Universal Scaling and Effective Temperatures

in Colloidal Glass

Ping Wang

Levich Institute and Physics Department

of City College of New York

Metastability and Crystallization in Hard-Sphere Systems.

D. Rintoul and S. Torquato, P.R.L. 11, 4198 (1996)

Glass Transition at: 58.0g

Supercooled Liquids and The Glass

Transition, Pablo G. Debenedetti & Frank

H. Stillinger, Nature, (2001)

Molecular Glasses

monodisperse colloidal glasses

Phase Diagram for Hard Sphere

Dynamical measurement of an effective temperature

In our experiment,

drag force will be

applied on magnetic

beads by external

magnetic field,

And the force also

should be small enough

to reach linear

response region.

Colloidal suspensions

Schematic diagram of the light path in confocal microscopy

Confocal Microscopy and 3D Information

in Colloid Suspension

PMMA beads ~ 2.8 µm

Magnetic Bead ~ 3.2 µm

F

Measuring effective temperatures in colloidal

suspensions with magneto-manipulation

Glass transition in colloidal hard spheres: Measurement and mode-

coupling-theory analysis of the coherent intermediate scattering

function. W.van Megen and S.M. Underwood, P.R.E 49, 4206 (1994)

Cage dynamic in colloidal hard spheres

Properties of Cage Rearrangements

Observed near the Colloidal Glass

Transition. Eric R. Weeks and D. A.

Weitz, P.R.L 89, 095704-1 (2002)

Structural rearrangements:

cage relaxation

Inside the cage relaxation

glass holder

air bubble

transmission light

capillary cell

Sample

Experimental Setting Up

50 x Objective

Electromagnet (0.15T)

Sample cell field of view

Magnetic force is perpendicular to diagram plane

4 hours

Cage Dynamic With and Without Magnetic Force

avF 6

Measure drag force by measuring velocity of magnetic

beads in glycerol-water solution

Force Direction

PMMA beads ~ 2.8 µm

Magnetic Bead ~ 3.2 µm

36 minutes

Step Jump at large force

60.0Force Direction

Forced motion of a probe particle near the colloidal glass

transition. P. Habdas, D. Schaar, Andrew C. Levitt, and

Eric R. Weeks, Emory University, cond-mat/0308633v1

(2003)

threshold force ~ 0.6 pN

Aging Phenomena

Linear Response Regime

The collapsing of correlations guarantee that at a given ratio , all the

PDF of the displacements have the same standard deviation. The question

is that does all these PDF of the displacements also have the same

distribution profiles?

Scaling Behavior of the Probability

Distribution Function of the Displacement

Measure Effective Temperature

ttMFxttt

ttforttDxtttC

www

wwww

)(~/),(

,)(~2/),( 2

08.031.0

08.033.0

)(

)(

ww

ww

ttM

ttD

power law decay

a Effective Temperature

Higher than Bath

)(

)(

w

weff

tM

tDT

Master Curves of Autocorrelation and Response

yyf

yyyf

M

D

~)(

1,~)(

asymptotic behavior

tt

ttttC

w

ww

)(

)(

~

,~

Power law decay

)(~

)(~

w

Mw

w

Dw

t

tft

t

tftC

Scaling behavior

Insight comes from glass theory: Violation of FDT in glasses

Light ScatteringSupercooled Liquids and The Glass Transition, Pablo G.

Debenedetti & Frank H. Stillinger, Nature, (2001)

Molecular glasses

Spin glasses

β decay

α decay

Short timescale

Long timescale

Analytical solution of the off-equilibrium dynamics of a

long-range spin-glass model, L. F. Cugliandolo, J.

Kurchan P. R. L., (1993)

Search the Best Collapsing

)(

wt

wt

wt

2

)/ln( )ln(

2

])/,())/,([ln(

wwwwww

tt t

tttCttttCt

w w

Minimize the standarddeviation of collapsing

05.034.0

05.048.0

the best collapsing

Spatial Heterogeneous and Local Fluctuations

Heterogeneous Aging in Spin Glasses. H.

E. Castillo, et al, P.R.L 88, 237201 (1994)

The autocorrelation and response for an individual particle can be regarded

as the coarse-grained local fluctuations of the observables

Local Fluctuations of Autocorrelation and Responses

)()( 0CCtCPt ww

modified power-law

Gaussian Fitting

Summary

We present experimental results on an aging colloidal glass showing a well-defined temperature for the slow modes of relaxation of the system. This Teff is larger than the bath temperature since it implies large scale structural rearrangements of the particles.

Temperature remains constant independent of the age, even though both the diffusivity and the mobility are age dependent.

The power-law scaling are found to describe the transport coefficients indicates the slow relaxation of the system.

A universal scaling form is found to describe all the observables. That is, not only the global averages, but also the local fluctuations.