some comments on the
Experimental tests of the fluctuationdissipation relation in aging glassy
systems
D. L’Hôte
SPEC CE Saclay
Local measurements
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 ...
Direct observation of the heterogeneities
0
2500s
301.5 K
0
700nm
E. Vidal Russel & N. E. Israeloff
Nature 408 (2000) 695
Very beautiful (and difficult) experiments
Grigera & Israeloff: First measurement of FDT violation in a structural glass (glycerol)
Test of FDTviolation in ageing PVAc (bulk)
Slow quench
Little or no FDR violation
T (K)
PVAc
335
330
330
Initial dT/dt=0.15 K/s
325
320
relaxation time
T (K)
“slow quench”
315
310
305
300
300
00
100
time (s)
200
300
400
400
aging
Quench duration not small in comparison with relaxation time at 300K
Test of FDT violation in ageing PVAc (bulk)
Fast quench
335
PVAc
330
“fast quench”
initial dT/dt=10 K/s
T (K)
325
320
315
310
305
300
0
0
2
1
4
2
3
6
4
5
6
7
time (s)
Glycerol
dT/dt=0.025 K/s
Ti=206K
PVAc
Log f tw
N.E. Israeloff et al.
R.L. Leheny & S.R. Nagel PRB57, 5154 (98).
Test of FDT in ageing PVAc (bulk)
Fast quench
wtw1
Teff
Large Teff (comp. glycerol)
Teff (K)
Ti
wtw>1
Tg
f fixed
Tf
Teff < Tf
tw
tw(s)
2 Hz
Polycarbonate
Tg=419K
Tf=0.93Tg
quench: 1 K/s
7 Hz
Not gaussian
intermittency (spikes)
L. Buisson & S. Ciliberto Physica D204, 1 (04)
Origin of large Teff ? of different Teff’s ?
of Teff < Tf ?
Test of FDT in ageing PVAc (bulk)
Scaling ?
800
tw :
700
1.
5
3
Teff < Tf ??
4.
6
9.
2
14
Teff(K)
600
500
400
19
300
200
0.01
0.1
0.450.45
1
f tft
ww
10
Scaling for spin glasses :
Same scaling for response and correlation
vs. (t-tw)/twm. If m<1, time replaced by effective time l
(comes from polymers !)
same m close to 1 (0.87); but ac  m ≈1
"subaging" (i.e; m < 1): due to quench rate ?
Parker et al. PRB74, 184432 (06)
Rodriguez et al. PRL91, 037203 (03)
D. Hérisson and M. Ocio, EPJB40, 283 (04)
Test of FDT in ageing PVAc
What about T during the quench ?
DH DH DH DH DH DH DH
Ti
t1 >t2 >t3 >t4 >t5 >t6 >t7 >...
Phonon bath
Ti
time
quench (t) t4 > t > t5
DH DH DH DH DH DH DH
??
t1 >t2 >t3 >t4 >t5 >t6 >t7 >...
Phonon bath
Tf
DH DH DH DH DH DH DH
Tf
t1 >t2 >t3 >t4 >t5 >t6 >t7 >...
Phonon bath
Tf
relaxation time of Dynamic Het. ti
= 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)
...
Test of FDT in ageing PVAc (bulk)
The meaning of large Teff , Teff < Tf , several Teff’s ?
Physics of aging
e.g.. Domain growth models: Teff  ∞ ; Molecular dynamics simulation
(A. Barrat PRE57, 3629 (98))
e.g.: Teff = 2.2 Tf (660K !)
Teff < Tf ?
Negative FD ratio for KCModels
(heterogeneous dynamics)
J.L. Barrat & W. Kob,
EPL46, 637 (99)
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)
Additional noise. Nathan’s model
Possible other origin ?
density are also the physics...)

Internal constraints ? release  noise
Thermal contraction during quench (but the rearrangements to
Weak Teff in glycerol, large Teff in polymers ?
Local polarization measurements
0
100 200 300
0 400 500 600nm
500
400
300
200
100
t =48mn
t =17mn
t =0
Spatial fluctuations of the
polarization due to DH’s ?
0
PVAc
Convol. resol.P(x)
P
DH
glass trans.
x
DH
DH
PVAc
DH
Assuming each DH has its own polarization.
DH size  3nm
Probed volume: 203030 nm3
 103 DH among which only a few are "active"
C. Dalle-Ferrier et al. Phys. Rev. E76, 041510 (07)
Direct observation of the DH’s in a polymer ?
0
2500s
301.5 K
0
2500
305.5 K
0
700nm
What do we see ?
"active" DH’s (33nm3)303020nm3 ?
Issues:
Correlations between DH’s: fusions/splitting,
fast DH’s close (or not) to slow DH’s ?
Spatial structure DH’s
Do DH’s move?
Correlation (Charac. time) – (DH size) ?
Birth, death: comes from what, replaced by what ?
etc.
Or what ?
Issues:
The same with something else than DH’s...
Response/Correlation => spatio-temporal
distribution of FDR violation/Teff
H.E. Castillo, C. Chamon, L.F. Cugliandolo,
M.P. Kennett, PRL88, 237201 (2002)
Test of FDR in ageing PVAc (local)
-1/kB slope
305.5
303.5
302.5
262 ± 15
258 ± 30
253 ± 40
R(t)
T (K)
303.5 K
302.5 K
305.5 K
Q=Ceff VP
Ceff = 7.2x10-18 F
R(t)=A-Q(t)/V
C(t)=<Q(t’)Q(t’+t)>
If Q=(corr.)Q,
Teff  (corr.)Teff
0
0
C (t)
Corrections:
Geometry of dipoles acting on the tip
Effective field
Q = S f(pi,ri)
C = S <f(pi,ri).f(pj,rj)>
correlations between DH’s
1/2
NHD
Ageing : growing of a correlation length ?
tw
E. Vidal Russel & N. E. Israeloff
Nature 408 (2000) 695
time
K.S. Sinnathamby, H. Oukris & N. E. Israeloff
PRL 95 (05) 067205
Simple model: Independent DH’s 
superposition of Lorentzians
But:
- Correlations size – char. time
- Correlations between DH’s
- etc.
position
Heisenberg spin glass
L. Berthier & A.P. Young
PRB69, 184423 (04)
0.1
Calculation ?
s2 (C) 0.05
0
0
500 1000
Open issues
Violation of Fluctuation-dissipation theorem: Very attractive experiments
But:
• Teff < Tf
• No unique Teff (> Tf) for wtw  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