‘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 CNRS
2Politecnico di Milano
V. Trappe
Fribourg 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
Keys et al. Nat. Phys. 2007
Colloidal Hard Spheres
Weeks et al. Science 2000
Repulsive disks
A. Widmer-Cooper Nat. Phys. 2008
CCD-based Dynamic Light Scattering
sample
CCD
diaphragm
Time Resolved Correlation (TRC)
lag t
degree of correlation cI(t,t) =
time t
< Ip(t) Ip(t +t)>p
< Ip(t)>p<Ip(t +t)>p
-1
Cipelletti et al. J. Phys:Condens. Matter 2003,
Duri et al. Phys. Rev. E 2006
degree of correlation cI(t,t) =
Average over t
g2(t)-1
intensity correlation
function g2(t) - 1
0.4
0.2
0.0
2
10 10
10
3
t (sec)
g2(t) - 1 ~ f(t)2
4
10
10
5
Average
dynamics
< Ip(t) Ip(t +t)>p
< Ip(t)>p<Ip(t +t)>p
-1
degree of correlation cI(t,t) =
< Ip(t) Ip(t +t)>p
< Ip(t)>p<Ip(t +t)>p
Average over t
fixed t, vs. t
intensity correlation
function g2(t) - 1
fluctuations of the dynamics
0.4
cI(t,t)-1
g2(t)-1
-1
0.2
0.0
2
10 10
10
3
t (sec)
g2(t) - 1 ~ f(t)2
10
4
10
5
0
10
4
2x10
4
t (sec)
Average
dynamics
var[cI(t)] ~ c(t)
10mm
Brownian particles
100mm
Gillette Comfort Glide Foam
Intensity correlation function
Homogeneous vs heterogeneous dynamics
Dynamical susceptibility
Colloids close to rcp
0.4
c*
0.02
Supercooled liquid (Lennard-Jones)
0.2
0.01
g2(t)-1
var(cI)
0.3
0.1
0.00
0.0
2
10
3
4
10
10
t (sec)
5
10
Ballesta et al., Nature Physics 2008
• PVC in DOP
• a ~ 5 µm
• polidispertsity ~33%
• j close to rcp
Lacevic et al., Phys. Rev. E 2002
Speckle Visibility Spectroscopy
By the group of Doug Durian
Speckel contrast cI(t,t = 0) =
< Ip(t) Ip(t)>p
< Ip(t)>p<Ip(t)>p
-1
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
Space-resolved DLS: Photon Correlation
Imaging
sample
object
plane
Dq
Dq
lens
focal plane
CCD
diaphragm
image plane
2.3 mm
Duri et al., Phys. Rev. Lett. 2009
q = 90°
1/q ~ 45 nm
Local, instantaneous dynamics: cI( t, t, r)
< Ip(t) Ip(t +t)>p(r)
cI(t, t , r) =
-1
< Ip(t)>p<Ip(t +t)>p(r)
Note: << cI(t, t , r) >t>r = g2(t)-1
[g2(t)-1] ~ f(t)2
2.3 mm
Dynamical Activity Maps: foam
Dynamical Activity Map
no motion
1.0
cI
0.0
cI (r, tw,t)
DAM movie: 2x real time,
6.15 x 4.69 mm2 , lag t = 40 msec
local
rearrangement
Dynamical Activity Maps: foam
Dynamical Activity Map
no motion
1.0
cI
0.0
cI (r, tw,t)
DAM movie: 2x real time,
6.15 x 4.69 mm2 , lag t = 40 msec
local
rearrangement
Random in time, correlated in space
Sessoms et al., Soft Matter 2010
Strain field and µ-scopic dynamics
Dynamics of actin/fascin networks
D u rin g p olym erization
strain field
@lacem
lateen tstages
formation
(d isp
m ap o v erof
3 3 0network
sec)
Y coordinate (µ m )
250
cos q , w h ere q is th e an gle
w / resp ect to x ax is
200
-1.0 00
-0.8 00 0
150
-0.6 00 0
-0.4 00 0
100
-0.2 00 0
0
0 .2 0 00
50
0 .4 0 00
0 .6 0 00
0
0 .8 0 00
J. Kaiser, O. Lielig,, G. Brambilla,
LC, A. Bausch, Nature Materials
2011
1 .0 0 0
0
100
200
300
40 0
5 µm
50 0
60 0
7 00
8 00
9 00
1000
1 10 0
1 20 0
1 30 0
X c oordinate (µ m )
A v erage
d isplacem
en t : 0 .7 5 µ m
average
strain
field
microcopic dynamics
S tan dard d ev iatio n : 0 .48 µ m
<Dr(t =330 s)>
A ctinF ascin Jon aR 0 .1 _ n ig ht.av i: d ata tak en fro m
F:\4 C A M S1
\Jo na\0 9 02 2 0_ sam ple4 \C C D 3 \N ig h t
D isplacem en t m ap calcu lated for im ag es 3 9 3 5 an d 4 10 0 (M I0 0 00 1 .d at),
co rresp on d in g to 1 05 1 0 sec after p rep arin g th e sam p le.
bo x size 4 0 pixels, av erag e ov er 4 fram es, tim e lag is 3 30 sec. 1 pixel = 2 .2 µ m
0.1
4
10
time after preparing sample (sec)
10
5
age
Dynamic Activity Maps: gels
Colloidal gel
g2(t)-1~ exp[-(t/tr)1.5]
tr = 5000 s
cI (t0,tr/10 , r)
Movie accelerated 500x
2 mm
1.0
Onion gel
Colloidal gel
"Artificial skin", RH = 12%
"Artificial skin" AS, RH = 62%
Soft spheres, T = 24.5°C, j ~0.69
Soft spheres, T = 28°C, j ~0.57
Hard Spheres, j ~0.5468
Hard Spheres j ~0.5957
4
~
G (Dr), G (Dr)
Spatial correlation of the dynamics:
x ~ system size in jammed soft matter!
4
0.5
0.0
0
2
4
Dr (mm)
6
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 r.
- 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 COLLOIDS
ADDING TO A SUSPENSION OF LARGE SPHERES
SMALLER SPHERES (POLYMERS, SURFACTANT MICELLES)…

