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

lucacip@lcvn.univ-montp2.fr

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