1. Relaxation dynamics in a colloidal glass
SAPIENZA
UNIVERSITÀ DI ROMA
Relaxation dynamics in a colloidal glass
Outline
Laponite
Aging and Phase Diagram.
Microscopic and structural relaxations across the glass transition.
Conclusions.
Barbara Ruzicka
101° Congresso Nazionale della Società Italiana di Fisica
Rome, September 2015 1

2. Laponite Sinthetic clay: Na+0.7 [(Si8Mg5.5Li0.3)O20(OH)4]-0.7
Idealised structural formula: .
Dispersed in water Laponite originates a
charged colloidal suspension
of disks of nanometric size
with inhomogeneous charge distribution

3. Viscosity increases with waiting time up to when Laponite reaches an
Laponite Aging
Initially LIQUID.
Viscosity increases with waiting time up to when Laponite reaches an
ARRESTED state

4. Phase diagram and Arrested States Next talk by Roberta Angelini
Small Angle
X-ray
Scattering tw
Cw=2.8 % a)
C=0.3% b)
C=1.5% c)
C=3.0%
Photographs
&
Representation
Phase
Separation
Equilibrium
Gel
Wigner Glass
Dynamic Light
Scattering
Fluid
Nature Materials 10, 56 (2011).
Nature Commun. 5, 4049(2014).
Next talk by Roberta Angelini

5. Aging in colloidal systems
The dynamics is not stationary but changes with waiting time (tw) as the sample evolves towards an arrested state.
t1: related to the interactions between a particle and the cage of its nearest neighbors.
Microscopic relaxation: t1
Structural relaxation: t2
One of the most striking features of soft matter systems is their ageing behavior: the dynamics is not stationary but changes with waiting time as the sample evolves towards an arrested state.
MCT predicts that the relaxation of the intermediate scattering function proceeds in two stages: alfa and beta. In the glass the alfa process is arrested but the beta process persists and saturates at long times. These predictions were first confirmed in hard sphere system by van Megen and coworkers.
t2: related to a structural rearrangement of the particles.

6. Aging of Laponite samples
G. Grubel et al. J Alloys Comp. 362, 3, 2004.

7. Multiangle Dynamic Light Scattering (DLS) Setup

8. MultiAngle Dynamic Light Scattering (DLS)
DLS on a Cw=3.0 % in D2O in the ERGODIC (Early aging) regime
6.2 x 10-4 < Q < 2.1 x 10-3 Å-1
10-6 < t < 1 s
τ1 microscopic relaxation time
t1 ≈ Q-2
τ2 structural relaxation time
t2 ≈ Q-2
b < 1
Diffusive dynamics for both microscopic and structural relaxation times

9. Neutron Spin Echo (NSE)
NSE at IN15 (ILL, Grenoble) on a Cw=3.0 % in D2O
ERGODIC and NON ERGODIC regime (glass transition at tw ≈600 min)
1.3 x 10-2 < Q < 1.3 x 10-1 Å-1
10-9 < t < 2 x 10-7 s
τ1 microscopic relaxation time
t1 ≈ Q-2

10. Microscopic Dynamics across the glass transition
Early aging regime
Full-aging regime
t1 ≈ Q-2
Microscopic dynamics remains DIFFUSIVE across the glass transition

11. X-rays Photon Correlation Spectroscopy (XPCS)
XPCS at ID10 (ESRF, Grenoble) on a Cw=3.0 %in D2O. NON ERGODIC regime
(glass transition at tw = 560 min)
3.1 x 10-3 < Q < 2.2 x 10-1 Å-1
1 < t < 4 x 103 s
Kohlrausch-Williams-Watts (KWW)
τ2 structural relaxation time
t2 ≈ Q-1
b < 1
Structural relaxation time NON DIFFUSIVE across the glass transition 11

12. Structural relaxation across the glass transition
Early aging regime
probed by DLS
Full-aging regime
probed by XPCS
t2 ≈ Q-2→ Q-1
The structural relaxation changes across the glass transition

13. Molecular Dynamics Simulations
Simple model of low density glass former: non-crystallizing binary mixture of N=1000 Yukawa particles of equal screening length and different repulsion strength.
b < 1
Increasing tw gradual transition
MD simulations were performed for a simple modelof low-density glass-former, i.e. a 50 ¡ 50 non-crystallising binary mixture of N = 1000 Yukawa particles of equal screening length and different repulsion strength. Self intermediate scattering function calculated for different wavevectors as a function of waiting time, averaging over 20 independent quenches to improve the statistics.
Microscopic dynamics is Newtonian, so alpha=2 and the corresponding t1 is not relevant to describe the experimental (Brownian) fast relaxation.
Restrict at larger waiting times (tw>=20 000) where full aging starts and double exponential describe the correlators and for wavevectors small enough that beta<1
t2 ≈ Q-2→ Q-1 13

14. Dynamics across the glass transition
T decreasing 14

15. Conclusions DLS & NSE DLS & XPCS MD Early-aging regime
Diffusive nature of particles motion
Full-aging regime
DLS & XPCS
Full-aging regime
Early-aging regime
Diffusive nature of the structural relaxation
Discontinuous hopping of caged particles MD
Intrinsic generality, occurring also in numerical and theoretical studies on different glass-formers.
Gradual transition from Q-2 to Q-1
F.A. Marques, R. Angelini, E. Zaccarelli, B. Farago, B. Ruta, G. Ruocco and B. Ruzicka Soft Matter 11, 466 (2015).

