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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.
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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 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 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 “slow quench” 330 Initial dT/dt=0.15 K/s T (K) relaxation time 300 0 400 time (s) aging Quench duration not small in comparison with relaxation time at 300K
330 320 310 300 PVAc T (K) 0 1 2 3 4 5 6 7 Test of FDT violation in ageing PVAc (bulk) Fast quench “fast quench” initial dT/dt=10 K/s time (s) Glycerol dT/dt=0.025 K/s Ti=206K PVAc Log ftw N.E. Israeloff et al. R.L. Leheny & S.R. Nagel PRB57, 5154 (98).
Test of FDT in ageing PVAc (bulk) Fast quench Large Teff (comp. glycerol) wtw1 Teff Ti Tg Teff (K) f fixed Teff < Tf wtw>1 Tf tw tw(s) • Origin of large Teff ? of different Teff’s ? • of Teff < Tf ? Polycarbonate Tg=419K Tf=0.93Tg quench: 1 K/s 2 Hz 7 Hz Not gaussian intermittency (spikes) L. Buisson & S. Ciliberto Physica D204, 1 (04)
Test of FDT in ageing PVAc (bulk) ftw 0.45 Scaling ? Teff < Tf ?? Scaling for spin glasses : Same scaling for response and correlation vs. (t-tw)/twm. Ifm<1, time replaced by effective timel (comes from polymers !) samem close to 1 (0.87); but acm≈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 time Tf DH DH DH DH DH DH DH >t2 >t3 t1 >t4 >t5 >t6 >t7 >... Tf Phonon bath What about T during the quench ? relaxation time of Dynamic Het. ti = thermal coupling time to phonon bath Ti DH DH DH DH DH DH DH >t2 >... >t3 t1 >t4 >t5 >t6 >t7 Ti R. Richert, S. Weinstein PRL97, 095703 (06) K. Schröter and E. Donth, J. Chem. Phys. 113, 9101 (00) R. V. Chamberlin, PRL82, 2520 (99) ... Phonon bath quench (t) t4 > t > t5 ?? DH DH DH DH DH DH DH >t2 >t3 t1 >t4 >t5 >t6 >t7 >... Tf Phonon bath
Test of FDT in ageing PVAc (bulk) Molecular dynamics simulation e.g.: Teff = 2.2 Tf (660K !) J.L. Barrat & W. Kob, EPL46, 637 (99) • 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 ? The meaning of large Teff , Teff < Tf , several Teff’s ? • 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) • Additional noise. Nathan’s model
Local polarization measurements 400 600nm 100 300 0 500 0 200 500 400 300 200 100 t=48mn t=17mn t=0 0 PVAc DH DH DH DH PVAc Assuming each DH has its own polarization. DH size 3nm Probed volume: 203030 nm3 103 DH among which only a few are "active" Spatial fluctuations of the polarization due to DH’s ? Convol. resol.P(x) P x glass trans. C. Dalle-Ferrier et al. Phys. Rev. E76, 041510 (07)
Direct observation of the DH’s in a polymer ? 301.5 K • What do we see ? • "active" DH’s (33nm3)303020nm3 ? • Or what ? • Response/Correlation => spatio-temporal • distribution of FDR violation/Teff 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. 0 2500s 305.5 K 0 2500 0 700nm Issues: The same with something else than DH’s... H.E. Castillo, C. Chamon, L.F. Cugliandolo, M.P. Kennett, PRL88, 237201 (2002)
Test of FDR in ageing PVAc (local) T (K) -1/kB slope 305.5 262 ± 15 303.5 258 ± 30 302.5 253 ± 40 Q=Ceff VP Ceff = 7.2x10-18 F R(t)=A-Q(t)/V C(t)=<Q(t’)Q(t’+t)> 305.5 K If Q=(corr.)Q, Teff (corr.)Teff 303.5 K 302.5 K Corrections: Geometry of dipoles acting on the tip Effective field Q = Sf(pi,ri) C = S <f(pi,ri).f(pj,rj)> correlations between DH’s
Ageing : growing of a correlation length ? 1/2 NHD tw time position E. Vidal Russel & N. E. Israeloff Nature 408 (2000) 695 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. Calculation ? Heisenberg spin glass L. Berthier & A.P. Young PRB69, 184423 (04) s2 (C)
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