A new control parameter for the glass transition of glycerol.

1. D. L’Hôte, R. Tourbot,F. Ladieu, P. Gadige A new control parameter for the glass transition of glycerol. Service de Physique de l’Etat Condensé (CNRS, MIPPU/ URA 2464), DSM/IRAMIS/SPEC/SPHYNXCEA Saclay, France Main Funding: AdditionnalFunding:

2. The mostemblematic claim of thiswork :  Est is a new control parameter in Glycerol.  Previously, the unique way to change Tg was the Pressure P • Small effect: discovered through a nonlinear technique  The most interesting is not dTgbut what we learn when varying P, Est.

3. Outline: • Motivations for nonlinearexperiments • II) Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives.

4. Whathappensaround Tg ??? tα Glass Supercooled liquid Liquid (Crystal) ta=100s tα~10-12s No (static) cristalline order T Tm Tg Angell, Science 267 (1995) 12 10 8 6 4 2 0 -2 -4 Log (viscosity)  ta Ea when T   Correlationswhen T  Polybutadiene, Tg 180K S(q) [a.u.] 0 0.2 0.4 0.6 0.8 1.0 Tg /T Tg/ T Relaxation time ta How to combine the existence of correlationswith the absence of order ?

5. DynamicalHeterogeneities in supercooledliquids … directly observed in granular matter or in numerical simulations. Example : numerical simulations on soft spheres : Hurley, Harowell, PRE, 52, 1694, (1995) • Ncorr = average number of dynamically correlated molecules : • …Experimentally, the heterogeneous nature of the dynamics has been established through various breakthroughs: • NMR experiments • Local measurements Tracht et al. PRL81, 2727 (98), J. Magn. Res. 140 460 (99),… E. Vidal Russell and N.E. Israeloff , Nature 408, 695 (2000). « clusters » of 30-90 monomers  Hole burning experiments When T:Ncorrwould, whichwouldexplainwhytaincreasessomuch

6. Dynamical Heterogeneities and NHB.  ManyimprovementssinceSchiener, Böhmer, Loidl, ChamberlinScience, 274, 752, (1996) e.g. R.Richert’sgroup: PRL, 97, 095703 (2006); PRB 75, 064302 (2007); EPJB, 66, 217, (2008); PRL, 104, 085702, (2010)…  The central idea in Schiener et al ’s seminalpaper in 1996: e(t,w) : shouldbegloballyshifted in w No distribution of t Strongfield (V0) at W e(t,w) : shouldbemainlymodified close to W A distribution of t’s exists Non ResHoleBurning: supercooleddynamics IS heterogeneous (at least in time) … Can nonlinearexperimentsgive MORE thanoriginallyexpected ??....

7. The predictionof Bouchaud-Biroli (B&B): PRB 72, 064204 (2005) H Natural scale of c3 cs= static value of cLin a3= molecular volume Ncorr= number of dynamic. correlatedmolec. ta (T) : typical relaxation time H: scaling function wta  « 1 » Systematicc3(w,T) measurementsto test the prediction and possiblygetNcorr(T) AND Ncorr « large enough »

8. The issue of interpretations : Box Model versus B&B c3 wta  « 1 » Box model assumptions (designed for NHB): → Each DH « k » has a Debye dynamics. {tk} chosen to recoverclin(w) at eachgiven T. → Applying E: each DH « k » isheated by dTk(ttherm) withtthermtk. as{tk}taheat diffusion over one DH takes a macroscopic time close to Tg. For a pure acfieldEac cos(wt): w and T dependences arequalitativelysimilarin the Box model and in B&B c3does NOT containNcorr (Box model isspace free) c3(w,T) : Ncorr(T) or not ?

9. SomeexperimentsdonesinceB&B’sprediction (2005) B&B: Box model : e.g. R.Richert’sgroup: PRL, 97, 095703 (2006); PRB 75, 064302 (2007); EPJB, 66, 217, (2008); PRL, 104, 085702, (2010)… Our group:PhD’s of C. Thibiergeand C. Brun. PRL (2010); (2012) PRB (2011) (2012); JChemPhys (2011) , Augsburg group: PhD of Th. Bauer : 2 PRL’s in (2013); etc… → Test of B&B’sprediction: OK → Very good fits at 1w (betterthan at 3w) → Evolution of Ncorr(T) or of Ncorr(ta) → Accounts for the transientregime at 1w → Severalliquidstested (Lunkenheimer& Loidl) → Severalliquidstested (Richert PRL (2007)) Using Estwill shed a new light on thisinterpretation issue

10. Outline: • Motivations for nonlinearexperiments • II) Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives.

11. Dielectric setup and orders of magnitude VS (t) Supercooledliquid, controlled T e P  Speciallydesigned setup For “low enough” E Linear term First non-linear term

12. Our setup to measure cubic susceptibilities C. Thibierge et al, RSI 79, 103905 (2008)) Bridge with two glycerol-filled capacitors of different thicknesses Vace jwt + Vst Z2 = thick capacitor (2×thin) Z1 = thin capacitor DV= Vmeas(Vac,Vst) Vmeas - Vmeas(Vac,0) 2 ILin+ 8INonlLin ILin+ INonlLin r1 r2  when r1Z1=r2Z2 : Plincancels gives PNonLin DV~ Vst2Vac Phase (DV) = cte

