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:
The most emblematic claim of this work : Glycerol (T g =187K at E st =0) T g (E st )-T g (0) , [mK] 6 E st is a new control parameter in Glycerol. 4 Previously, the unique 2 way to change Tg was the Pressure P 0 -4 -2 0 2 4 Est , [MV/m] Small effect: discovered through a nonlinear technique (see L’Hôte , Tourbot, Ladieu, Gadige PRB 90, 104202 (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.
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.
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.
What happens around Tg ? t α Glass Supercooled Liquid Relaxation time t a liquid (Crystal) t a =100s t α ~ 10 -12 s T T g T m Angell, Science 267 (1995) Polybutadiene, T g 180K Log ( viscosity ) t a 12 E a S(q) [a.u.] t 10 T ~ ~ e a 8 6 E a when T 4 2 Correlations 0 when T -2 -4 0 0.2 0.4 0.6 0.8 1.0 T g / T No (static) order T g / T How to combine the existence of correlations with the absence of order ?
Dynamical Heterogeneities in supercooled liquids • N corr = average number of dynamically correlated molecules : 3 N corr … directly observed in granular matter …Experimentally, the heterogeneous nature or in numerical simulations. of the dynamics has been established through various breakthroughs: Example : numerical simulations on soft • NMR experiments Tracht et al. PRL81, 2727 (98), spheres : J. Magn. Res. 140 460 (99),… • Local measurements E. Vidal Russell and N.E. Israeloff , Nature 408, 695 (2000). Hurley, Harowell, « clusters » PRE, 52, of 30-90 1694, (1995) monomers Hole burning experiments When T : N corr would , which would explain why t a increases so much
Dynamical Heterogeneities and NHB. Many improvements since Schiener, Böhmer, Loidl, Chamberlin Science, 274 , 752, (1996) e.g. R.Richert’s group: PRL, 97 , 095703 (2006); PRB 75 , 064302 (2007); EPJB, 66 , 217, (2008); PRL, 104 , 085702, (2010)… The central idea in Schiener et al ’s seminal paper in 1996: e (t, w ) : should be globally No distribution of t shifted in w Strong field (V 0 ) at W e (t, w ) : should be mainly A distribution of t ’s exists modified close to W Non Res Hole Burning: supercooled dynamics IS heterogeneous (at least in time) … Can nonlinear experiments give MORE than originally expected ??....
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.
The prediction of Bouchaud-Biroli ( B&B): PRB 72, 064204 (2005) DH characteri sation AND N corr « large enough » g ( r , t ) p ( 0 , 0 ) p ( 0 , t ) p ( r , 0 ) p ( r , t ) 4 c P c c w 3 i t E E ... E ( t ) E e e Lin 3 0 e c 2 3 a c w wt 0 s ( , ) ( ) ( ) T N T H T a 3 corr k T B H Natural scale of c 3 N corr = number of dynamic. correlated molec. c s = static value of c Lin t a (T) : typical relaxation time a 3 = molecular volume H: scaling function wt a « 1 » Systematic c 3 ( w ,T) measurements to test the prediction and possibly get N corr (T)
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 d T 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. d ( T ) heat power density P t d d k d 2 T k , Lin T k ~ E 3 P P T ~ E k k k k , Lin k t c T c w c 2 (heat power density ~ ' ' E ) ( P ~ E ) k k , Lin k c 3 For a pure ac field E ac cos( w t): c 3 does NOT contain w and T dependences are N corr (Box model is qualitatively similar in the Box space free) model and in B&B wt a « 1 » c 3 ( w ,T) : N corr (T) or not ?
Some experiments done since B&B’s prediction (2005) c ( 1 ) Im( ) E ² c c d e ( 1 ) ( 3 ) 3 as well as B&B: ln ' ' Box model : c 3 3 Im( ) Lin e.g. R.Richert’s group: PRL, 97 , 095703 Our group : PhD’s of C. Thibierge and C. Brun . (2006); PRB 75 , 064302 (2007); EPJB, 66 , PRL (2010); (2012) PRB (2011 ) (2012); JChem Phys (2011) , 217, (2008); PRL, 104 , 085702, (2010)… Augsburg group : PhD of Th. Bauer : 2 PRL’s in (2013); etc… → Very good fits at 1 w (better than at 3 w → Test of B&B’s prediction: OK → Accounts for the transient regime at 1 w → Evolution of N corr (T) or of N corr (t a ) → Several liquids tested ( Bauer, Lunkenheimer, → Several liquids tested (Richert PRL (2007)) Loidl, PRL 111 , 225702 (2013) ) Using E st will shed a new light on this interpretation issue
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.
Dielectric setup and orders of magnitude V S (t) Supercooled liquid, e P controlled T For “low enough” E P ( t ) c c ... ' ' ' ' ' ' ' ' ' ( t t ' ) E ( t ' ) dt ' t t , t t , t t E ( t ) E ( t ) E ( t ) dt dt dt e lin 3 1 2 3 1 2 3 1 2 3 0 Linear term First non-linear term w E ( t ) E ac cos( t ) E st 1 c w w P ( t ) P c w w c w w 2 ( 1 ) j t 3 ( 1 ) j t ( 3 ) j 3 t 3 E E Re ( ) e even harmonics E Re 3 ( ) e ( ) e Lin st ac 2 ; 1 e ac 3 3 4 0 { { c w c c w c ( 1 ) ( 1 ) ( ) F . T . ( ) . . F T w w w w ( , , ) ( 0 , 0 , ) 3 3 2 ; 1 3 { c w c ( 3 ) ( ) F . T . w w w ( , , ) 3 3 cubic terms 6 10 Specially designed setup 4 For E 1 MV/m, 10 - linear term
Our setup to measure cubic susceptibilities C. Thibierge et al, RSI Bridge with two glycerol-filled capacitors of different thicknesses 79 , 103905 (2008)) 3 V ac e j w t + V st P P w c w 3 ( 1 ) j t Lin E Re ( ) e e ac 3 4 w 1 Z 2 = thick 0 Z 1 = thin c w w 2 ( 1 ) j t capacitor 3 E E Re ( ) e capacitor st ac 2 ; 1 ( 2 × thin ) D V = V meas (V ac ,V st ) V meas - V meas (V ac ,0) 2 I Lin + I Lin + -3 10 r 1 r 2 8 I NonlLin I NonlLin 300 Modulus, [V] Phase, [deg] -4 200 10 P 100 N.B. : I S t -5 10 0 when r 1 Z 1 =r 2 Z 2 : P lin cancels -100 -6 gives P NonLin 10 1 10 V st , [V] D D V~ V st V 2 V ac c ( 1 ) 2 ; 1 2 Phase ( D V) = cte V V st ac
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. 1,E-08 C or G/ w [Farads] wt a f/f a NB: c ~ ' Lin 1,E-09 f a peak of c lin ’’( w ) c ~ ' ' Lin |c lin ( w )| has no peak 1,E-10 1,E+00 1,E+02 1,E+04 1,E+06 frequency [Hz]
c w ( 1 ) Main features of ( , T ) 2 ; 1 50 -15 10 At constant T: 0 humped shape 2;1 ), [Deg] 2 ] for | c 2;1 -50 (1) | 2 / V 197K (f a = 0.3 Hz) maximum 202K (f a = 2.1 Hz) 2;1 |, [m -100 211K (f a = 60 Hz) happens in the -16 (1) 10 218K (f a = 520 Hz) Arg( c range of f a (1) -150 | c Scaling of the -200 hump in T -17 10 -250 0.1 1 10 100 f/f a Same qualitative trends as for c 3 (1) and c 3 (3)
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