FORCE VIEW

SMALL SPHERES
CANNOT ENTER HERE!



Osmotic pressure unbalance
yields an ATTRACTIVE
force between colloids
IF the depletant can be regarded as an IDEAL GAS
AO POTENTIAL
U = Vexc
ENTROPY VIEW
Large particles subtract
free volume to the small ones
(which DOMINATE ENTROPY)
Small spheres gain entropy by
PHASE SEGREGATION
of the large colloids
DEPLETANT: Triton X100
● A nonionic surfactant forming globular micelles in a wide conc. range
Hydrophilic head
Hydrophobic tail
r ≈3.4 nm
Aggregation number
N ≈ 100
● When added to a MFA suspension, first adsorbs on the particles,
leading to colloid stabilization even in the presence of salt
● At higher surfactant concentration:
MICELLAR DEPLETION
TO THE ROOTS OF GELATION
0.15
GELATION AS
ARRESTED SPINODAL
DECOMPOSITION
GEL
0.10
s
Miller & Frenkel
coex. line for AHS
0.05
FLUID
0
SOLID
0
0.2
0.4
P
0.6
0.8
BIRTH OF A GEL
Quenching into the L-L gap:
FAST SEDIMENTATION
(hours vs. months!)
A MUCH MORE EXPANDED PHASE
COMPRESSION MODULUS: A POWER LAW BEHAVIOR
1
3
B
 / k T
10
0 .1
0 .0 1
0 .0 5
0 .1
0 .2

