‘Colloids in space’: recent work and outlook for the Milano and

Montpellier Groups

G. Brambilla1, L. Cipelletti1, L. Berthier1, S. Buzzaccaro2, R. Piazza2

1L2C, Université Montpellier 2 and CNRS2Politecnico di Milano

V. TrappeFribourg University

Outlook

1) Research in Montpellier/Milano : Slow dynamics and dynamical heterogeneity in soft glasses / jammed materials.

2) Space Proposal: Solidification of colloids in space

3) Foam - C

Dynamical heterogeneity is ubiquitous!

Granular matter Colloidal Hard Spheres Repulsive disks

Weeks et al. Science 2000Keys et al. Nat. Phys. 2007 A. Widmer-Cooper Nat. Phys. 2008

CCD-based Dynamic Light Scattering

diaphragm

sample

CC

D

Time Resolved Correlation (TRC)

time tlag

degree of correlation cI(t,) = - 1< Ip(t) Ip(t +)>p

< Ip(t)>p<Ip(t +)>p

Cipelletti et al. J. Phys:Condens. Matter 2003,Duri et al. Phys. Rev. E 2006

10 102 103 104 105

0.0

0.2

0.4

g 2(t)-

1

(sec)

intensity correlation function g2(1

Average over t

degree of correlation cI(t,) = - 1< Ip(t) Ip(t +)>p

< Ip(t)>p<Ip(t +)>p

Average dynamicsg2(1 ~ f()2

intensity correlation function g2(1

Average over t

degree of correlation cI(t,) = - 1< Ip(t) Ip(t +)>p

< Ip(t)>p<Ip(t +)>p

fixed , vs. t

fluctuations of the dynamics

c I(t,)

-1

t (sec)0 10

4 2x10

410 102 103 104 1050.0

0.2

0.4

g 2(t)-

1

(sec)

Average dynamicsg2(1 ~ f()2 var[cI()] ~ ()

10m

Homogeneous vs heterogeneous dynamics

100m

Gillette Comfort Glide Foam

Brownian particles

Inte

nsit

y co

rrel

atio

n fu

ncti

on

Dynamical susceptibility

• PVC in DOP• a ~ 5 µm• polidispertsity ~33%• close to rcp

Supercooled liquid (Lennard-Jones)

Lacevic et al., Phys. Rev. E 2002

Colloids close to rcp

Ballesta et al., Nature Physics 2008

Speckle Visibility SpectroscopyBy the group of Doug Durian

Speckel contrast cI(t,) = - 1

< Ip(t) Ip(t)>p

< Ip(t)>p<Ip(t)>p

Dynamics on the time scale of the CCD exposure time

Pros:• “Light” algorithm (can be calculated on the fly)• Fast time scales (µsec – msec)

Cons:• Time delays larger than the exposure time are not accessible• Need to adjust laser power to probe different time scales• Different time scales require separated runs

2.3 mm

Space-resolved DLS: Photon Correlation Imaging

diaphragm

lens

object plane

image plane

focal plane

CC

D

sample

= 90° 1/q ~ 45 nm

Duri et al., Phys. Rev. Lett. 2009

2.3 mm

Local, instantaneous dynamics: cI( t, ,r)

< Ip(t) Ip(t +)>p(r)

< Ip(t)>p<Ip(t +)>p(r)

cI(t, , r) = - 1

Note: << cI(t, , r) >t>r = g2()-1

[g2()-1] ~ f()2

DAM movie: 2x real time, 6.15 x 4.69 mm2 , lag = 40 msec

Dynamical Activity Maps: foam

cI

0.0

1.0

Dynamical Activity MapDynamical Activity Map

cI (r, tw,)local

rearrangement

no motion

DAM movie: 2x real time, 6.15 x 4.69 mm2 , lag = 40 msec

cI

0.0

1.0

Dynamical Activity MapDynamical Activity Map

cI (r, tw,)local

rearrangement

no motion

Dynamical Activity Maps: foam

Random in time, correlated in space

Sessoms et al., Soft Matter 2010

Strain field and µ-scopic dynamics

J. Kaiser, O. Lielig,, G. Brambilla, LC, A. Bausch, Nature Materials 2011

Dynamics of actin/fascin networks

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300

0

50

100

150

200

250

Average displacement : 0.75 µmStandard deviation: 0.48 µm

cos, where is the angle w/ respect to x axis

ActinFascinJonaR0.1_night.avi: data taken fromF:\4CAMS\Jona\090220_sample4\CCD3\NightDisplacement map calculated for images 3935 and 4100 (MI00001.dat), corresponding to 10510 sec after preparing the sample.boxsize 40 pixels, average over 4 frames, time lag is 330 sec. 1 pixel = 2.2 µm