16. THEORY and SIMULATIONS Thank you for your attention!
Coworkers
M. Sztucki
THEORY and SIMULATIONS
SAXS
E. Zaccarelli
EXPERIMENTS
R. Angelini
T. Narayanan
A. Fluerasu
F. A. de Melo Marques
XPCS
NSE
G. Ruocco
B. Farago
Thank you for your attention!
B. Ruta
A. Madsen

18. Aging of Laponite samples
Two different non ergodic states below and above Cw =2.0 %
Above Cw =2.0 %:
~37 nm
~14 nm
Structure does not change much with waiting time.
Fast aggregation.
First peak at distances larger than contact.
WIGNER GLASS.
Short-time REPULSIVE dominated tw tw
Below Cw =2.0 %:
Structure changes considerably
with waiting time.
Slow aggregation.
First peak compatible with rim-face bonding.
HOUSE of CARDS structure GEL
Long time ATTRACTIVE
dominated
0.17
0.45
Phys Rev Lett 93, (2004); JPCM 16, S4993 (2004); Langmuir 22, 1106 (2006); Phys Rev E 77, (2008);
Phys Rev Lett 104, (2010); Soft Matter 7, 1268 (2011); Nat Mat 10, 56 (2011), 18

19. Long waiting time – full aging regime – Dichotomic Aging Behaviour
Aging Dynamics
XPCS measurements at ID10-ESRF
Spontaneously Aged sample
Long waiting time – full aging regime – Dichotomic Aging Behaviour
b < 1
Stretched
b > 1
Compressed
In the case of rejuvenated samples the shear applied by
the syringe induces internal stresses responsible for the compressed
exponential relaxations in agreement with several
models explaining this type of phenomenology in aging soft
materials: both a heuristic interpretation 6 and a microscopic
model24 underline the importance of internal stresses in these
complex systems.
Anomalous behaviour
Same tQ≈Q-1 behaviour
Rejuvenated sample
(tR≈3.5 days)
R. Angelini, L. Zulian, A. Fluerasu, A. Madsen, G. Ruocco and B. Ruzicka Soft Matter 9, (2013).

20. Waiting time dependence of t2
Early aging regime
Full-aging regime

22. Gold/polystyrene nanocomposite thin films (70 nm)

23. Activated MCT. Discontinuos hopping of caged particles.
Theory that unifies the MCT for continuous dynamics with the random first order transition theory treatment of activated discontinuous motion. Predicted smooth change in mechanism of relaxation from diffusive to activated.

24. At low T tl seems to cross from a Q-2 to a Q-1 behaviour
T decreasing
At low T tl seems to cross from a Q-2 to a Q-1 behaviour

25. Fitting Expressions b: distribution width of the slow relaxation time.
t1: Fast or microscopic relaxation time.
t2: Slow or structural relaxation time.
B. Ruzicka, L. Zulian G. Ruocco Phys. Rev. Lett. 93, (2004).

26. Waiting Time Dependence
tw = 0 defined at sample filtration

27. Waiting Time Dependence of the structural relaxation time
b parameter has been found to be lower than 1 (stretched behaviour) for all measured waiting times and Q-values differently from the anomalous dynamics normally found in different glass-formers with b > 1, i.e. compressed behaviour.

28. NON ERGODIC regime probed by XPCS Correlation functions stretched.
Q-Dependence of the structural relaxation time
NON ERGODIC regime probed by XPCS
Structural relaxation times NON DIFFUSIVE across the glass transition (at tw ≈600 min).
Correlation functions stretched.

29. Anomalous dynamics Q-1 tw0.9 exp tw Ballistic motion Power law
polystyrene
Q-1
Ballistic
motion
vs Q
tw0.9
Power law
behaviour
A pioneering work by Cipelletti on a gel of colloidal Polystirene has shown the existence of anomalous dynamics.
exp tw
=1.5
Compressed Behaviour
Exponential
behaviour

30. Anomalous dynamics in Laponite Glass
FULL AGING
(Compressed)
AGING (Stretched)
β >1
β <1

31. XPCS and DLS on Laponite
Large tw
(XPCS region)
b<1
tQ ≈ Q-1
Small tw
(DLS region)
b<1
tQ ≈ Q-2
Increasing tw tQ cross from a Q-2 to a Q-1 behaviour.