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, 21 - 25 September 2015 1

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

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

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

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.

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

Multiangle Dynamic Light Scattering (DLS) Setup

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

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

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

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

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

Molecular Dynamics Simulations Simple model of low density glass former: 50 - 50 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

Dynamics across the glass transition T decreasing 14

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).

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

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, 258301 (2004); JPCM 16, S4993 (2004); Langmuir 22, 1106 (2006); Phys Rev E 77, 020402 (2008); Phys Rev Lett 104, 085701 (2010); Soft Matter 7, 1268 (2011); Nat Mat 10, 56 (2011), 18

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, 10955 (2013).

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

Gold/polystyrene nanocomposite thin films (70 nm)

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.

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

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, 258301 (2004).

Waiting Time Dependence tw = 0 defined at sample filtration

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.

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.

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

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

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.