Experimental tests of the fluctuation- dissipation relation in aging glassy systems some comments on the D. L’Hôte SPEC CE Saclay

Very beautiful (and difficult) experiments Direct observation of the heterogeneities E. Vidal Russel & N. E. Israeloff Nature 408 (2000) s 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 T (K) Quench duration not small in comparison with relaxation time at 300K Slow quench Little or no FDR violation relaxation time 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). Glycerol dT/dt=0.025 K/s T i =206K PVAc Fast quench T (K) Log f t w

Test of FDT in ageing PVAc (bulk) Large T eff (comp. glycerol) f fixed TiTi TgTg TfTf twtw L. Buisson & S. Ciliberto Physica D204, 1 (04) Polycarbonate Tg=419K Tf=0.93Tg quench: 1 K/s 2 Hz 7 Hz Not gaussian intermittency (spikes) Origin of large T eff ? of different T eff ’s ? of T eff < T f ? Fast quench tw1tw1  t w >1 t w (s) T eff (K) T eff < T f T eff

Test of FDT in ageing PVAc (bulk) Scaling for spin glasses : Same scaling for response and correlation vs. (t-t w )/t w . 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, (06) Rodriguez et al. PRL91, (03) T eff < T f ?? f twf tw 0.45

Test of FDT in ageing PVAc What about T during the quench ? Phonon bath DH        Phonon bath DH         time TiTi TiTi ? TfTf Phonon bath DH         TfTf TfTf quench ( t )    t   relaxation time of Dynamic Het.  i = thermal coupling time to phonon bath R. Richert, S. Weinstein PRL97, (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: T eff  ∞ ; (A. Barrat PRE57, 3629 (98)) T eff < T f ? Negative FD ratio for KCModels (heterogeneous dynamics) P. Mayer et al. PRL96, (06): Also: Barrat & Kob (Nathan) Many T eff ’s ? "Unusual" scaling ? More than two “time sectors“ ? (2 time sectors: FDVratio = 1 or T f /T eff in e.g. mean field models) Test of FDT in ageing PVAc (bulk) The meaning of large T eff, T eff < T f, several T eff ’s ? Possible other origin ? Internal constraints ? release  noise Thermal contraction during quench (but the rearrangements to density are also the physics...) Weak T eff in glycerol, large T eff in polymers ?  J.L. Barrat & W. Kob, EPL46, 637 (99) Molecular dynamics simulation e.g.: T eff = 2.2 T f (660K !) Additional noise. Nathan’s model

Local polarization measurements t =0 t =17mn t =48mn nm Spatial fluctuations of the polarization due to DH’s ? P x Assuming each DH has its own polarization. DH size  3nm Probed volume: 20  30  30 nm 3  10 3 DH among which only a few are "active" PVAc DH Convol. resol.  P(x) C. Dalle-Ferrier et al. Phys. Rev. E76, (07) PVAc glass trans.

What do we see ? "active" DH’s (3 3 nm 3 )  30  30  20nm 3 ? Or what ? Response/Correlation => spatio-temporal distribution of FDR violation/T eff s 0 700nm K K 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. 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, (2002)

Test of FDR in ageing PVAc (local) Q=C eff V P C eff = 7.2x F R(t) =A-Q(t)/V C(t)= T (K)-1/k B slope ± ± ± K K K If Q=(corr.)  Q, T eff  (corr.)  T eff Corrections: Geometry of dipoles acting on the tip Effective field Q =   f(p i,r i ) C =   f(p i, r i ). f(p j,r j )  correlations between DH’s

Heisenberg spin glass L. Berthier & A.P. Young PRB69, (04) twtw Ageing : growing of a correlation length ? E. Vidal Russel & N. E. Israeloff Nature 408 (2000) 695  2 (C) time position K.S. Sinnathamby, H. Oukris & N. E. Israeloff PRL 95 (05)  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: T eff < T f No unique T eff (> T f ) for  t w  1 Unusual scaling of T eff 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