A new control parameter for the glass transition of glycerol. P. - - PowerPoint PPT Presentation
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 lEtat Condens (CNRS, MIPPU/ URA 2464), DSM/IRAMIS/ SPEC/SPHYNX CEA Saclay, France Main
Service de Physique de l’Etat Condensé (CNRS, MIPPU/ URA 2464), DSM/IRAMIS/SPEC/SPHYNX CEA Saclay, France
2 4 2 4 6
Small effect: discovered through a nonlinear technique (see L’Hôte, Tourbot, Ladieu, Gadige PRB 90, 104202 (2014) )
As for P expts, the most interesting is not Tg(P) in itself but what we learn about the glass transition when varying the control parameter.
Previously, the unique way to change Tg was the Pressure P Est is a new control parameter in Glycerol.
How to combine the existence of correlations with the absence of order ?
12 10 8 6 4 2
Tg / T Log (viscosity) ta
Angell, Science 267 (1995) Tg / T 0 0.2 0.4 0.6 0.8 1.0
Ea when T
T Ea
a
Correlations when T No (static) order
S(q) [a.u.] Polybutadiene, Tg 180K
Relaxation time ta
tα~ 10-12s
T Tm Tg
Liquid Supercooled liquid Glass
ta=100s
(Crystal)
Hurley, Harowell, PRE, 52, 1694, (1995)
… directly observed in granular matter
Example : numerical simulations on soft spheres :
3 corr
N
…Experimentally, the heterogeneous nature
through various breakthroughs:
Tracht et al. PRL81, 2727 (98),
Israeloff , Nature 408, 695 (2000).
« clusters »
monomers
When T: Ncorr would , which would explain why ta increases so much
Hole burning experiments
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
Natural scale of c3 cs= static value of cLin a3= molecular volume
Ncorr= number of dynamic. correlated molec. ta (T) : typical relaxation time H: scaling function
3 3
Lin
t i
e E t E
w
) (
3 2 3
corr B s a
Systematic c3(w,T) measurements to test the prediction and possibly get Ncorr(T)
c
t r p r p t p p t r g ) , ( ) , ( ) , ( ) , ( ) , ( sation characteri DH
4
AND Ncorr « large enough »
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
~ E Tk d
) ~ ( ~
, 3 , ,
E P E T T P P P
k Lin k k Lin k Lin k k
c d
c3 does NOT contain Ncorr (Box model is space free)
) E ' ' ~ density power (heat c density power heat ) (
2
w c d d t
k k k k
T t T
For a pure ac field Eac cos(wt): w and T dependences are qualitatively similar in the Box model and in B&B
Using Est will shed a new light on this interpretation issue
→ Very good fits at 1w (better than at 3w 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( ² ) Im( ' ' ln
) 1 ( 3 Lin
E c c e d
) 3 ( 3 ) 1 ( 3
as well as c c
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 (Bauer, Lunkenheimer,
Loidl, PRL 111, 225702 (2013))
) cos( t Eac w
' ) ' ( ) ' ( ) ( dt t E t t t P
lin
c e
' 3 ' 2 ' 1 ' 3 ' 2 ' 1 ' 3 ' 2 ' 1 3
) ( ) ( ) ( , , dt dt dt t E t E t E t t t t t t
c
Linear term First non-linear term
t j t j ac
e e E
w w
w c w c
3 ) 3 ( 3 ) 1 ( 3 3
) ( ) ( 3 Re 4 1
) ( e
Lin
P t P
{
) , , ( . . ) (
3 ) 1 ( 3
w w w c w c T F
{
) , , ( . . ) (
3 ) 3 ( 3
w w w c w c T F
4 6 10
term linear terms cubic MV/m, 1 For
E
Specially designed setup
P e Supercooled liquid, controlled T VS (t)
st
E
harmonics even ) ( Re 3
) 1 ( 1 ; 2 2
t j ac st
e E E
w
w c
) (t E
{
) , , ( . . ) (
3 ) 1 ( 1 ; 2
w c w c T F
...
For “low enough” E
Vmeas
r1
Z2 = thick capacitor (2×thin) Z1 = thin capacitor
r2
Vac e j w t + Vst Bridge with two glycerol-filled capacitors of different thicknesses
79, 103905 (2008))
DV~ Vst
2 Vac
Phase (DV) = cte
ac V st V V 2
) 1 ( 1 ; 2
D c
when r1Z1=r2Z2 : Plin cancels
ILin + INonlLin
t P S I : N.B.
