Experimental tests of the fluctuation-dissipation relation in aging glassy

systems

some comments on the

D. L’HôteSPEC CE Saclay

Very beautiful (and difficult) experiments

Direct observation of the heterogeneities

E. Vidal Russel & N. E. Israeloff Nature 408 (2000) 695

0

25

00

s

301.5 K

0 700nm

Electric Force Microscopy: realizes (almost) the dream to visualize molecular systems as (e.g.) a microscope for colloids, a camera for granular systems, a plotter for simulations ...

Grigera & Israeloff: First measurement of FDT violation in a structural glass (glycerol)

Local measurements

PVAc

Test of FDTviolation in ageing PVAc (bulk)

time (s)

Initial dT/dt=0.15 K/s

“slow quench”

aging

300

330

T (

K)

0 400

Quench duration not small in comparison with relaxation time at 300K

Slow quench

Little or no FDR violation

rela

xati

on ti

me

T (K)

Test of FDT violation in ageing PVAc (bulk)

time (s)

“fast quench”initial dT/dt=10 K/s

PVAc

N.E. Israeloff et al.R.L. Leheny & S.R. Nagel PRB57, 5154 (98).

GlyceroldT/dt=0.025 K/sTi=206K

PVAc

0 1 2 3 4 5 6 7

Fast quenchT

(K

)

330

320

310

300

Log f tw

Test of FDT in ageing PVAc (bulk)

Large Teff (comp. glycerol)

f fixed

Ti

Tg

Tf

tw

L. Buisson & S. Ciliberto Physica D204, 1 (04)

PolycarbonateTg=419KTf=0.93Tgquench: 1 K/s2 Hz

7 Hz

Not gaussianintermittency (spikes)

Origin of large Teff ? of different Teff’s ?of Teff < Tf ?

Fast quench

tw1

tw>1

tw(s)

Tef

f (K

)

Teff < Tf

Teff

Test of FDT in ageing PVAc (bulk)

Scaling for spin glasses :Same scaling for response and correlationvs. (t-tw)/tw

. If <1, time replaced by effective time (comes from polymers !)same close to 1 (0.87); but ac ≈

D. Hérisson and M. Ocio, EPJB40, 283 (04)

Scaling ?

"subaging" (i.e; < 1): due to quench rate ?Parker et al. PRB74, 184432 (06)Rodriguez et al. PRL91, 037203 (03)

Teff < Tf ??

f tw0.45

Test of FDT in ageing PVAc What about T during the quench ?

Phonon bath

DH DH DH DH DH DH DH

Phonon bath

DH DH DH DH DH DH DH

time

Ti

Ti

??

Tf

Phonon bath

DH DH DH DH DH DH DH

Tf

Tf

quench (t) t

relaxation time of Dynamic Het. i

= thermal coupling time to phonon bath

R. Richert, S. Weinstein PRL97, 095703 (06)K. Schröter and E. Donth, J. Chem. Phys. 113, 9101 (00)R. V. Chamberlin, PRL82, 2520 (99)...

Physics of aging e.g.. Domain growth models: Teff ∞ ; (A. Barrat PRE57, 3629 (98))

Teff < Tf ?Negative FD ratio for KCModels (heterogeneous dynamics)P. Mayer et al. PRL96, 030602 (06):

Also: Barrat & Kob (Nathan)

Many Teff’s ? "Unusual" scaling ?More than two “time sectors“ ?(2 time sectors: FDVratio = 1 or Tf/Teff in e.g. mean field models)

Test of FDT in ageing PVAc (bulk)

The meaning of large Teff , Teff < Tf , several Teff’s ?

Possible other origin ? Internal constraints ? release noise Thermal contraction during quench (but the rearrangements to density are also the physics...) Weak Teff in glycerol, large Teff in polymers ?

J.L. Barrat & W. Kob, EPL46, 637 (99)

Molecular dynamics simulatione.g.: Teff = 2.2 Tf (660K !)

Additional noise. Nathan’s model

Local polarization measurements

t =0 t =17mn t =48mn

0 100 300200 0 400 600nm500

0

100

300

200

500

400

Spatial fluctuations of the polarization due to DH’s ?

P

x

Assuming each DH has its own polarization.DH size 3nmProbed volume: 203030 nm3 103 DH among which only a few are "active"

PVAc

DH

DH

DH

DH

Convol. resol.P(x)

C. Dalle-Ferrier et al. Phys. Rev. E76, 041510 (07)

PVAc

gla

ss t

ran

s.

What do we see ? "active" DH’s (33nm3)303020nm3 ?

Or what ?

Response/Correlation => spatio-temporal distribution of FDR violation/Teff

0

2

500s

0 700nm

301.5 K

305.5 K

0

250

0

Issues:Correlations between DH’s: fusions/splitting, fast DH’s close (or not) to slow DH’s ?Spatial structure DH’sDo DH’s move?Correlation (Charac. time) – (DH size) ?Birth, death: comes from what, replaced by what ?etc.

Issues:The same with something else than DH’s...

Direct observation of the DH’s in a polymer ?

H.E. Castillo, C. Chamon, L.F. Cugliandolo, M.P. Kennett, PRL88, 237201 (2002)

Test of FDR in ageing PVAc (local)

0

0

R(t

)

C (t)

Q=Ceff VP

Ceff = 7.2x10-18 F R(t)=A-Q(t)/VC(t)=<Q(t’)Q(t’+t)>

T (K) -1/kB slope

305.5 262 ± 15303.5 258 ± 30302.5 253 ± 40

305.5 K303.5 K

302.5 K

If Q=(corr.)Q,Teff (corr.)Teff

Corrections:Geometry of dipoles acting on the tipEffective field

Q = f(pi,ri)

C = f(pi,ri).f(pj,rj)correlations between DH’s

Heisenberg spin glassL. Berthier & A.P. Young PRB69, 184423 (04)

t w

Ageing : growing of a correlation length ?

E. Vidal Russel & N. E. Israeloff Nature 408 (2000) 695

2 (C)

tim

e

position

K.S. Sinnathamby, H. Oukris & N. E. Israeloff PRL 95 (05) 067205

N

HD

1/2

Simple model: Independent DH’s superposition of Lorentzians

But: - Correlations size – char. time - Correlations between DH’s - etc.

Calculation ?

Open issues

Violation of Fluctuation-dissipation theorem: Very attractive experiments

But:• Teff < Tf

• No unique Teff (> Tf) for tw 1• Unusual scaling of Teff

• Additional noise ? Nathan’s model• Extrinsic noise ?• « DHs temperature" vs. phonon temperature

Electric force microscopy: a fantastic tool for local FDT violations, and many other things (spatio-temporal correlations...)What are the observed structures ?Calculations/simulations of the experimental situation ?

Simple dynamic heterogeneity

Correlated dynamic herogeneities