Plasticity and Flow ofSoft Materials
Laurence Ramos
Laboratoire des Colloïdes, Verres et Nanomatériaux
CNRS-Univ. Montpellier 2, Montpellier, Francelaurence.ramos@univ-montp2.fr
www.lcvn.univ-montp2.fr/~ramos/Complex Fluids under Mechanical Stress
From the process of industrial fluids

http://mocoloco.com/art/archives/001001.php......

to the flow of soft glasses

E. Weeks, Emory U.

• shear-induced transitions• solid-liquid transition

Outline
I. Soft 2D columnar crystalA) Designing a versatile self-assembled structured system
B) Flow - characterizing and modeling the shear-inducedtransitionC) Plasticity - Understanding the solid-liquid transition incomplex fluids

II. Towards the plasticity of soft 3D polycrystals
III. Plasticity and spontaneous dynamics of soft glasses

Self-Assembled Hexagonal Phases
as Templates for Nanomaterials

10 nm

In situ templating of PbS nanorods
in reverse hexagonal liquid crystal
Huang et al. Colloids and Surf. A 2004

Experimental System
Soft columnar crystal
self-assembled systemsurfactant molecules
solvent
Intensity (arb. u.)1010107q0
6

3q0
2q0

57q0
10

40.20.3-1

triangular array of tubes
1D liquid, 2D solidq (nm )0.4

0.5 0.6

Experimental System
Soft columnar crystal
self-assembled systemsurfactant molecules
solvent

OIL+ tuning of the spontaneous
curvature of the surfactant film

triangular array of tubes
1D liquid, 2D crystal

R
1.5 -15 nm
LR and Fabre, Langmuir (1997)hR, h (nm)151050R
h0SAXS @ ESRF

246810

Water/Surfactant

12Our strategy to Increase the Spacing
between the Tubes

Amphiphilic di-block polymer (home-synthesized)
C18 - POE5K (RG = 2.4 nm)

2RhhR, h (nm)1510R h50,,,,0246without polymer
β=1%
β=2%
β=3%

8

Water/Surfactant

1012

Effective Polymer Thickness
Excluded volume interaction between the tubes
Same effective surface density upon addition of polymere (nm)

ρ0 /ρmeasur.= (1+e/R)2e5432
100

LR and Ligoure, Langmuir (2008)

12β (%)

3

A Versatile Soft Columnar Crystal
LR and Fabre, Langmuir (1997)
LR and Ligoure, Langmuir (2008)

hexagonal phaseoilR

R = 1.5 - 15 nm
hh = 2 - 15 nm

Specificities of the Soft Columnar Crystals
Soft hexagonal phase : a unique system● Tunable characteristic sizes

Template for nanomaterials… one example

Chemistry Outside the Surfactant Tubes:
Pt and Pd Porous Nanoballs

Metallic salt
20 nm

200 nm2 required conditions

10Confinement (in a hexagonal matrix)

10(γ irradiation)

4I (arb. un.)Slow and homogeneous reduction in the bulk

5SAXS of nanoballs-2310-3210

110010Surendran, LR et al. Chem. Mater (2007)
Surendran et al. J. Phys. Chem. C (2008)

0.1

1-1q (nm )10Specificities of the Soft Columnar Crystals
Soft hexagonal phase : a unique system● Tunable characteristic sizes● Tunable elasticity

Template for nanomaterials

Elasticity of Surfactant Hexagonal Phase

polycrystalline samples
1040swelling

G (Pa)

-3
10

1010

321345 6 7 8 910

20R (nm)G0 ~LR and Molino, EPL. (2000)

κR3

bending constant ofthe surfactant film

Specificities of the Soft 2D Crystals
Soft hexagonal phase : a unique system● Tunable characteristic sizes● Tunable elasticity● Structural signatureSAXSFlow Curves

stress (Pa)30

1086IIIIII

4110100

1000-1

shear rate (s )Ishear-thinning

IIIII

stress plateau and hysteretic loop
low viscosity Newtonian fluid

Flow Curves

1086IIII

shear-thinning

IIIII

stress plateau and hysteretic loop
low viscosity Newtonian fluidIII

4110100

stiffer

30

1000
-1

shear rate (s )σ (Pa)

stress (Pa)30

1086softer

42
110.

