A new control parameter for the glass transition of glycerol.

Transcription

1 A new control parameter for the glass transition of glycerol. P. Gadige, S. Albert, C. Wiertel-Gasquet, R. Tourbot, F. Ladieu Service de Physique de l Etat Condensé (CNRS, MIPPU/ URA 2464), DSM/IRAMIS/SPEC/SPHYNX CEA Saclay, France Main Funding: Additionnal Funding:

2 T g (E st )-T g (0), [mk] The most emblematic claim of this work : Glycerol (T g =187K at E st =0) 6 4 E st is a new control parameter in Glycerol Est, [MV/m] Previously, the unique way to change Tg was the Pressure P Small effect: discovered through a nonlinear technique (see L Hôte, Tourbot, Ladieu, Gadige PRB 90, (2014) ) As for P exp ts, the most interesting is not T g (P) in itself but what we learn about the glass transition when varying the control parameter.

3 Outline: I) Motivations for nonlinear experiments What happens around Tg? Dynamical Heterogeneities Special interest of nonlinear responses! II) Our specially designed experiment it works! III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to N corr Tg shift Summary and Perspectives.

4 Outline: I) Motivations for nonlinear experiments What happens around Tg? Dynamical Heterogeneities Special interest of nonlinear responses! II) Our specially designed experiment it works! III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to Ncorr Tg shift Summary and Perspectives.

5 S(q) [a.u.] What happens around Tg? Relaxation time t a t α Glass Supercooled liquid (Crystal) Liquid t a =100s T g T m t α ~ s T Angell, Science 267 (1995) E a T ~ t a ~ e E a when T Correlations when T Log (viscosity) t a T g / 0.6 T T g / T Polybutadiene, T g 180K No (static) order How to combine the existence of correlations with the absence of order?

6 Dynamical Heterogeneities in supercooled liquids N corr = average number of dynamically correlated molecules : N corr directly observed in granular matter or in numerical simulations. Example : numerical simulations on soft spheres : Experimentally, the heterogeneous nature of the dynamics has been established through various breakthroughs: NMR experiments Tracht et al. PRL81, 2727 (98), J. Magn. Res (99), Hurley, Harowell, PRE, 52, 1694, (1995) Local measurements E. Vidal Russell and N.E. Israeloff, Nature 408, 695 (2000). «clusters» of 0-90 monomers Hole burning experiments When T: N corr would, which would explain why t a increases so much

7 Dynamical Heterogeneities and NHB. Many improvements since Schiener, Böhmer, Loidl, Chamberlin Science, 274, 752, (1996) e.g. R.Richert s group: PRL, 97, (2006); PRB 75, (2007); EPJB, 66, 217, (2008); PRL, 104, , (2010) The central idea in Schiener et al s seminal paper in 1996: Strong field (V 0 ) at W No distribution of t A distribution of t s exists e(t,w) : should be globally shifted in w e(t,w) : should be mainly modified close to W Non Res Hole Burning: supercooled dynamics IS heterogeneous (at least in time) Can nonlinear experiments give MORE than originally expected??...

8 Outline: I) Motivations for nonlinear experiments What happens around Tg? Dynamical Heterogeneities Special interest of nonlinear responses! II) Our specially designed experiment it works! III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to N corr Tg shift Summary and Perspectives.

9 The prediction of Bouchaud-Biroli (B&B): PRB 72, (2005) c DH characterisation g ( r, t) p(0,0) p(0, t) p( r,0) p( r, t) 4 2 E( t) E e iwt P e 0 c Lin E c E e c a ( w, T ) 0 s N ( T ) H wt ( T corr k T a B c AND N corr «large enough»... ) Natural scale of c N corr = number of dynamic. correlated molec. H c s = static value of c Lin t a (T) : typical relaxation time a = molecular volume H: scaling function «1» wt a Systematic c (w,t) measurements to test the prediction and possibly get N corr (T)

10 The issue of interpretations : Box Model versus B&B Box model assumptions (designed for NHB): Each DH «k» has a Debye dynamics. {t k } chosen to recover c lin (w) at each given T. Applying E: each DH «k» is heated by dt k (t therm ) with t therm t k. as{t k }t a heat diffusion over one DH takes a macroscopic time close to Tg. ( dtk ) heat power density t k dtk t c 2 (heat power density ~ c '' w E ) k dt k 2 ~ E P k P k, Lin ( P k, Lin P k, Lin T ~ c k dt E) k ~ E c «1» wt a For a pure ac field E ac cos(wt): w and T dependences are qualitatively similar in the Box model and in B&B c does NOT contain N corr (Box model is space free) c (w,t) : N corr (T) or not?

