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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/SPHYNX CEA Saclay , France. Main Funding :. Additionnal Funding :. - PowerPoint PPT Presentation
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A new control parameter for the glass transition of glycerol.
D. L’Hôte, R. Tourbot, F. Ladieu, P. Gadige
Service de Physique de l’Etat Condensé (CNRS, MIPPU/ URA 2464), DSM/IRAMIS/SPEC/SPHYNX
CEA Saclay, France
Main Funding:
Additionnal Funding:
-4 -2 0 2 4
0
2
4
6
Tg(E
st)-
Tg(0
) , [
mK
]
Est , [MV/m]
Glycerol (Tg=187K at E
st=0)
The most emblematic claim of this work :
· Small effect: discovered through a nonlinear technique
The most interesting is not dTg but what we learn when varying P, Est.
Previously, the unique way to change Tg was the
Pressure P
Est is a new control parameter in Glycerol.
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
IV) Some naives questions/ideas.
Summary and Perspectives.
How to combine the existence of correlations with the absence of order ?
12
10
8
6
4
2
0
-2
-4
Tg / T
Lo
g (
visc
osi
ty) t a
Angell, Science 267 (1995)
Tg / T0 0.2 0.4 0.6 0.8 1.0
Ea when T
T
Ea
e~~
Correlations when T
No (static) cristalline orderS
(q)
[a.u
.]
Polybutadiene, Tg 180K
What happens around Tg ???Relaxation time ta
tα
tα~ 10-12sTTmTg
LiquidSupercooled
liquid
Glass
ta=100s
(Crystal)
Dynamical Heterogeneities in supercooled liquids• Ncorr = average number of dynamically correlated molecules :
Hurley, Harowell, PRE, 52, 1694, (1995)
… directly observed in granular matter or in numerical simulations.
Example : numerical simulations on soft spheres :
3corrN
…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
When T: Ncorr would , which would explain why ta increases so much
Hole burning experiments
Dynamical Heterogeneities and NHB.
Non Res Hole Burning: supercooled dynamics IS heterogeneous (at least in time)
e.g. R.Richert’s group: PRL, 97, 095703 (2006); PRB 75, 064302 (2007); EPJB, 66, 217, (2008); PRL, 104, 085702, (2010)…
A distribution of t’s exists
e(t,w) : should be globally shifted in w
Many improvements since Schiener, Böhmer, Loidl, Chamberlin Science, 274, 752, (1996)
The central idea in Schiener et al ’s seminal paper in 1996:
… Can nonlinear experiments give MORE than originally expected ??....
Strong field (V0) at W No distribution of t
e(t,w) : should be mainly modified close to W
The prediction of Bouchaud-Biroli (B&B): PRB 72, 064204 (2005)
Natural scale of c3
cs= static value of cLin
a3= molecular volume
H
wta « 1 »
Ncorr= number of dynamic. correlated molec.
ta (T) : typical relaxation time
H: scaling function
...33
0
EEP
Lin
tieEtE )(
)()(),(32
03 THTN
Tk
aT corr
B
s
Systematic c3(w,T) measurements to test the prediction and possibly get Ncorr(T)
ctrprptpptrg ),()0,(),0()0,0(),(
sation characteriDH
4
AND Ncorr « large enough »
The issue of interpretations : Box Model versus B&B
c3(w,T) : Ncorr(T) or not ?
→ Each DH « k » has a Debye dynamics. {tk} chosen to recover clin(w) at each given T.
Box model assumptions (designed for NHB):
→ Applying E: each DH « k » is heated by dTk (ttherm) with ttherm tk.
as{tk}ta heat diffusion over one DH takes a macroscopic time close to Tg.
