Long range correlations and intermittency in the slow dynamics of a soft glass

(1)

0 1 2 3 4 5 6 7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.8 0.9 1.0 1.1 1.2 -0.05 0.00 0.05 0.10 0.15 0.20 corr ( t, D r/r) Dr/r (1 - Dr/r)

Agnès Duri and Luca Cipelletti

Groupe de Dynamique des Phases Condensées, UMR 5581, Université Montpellier II, 34095 Montpellier, France

time t

References :

Ip(t): intensity p-th pixel, time t

Long Range Correlations and Intermittency

In the Slow Dynamics of a Soft Glass

Dynamic Light Scattering (DLS) Multispeckle Set Up

Imaging Geometry

Sample Scattering_Volume

Lens

Speckled Image of the Scattering Volume

CCD

Laser beam

lag t

Speckled Images of the Scattering Volume

q=90 °

( )

_{( )} ( )

( )

1 -τ

t

I

(t)

I

τ

t

I

(t)

I

)

r

τ,

(t,

c

r V p p r V p p r V p p p I ! ! !

!

Î Î Î

+

=

vSpace and Time Resolved Degree of Correlation :

Experimental Results

ØTEST : Diluted Brownian Suspension [2

]

vSample : 100 ₁₀1 ₁₀2 ₁₀3 ₁₀4 0.0 0.1 0.2 0.3 0.4 0.5 g2 ( t ) - 1 t (sec) Fit : g2(t)-1 = A exp(-t/ts) ts = 2.35 sec 0.38 0.40 0.42 0.44 0.46 0.48 10-1 100 101 102 cI PDF (cI ) t =0.5 sec 0.0 5.0x103 _1.0x104 _1.5x104 0.0 0.1 0.2 0.3 0.4 0.5 cI (t, t) t= 15 sec t=3 sec t=1.5 sec t=0.5 sec t (sec)

[1] L. Cipelletti, H. Bissig, V. Trappe, P. Ballesta, S. Mazoyer, J. Phys. : Condens. Matter, 2003, 15, S257

[2] A. Duri, H. Bissig, V. Trappe, P. Ballesta, L. Cipelletti, Conference Proceedings of the SPIE Fluctations and Noise, Meeting [3] F. Castro-Roman, G. Porte, C. Ligoure, Phys.Rev.Lett, 1999, 82, 109

vAverage Dynamics :

t = 0.5 sec

r

spheres

=

530 nm,

F

=

3.7 10-5

BROWNIAN DYNAMICS :

- cI(t,t) : Stationary and Temporally Homogeneous Dynamics

- PDF (cI) : Gaussian (fluctuations due to measurement noise)

- Dynamics Spatially Uncorrelated (0< Dr/r< 1, Corr (t,Dr/r) = (1 – Dr/r), Regions overlaped)

ØONIONS GEL [3]

vSample : Octanol + CpCl decorated with F68

0.032´0.39 mm 0.32´0.39 mm

Space and Time Resolved Correlation (TRC)

vSpatially Resolved Intensity Correlation Function :

vSpatial Correlation of the Dynamics :

( )

τ,

r

-

1 c

(t,

τ,

r

)

g

2

"

=

I

!

( )

_τ,

_r

c

(t,

τ,

r

)

c

(t,

τ,

r

)

-

c

(t,

τ,

r

)

c

(t,

τ,

r

)

corr

r I I I I !

!

₌

+

D

+

D

)

r

τ,

(t,

c

)

r

τ,

(t,

c

I

!

I

!

2 2

vDistribution of cI: vSpatial Correlation Dynamics :

vTime Resolved Dynamics :

INTERMITTENT DYNAMICS :

- cI(t,t) : Large Fluctuations, Heterogeneous Dynamics

- PDF (cI) : Non-Gaussian

- Very Long Range Spatial Correlations of the Dynamics

vAverage dynamics : vTime Resolved Dynamics : vDistribution of cI: vSpatial Correlation Dynamics :

2x104 _3x104 _4x104 _5x104 _6x104 0.0 0.1 0.2 0.3 cI (t, t) t= 20000 sec t=10000 sec t=5000 sec t=1000 sec t (sec) 101 ₁₀2 ₁₀3 ₁₀4 ₁₀5 0.0 0.1 0.2 0.3 t = 20000 sec g2 ( t ) - 1 t (sec) Fit : g2(t)-1 = A exp(-t/ts) p ts = 11240 sec p=1.02 OV E R L A P 0.24 0.26 0.28 0.30 0.32 100 101 102 cI PDF (cI ) t =1000 sec 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 corr ( t ,r) r (mm) 0.13´0.13 mm 0.26´0.26 mm t = 1000 sec