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Dynamical heterogeneity at the jamming transition of concentrated colloids

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LCVN

P. Ballesta1, A. Duri1, Luca Cipelletti1,2

1LCVN UMR 5587

Université Montpellier 2 and CNRS, France

2Institut Universitaire de France

homogeneous

heterogeneous

homogeneous

heterogeneous

homogeneous

Supercooled liquid (Lennard-Jones)

Lacevic et al., PRE 2002

c4~ var[Q(t)]

N regions

c4~ var[Q(t)]

c4 dynamics spatially correlated

Decreasing T

Glotzer et al.

c4 increases when decreasing T

- Measuring average dynamics and c4 in colloidal suspensions
- c4 at very high j : surprising results!
- A simple model of heterogeneous dynamics

PVC xenospheres in DOP

radius ~ 10 mm, polydisperse

j = 64% – 75%

Excluded volume interactions

CCD-based (multispeckle)

Diffusing Wave Spectroscopy

CCD

Camera

Laser beam

Change in speckle field mirrors change in sample configuration

Probe d << Rparticle

lag t

time tw

fixed tw, vs.t

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

degree of correlationcI(tw,t) = - 1

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

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

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

f = 66.4%

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

Average dynamics :

< ts >tw , < p >tw

Average relaxation time

Average relaxation time

Average stretching exponent

lag t

time tw

fixed t, vs.tw

fluctuations of the dynamics

var(cI)(t)

c (t )

degree of correlationcI(tw,t) = - 1

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

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

j = 0.74

var(cI) c4

(dynamical susceptibility)

j = 0.74

var(cI) c4

(dynamical susceptibility)

Max of var (cI)

fully decorrelated

r

Durian, Weitz & Pine (Science, 1991)

Random number of rearrangements

g2(t,t) – 1 fluctuates

r

Random number of rearrangements

g2(t,t) – 1 fluctuates

r

r increases

fluctuations increase

increasing r,j

r

r increases

fluctuations increase

partially decorrelated

r

partially decorrelated

Correlation after n events

r

Probability of n events during t

r

Poisson distribution:

r

Poisson distribution:

Random change of phase

Correlated change of phase

r

Poisson distribution:

Random change of phase

Correlated change of phase

r

Poisson distribution:

b»1.5

increasing j

decreasing sf2

increasing j

r

Moderate j : large sf2 few events large flucutations

Near jamming : small sf2 many events small flucutations

increasing j

decreasing sf2

Dynamics heterogeneous

Non-monotonic behavior of c*

Competition between

increasing size of dynamically

correlated regions ...

Dynamics heterogeneous

Non-monotonic behavior of c*

Competition between

increasing size of dynamically

correlated regions

and

decreasing effectiveness of

rearrangements

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

Single scattering, colloidal fractal gel (Agnès Duri)

sf2 ~q2d 2look at different q!

sf2 ~q2d 2look at different q!

sf2 ~q2d 2look at different q!

St. dev. of stretching

exponent

St. dev. of relaxation time

Average relaxation time

Supercooled liquid (Lennard-Jones)

Glotzer et al.,

J. Chem. Phys. 2000

c4 increases when approaching Tg

Dynamics heterogeneous

Non-monotonic behavior of c*

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements

Many extended, poorly effective

rearrangements

Dynamics heterogeneous

Non-monotonic behavior of c*

Many localized, highly effective

rearrangements

Many extended, poorly effective

rearrangements

Few extended, quite effective

rearrangements

General behavior

lag t

time tw

degree of correlationcI(tw,t) = - 1

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

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