11 Some experiments done since B&B s prediction (2005) Box model : d lne '' Im( c Im( c Lin ) E² ) B&B: c as well as c () e.g. R.Richert s group: PRL, 97, (2006); PRB 75, (2007); EPJB, 66, 217, (2008); PRL, 104, , (2010) Very good fits at 1w (better than at w Accounts for the transient regime at 1w Several liquids tested (Richert PRL (2007)) Our group: PhD s of C. Thibierge and C. Brun. PRL (2010); (2012) PRB (2011) (2012); JChem Phys (2011), Augsburg group: PhD of Th. Bauer : 2 PRL s in (201); etc Test of B&B s prediction: OK Evolution of N corr (T) or of N corr (t a ) Several liquids tested (Bauer, Lunkenheimer, Loidl, PRL 111, (201)) Using E st will shed a new light on this interpretation issue

12 Outline: I) Motivations for nonlinear experiments II) Our specially designed experiment III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to N corr Tg shift Summary and Perspectives.

13 Dielectric setup and orders of magnitude V S (t) Supercooled liquid, controlled T P e P( t) e 0 c lin ( t t') E( t') dt' c For low enough E ' ' ' ' ' ' ' ' ' t t, t t, t t E( t ) E( t ) E( t dt dt dt ) Linear term First non-linear term E(t) E ac cos( wt) E st P( t) e 0 c c P Lin 1 j w E t () j w t ac Re c ( w) e c ( w) e 4 ( w) F. T. { c ( w, w, ) w ( w) F. T. { c ( w, w, ) () w c E ( w) F. T. 2 st E ac Re { c (0,0, ) w jwt c ( w) e even harmonics For E 1MV/m, cubic terms linear term Specially designed setup

14 Modulus, [V] Phase, [deg] Our setup to measure cubic susceptibilities Bridge with two glycerol-filled capacitors of different thicknesses C. Thibierge et al, RSI 79, (2008)) Z 2 = thick capacitor (2 thin) V ac e j w t + V st Z 1 = thin capacitor P P Lin (1 E j w t ac Re c ) ( w) e e 0 1w 4 E E Re c ( w) e 2 st ac j w t I Lin + I NonlLin r 1 V meas r 2 2 I Lin + 8 I NonlLin 10 - DV = V meas (V ac,v st ) - V meas (V ac,0) 00 P N.B.: I S t when r 1 Z 1 =r 2 Z 2 : P lin cancels gives P NonLin V st, [V] DV~ V st 2 V ac Phase (DV) = cte c DV V 2 V st ac

15 Outline: I) Motivations for nonlinear experiments C or G/w [Farads] II) Our specially designed experiment III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to N corr Tg shift Summary and Perspectives. 1,E-08 NB: wt a f/f a f a peak of c lin (w) c lin (w) has no peak 1,E-09 ~ c Lin ' ~ c Lin '' 1,E-10 1,E+00 1,E+02 1,E+04 1,E+06 frequency [Hz]

16 Arg(c ), [Deg] Main features of c ( w, ) c, [m2 / V 2 ] T 197K (fa = 0. Hz) 202K (fa = 2.1 Hz) 211K (fa = 60 Hz) 218K (fa = 520 Hz) At constant T: humped shape for c maximum happens in the range of f a Scaling of the hump in T f/f a -250 Same qualitative trends as for c and c ()

17 c c, [m²/v²] Comparing P e 0 or c or /4 c /4 P Lin 1w 2x x x x10-17 c ( w, ) and c ( w, ) T T (1 j w Re c ( w) t 2 E E e j w Re c ( w) t ) E ac e 4 st ac X 2,1, T=202 K X /4 For the first time, Box Model is unable to account for a cubic response: X 2,1, T= K 10 2 X /4 f/f a Box model s prediction : c << c f/f a (ions) Decisive point for the interpretation issue Compare c /4 and c Same order of magitude Measurements ( ) are in the stationnary regime (t st >> t a E st t st t Varying E st ZERO dissipated power dt k In the Box Model : ~ dissipated power Box model s prediction is too small by a factor 00 for c