2 ILin + 8 INonlLin
w e 1
Lin
P P
t j ac
e E
w
w c
) ( Re 4 3
) 1 ( 3 3
t j ac st
e E E
w
w c
) ( Re 3
) 1 ( 1 ; 2 2
DV = Vmeas(Vac,Vst)
1 10
10
10
10
10
100 200 300
Modulus, [V] Vst , [V] Phase, [deg]
gives PNonLin
NB:
1,E-10 1,E-09 1,E-08 1,E+00 1,E+02 1,E+04 1,E+06
frequency [Hz] C or G/w [Farads]
' ~
Lin
c ' ' ~
Lin
c fa peak of clin’’(w) |clin(w)| has no peak
0.1 1 10 100 10
10
10
50
197K (fa = 0.3 Hz) 202K (fa = 2.1 Hz) 211K (fa = 60 Hz) 218K (fa = 520 Hz)
(1) 2;1|, [m 2/ V 2]
Arg(c
(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
) 1 ( 1 ; 2
Same qualitative trends as for c3
(1) and c3 (3)
) 1 ( 1 ; 2
) 1 ( 3
For the first time, Box Model is unable to account for a cubic response: Decisive point for the interpretation issue …
w e 1
Lin
P P
t j ac
e E
w
w c
) ( Re 4 3
) 1 ( 3 3
t j ac st
e E E
w
w c
) ( Re 3
) 1 ( 1 ; 2 2
Compare |c3
(1)|/4 and |c2;1 (1)|
→ Same order of magitude
10
10 10
1
10
2
2x10
2x10
2x10
|X2,1
(1)|, T=202 K
|X3
(1)|/4
c2;1 c3
, [m²/V²]
2
|c
(1) 2;1| or |c (1) 3 |/4
a
→ Measurements ( ) are in the stationnary regime (tst>> ta
Est tst
t Varying Est ZERO dissipated power power dissipated ~ : Model Box In the
k
T d
Box model’s prediction :|c2;1
(1)|<< |c3 (1)|
Box model’s prediction is too small by a factor 300 for |c2;1
(1)|
(ions)
0.01 0.1 1 10 100 0.01 0.1 1
0.01 0.1 1 10 100
100 200 300
X
(3) 3
X
(1) 3
X
(1) 2;1
X
(1) 2;1
X
(3) 3
X
(1) 3
X
(1) 2;1 , X (1) 3 & X (3) 3
f/fa
w w
X
(3) 3 phaseX
(1) 3 PhaseX
(1) 2;1PhaseX
(1) 2;1Phase+ f/fa
Phase
2 1 2
static g c α static
) 3 ( 3 ) 1 ( 3 ) 1 ( 1 ; 2 ac static
Very unlikely due to the similarities of c2;1
(1) , c3 (1) ,
and c3
(3) .
Two different mechanisms at play ?
) 1 ( 1 ; 2
st E T
Lin
c
Direct link with
dT dχ T n
Lin estim corr ~
Berthier et al., Science (2005);
JCP, (2007); PRE (2007).
For f/fa > 0.2: w c w c , , ) , (
) 1 ( 1 ; 2
T T T
Lin
80 . ,
² ² 16
10 2 . 1
V Km
with
expected from
for both Re and Im parts T
For f/fa < 0.2: “Trivial” dominates Reshuffling Ideal gas at t >>ta
T T
Lin
c w c ) , (
) 1 ( 1 ; 2
0.1 1 10 100 10
10
10
50
|c
(1) 2;1| or | dcLin/dT|, [m 2/ V 2]
f/faor f/fa Arg(c
(1) 2;1) or Arg(- dcLin/dT), [Deg]
218K 197K
) (k n
195 200 205 210 215 220 0.6 0.8 1.0 1.2 1.4 1.6
10
10 10
1
0.05 0.1
(1) 2;1|
|Z (T)|/|Z (202K)| T, [K]
|X2;1
(1)|
|TcT| |X3
(1 or 3)(T<204.7K)|
f/fa
T k a T T X
B s k n k n 3 2 ) ( ) (
, ) , ( c e w c w
is T-independent in the trivial limit (ideal gas)
)) ( ( ) ( T H T N
k n corr a
wt
if B&B’s prediction holds
“Trivial”
) 1 ( 1 ; 2
looks OK Similar T dependences for
Lin k n
) (
w and T dependences consistent with X2;1
(1) ~ Ncorr (OK within MCT)
Each Dyn.Het. µ = µm 𝑶𝒅𝒑𝒔𝒔
corr B corr
N T k t E N m µ e ~ ) ( where
corr corr corr
N a N N m µ 1 ~
3
M
corr Lin
3
corr corr corr corr Lin
N E N e P E N N e P 3 ~ ~ ~ ~
3 3
Μ Μ
e P t P e th ch M t
Simplest example: D=0=q1 can it fit the data ? … Two key points Amorphous Order («as» in S.G.)
corr
N µ ~ Crossover to trivial is enforced at f<<fa
in a double well (to get long t),
Ncorr has the right
good fits for ALL the Xn
(k)
… but with different values of Ncorr (toy model)
Ncorr=10 d=0.60 Ncorr=15 d=0.60
Ladieu, Brun, L’Hôte, PRB 85, 184207, (2012) L’Hôte, Tourbot, Ladieu, Gadige PRB 90, 104202 (2014)
Hensel-Bielowka et al. , PRE (2004)
(1) as a dTg shift
Pressure experiments: dTg(P) is drawn from :
Slight trivial distortion
(1) ≠1
) ( ; ; ; ; P P
g
T T P T P d w w
Same method for Est:
) ( ; ; ; ;
st st
E T T P T E P
g
d w w
1 with , , ) , (
) 1 ( 1 ; 2
w c w c T T T
Lin
dTg=3Est
2 Est is a new control parameter in glycerol
2 st E 3 ) st (E g T d
Density … S and ta Increasing Est … Est … S and ta Increasing Pressure …
Our very sensitive setup has successfully measured c2;1
(1)(w,T)
The interpretation issue is now clarified since : the Box Model cannot account for the order of magnitude of c2;1
(1)
(k) ~ Ncorr:
w and T dependences, fits with the toy model Perspectives = systematic studies of Ncorr the scale on which the systems is solid, during ta : study c3(w1;w2;w3) in other directions than (0,0,w) or (±w,w,w) study c2;1
(1)at high temperatures (no heating)
(1) at higher fields or in other liquids
For the nice discussions and/or long time support, warm thanks to:
well as P. Lunkenheimer, A. Loidl and the Augsburg group.