unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming...
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![Page 1: Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition Luca Cipelletti 1,2, Pierre Ballesta 1,3, Agnès](https://reader031.vdocument.in/reader031/viewer/2022012919/56649eef5503460f94bff41f/html5/thumbnails/1.jpg)
Unexpected drop of dynamical heterogeneities in colloidal suspensions
approaching the jamming transition
Luca Cipelletti1,2, Pierre Ballesta1,3, Agnès Duri1,4
1LCVN Université Montpellier 2 and CNRS, France2Institut Universitaire de France3SUPA, University of Edinburgh
4Desy, Hamburg
P. Ballesta, A. Duri, and L. Cipelletti, Nature Physics 4, 550 (2008).
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Soft glassy materials
Eric Weeks
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Soft glassy materials
Eric Weeks
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Outline
• What are dynamical heterogeneities ?
• Why should we care about DH ?
• How can we measure DH ?
• Shaving cream: a model system for DH
• Colloids: DH (very) close to jamming
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What quantities should we measure?
Space and time-resolved correlation functions f(t,t+,r) or particle displacement
• Simulations (« far » from Tg!)
• Granular systems (2D, athermal, see Dauchot’s talk)
• (Confocal) microscopy on colloidal systems
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Simulations (LJ)
L. Berthier, PRE 2002
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Dynamical length scale in 2D granular media
Keys et al., Nat. Phys. 2007 Lechenault et al., EPL 2008
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Confocal microscopy on colloidal HS
Weeks et al. Science 00 Weeks et al., J. Phys. Cond. Mat 07
« »
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What quantities should we measure?
Space- and time-resolved correlation functions f(t,t+,r) or particle displacement
• Simulations (far from Tg!)
• Granular systems (2D, athermal)
• (Confocal) microscopy on colloidal systems
( stringent requirements on particles (size, optical
mismatch…), difficult close to jamming)
Time-resolved correlation functions f(t,t+) (no space resolution)
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Temporally heterogeneous dynamics
homogeneous
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Temporally heterogeneous dynamics
homogeneous heterogeneous
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Temporally heterogeneous dynamics
homogeneous heterogeneous
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Dynamical susceptibility in glassy systems
Supercooled liquid (Lennard-Jones)
Lacevic et al., PRE 2002
4 N var[Q(t)]
<Q
(t)>
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Dynamical susceptibility in glassy systems
4 N var[Q(t)] ~ N (1/Nblob) = N/Nblob
Nblob regions
4 () ~ '
3 ',',',',0t
tttftttfd rr
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How can we measure 4?
Time-resolved light scattering experiments (TRC)
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Experimental setup
CCD-based (multispeckle)Diffusing Wave Spectroscopy
CCDCamera
Las
er b
eam
Change in speckle field mirrors change in sample configuration
Random walk w/ step l*
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Time Resolved Correlation
time twlag
2-time correlation function
Cipelletti et. Al JPCM 03, Duri et al. PRE 2005
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intensity correlation function g2(1
Average over tw
Average dynamicsg2(1
fixed , vs. tw
fluctuations of the dynamics
var(g2)() ‘dynamical susceptibility’
tw (sec)g 2(
t w,
)
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Outline
• What are dynamical heterogeneities ?
• Why should we care about DH ?
• How can we measure DH ?
• Shaving cream: a model system for DH
• Colloids: DH (very) close to jamming
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A « model system »: shaving creamD.J. Durian, D.A. Weitz, D.J. Pine (1991) Science 252, 686
g2-1 = fraction of paths not rearranged
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A « model system »: shaving cream
3D foam (DWS)
Mayer et al. PRL 2004
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age dependence of
10-2 10-1 100
10-8
10-7
10-6
10-5
10-4
10-3
tw (sec)
3348 5250 6760 1769610295 2180114265 26118
(t w
,t)
t (sec)
Coarsening of the foam
t
w
tw
tw
4
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Scaling of during coarsening
10-1 100 101
10-4
10-3
10-2
10-1
100
101
tw (sec)
3348 5250 6760 17696 10295 21801 14265 26118
(t w
,t)
/l*3 (
cm-3)
(tw)t
Less bubbles more fluctuations!