100

γ (s-1)1000

SAXS under Shearv

∆v

∆v

v

2D detector

X-beam

Structure under controlled shear rateradialtangential

SAXS under Low Shear∇v tangential

ωv

stress (Pa)ω30

radial

III

1086III

4110100

1000-1shear rate (s )• Polydomain• Preferential orientation of the tubes
along v
25v

32.5

15

2I (a.u.)∆θ (deg)

20

10

∆θ

1.5
1
0.5
0050 100 150 200 250 300 350

θ (deg)

5
1

10100
-1

shear rate (s )Progressive alignment of thetubes along v

Structural Transition under Shear
Flow curveHigh shear

stress (Pa)Low shear10ωωv

110100-11000v

shear rate (s )Perfect alignmentof the tubes along v

Structural Transition under Shear
Flow curveHigh shear

stress (Pa)Low shear10ωωv

1101001000-1v

shear rate (s )crystal-like pattern

I (arb. un.)610liquid-like pattern
5104100.1-1q (nm )1

SHEAR-MELTING

Role of Dislocations
Nabarro et al. (1964)
Work-hardening of crystals

dimensional arguments

σ /G0= f(b ρ 1/2)

Driving force F1~ bσ (Peach-Kohler)

G0 : shear modulus
b: Burgers vector
ρ :density of dislocations

σ ~bResistive force F2~ b2 (line tension of a dislocation)

σ ~ G0 b ρ1/2

3 types of dislocations in columnar crystal

Marchetti and Nelson(1990)

Role of Dislocations
Nabarro et al. (1964)
Work-hardening of crystals

dimensional arguments

σ /G0= f(b ρ 1/2)

Driving force F1~ bσ (Peach-Kohler)
Resistive force F2~ b2 (line tension of a dislocation)

OrowanG0 : shear modulus
b: Burgers vector
ρ :density of dislocations

σ ~b
σ ~ G0 b ρ1/2.

γ =ρ bvv~σ. 1/3

σ~γ.

(geometrical argument)

ρ ~ σ 2 ~ γ 2/3.

Determination of ρ =f(γ) from Rheology DataI.

low γ regime

stress (Pa)

30

IIIII

1086σ (Pa)

415°C
16°C
18°C
20°C

0.32

22°C
26°C
28°C
30°C

1101001000-1shear rate (s )10shear-thinning regime
010

110-1

γ (sec )σ ∝ γ& 1/ 3

2/3&ρ ∝γ.
Determination of ρ =f(γ) from SAXS Data
Broadening of the diffraction peaks
Irest-1
5.8 sec-1
29 secstress (Pa)I (arb. units)

30

IIIII

10864
1010100

1000-1

shear rate (s )0.18 0.20 0.22 0.24 0.26-1q (nm )100ξ ≡ mean distance between dislocationsρ ≡ 1/ ξ 2

ρ ∝ γ& 2 / 3-1/3

ξlength/a2πcorrelation length ξ =∆q10110.γ (sec100-1)

1000

Broadening of the diffraction peaks

2/3&ρ ∝γ

Shear-thinning regime

Scaling in agreement with simple theory ofwork-hardening of crystals
Shear-melting due to a proliferation of dislocations

LR and F Molino, PRL (2004)

Analogies with Flux Line Lattices in Superconductors
FFL

soft hexagonal phase
Shear-melting due to a proliferation of dislocationsvv

Corbino disk
geometry

HOWEVER
coupling between orientationof the tubes and density ofdislocations

Benetatos and Marchetti
PRB (2002)

Intermediate hexatic phase ?

hexatic flux liquidazimuthal scan
I (arb. u.)

γ=390 s-1

00

Marchetti and Nelson
PRB (1990)

60 120 180 240 300 360

θ (deg.)Shear-Melting… and Re-Crystallization
ω

ωv

∇v

γ& = 1400 s −1

After abrupt cessation of shear
MONOCRYSTAL•Time scale ~ 100 sec•Stable at rest

Nanostructured materials !!

Summary

Soft 2D crystal

MONOCRYSTALat rest
σ >σcγ& > γ&cMELTING

Proliferationof dislocations

Summary

Soft 2D crystal

MONOCRYSTAL

at restSolid-Fluid transition

σ >σcγ& > γ&c?

