surfactant
100 %cosurfactant
100 %surfactant
100 %water
Zones of self-assembled structures interface
cosurfactant
surfactant
L1
Lα
L3
cylinder
sphere
bilayer
(Porte)
Wormlike micellesLong polymer-like chains resulting from the association of surfactant
Polar head Aliphatic chain
Usually : C16-surfactants and cationic
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 2
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ITP 27 March 2002
+
Growth of cylindrical micelles (Israelachvil i 1976)
The end-cap enery E drives the unidimensional growth of the aggregates
End-cap
E ~ 20 kBT (~ 1 kBT per surfactant in the endcap)End-cap
Number density c(n) of micelles of aggregation number n :
c(n) =
c
n 2exp(−
n
n )
c is the concentrationn is the average aggregation number
n = c ×exp(E/ kBT)
Predictions are that micelles are broadly distributed in size, polydispersity index 2Experimentally : 100 Å in length correspond to 200 molecules
Dynamic of breaking/recombination (Cates 1987)
Probabil ity of breakage ~ c1×L(c1 and L are thermally activated)
Micelle of contour length L
L L’’L’ Equilibrium properties are based on curvature of the
surfactant film (or packing of surfactants)
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Experiments : How to make micelles grow ?
1. Add cosurfactant as in CPCl/Hexanol/water (Porte)2. Add salt (to screen electrostatics) as in CTAB/KBr (Lequeux, Candau)3. Add strongly binding counterions Rehage, Hoffmann and others4. …. Gemini surfactant (In, Zana)
Cationic-anionic mixtures (Kaler)
COO
OH
-Salicylate S
OO
O
H3C -Tosylate
Salicilate etc… are not simple salt : they are incorporated to the body of the micelles(Estimation from the effective charge per unit lenth : 90 % are in the micelles)
water
Micellar core
+ -- - -+ ++ +
With strongly binding counterions
Strongly viscoelasticity in entangled stateThe viscoelasticity is Maxwellian
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 3
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ITP 27 March 2002
Illustrations of a Maxwellian behavior
0
0.2
0.4
0.6
0.8
1
0.01 0.1 1 10 100
20 °C25 °C30 °C40 °C45 °C
G'/G
0(ω)
G"/
G0(ω
)
ω τR
CPCl-NaSal-H2O (0.5 M NaCl)
Rehage and Hoffmann (88)
CPCl-NaSal-H2O
Viscoelasticity arises from entangled network
1. Unicity of relaxation time is explained by the combination of reptation and breaking2. Scaling laws for viscoelastic parameters versus concentration η0 ~ c7/2 and G0 ~ c9/4
Cates Model (1987)
1 is almost always observed, 2 not always !
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ITP 27 March 2002
2 - Rehage and Hoffmann (88)
Static viscosity
Maxwellianbehavior
Not all Maxwellian fluids are equivalent (shear thinning, shear tickening, or both)
Theoretical predictions (growth law, scaling) might not apply
There is a specificity for micelles made with counterions, especially for the
dynamics of the network ?
No change of morphology(Except from sphere to worms)
cosu
rfac
tant
surfactant
L1
Lα
L3
cylinder
sphere
bilayer
Specificity of the strongly binding counterions1 - With increasing counterions concentration
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 4
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ITP 27 March 2002
Rheology of Wormlike MicellesSystem investigated : CPCl, NaSalRequirements : 1 - Fix the ratio counterion /surfactant (here 0.5)
2 - Saturate the solutions with salt (screening electrostatics)
0.001
0.01
0.1
1
10
100
1000
0.1 1 10
0 (P
a.s)
, G 0 (
Pa)
[Sal]/[CP] = 0.50T = 25° C
η0 ~ c3.3
concentration (wt%)
G0 ~ c2.2
Scaling in agreement with Cates Model
Changing counterion/surfactant ratio and the agreement is less good
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ITP 27 March 2002
General Flow curveMicellar system : CPCl-NaSal-H2O (0.5 M NaCl)
Experiments made at stationary state
At the stationary state, the stress shows a plateau (above γ1). The stress plateau is robust
0
50
100
150
200
250
0.1 1 10
σstationary
σM
σovershoot
η0γ
She
ar s
tres
s (P
a)
shear rate (s-1)
.
σP
c = 12 %
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 5
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Transient rheology of Wormlike Micelles
Before the plateau
0
50
100
150
200
250
0.1 1 10
She
ar s
tres
s (P
a)
shear rate (s-1)
A
BC D E
A
B
Linear regime : in agreement with stress relaxation function
Nonlinear regime : overshoot
G0 = 240 Pa, τ = 1 s
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Sh
ea
r st
ress
(P
a)
time (s)
γ = 0.1 s-1.
