Dynamical heterogeneity at the jamming transition of concentrated colloids
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LCVN. Dynamical heterogeneity at the jamming transition of concentrated colloids. P. Ballesta 1 , A. Duri 1 , Luca Cipelletti 1,2 1 LCVN UMR 5587 Université Montpellier 2 and CNRS, France 2 Institut Universitaire de France. [email protected] Heterogeneous dynamics. homogeneous.

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Dynamical heterogeneity at the jamming transition of concentrated colloids

LCVN

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

[email protected]



Heterogeneous dynamics1
Heterogeneous dynamics

heterogeneous

homogeneous


Heterogeneous dynamics2
Heterogeneous dynamics

heterogeneous

homogeneous


Dynamical susceptibility in glassy systems
Dynamical susceptibility in glassy systems

Supercooled liquid (Lennard-Jones)

Lacevic et al., PRE 2002

c4~ var[Q(t)]


Dynamical susceptibility in glassy systems1
Dynamical susceptibility in glassy systems

N regions

c4~ var[Q(t)]

c4 dynamics spatially correlated


Decreasing T

Glotzer et al.

c4 increases when decreasing T


Outline
Outline

  • Measuring average dynamics and c4 in colloidal suspensions

  • c4 at very high j : surprising results!

  • A simple model of heterogeneous dynamics


Experimental system setup
Experimental system & setup

PVC xenospheres in DOP

radius ~ 10 mm, polydisperse

j = 64% – 75%

Excluded volume interactions


Experimental system setup1
Experimental system & setup

CCD-based (multispeckle)

Diffusing Wave Spectroscopy

CCD

Camera

Laser beam

Change in speckle field mirrors change in sample configuration

Probe d << Rparticle


Time resolved correlation

lag t

time tw

fixed tw, vs.t

2-time intensity correlation function g2(tw,t) - 1

Time Resolved Correlation

degree of correlationcI(tw,t) = - 1

< Ip(tw) Ip(tw+t)>p

< Ip(tw)>p<Ip(tw+t)>p


2 time intensity correlation function
2-time intensity correlation function

f = 66.4%

Fit: g2(tw,t) ~ exp[-(t /ts (tw))p(tw)]

  • Initial regime: « simple aging » (ts ~ tw1.1 ± 0.1)

  • Crossover to stationary dynamics, large fluctuations of ts


2 time intensity correlation function1
2-time intensity correlation function

f = 66.4%

Fit: g2(tw,t) ~ exp[-(t/ts(tw))p(tw)]

Average dynamics :

< ts >tw , < p >tw


Average dynamics vs j
Average dynamics vs j

Average relaxation time


Average dynamics vs j1
Average dynamics vs j

Average relaxation time

Average stretching exponent


Fluctuations from trc data

lag t

time tw

fixed t, vs.tw

fluctuations of the dynamics

var(cI)(t)

c (t )

Fluctuations from TRC data

degree of correlationcI(tw,t) = - 1

< Ip(tw) Ip(tw+t)>p

< Ip(tw)>p<Ip(tw+t)>p


Fluctuations of the dynamics vs j
Fluctuations of the dynamics vs j

j = 0.74

var(cI) c4

(dynamical susceptibility)


Fluctuations of the dynamics vs j1
Fluctuations of the dynamics vs j

j = 0.74

var(cI) c4

(dynamical susceptibility)

Max of var (cI)



A simple model of intermittent dynamics1
A simple model of intermittent dynamics…

fully decorrelated

r

Durian, Weitz & Pine (Science, 1991)


Fluctuations in the dwp model
Fluctuations in the DWP model

Random number of rearrangements

g2(t,t) – 1 fluctuates

r


Fluctuations in the dwp model1
Fluctuations in the DWP model

Random number of rearrangements

g2(t,t) – 1 fluctuates

r

r increases

fluctuations increase


Fluctuations in the dwp model2
Fluctuations in the DWP model

increasing r,j

r

r increases

fluctuations increase


Approaching jamming
Approaching jamming…

partially decorrelated

r

partially decorrelated


Approaching jamming1
Approaching jamming…

Correlation after n events

r

Probability of n events during t


Approaching jamming2
Approaching jamming…

r

Poisson distribution:


Approaching jamming3
Approaching jamming…

r

Poisson distribution:

Random change of phase

Correlated change of phase


Approaching jamming4
Approaching jamming…

r

Poisson distribution:

Random change of phase

Correlated change of phase


Approaching jamming5
Approaching jamming…

r

Poisson distribution:

b»1.5


Average dynamics
Average dynamics

increasing j

decreasing sf2

increasing j


Fluctuations
Fluctuations

r

Moderate j : large sf2 few events large flucutations

Near jamming : small sf2 many events small flucutations


Fluctuations1
Fluctuations

increasing j

decreasing sf2


Conclusions
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Competition between

increasing size of dynamically

correlated regions ...


Conclusions1
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Competition between

increasing size of dynamically

correlated regions

and

decreasing effectiveness of

rearrangements


Conclusions2
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Competition between

increasing size of dynamically

correlated regions

and

decreasing effectiveness of

rearrangements

Dynamical heterogeneity dictated by the number of rearrangements

needed to decorrelate


A further test
A further test…

Single scattering, colloidal fractal gel (Agnès Duri)


A further test1

sf2 ~q2d 2look at different q!

A further test…


A further test2

sf2 ~q2d 2look at different q!

A further test…


A further test3

sf2 ~q2d 2look at different q!

A further test…


Fluctuations of the dynamics vs j 1 2
Fluctuations of the dynamics vs j (1/2)

St. dev. of stretching

exponent

St. dev. of relaxation time


Average dynamics vs j2
Average dynamics vs j

Average relaxation time


Dynamical hetereogeneity in glassy systems
Dynamical hetereogeneity in glassy systems

Supercooled liquid (Lennard-Jones)

Glotzer et al.,

J. Chem. Phys. 2000

c4 increases when approaching Tg


Conclusions3
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*


Conclusions4
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements


Conclusions5
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements

Many extended, poorly effective

rearrangements


Conclusions6
Conclusions

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements

Many extended, poorly effective

rearrangements

Few extended, quite effective

rearrangements

General behavior


Time resolved correlation1

lag t

time tw

Time Resolved Correlation

degree of correlationcI(tw,t) = - 1

< Ip(tw) Ip(tw+t)>p

< Ip(tw)>p<Ip(tw+t)>p


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