MELTING

Proliferationof dislocations

Solid-Fluid Transition

Yield Stress Fluids
Nature of the solid to fluid transition?

stress

Prediction whether and when a material will flow
Structural modifications at the onset of flow?

…

shear rate

Behavior under Low Stress

Low stress
σ = 2 Pa

Higher stressσ = 5 Paγ ~ t m (m < 1)

γ ~t

No steady state

Stationary regime“creep”“flow”

Behavior under Low Stress1000

12 Pa
13 Pa
15 Pa
19 Pa21 Pa22 Pa
30 Pa
35 Pa

dγ /dt (x10-2 sec-1)

100-1/3
1010.10.1

1

10100time (sec)

1000

10000

Behavior under Low Stresssurfactant hexagonal phase

polymer composite

1000

dγ /d/dt (x10-2 sec-1)

100-1/3
101

0.1

0.1

1

10100

1000

10000

time (sec)
Nechad, PRL (2005)

Analogies withheterogeneous composite polymer materials
EXCEPT flow with low viscosity instead of ruptureBehavior under Low Stress
100000

12 Pa
13 Pa
15 Pa
19 Pa
21 Pa
22 Pa
30 Pa
35 Pa

η=σ/γviscosity (Pa.sec)

1/310000
1000
10010CREEPFLUIDIZATION

10.1

1

10100time (sec)

1000

10000

Onset of Flow
Fluidization time τfτf (sec)

10000

1000

3200 Pa
2240 Pa760 Pa
250 Pa100

101

10100stress (Pa)τfwhen στf vs σ shifted towards smaller stresses
for softer materials

Onset of Flow
Fluidization time τf

Strain at τf
1000

strain at τf (%)τf (sec)

10000

1000

3200 Pa
2240 Pa760 Pa
250 Pa100

10101

110100stress (Pa)

τf

100

when στf vs σ shifted towards smaller stresses
for softer materials

110stress (Pa)γc ~ 70 %independent of σ and G0100

τf (sec)
Fluidization
time τf (sec)Onset of Flow
10000

G0 = 3200 Pa
G0 = 2240 Pa
G0 = 760 Pa
G0 = 250 Pa

1000

100

G0 ~
slope: -3.1 +- 0.2
100.010.1

1σ/G00.64
Powerlaw variation of the time with stress
No yield stress?

Collapse when stress normalized by G02/3
Fluidization time depends only on the force applied per tube
Bulk properties?

κR3

SAXS under Controlled Stressv∆v
radial2D detector

X-beamStress-controlled rheometerconcomitant measurements of SAXS and rheology

Structures in the creep regime and at the onset of flow?

I (arb. u.)

Time Evolution of the Angular Scan

101150

180

210

240

270

angle (deg.)

ωv

300

330

t = 0 sect = 120 sec
t = 240 sec
t = 360 sec
t = 480 sec
t = 600 sec
t = 720 sec
t = 840 sec
t = 960 sec
t = 1080 sec
t = 1200 sec
t = 1320 sec
t = 1440 sec
t = 1560 sec
t = 1680 sec
t = 1800 sec
t = 1920 sec

Time Evolution of the Peaks’ Positions and Intensity

ωpeak positions (deg.)

330
300
270
240
210
180
150
01000

time (sec)

2000

3000v

Time Evolution of the Peaks’ Positions and Intensity
ω
1.0

300

0.8

2700.6240
0.4
2100.218015001000

2000time (sec)Contrast = (I max – I min) / (I max + I min)

0.0
3000

contrast

peak positions (deg.)

330v

Correlation Structure / Rheological Behavior

300

1.0

2000

0.8

1500

0.6
240
0.4
210

1000

500

0.2

180

0
150
01000

2000

0.0
3000

time (sec)contrast

viscosity

viscosity (Pa.sec)

270

contrast

peak positions (deg.)

330

330
300

1.0

2000

0.8

1500

0.6
240
0.4
210

1000

500

0.2

180

viscosity (Pa.sec)

270

contrast

contrast

peak positions (deg.)

viscosity

0150
01000

2000

0.03000time (sec)At the onset of flow:
Collective rearrangements of all crystallites- All oriented along the flow (90 deg) but wide angular distribution (35deg)- In agreement with the scaling for fluidization time

Not due to wall slip !!