Y c

oord

inat

e (µ

m)

X coordinate (µm)5 µm

-1.000

-0.8000

-0.6000

-0.4000

-0.2000

0

0.2000

0.4000

0.6000

0.8000

1.000

During polymerization(displacement map over 330 sec)strain field @ late stages of network formation

104 105

0.1

1

<r

( =

330

s)>

time after preparing sample (sec)

ageaverage strain field microcopic dynamics

Dynamic Activity Maps: gels

Colloidal gelg2()-1~ exp[-(/r)1.5]r = 5000 s

cI (t0,r/10 , r)

Movie accelerated 500x

2 mm

0 2 4 60.0

0.5

1.0 Onion gel Colloidal gel "Artificial skin", RH = 12% "Artificial skin" AS, RH = 62% Soft spheres, T = 24.5°C, ~0.69

Soft spheres, T = 28°C, ~0.57 Hard Spheres, ~0.5468 Hard Spheres ~0.5957

r (mm)

G4(

r), G

4(r)

~Spatial correlation of the dynamics: ~ system size in jammed soft matter!

Maccarrone et al., Soft Matter 2010

Space experiments

ESA Proposal (2004): Solidification of Colloids in space: structure and dynamics of crystal, gel, and glassy phases

Piazza (Milano), Van Blaaderen, Kegel (Utrecht), Cipelletti (Montpellier)

Motivation for µ-g: - Solid like structures -> gravitational stress transmitted over large distances.- Mixture of particles with different .- Slow dynamics -> long experiments, ISS

Space experiments

Original plan : investigate slow dynamics and DH in glassy colloidal systems (repulsive, attractive)

Difficulty: only a limited set of samples will (hopefully) be flown

Proposal: depletion force: a system with tunable (thermosensitive) attractive interactions

DEPLETION EFFECTS IN COLLOIDSADDING TO A SUSPENSION OF LARGE SPHERES

SMALLER SPHERES (POLYMERS, SURFACTANT MICELLES)…

SMALL SPHERES CANNOT ENTER HERE!

Osmotic pressure unbalance yields an ATTRACTIVE

force between colloids

U = Vexc

IF the depletant can be regarded as an IDEAL GAS

AO POTENTIAL

FORCE VIEW

Large particles subtract free volume to the small ones (which DOMINATE ENTROPY)

Small spheres gain entropy by PHASE SEGREGATION

of the large colloids

ENTROPY VIEW

DEPLETANT: Triton X100

● When added to a MFA suspension, first adsorbs on the particles, leading to colloid stabilization even in the presence of salt

● A nonionic surfactant forming globular micelles in a wide conc. range

Hydrophilic head

Hydrophobic tail

r ≈3.4 nmAggregation number

N ≈ 100

● At higher surfactant concentration:

MICELLAR DEPLETION

0

0.05

0.10

0.15

0 0.2 0.4 0.6 0.8P

s

FLUID

SOLID

GEL

TO THE ROOTS OF GELATION

GELATION ASARRESTED SPINODAL

DECOMPOSITION

Miller & Frenkel coex. line for AHS

BIRTH OF A GELQuenching into the L-L gap:

FAST SEDIMENTATION (hours vs. months!)

A MUCH MORE EXPANDED PHASE

0.01

0.1

1

10

0.05 0.1 0.2 0.5

3 /

k BT

COMPRESSION MODULUS: A POWER LAW BEHAVIOR

A) COLLAPSE OF

DEPLETION GELSG. Brambilla, S. Buzzaccaro, R. P.,

L. Berthier, and L. Cipelletti

(to appear in PRL)

D) Collapse and ageing of a gel: macroscopic dynamics Time evolution of the gel height (P ≈ 0.12,Uatt ≈ 4.5 kBT )

Spinodal decomposition and cluster formation

Settling of a cluster phase(linear in time)

GELATION

Poroelastic restructuringof an arrested gel

THE POROELASTIC REGIME

PICTURE: A FLUID (COUNTER)FLOWING THROUGH AN ELASTIC POROUS MEDIUM

zK

gzt

)()(

● FORCE BALANCE:

PERMEABILITYGRAVITATIONAL

STRESSELASTIC

RESPONSE

● INPUT FOR NUMERICAL SIMULATIONS:EFFECTIVE COMPRESSIONAL MODULUS

IN RESPONSE TO AN APPLIED STRESS FROM STEADY-STATE PROFILE

)(K

a

i)

m)1()( 0 WITH 0 AND m CHOSEN TO FIT THE

TIME-DEPENDENCE OF THE GEL HEIGHTii)

VELOCIMETRY

● THE VELOCITY PROFILE IS ALMOST LINEAR FOR ANY SETTLING TIME, EXCEPT IN THE UPPERMOST LAYER OF THE GEL.