2~ ETk
)~(
~
,
3,,
EP
ETT
PPP
kLink
kLink
Linkk
c3 does NOT contain Ncorr (Box model is
space free)
)E'' ~density power(heat
c
densitypowerheat)(
2
k
kk
k Tt
T
c3
wta « 1 »
For a pure ac field Eac cos(wt): w and T dependences are
qualitatively similar in the Box model and in B&B
Some experiments done since B&B’s prediction (2005)
Using Est will shed a new light on this interpretation issue
→ Very good fits at 1w (better than at 3 )w
Box model : B&B:
e.g. R.Richert’s group: PRL, 97, 095703 (2006); PRB 75, 064302 (2007); EPJB, 66, 217, (2008); PRL, 104, 085702, (2010)…
Our group: PhD’s of C. Thibierge and C. Brun. PRL (2010); (2012) PRB (2011) (2012); JChem Phys (2011) ,
→ Accounts for the transient regime at 1w
→ Several liquids tested (Richert PRL (2007))
)Im(
)Im(''ln
)1(3
Lin
)3(3
)1(3 aswellas
Augsburg group: PhD of Th. Bauer : 2 PRL’s in (2013); etc…
→ Test of B&B’s prediction: OK
→ Evolution of Ncorr(T) or of Ncorr(ta)
→ Several liquids tested (Lunkenheimer & Loidl)
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
IV) Some naives questions/ideas.
Summary and Perspectives.
)cos( tEac
')'()'()(
0
dttEtttP
lin
'3
'2
'1
'3
'2
'1
'3
'2
'13 )()()(,, dtdtdttEtEtEtttttt
Linear term
First non-linear term
tjtjac eeE 3)3(
3)1(
33 )( )(3Re
4
1
0
)(
LinPtP
),,(..)( 3)1(
3 TF
),,(..)( 3)3(
3 TF
46 10-10termlinear
termscubic MV/m,1For E Specially designed setup
Dielectric setup and orders of magnitude
P eSupercooled liquid, controlled T
VS (t)
stE
harmonicseven)(Re3 )1(1;2
2 tjacst eEE
)(tE
),0,0(..)( 3)1(1;2 TF
...For “low enough” E
Our setup to measure cubic susceptibilities
Vmeas
r1
Z2 = thickcapacitor(2×thin)
Z1 = thincapacitor
r2
Vac e j w t + Vst
Bridge with two glycerol-filled capacitors of different thicknessesC. Thibierge et al, RSI 79, 103905 (2008))
DV~ Vst2 Vac
Phase (DV) = cte acV
stV
V2
)1(1;2
when r1Z1=r2Z2 : Plin cancels
ILin +INonlLin
t
PSI
:N.B.
2 ILin +8 INonlLin
10
LinPP tjac eE )(Re
4
3 )1(3
3
tjacst eEE )(Re3 )1(
1;22
DV = Vmeas(Vac,Vst)- Vmeas(Vac,0)
1 1010-6
10-5
10-4
10-3
-100
0
100
200
300
Mod
ulus
, [V
]
Vst , [V]
Pha
se, [
deg]
gives PNonLin
Outline:I) Motivations for nonlinear experimentsII) Our specially designed experiment
III) Results on Glycerol• Order of magnitude and comparison to the Box model • Relation to Ncorr
• Tg shiftIV) Some naives questions/ideas.
Summary and Perspectives.