What happens in the solid regime?
resistance to flow

resistance to flow

Bulk 3D polycrystalline sample=
Percolated network of resistive paths

resistance to flow

What happens in the solid regime?
2000
IntensitydegFractionof @180
resistivepaths

35

Viscosity
30
1500
25
1000

2015500105Viscosity (Pa.sec)

Intensity @ 180 deg

400001000

2000

3000

Time (sec)
Before onset of flow:
slow rearrangements to remove « most unfavorable » grain orientation(180 deg)

Correlation Structure / Rheological Behavior
A NAIVE PICTURE
De-percolation
FLUIDIZATIONNo resistive paths

Percolated network

FLOW
stationary state

CREEP

I

IIIII
.

Fraction of resistive paths

γ (s-1)
0.1

General mechanism?

0.01

1E-3

Bauer, Oberdisse and LR, PRL (2006)

0.0

0.5

t/tc

1.01.5

Correlation Structure / Rheological Behavior
A NAIVE PICTUREPercolated network

De-percolation

No resistive paths

CREEP

FLUIDIZATION

FLOW
stationary state

General mechanism?

F. Caton, Rheologica Acta (2008)

Summary

Soft 2D crystal

MONOCRYSTAL

at restSolid-Fluid transition

GRAIN ROTATION• de-percolation of a networkof resistive paths• collective rearrangementof the crystallites

MELTING

Proliferationof dislocations

Summary

Soft 2D crystal

MONOCRYSTAL

PLASTICITY
 of 3D soft crystals
 and spontaneous dynamics

at restPLASTICITY &ONSET OF FLOW

Grain rotation

MELTING

Proliferationof dislocations

Outline
I. Soft 2D columnar crystal
A) Designing a versatile self-assembled structured system
B) Flow - characterizing and modeling the shear-inducedtransition
C) Plasticity - Understanding the solid-liquid transition incomplex fluids

II. Towards the plasticity of soft 3D polycrystals
III. Plasticity and spontaneous dynamics of soft glasses

Plasticity of Polycrystals
DYNAMICS and PLASTICITY ofATOMIC POLYCRYSTALS
Original mechanical properties ofpolycrystals (e. g. superplasticity)

OUR APPROACH: USE of a
COLLOIDAL ANALOGUE
block-copolymer+nanoparticles

segregationin thegrain-boundaries

Physical mechanisms at the origin ofplasticity?
Role of grain boundaries?
cubic phase (fcc)
Simulation

Experiment
optical microscopy

20 µm
Schiotz, 1998

J. Weiss, LGGE/CNRS

Plasticity of Polycrystals
DYNAMICS and PLASTICITY ofATOMIC POLYCRYSTALS
Original mechanical properties ofpolycrystals (e. g. superplasticity)

OUR APPROACH: USE of a
COLLOIDAL ANALOGUE
block-copolymer+nanoparticles

segregationin thegrain-boundaries

Physical mechanisms at the origin ofplasticity?

cubic phase (fcc)
Simulation

Schiotz, 1998

Experiment

J. Weiss, LGGE/CNRS

20 µm

Role of grain boundaries?

Direct Visualization of Grain Refinement
2 control parameters

Φ, volume fraction of « impurities »R, speed of the crystallization ramp
R = 0.007°C/min

0.05%

0.25%

1%

Φ = 0.5%0.00025 °C/Min 0.007 °C/min

0.02 °C/Min

Super Preliminary Shear Experiments
z1z2
200
190

x displacement (µm)

12180

strain 75%

1701601501401301201103100

0 10 20 30 40 50 60 70 80 90100

z displacement (µm)

1350 µm

2Cf. simulations Shiba & Onuki (Poster 108)

on-going work …

Outline
I. Soft 2D columnar crystal
A) Designing a versatile self-assembled structured system
B) Flow - characterizing and modeling the shear-inducedtransitionC) Plasticity - Understanding the solid-liquid transition incomplex fluids

II. Towards the plasticity of soft 3D polycrystals
III. Plasticity and spontaneous dynamics of soft glasses

Slow Dynamics of Soft Glasses

still poorly understood
Associated with aging & dynamical
heterogeneities
Key role of elasticity & relaxationof internal stresses