LOCAL SETTLING VELOCITY v(t) (AT VARIOUS SETTLING TIMES)

t =30 h

t =80 h

● A z-INDEPENDENT (BUT t-DEPENDENT)

STRAIN RATE: dzdvt /)(

Collapse and ageing of a gel: microscopic dynamics

Local TRC correlationfunctions in the gel

SAME decay time at all values of z(like for strain rate!)

1/e scales as -1

B) CRITICAL DEPLETANTS(depletion vs. critical Casimir effect)

S. Buzzaccaro, J. Colombo, A. Parola, and R. P.Phys. Rev. Lett. 105, 198301 (2010)

COLLOID PHASE SEPARATION IN CRITICAL MIXTURES

CRITICAL CASIMIR EFFECT

Casimir forces pop up also when fluctuations are thermal instead of quantum, e. g. close to L-L demixing.

A “depletion” of critical fluctuations!

Fisher - De Gennes 1978 Dietrich & coworkers (1998)

Universal scaling of the force between a colloidal particle immersed in a critical binary mixture and the container walls

C. Bechinger & coworkers (2008):

TIRM measurements of forces between a silica plate and a polystyrene sphere dispersed in a critical liquid mixture.

SURFACE TRANSITIONS

(CRITICAL WETTING)

NOT NECESSARILY LINKED TO BULK

SEPARATION

!

Critical wetting layer ?

(Beysens & Estève, 1985) Beysens and Esteve, 1985

EXPERIMENTALRANGE

• Forms globular micelles in a wide conc. range

• Micellar radius r ≈ 3.4 nm → q = r/R ≈ 0.04

• Adsorbs on MFA, leading to steric stabilization

• MICELLAR DEPLETION at larger surfactant concentration

DEPLETANTC12E8 - nonionic surfactant

Hydrophilic head

Hydrophobic tail

C12E8 concentration

T

≈ 70°C

≈ 2%

L-L coexistence

LC r ≈3.4 nmAggregation number

N ≈ 100

GlobularMicelles

• PHASE SEPARATION WITH WATER BY RAISING T

0

10

20

30

40

50

60

70

2 4 6 8 10

volume fraction C12E8

T (C

)MINIMUM SURFACTANT AMOUNT TO INDUCE PHASE SEPARATION vs. T

C12E8/WATER COEXISTENCE GAP

-temperature

STABLE

PHASE SEPARATED

0.2

0.5

1

2

5

10

0.01 0.1 1

cs- cc =A2/3

(cs, Ts) (104 Pa)

c s - c

c (%

w/w

)SEPARATION vs. OSMOTIC PRESSURE

T - Tc ≈ 4°C: has decreased by a factor of 200.Two orders of magnitude increase in depletion “efficiency”!

0.1

1

10

1 2 5 10

csep - ccrit = a ; 1.8

(csep, Tsep) [nm]

c sep-

cc

(%)

SEPARATION POINTS vs.

2.03.03 TTc 3/2 csep cc

8.1 csep ccBUT:

ALMOST T-INDEPENDENT!

0

0.05

0.10

0.15

0 4 8 12

x 102

3 /k

BT

What we would need to use Foam C

Levels of confinement to be checked

Stirring capability

Temperature control would enable us to span a wide range of attractive forces with one single sample. T up to ~70°C, actual range/accuracy to be checked with R. Piazza

Long runs: moderate frame rate (down to 10 Hz), tens of tau spanning several decades -> image storage and post processing.~1 Gb / run, post processing time ~ 10'.

Ground tests on the setup!

Thanks!

Collaborators: V. Trappe (Fribourg)Students: P. Ballesta, G. Brambilla, A. Duri, D. El MasriPostdocs: S. Maccarrone, M. PiernoFunding: CNES, ESA, Région Languedoc Roussillon, ANR, MIUR.