NB: wta f/fa
1,E-10
1,E-09
1,E-08
1,E+00 1,E+02 1,E+04 1,E+06frequency [Hz]
C o
r G
/
[Far
ads]
'~ Lin
''~ Linfa peak of clin’’(w)
|clin(w)| has no peak
0.1 1 10 10010-17
10-16
10-15
-250
-200
-150
-100
-50
0
50
197K (f = 0.3 Hz) 202K (f = 2.1 Hz) 211K (f = 60 Hz) 218K (f = 520 Hz)
|
(1)
2;1|,
[m2 / V
2 ]
f/f
Arg
((1
)2;
1),
[Deg
]
At constant T:
humped shape for |c2;1
(1)|
maximum happens in the range of fa
Scaling of the hump in T
Main features of ),()1(1;2 T
Same qualitative trends as for c3(1) and c3
(3)
Comparing and ),()1(1;2 T ),()1(
3 T
For the first time, Box Model is unable to account for a cubic response:
Decisive point for the interpretation issue …
10
LinPP tjac eE )(Re
4
3 )1(3
3 tjacst eEE )(Re3 )1(
1;22 Compare |c3
(1)|/4 and |c2;1(1)|
→ Same order of magitude
10-1 100 101 1022x10-172x10-17
2x10-16
|X2,1
(1)|, T=202 K
|X3
(1)|/4
|(1)
2;1| o
r |(1
)
3|/4
f/f
, [m
²/V²]
10-1 100 101 1022x10-172x10-17
2x10-16
|X2,1
(1)|, T=202 K
|X3
(1)|/4
|(1)
2;1| o
r |(1
)
3|/4
f/f
→ Measurements ( ) are in the stationnary regime (tst>> ta)
Est
tst
tVarying Est ZERO dissipated power
powerdissipated~
:ModelBox In the
kTBox model’s prediction :|c2;1(1)|<< |c3
(1)|
Box model’s prediction is too small by a factor 300 for |c2;1(1)|
(ions)
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
IV) Some naives questions/ideas.
Summary and Perspectives.
Comparing the w dependences of and of ),()1(1;2 T
0
stET
Lin
Direct link withdT
dχTn Linestim
corr ~ Berthier et al., Science (2005); JCP, (2007); PRE (2007).
For f/fa > 0.2:
,,0
),()1(1;2
TTT Lin
80.0, ²
²16102.1V
Kmwith
expected from
for both Re and Im parts T
For f/fa < 0.2: “Trivial” dominatesReshuffling Ideal gas at t >>ta
T
T Lin ),()1(1;2
0.1 1 10 10010-17
10-16
10-15
-250
-200
-150
-100
-50
0
50
|(1
)
2;1| o
r |
d L
in/d
T|, [
m2 /
V2 ]
f/for f/f
Arg
((1)
2;1)
or
Arg
(- d L
in/d
T),
[D
eg
]
218K
197K
T-dependences of the dimensionless nonlinear suscept. )(knX
195 200 205 210 215 2200.6
0.8
1.0
1.2
1.4
1.6
10-1 100 1010.05
0.1
|X(1
)
2;1|
|Z (T
)|/|Z
(202
K)|
T, [K]
|X2;1
(1)|
|TT|
|X3
(1 or 3)(T<204.7K)|
f/f
Tk
a
TTX
B
s
knk
n 320
)()( ,
),(
is T-independent in the trivial limit (ideal gas)
))(()( THTN kncorr if B&B’s prediction holds
“Trivial”)1(
1;2X looks OK
Similar T dependences for TTX Lin
kn forand)(
w and T dependences consistent with X2;1(1) ~ Ncorr (OK within MCT)
Each Dyn.Het. µ = µm
Can we fit nonlinear resp. ? The ‘‘toy model’’ as an attempt :
//z
corrB
corr NTk
tENmµe ~
)(where
corrcorr
corr
NaN
Nmµ 1~
3M
corr
Lin
N~
1~
3
corr
corr
corr
corrLin
N
ENeP
EN
NeP
3~~
~~
33 Μ
Μ
ePt
P
eth
chM
Simplest example: D=0=q1
can it fit the data ? …
Two key points
Amorphous Order («as» in S.G.)corrNµ ~
Crossover to trivial is enforced at f<<fa
in a double well (to get long t),of assymetry D
Fits at Tg+17K:
Ncorr has the right order of magnitude good fits for ALL the Xn
(k)
… but with different values of Ncorr (toy model)
Ncorr=10d=0.60
Ncorr=15d=0.60
Ladieu, Brun, L’Hôte, PRB 85, 184207, (2012)
L’Hôte, Tourbot, Ladieu, Gadige to appear in PRB (2014)
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
IV) Some naives questions/ideas.