EXPERIMENTAL SYSTEM & METHOD
Slow dynamics after atemperature quench

20 µm

SLOW DYNAMICS of JAMMED MATTER

onion phase∆ri(τ,tw)
76 µm

Origin? Driving force?
colloids

E. Weeks, Emory U.

grainshttp://www.cijm.org/

Time- and spaceresolved
measurements

Time- and Space-Resolved Measurements

Role of Temperature ?
<∆R//> (µm)

Global displacement

τ =315 sec

3• Intermittent motion• Fluctuations aroundan average position

0-3030000
tw (sec)

60000

Role of Temperature ?
<∆R//> (µm)

Global displacement

τ =315 sec

3• Intermittent motion• Fluctuations aroundan average position

0-3030000
tw (sec)

60000

Zoom in20-2∆T (°C) = T (tw+τ) - T (tw)

0.4
0.0
29000

30000

tw (sec)

31000

Role of Temperature ?

τ =315 sec

3-30

30000
tw (sec)

Cross-correlation between<∆R//> and ∆T
1 .0

Cf, g• Intermittent motion• Fluctuations aroundan average position

00 .5

60000

∆T (°C)<∆R//> (µm)

Global displacement

Zoom in

20-2
0.4
0.0

0 .0-10 0 00t' (se c )1 0 00

29000

30000

tw (sec)

31000

Temperature-driven Intermittent SHEAR Deformations<∆R//> (µm)

20-2∆T (°C)

0.4

Global displacement

0.0(∆∆r//2)0.5 (µµm)

Relative displacement

1029000

30000

31000

tw (sec)

Spatial structure

SHEAR

25<∆r// > (µm )τ =315 sec

432
10222<∆r// > (µm )Temperature-driven Intermittent SHEAR Deformations10

τ =15000 sec

10.1

03000060000

tw (sec)

REVERSIBLE rearrangements

03000060000

tw (sec)

REVERSIBLE and IRREVERSIBLE
rearrangements

SHEAR

PLASTICITY

Identification of the Plastic events
Decoupling the purely plastic events fom the reversible shear deformations

Find plastic events

delayτ between images such that ∆R// (τ ) = 0∆R// (µm)

Global // displacement

10-1

Images taken at equal Ta)∆r// (µm)

Relative // displacement

1.00.50.0b)
2500

τ (s)

5000

on the baselineStructure of the Plastic Events

Correlated on large length scale (~ 1 mm >> onions)
Vortex-like
Analogy with simulation of 2D hard spheres deep in the glass phase(Brito and Wyart, J. Stat. Mech. 07)

Aging Dynamics of the Plastic Eventsirr∆r // (µm)

2.5
2.0
1.5

Vb

1.00.50.0025000

50000

75000

τ (s)
Same spatial structure but decrease of theamplitude with sample age-5Vb (µm/s)

4x10-52x100020000

40000 60000 80000

tw (s)

exponential decay
characteristic time: 72 000 s

Summary
Aging dynamics of a deeply jammed system (φ=1)
Origin::Originreversible rearrangements∆Tmechanical shear deformations
PLASTIC rearrangements

Mazoyer, Cipelletti & LR, PRL (2006) ; PRE (2009)

Ballistic motion
Vortex-like
Aging

General behavior?
Elastic systems (concentrated pastes, copolymer phase, emulsions, fractal colloidalgels, …)
Analogy withsheared athermal suspensions? (Pine and coll.)
granular materials under thermal cycling? (Géminard and coll.)

CONCLUSIONS
Probing the structure of soft materials under shear

2D crystal, 1D liquid
Fourrier space
Shear-induced transition interpretated using model for crystalline solids
Plasticity / a physical mechanism for the solid-to-fluid transition

3D amorphous solid
3D crystal
direct space
Plasticity ?

direct space
Plasticity and spontaneous
dynamics / a physicalmechanism at the originof the slow aging dynamics

Many thanks to
2D soft columnar crystals
Pascale Fabre (Paris, Bordeaux)
Christian Ligoure, Raymond Aznar & Ty Phou (Montpellier)François Molino, Julian Oberdisse & Teresa Bauer (Montpellier)Hynd Remita, Geeta Surendran & Prem Felix (Orsay)
Eric Prouzet (Montpellier, Waterloo)

OnionsSylvain Mazoyer & Luca Cipelletti (Montpellier)

3D soft polycrystals
Neda Ghofraniha, Elisa Tamborini & Luca Cipelletti (Montpellier)

AND YOU