13. Outline: • Motivations for nonlinearexperiments • Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives. wta f/fa  NB: fapeak of clin’’(w) |clin(w)| has no peak

14. Main features of At constant T:  humped shape for |c2;1(1)|  maximum happens in the range of fa Scaling of the hump in T Same qualitative trends as for c3(1) and c3(3)

15. Comparingand Est tst  Compare |c3(1)|/4 and |c2;1(1)| → Sameorder of magitude → Measurements (  ) are in the stationnaryregime(tst>>ta) , [m²/V²] t Varying Est ZERO dissipated power Box model’sprediction :|c2;1(1)|<<|c3(1)| (ions) Box model’spredictionistoosmall by a factor 300 for |c2;1(1)| For the first time, Box Model is unable to account for a cubic response: Decisive point for the interpretation issue …

16. Outline: • Motivations for nonlinearexperiments • Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives.

17. Comparing the wdependences ofand of  For f/fa > 0.2: 197K 218K with  T for bothRe and Im parts Berthier et al., Science (2005); JCP, (2007); PRE (2007). Direct link with expected from  For f/fa < 0.2: “Trivial” dominates Reshuffling  Ideal gas at t >>ta 

18. T-dependences of the dimensionlessnonlinearsuscept. is T-independent in the trivial limit (idealgas) if B&B’spredictionholds looks OK “Trivial” Similar T dependences for w and T dependences consistent with X2;1(1) ~ Ncorr(OK within MCT)

19. Can wefit nonlinearresp. ? The ‘‘toy model’’ as an attempt : EachDyn.Het.  µ = µm Simplestexample: D=0=q1 in a double well (to get long t), of assymetryD //z Two key points  AmorphousOrder(«as» in S.G.) canit fit the data ? … Crossover to trivial isenforced at f<<fa

20. Fitsat Tg+17K: L’Hôte, Tourbot, Ladieu, Gadige to appear in PRB (2014) Ncorr=10 d=0.60  Ncorr has the right order of magnitude  good fits for ALL the Xn(k)  … but withdifferent values of Ncorr (toy model) Ncorr=15 d=0.60 Ladieu, Brun, L’Hôte, PRB 85, 184207, (2012)

21. Outline: • Motivations for nonlinearexperiments • Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives.

22. Translatingc2,1(1)as adTgshift Hensel-Bielowka et al. , PRE (2004) Pressure experiments: dTg(P) is drawn from : Same method for Est: Slight trivial distortion of c2,1(1) l≠1 dTg=3kEst2  Estis a new control parameter in glycerol

23. A picture: D.H.  overcrowdedsubway Ncorr Increasing Pressure … Increasing Est … Density… S and ta Est… S and ta

24. Outline: • Motivations for nonlinearexperiments • Our speciallydesignedexperiment • III) Results on Glycerol • Order of magnitude and comparison to the Box model • Relation to Ncorr • Tg shift • IV) Somenaives questions/ideas. • Summary and Perspectives.

25. Does TKfollow Tg ? S.G: dTg (Hst) < 0 or “very negative” We find dTg (Est) > 0 |Est | |Hst| « Supercooledliquid » « true » glass Spin Glass Paramagnet T Tc T TK Tg Is itallowedthatdTK(Est)>0 ?  e.g. peculiarity of 1RSB ? S.G.: Hst speeds up the relaxation Est slows down the dynamics Y.G. Joh et al, PRL 82, 438 (1999) and Saclay data Not a contradiction since T>Tgdiffersfrom T<Tc

26. Can we test theorieswithcubicresponses? L. Levy et T. Oglieksi PRL57, 3288 (1986), L. Lévy, PRB, 38, 4963 (1988) Brun et al. PRB 84, 104204 (2011) Too narrow to test theories relating ta and Ncorr Above Tg Ncorr[a.u.] c3 (a.u.) ta, [s] Quench at Tg-7K Ncorr/Ncorr(eq) In Spin Glasses: critical behavior nicely evidenced Brun et al. PRL109, 175702 (2012) ta, [s] Quasi equilibrium

27. Can we test theorieswithcubicresponses? Brun et al. PRL109, 175702 (2012) Brun et al. PRB 84, 104204 (2011) Above Tg Below Tg Ncorr[a.u.] Ncorr[a.u.] AND ta, [s] ta, [s] Consistent withRFOT Consistent withCammarota et al, JCP (2009) NB: yields z>20 : not reasonnable We can test theories

28. Recentworks on cubicresponses → In colloids: experiments and MCT done for oscillatoryshear : See Brader et al, PRE, 82, 061401, (2010)  MCT for oscillatorystressiscoming: see Matthias Fuchs papers (Konstanzuniv.) → In supercooledliquids: BouchaudBiroli PRB 72, 064204 (2005) and Tarzia et al, JCP (2010) in MCT • G. Diezemann : PRE, (2012); JCP(2013); arXiv: 1407.4333v1 • no generallinkbetweenc3 and four times correlationfunctions(trapmodels…) • This linkdepends on the chosen model and chosen observable. How to choose a good model ? ANDcrossover to trivial A model accounting for c3willALSO capture dyn. spatial aspects ☺ t / ta 1 Why not simulate ? (d=3) with