Summary and Perspectives.
Hensel-Bielowka et al. , PRE (2004)Translating c2,1(1) as a dTg shift
Pressure experiments:
dTg(P) is drawn from :
Slight trivial distortion of
c2,1(1) l≠1
)(;0;;; gTTPTP
Same method for Est:
)(;0;;; stst ETTPTEP g
1with,,0
),()1(1;2
TT
T Lin
dTg=3kEst2 Est is a new control parameter in glycerol
2st
E3)st
(Eg
T
A picture: D.H. overcrowded subway
Density … S and ta
Increasing Est …
Est … S and ta
Increasing Pressure …
Ncorr
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
IV) Some naives questions/ideas.
Summary and Perspectives.
Does TK follow Tg ? We find dTg (Est) > 0
|Est |
TTK Tg
« true » glass
« Supercooled liquid »|Hst |
Tc
Spin Glass Paramagnet
S.G: dTg (Hst) < 0 or “very negative”
Is it allowed that dTK(Est)>0 ? e.g. peculiarity of 1RSB ?
T
Est slows down the dynamics
S.G.: Hst speeds up the relaxation
Not a contradiction since T>Tg differs from T<Tc
Y.G. Joh et al, PRL 82, 438 (1999)
and Saclay data
Can we test theories with cubic responses?L. Levy et T. Oglieksi PRL57, 3288 (1986), L. Lévy, PRB, 38, 4963 (1988)
c 3 (a
.u.)
0.01 0.1 1 10
0.8
1.0
1.2
1.4
(s)
Nco
rr [a
.u.]
Above Tg Too narrow to test
theories relating ta and Ncorr
Quench at Tg-7K
In Spin Glasses: critical
behavior nicely evidenced
Nco
rr /N
corr(e
q)
ta, [s]
Brun et al. PRL109, 175702 (2012)
Brun et al. PRB 84, 104204 (2011)
ta, [s]
Quasi equilibrium
𝑇 −𝑇𝑐𝑇 𝑐
Can we test theories with cubic responses?
AND
We can test theories
0.01 0.1 1 10
0.8
1.0
1.2
1.4
(s)
Nco
rr [a
.u.]
Above Tg
Brun et al. PRB 84, 104204 (2011)
ta, [s]10000 20000 30000
0.90
0.95
1.00
12mHz 36mHz 106mHz 1.1Hz 11Hz
Nco
rr [a
.u.]
ta, [s]
Brun et al. PRL109, 175702 (2012)
Consistent with RFOT
NB: yields z>20 : not reasonnable
Tk
N
B
corr3/
0Ln
2/3
TkB
)20(w
)(w)(
msW
0Ln)w(
10
0Ln)v(
T)20(v
)(v)(
msV
Consistent with
Cammarota et al, JCP (2009)
zNcorr )(~0
)20(N
)(N
mscorr
corr
Below Tg
Recent works on cubic responses
kjikji
kji SSStJH
,,
,,
How to choose a good model ? corrNµ ~
A model accounting for c3 will ALSO capture dyn. spatial aspects ☺
→ In colloids: experiments and MCT done for oscillatory shear : See Brader et al, PRE, 82, 061401, (2010) MCT for oscillatory stress is coming: see Matthias Fuchs papers (Konstanz univ.)
t / ta 1
tJJ kjikji ,,,, 0
→ In supercooled liquids: Bouchaud Biroli PRB 72, 064204 (2005) and Tarzia et al, JCP (2010) in MCT· G. Diezemann : PRE, (2012); JCP(2013); arXiv: 1407.4333v1
Þ no general link between c3 and four times correlation functions (trap models…)Þ This link depends on the chosen model and chosen observable.
AND crossover to trivial
withWhy not simulate ? (d=3)
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