t
wl
(c
m-3)
tw
10-2 10-1 100
10-8
10-7
10-6
10-5
10-4
10-3
tw (sec)
3348 5250 6760 1769610295 2180114265 26118
(t w
,t)
t (sec)
4
4
Mayer et al. PRL 2004
Nblob
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Outline
• What are dynamical heterogeneities ?
• Why should we care about DH ?
• How can we measure DH ?
• Shaving cream: a model system for DH
• Colloids: DH (very) close to jamming
![Page 25: Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition Luca Cipelletti 1,2, Pierre Ballesta 1,3, Agnès](https://reader031.vdocument.in/reader031/viewer/2022012919/56649eef5503460f94bff41f/html5/thumbnails/25.jpg)
Experimental system
PVC xenospheres in DOP• radius R ~ 5 m• Polydisperse (~ 33%)• Brownian• Excluded volume interactions• = 64% – 75% (close to jamming)• L = 2 mm• l* = 200 m
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« Diluted » samples
10-6 10-5 10-4 10-3 10-2 10-1 10010-20
10-19
10-18
10-17
10-16
10-15
= 28% = 46%
<r
2 ()>
(m
2 )
(sec)
1Brownian behavior
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« Diluted » samples
10-6 10-5 10-4 10-3 10-2 10-1 10010-20
10-19
10-18
10-17
10-16
10-15
= 28% = 46%
<r
2 ()>
(m
2 )
(sec)
1
R/100 !!
DWS probes dynamics on a length scale
l*/L ~ 10 – 35 nm << R
L
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Concentrated samples: slow dynamics
1E-4 1E-3 0.01 0.1 1 100.0
0.2
0.4
0.6
0.8
1.0
C:\lucacip\ParisToCopy\FluctuationsTheoryg 2
- 1
(arb .un.)
B ###
Fast dynamics(phototube)
Slow dynamics(CCD)
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2-time intensity correlation function
• Initial regime: « simple aging » (0 ~ tw1.1 0.1)
• Crossover to stationary dynamics, large fluctuations of s
101 102 103 104 105
0,00
0,02
0,04
0,06
C:\lucacip\doc\papers\WorkInProgress\2004JapanMeeting2003\Figures\Pierre40pcr030422
tw (sec)
1194 4400 7900 14900 21900 44083 54800
n42 n500 n1000 n2000 n3000 n6169 n7700
g 2(t
w,t w
)-1
(sec)
0 40000 800000
500
1000
C:\lucacip\doc\papers\WorkInProgress\2004JapanMeeting2003\Figures\Pierre40pcr030422
s (se
c)
tw (sec)
TODO: check tw = 0
Fit: g2(tw,tw+1 = aexp[-(/)]
= 66.4%
(
sec)
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Average dynamics
Relaxation time 0 ~ 04.001.1
1 c
c = 0.752
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Average dynamics
Stretching exponent
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Fluctuations of the dynamics:
= 0.738
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vs 4: different normalization
In our experiments:
No N factor
~ correlation volume*4
• N is not known precisely• Need model to extract correlation volume 3 from
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Fluctuations of the dynamics: vs
2.05.1
1 c
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Measurement time issue?
Merolle et al., PNAS 2005
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Measurement time issue?
tseg tseg tseg tseg tseg tseg
g2(t,)-1
Does *(tseg,) depend on tseg ?
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Not a measurement time issue !