0 .5
A) COLLAPSE OF
DEPLETION GELS
G. 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 restructuring
of an arrested gel
THE POROELASTIC REGIME
PICTURE: A FLUID (COUNTER)FLOWING
THROUGH AN ELASTIC POROUS MEDIUM
● FORCE BALANCE:
    ( ) 
K ( ) 
=
 Drg 

t
z  

z


PERMEABILITY
GRAVITATIONAL
STRESS
● INPUT FOR NUMERICAL SIMULATIONS:
i)
K ( ) = 
ii)  (  ) =  0

EFFECTIVE COMPRESSIONAL MODULUS

IN RESPONSE TO AN APPLIED STRESS

FROM STEADY-STATE PROFILE
(1 -  )

m
WITH 0 AND m CHOSEN TO FIT THE
TIME-DEPENDENCE OF THE GEL HEIGHT



ELASTIC
RESPONSE
 = a30.3
VELOCIMETRY
LOCAL SETTLING VELOCITY v(t) (AT VARIOUS SETTLING TIMES)
● THE VELOCITY PROFILE IS ALMOST
LINEAR FOR ANY SETTLING TIME, EXCEPT
IN THE UPPERMOST LAYER OF THE GEL.
t =30 h
● A z-INDEPENDENT (BUT t-DEPENDENT)
STRAIN RATE:
 ( t ) = dv / dz
t =80 h
Collapse and ageing of a gel: microscopic dynamics
Local TRC correlation
functions in the gel
SAME decay time at all values of z
(like for strain rate!)
t1/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
(Beysens & Estève, 1985)
Beysens and Esteve, 1985
SURFACE
TRANSITIONS
(CRITICAL
WETTING)
Critical wetting layer ?NOT NECESSARILY
LINKED TO BULK
CRITICAL CASIMIR EFFECT
SEPARATION
Fisher - De Gennes 1978
Dietrich & coworkers (1998)
C. Bechinger & coworkers (2008):
Casimir forces pop up also when
fluctuations are thermal instead of
quantum, e. g. close to L-L demixing.
Universal scaling of the
force between a colloidal
particle immersed in a
critical binary mixture and
the container walls
TIRM measurements of forces
between a silica plate and a
polystyrene sphere dispersed in
a critical liquid mixture.
A “depletion” of critical fluctuations!
!
Hydrophilic head
DEPLETANT
C12E8 - nonionic surfactant
Hydrophobic tail
• 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
• PHASE SEPARATION WITH WATER BY RAISING T
T
L-L coexistence
≈ 70°C
Globular
Micelles
LC
EXPERIMENTAL
RANGE
≈ 2%
C12E8 concentration
r ≈3.4 nm
Aggregation number
N ≈ 100
MINIMUM SURFACTANT AMOUNT TO INDUCE PHASE SEPARATION vs. T
70
C12E8/WATER COEXISTENCE GAP
60
PHASE
SEPARATED
T (C)
50
40
q-temperature
30
20
STABLE
10
0
2
4
6
volume fraction C12E8
8
10
SEPARATION vs. OSMOTIC PRESSURE
10
cs- cc =A2/3
cs - cc (% w/w)
5
2
1
0.5
0.2
T - Tc ≈ 4°C:  has decreased by a factor of 200.
Two orders of magnitude increase in depletion “efficiency
0.01
0.1
 (cs, Ts) (104 Pa)
1
SEPARATION POINTS vs. x
csep- cc (%)
10
1
csep - ccrit = ax- ;
0.1
1
2
  1.8
5
x(csep, Tsep) [nm]
10
c sep - c c  
BUT:
c sep - c c  x
2/3
x
- 1 .8
3
x
0 .3
 T c - T )
ALMOST T-INDEPENDENT!
0.15
3
B
x /k T
0.10
0.05
0
0
0 .2
4
8
2
 x 10
12
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!
Collaborators: V. Trappe (Fribourg)
Students: P. Ballesta, G. Brambilla, A. Duri, D. El Masri
Postdocs: S. Maccarrone, M. Pierno
Funding: CNES, ESA, Région Languedoc Roussillon, ANR, MIUR.
Thanks!