Colloids in space
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Transcript Colloids in space
‘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
= a30.3
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 =A2/3
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!