Dynamics of a Colloidal Glass During Stress-Mediated Structural Arrest (“Relaxation in Reverse”) Dynamics of a Colloidal Glass During Stress-Mediated Structural Arrest (“Relaxation in Reverse”) Ajay Singh Negi and Chinedum Osuji Department of Chemical Engineering, Yale University, New Haven, CT.

Motivation Structural Glass At high temperatures (above T g ), system is liquid. Below T g, the viscosity is very high. Below T g, the system shows aging behavior. Colloidal Glass Under high shear, the system flows. At low shear rates or rest, the system does not flow. Aging behavior is seen at rest or low shear. Is shear temperature ?

Motivation EXPERIMENTS: Ediger et al, Science, 323, 231 (2009) At higher creep stresses, the dynamics was faster and distribution narrower. SIMULATIONS: Warren and Rottler, 2010: At higher stresses, dynamics is accelerated and distribution is narrowed.

How does stress influence the structural arrest of a colloidal glass? Motivation What is the role of stress on the arrest timescale? How does stress affect the trajectory of the system during arrest? (peak-width in time-dependent viscosity)

System and Method Laponite XLG (a) Electrostatic screening length at pH 10 ≈ 30 nm. (b) Non-ergodic state at concentration of 1 wt %. Bulk Rheology (a) Constant stress measurements. (b) Oscillation over a background steady flow.

time (s) Solid lines: Controlled variable Dashed lines: Measured variable Schematic of Protocol (constant stress) shear rate stress Rejuvenation (Fluid State) Aging Quench t=0

Dynamical Arrest Shear rate measured as a function of time for a constant applied stress. The time for arrest increase with increase in the applied stress. Above a certain stress the system will NOT arrest. Viscosity Bifurcation Coussot et al, PRL 2002

time (s) Solid lines: Controlled variable Dashed lines: Measured variable Superposition Rheology Protocol shear rate stress Rejuvenation (Fluid State) Aging Quench t=0

Linearity of Superposition Rheology Same background stress and different probe stresses give the same result. This ensured that we are measuring the linear properties of the system under flow.

Waveforms Waveforms are NOT distorted  linear properties are being measured. Finite phase lag for a liquid sample. The phase lag vanishes when the system solidifies.

Oscillation Over Flow Oscillation Over Flow Dynamic measurements on the sample under steady flow. Probe stress = 1 Pa.

Bentonite Ovarlez and Coussot, PRE, 76, (2007) Shahin and Joshi, Langmuir, 26, 4219 (2010) melting stress > yield stress (yield stress)

Oscillation Over Flow Oscillation Over Flow Dynamic measurements on the sample under steady flow. Probe stress = 1 Pa.

Oscillation Over Flow Oscillation Over Flow Dynamic measurements on the sample under steady flow. Probe stress = 1 Pa.

Oscillation Over Flow Oscillation Over Flow Dynamic measurements on the sample under steady flow. Varying background stresses, σ m. Probe stress = 1 Pa. The cross-over between G’ and G” is delayed as the background stress was increased.

τ vs σ m System will not arrest above a stress σ 0. VFT equation

τ vs σ m System will not arrest above a stress σ 0. VFT equation Evolution of the arrest time with applied stress? VFT dependence Width of the loss mode peak with applied stress?

Width of Loss Peak G” peaks broaden as stress is decreased, precluding time- stress superposition. It is similar to broadening of loss peak on approaching glass transition temperature.

Peak Width of Loss Modulus Lines are fit to Lorentzian function Loss mode peak narrows with increasing stress.

Cole Davidson Exponent ~ 1/peak width Stickel et al (1993): decreases on approaching glass transition for PDE, an organic glass former.

Summary Stress delays the onset of structural arrest. Dynamic measurement gives a temporal response similar to frequency dependence observed in non-aging systems. The arrest time τ has an exponential dependence on inverse stress. Above a critical stress σ 0, the arrest time diverges. Loss peak narrows with increasing stress. Negi and Osuji, EPL, 90, (2010)

Effect of Frequency The frequency of the probe stress was varied.

Frequency Dependence At higher frequency system arrests much faster.

Width of Loss Modulus The lines are fitted to logistic power peak function to estimate the width.

Summary The response of the system at higher frequency is qualitatively similar to its response at the lower stresses. The system seem to be more arrested at higher frequencies. POSSIBLE REASON At higher frequency or at short times, the system seems more solid like.

Acknowledgements Funding. Osujilab group. Thank you for your attention!!! Questions?