Rheology of W ormlike Micelles -...

Rheology of Wormlike Micelles (ITP Complex Fluids Program 3/27/02)

Dr. Jean-Francois Berret, ITP & Rhodia CRTC-CNRS 1

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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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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



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+

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



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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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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



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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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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 %



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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



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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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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



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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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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



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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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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



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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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