experimental tests of the fluctuation-dissipation relation in aging glassy systems
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Experimental tests of the fluctuation-dissipation relation in aging glassy systems. some comments on the. D. L’Hôte SPEC CE Saclay. Local measurements. 301.5 K. 0 2500s. 0 700nm. - PowerPoint PPT PresentationTRANSCRIPT
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