0
50
100
150
200
0 20 40 60 80 100S
he
ar
stre
ss
(Pa
)time (s)
γ = 0.8 s-1.
shear thinning
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Transient rheology of Wormlike MicellesAt the stress plateau
0
50
100
150
200
250
0.1 1 10
Sh
ea
r st
ress
(P
a)
shear rate (s-1)
A
BC D E
C
E
D
• Long-time relaxations• Oscillations
• σM : « mechanical » stress
0
50
100
150
200
0 50 100 150 200 250 300 350 400
Sh
ea
r st
ress
(P
a)
time (s)
γ = 1.2 s-1.
0
50
100
150
200
250
300
0 20 40 60 80
Sh
ea
r st
ress
(P
a)
time (s)
γ = 2 s-1.
σP
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50
Sh
ea
r st
ress
(P
a)
time (s)
γ = 5 s-1.
σM
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 6
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ITP 27 March 2002
General Flow Phase diagram
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.1 1 10 100
Nor
mal
ized
she
ar s
tres
s
σ /G
0
normalized shear rate γ τR
CPCl-Sal
.
12 %10 %
6 %
8 %
4 %
c = 2 %
Playing with concentration and temperature
critical concentration
Stress plateaus are robustStrong analogy with phase transition
In this case : isotropic-to-nematic induced by shear
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ITP 27 March 2002
Arguments in favor of the I-N transition (1994)
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40
σ P/G0
c (wt %)
isotropic
critical c
cI-N
N
1 - σP/G0 extrapolates at 0 for c = cI-N
2 - Kinetics at the onset of stress plateau
• The stress decrease coincides with the nucleation and growth of the aligned (nematic) state
• The exponent 2 is related to a one-dimension mechanism• Strongly aligned phase is the high shear rate band
160
180
200
220
240
0 100 200 300
she
ar
stre
ss (
Pa
)
time (s)
∆σ0
σP
SANS and FB
Inconclusive !
(found in two different systems)
V
∇v
σ(t) = σP + ∆σ0exp−t
τI −N
2
Nematicstate
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 7
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ITP 27 March 2002
0
10
20
30
40
50
1 10 100 1000
stress controlledstrain controlled
shea
r st
ress
(P
a)
shear rate (s-1)
The «ideal » example : CTAB/D20 (Cappelaere et al. 1997)
ω
v∇v
A
P
(λ)
h
• Rheology (rate and stress controlled)
• SANS• Flow birefringence
(J.P. Decruppe)A
B
C
A B C
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ITP 27 March 2002
New results (1) : Fisher and Callaghan (2000)
NMR measurementsDoes the highly birefringent band correspond to a high shear rate band ?
Micellar system : CTAB-D2O
Proportion of nematic phase
The agreement between SANSand NMR is excellent
Velocity profil e Birefringent band
The highly birefrigent phase is not the high shear rate band
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 8
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ITP 27 March 2002
New results (2) : Lerouge et al. (2000)
Transient flow birefringence
I(t) ~ sin2 φ(t)
2sin2 2χ(t) −θ( )
∆n =
λφ2πh
Flow birefringence
Εxtinction angle
φ : phase shiftχ : extinction angleθ : angle between polarizer and V∆n : birefringenceh : height of the Couette cell
The long-time kinetics in FB coincides precisely with the kinetics seen in transient rheology
Micellar system : CTAB-NaNO3
Rheology identical to CPCl-NaSal
Appearence of a thin band
×
~ exp −tτ
n
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ITP 27 March 2002
Evidence of multibanded flow / the stress remains constant
Transient birefringence
Short time Long time
multibandsOne band
inner wall
outer wallouter wall
inner wall
Final bands are 100 µm broad and not stationary
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 9
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ITP 27 March 2002
conclusions1. In entangled state, wormlike micelles are Maxwellian fluids2. The nonlinear rheology of wormlike micelles show stress plateaus3. Stress plateaus are associated to shear banding (flow birefringence)4. The picture of an isotropic-to-nematic transition is not appropriate5. A description in terms of a mechanical instability related to
the existence of a non monotonic constitutive equation is plausible
Possible routes :Determine experimentally the non-monotonic constitutive equation for wormlike micelles (?)Investigate simultaneously the temporal and spatial (at the micron length scale) responses of the sheared fluids using FB, NMR, scattering
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ITP 27 March 2002
Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)
Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 10
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ITP 27 March 2002
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ITP 27 March 2002