18 X & X () The latest paper: Samanta, Richert, J.Chem.Phys. 142, (2015). 2 ( Dc1) A D S e 0 Estatic plugged in Ln(τα ) dtg ~ E T T S (T) 2 ~ static c Glycerol supercooled liquid 202 K Comparison of three cubic nonlinear responses: 1w w and static field induced X () X X X f/f a X X () c c and : c E () static : E entropy variation ac heating (boxmodel) Two different mechanisms at play? X () phase X Phase Phase X Phase X Phase+ Very unlikely due to the similarities of c, c, and c () f/f a

19 Outline: I) Motivations for nonlinear experiments II) Our specially designed experiment III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to N corr Tg shift Summary and Perspectives.

20 Arg(c ) or Arg(- dc Lin /dt), [Deg] Comparing the w dependences of c ( w, T ) c or dc /dt, Lin [m2 / V 2 ] f/f a or f/f a 197K 218K For f/f a > 0.2: and of T c Lin E st estim dχ Lin Direct link with ncorr ~ T expected from Berthier et al., Science (2005); dt JCP, (2007); PRE (2007). with 0 c c ( T, w) Lin T w 0, T, 16 Km² 1.210, 0.80 V ² T for both Re and Im parts For f/f a < 0.2: Trivial dominates Reshuffling Ideal gas at t >>t a c Lin c ( w, T ) T

21 w and T dependences consistent with X ~ N corr (OK within MCT) (k ) T-dependences of the dimensionless cubic susceptibility X n X ( k ) ( k ) cn, n ( w, T ) w T 2 e 0c s a kbt is T-independent in the trivial limit (ideal gas) N corr k ( T ) H ( wt ( T )) n a if B&B s prediction holds 1.6 Z (T) / Z (202K) X Tc T X X (1 or ) (T<204.7K) T, [K] f/f a Trivial X looks OK Similar T dependences ( k ) for X n and fort c Lin T

22 Can we fit nonlinear resp.? The toy model as an attempt : Each Dyn.Het. µ = µ m N corr in a double well (to get long t), of assymetry D Simplest example: D=0=q 1 t P ch e t where P M th e µ m Ncorr E( t) e ~ N kbt µ m Ncorr 1 M ~ N a N corr corr corr E //z Two key points µ ~ N corr P Lin P ~ Μ ~ Μ e ~ e ~ N N N corr N corr corr E corr Amorphous Order («as» in S.G.) Crossover to trivial is enforced at f<<fa E c Lin c ~ 1 ~ N corr can it fit the data?

23 Fits at Tg+17K: L Hôte, Tourbot, Ladieu, Gadige PRB 90, (2014) N corr =10 d=0.60 N corr =15 d=0.60 N corr has the right order of magnitude good fits for ALL the X n (k) but with different values of N corr (toy model) Ladieu, Brun, L Hôte, PRB 85, , (2012)

24 Outline: I) Motivations for nonlinear experiments II) Our specially designed experiment III) Results on Glycerol Order of magnitude and comparison to the Box model Relation to Ncorr Tg shift Summary and Perspectives.

25 Translating c 2,1 as a dtg shift Hensel-Bielowka et al., PRE (2004) Pressure experiments: P dt g (P) is drawn from : w; P; T Pw ;0; T dt ( P) g Same method for E st : P w E ; T Pw ;0; T dt ( E ) ; st g st dt g (E ) st E 2 st c Lin c ( T, w) with 1 T w 0, T, Slight trivial distortion of c 2,1 1 dt g =E st 2 E st is a new control parameter in glycerol

26 A picture: D.H. overcrowded subway N corr Increasing Pressure Increasing E st Density S and t a E st S and t a

27 Summary and Perspectives. Our very sensitive setup has successfully measured c (w,t) The interpretation issue is now clarified since : the Box Model cannot account for the order of magnitude of c Global consistency with c n (k) ~ N corr : w and T dependences, fits with the toy model Perspectives = systematic studies of N corr the scale on which the systems is solid, during t a : study c (w 1 ;w 2 ;w ) in other directions than (0,0,w) or (±w,w,w) study c at high temperatures (no heating) Study c at higher fields or in other liquids For the nice discussions and/or long time support, warm thanks to: G. Biroli, J.-P. Bouchaud, G. Tarjus, C. Alba-Simionesco, P.M. Déjardin, as well as P. Lunkenheimer, A. Loidl and the Augsburg group. Thank you for your attention