10-3 10-2 10-1 100 101 102 103
10-2
10-1
100
eff
0.637 0.6638 0.693 0.7152 0.7247 0.7377 0.7383 0.7442 0.7455
F F F F F F F F F
*(t
seg)
/*(t
exp)
tseg/0
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Proposed physical mechanism
Competition between :
Growth of on approaching c
Smaller displacement associated with each rearrangement event (tigther packing)
Nblob *
More events *required torelax system
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DWS and intermittent dynamicsInspired by Durian, Weitz & Pine (Science, 1991)
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Light is decorrelated
DWS and intermittent dynamicsInspired by Durian, Weitz & Pine (Science, 1991)
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Light is decorrelated
DWS and intermittent dynamicsInspired by Durian, Weitz & Pine (Science, 1991)
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Light is decorrelated
DWS and intermittent dynamicsInspired by Durian, Weitz & Pine (Science, 1991)
Number of events betweent and t +
Mean squared change of phase for1 event
2
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Light is decorrelated
DWS and intermittent dynamicsInspired by Durian, Weitz & Pine (Science, 1991)
p = 1 « brownian » rearrangements
p = 2 « ballistic » rearrangements
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Simulations
• Photon paths as random walks on a 3D cubic lattice
• Lattice parameter = l*, match cell dimensions
• Random rearrangement events of size 3
• Calculate with
Parameters :
• p (use one single p for all )3
2 (we expect 2
as
c )
2)(12 ),(1),(
s
s tgtg
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Simulations vs. experiments
simulations
experiments
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Simulation parameters
p = 1.65 supradiffusive motion
3 - grows continuously with -very large!!
Cell thickness!
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Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
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Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Competition between- increasing size of dynamically correlated regions
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Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Competition between- increasing size of dynamically correlated regions
- decreasing effectiveness of rearrangements
Dynamical heterogeneity dictated by the number of rearrangements needed to relax the system on the probed length scale
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Thanks to…
V. TrappeD. WeitzL. BerthierG. BiroliM. Cloître
CNESSoftcompACIIUF
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Scaling of * (revisited)
* ~ 1 / (# rearrangements in the scattering volume needed to decorrelate the scattered light)
* ~ 1/(Nblob Nev)
Nblob , Nev depend on , q, tw, …
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Length scale dependence of
Increasing q
104 105
0.01
0.1
*
q (cm-1)
slope 1.14 +/- 0.11
Duri & LC, EPL 76, 972 (2006)
Strongly attractive colloidal gel (Nblob = 1)
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Strongly attractive gels: scaling of *
* ~ var(Nev)/<Nev>2 ~ <Nev>-1
< Nev > ~ f ~ q-1
* ~ q
Duri & LC, EPL 76, 972 (2006)
104 105103
104 1.05 ± 0.04
f (se
c)
q (cm-1)
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Jump size
2 2
~[/l*]2~1/R2
~1/10
~ R ~ 10-3R
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Colloidal gel
• buoyancy-matched polystyrene colloids
• low volume fraction 10-4 ÷ 10-3
• screen charges “fast” aggregation (DLCA)
21 nm diam suspended in H2O/D2O
MgCl2 16 mM
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Time-averaged dynamics
g2(q,) - 1 ~ [f(q,)]2 kj kjiqf
,)0()(exp),( rrq
• Fast dynamics: overdamped vibrations(~ 500 nm) Krall & Weitz PRL 1998
• Slow dynamics: rearrangements
pfqg exp~1),(2
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q dependence of f and p
« compressed » exponential
104 105103
104 1.05 ± 0.04
f (se
c)
q (cm-1)
« ballistic » motion
pfqg exp~1),(2
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A surprising but quite general behavior!
Onion gel Micellar polycrystal Conc. Emulsion
f(q,) exp[-(t/f) p], f q-1, p > 1
Laponite Depletion gels, …
Ramos & Cipelletti PRL 2001 Cipelletti et al Faraday Discuss 2003
Bandyopadhyay et al. PRL 2004 Chung et al. PRL 2006
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Compressed exponential
f(q,) exp[-(t/f) 1.5]
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4 increases when decreasing T
Glotzer et al.
Decreasing T