dynamical heterogeneity at the jamming transition of concentrated colloids p. ballesta 1, a. duri 1,...
TRANSCRIPT
Dynamical heterogeneity at the jamming transition of concentrated
colloids
P. Ballesta1, A. Duri1, Luca Cipelletti1,2
1LCVN UMR 5587 Université Montpellier 2 and CNRS, France
2Institut Universitaire de France
Heterogeneous dynamics
homogeneous
Heterogeneous dynamics
homogeneous heterogeneous
Heterogeneous dynamics
homogeneous heterogeneous
Dynamical susceptibility in glassy systems
Supercooled liquid (Lennard-Jones)
Lacevic et al., PRE 2002
4 var[Q(t)]
Dynamical susceptibility in glassy systems
4 var[Q(t)] 4 dynamics spatially correlated
N regions
4 increases when decreasing T
Glotzer et al.
Decreasing T
Outline
• Measuring average dynamics and 4 in colloidal suspensions
• 4 at very high : surprising results!
• A simple model of heterogeneous dynamics
Experimental system & setup
PVC xenospheres in DOPradius ~ 10 m, polydisperse = 64% – 75%Excluded volume interactions
Experimental system & setup
CCD-based (multispeckle)Diffusing Wave Spectroscopy
CCDCamera
Las
er b
eam
Change in speckle field mirrors change in sample configuration
Probe << Rparticle
Time Resolved Correlation
time twlag
degree of correlation cI(tw,) = - 1< Ip(tw) Ip(tw +)>p
< Ip(tw)>p<Ip(tw +)>p
2-time intensity correlation function g2(tw,1
fixed tw, vs.
2-time intensity correlation function
• Initial regime: « simple aging » (s ~ 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
= 66.4%
Fit: g2(tw,exp[-(/s
(tw))p(tw)]
2-time intensity correlation function
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
= 66.4%
Fit: g2(tw,exp[-(/s(tw))p(tw)]
Average dynamics :
< s >tw , < p >tw
Average dynamics vs
Average relaxation time
Average dynamics vs
Average relaxation time Average stretching exponent
fixed , vs. tw
fluctuations of the dynamics
var(cI)()
Fluctuations from TRC data
time twlag
degree of correlation cI(tw,) = - 1< Ip(tw) Ip(tw +)>p
< Ip(tw)>p<Ip(tw +)>p
Fluctuations of the dynamics vs
var(cI) 4
(dynamical susceptibility)
= 0.74
Fluctuations of the dynamics vs
var(cI) 4
(dynamical susceptibility)
Max of var (cI)
= 0.74
A simple model of intermittent dynamics…
A simple model of intermittent dynamics…
r
Durian, Weitz & Pine (Science, 1991)
fully decorrelated
Fluctuations in the DWP model
r
Random number of rearrangements
g2(t,) – 1 fluctuates
Fluctuations in the DWP model
r
Random number of rearrangements
g2(t,) – 1 fluctuates
r increases
fluctuations increase
Fluctuations in the DWP model
r
r increases
fluctuations increase
increa
sing
r,
Approaching jamming…
r
partially decorrelated
partially decorrelated
Approaching jamming…
r
Probability of n events during
Correlation after n events
Approaching jamming…
r
Poisson distribution:
Approaching jamming…
r
Poisson distribution:
Random change of phase
Correlated change of phase
Approaching jamming…
r
Poisson distribution:
Random change of phase
Correlated change of phase
Approaching jamming…
r
Poisson distribution:
1.5
Average dynamics
increasing
decreasing 2
10-3 10-2 10-1 1 10 1020.5
1.0
1.5
2.0
p
increasing
Fluctuations
r
Near jamming : small 2 many events small flucutations
Moderate : large 2 few events large flucutations
Fluctuations
10-2 10-1 1 10 102
10-3
10-2
10-1
0.01
0.1
10
var(
c I)
(arb. un.)
1
increasing
decreasing 2
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Competition betweenincreasing size of dynamically correlated regions ...
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Competition betweenincreasing size of dynamically correlated regions anddecreasing effectiveness ofrearrangements
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Competition betweenincreasing size of dynamically correlated regions anddecreasing effectiveness ofrearrangements
Dynamical heterogeneity dictated by the number of rearrangements needed to decorrelate
A further test…
Single scattering, colloidal fractal gel (Agnès Duri)
A further test…
2 q2 2look at different q!
A further test…
2 q2 2look at different q!
A further test…
104
0.01
0.1
*
q (cm-1)
2
~ (q)2
2 q2 2look at different q!
Fluctuations of the dynamics vs
St. dev. of relaxation time St. dev. of stretching exponent
Average dynamics vs
0.64 0.68 0.72 0.76
103
104
c= 0.752
s (se
c)
eff
s ~ |
eff
c|-1.01
Average relaxation time
Dynamical hetereogeneity in glassy systems
Supercooled liquid (Lennard-Jones)
Glotzer et al., J. Chem. Phys. 2000
4 increases when approaching Tg
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Many localized, highly effective rearrangements
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Many localized, highly effective rearrangements
Many extended, poorly effective rearrangements
Conclusions
Dynamics heterogeneous
Non-monotonic behavior of *
Many localized, highly effective rearrangements
Many extended, poorly effective rearrangements
Few extended, quite effectiverearrangements
General behavior
Time Resolved Correlation
time twlag
degree of correlation cI(tw,) = - 1< Ip(tw) Ip(tw +)>p
< Ip(tw)>p<Ip(tw +)>p
