Role of length and time scales of dynamic heterogeneities on - PowerPoint PPT Presentation

Niigata 311epicenter Tokyo Kyoto IMS Role of length and time scales of dynamic heterogeneities on fragility in various model glasses Kang Kim (IMS → Niigata Univ.) Shinji Saito (IMS) K. Kim and S. Saito, J. Chem. Phys. 138, 12A506 (2013)

Outline ✓ Purpose ‣ fragility in glass transition ‣ dynamic heterogeneities ‣ MD for various model glasses ✓ Spatiotemporal structures of DH ‣ multi-point and multi-time correlations ‣ fragility vs. length scale ξ and lifetime τ hetero ‣ model detail dependence ✓ Summary

Vogel-Fulcher-Tammann Fragility P. G. Debenedetti and F. H. Stillinger, Nature 410, 259-267 (2001) � � 1 η ∼ exp K ( T/T g − 1) Log(Viscosity in poise) K : Fragility index Fragile: o-Terphenyl K : large van der Waals super-Arrhenius Strong: SiO 2 T g / T K : small Physical implication of network-formation Arrhenius fragility K ？

It looks like a universal hallmark, doesn’t it? Simulations visualize Dynamic Heterogeneity (1995 ～ ) Binary hard spheres Schematic illustration of DH Binary LJ disks (Flenner-Zhang-Szamel) (Ediger) (Berthier) ξ Polydisperse WCA spheres Binary soft disks Binary LJ spheres (Kawasaki-Tanaka) (Hurley-Harrowell) (Donati-Douglas-Poole-Kob-Glotzer)

How do collective motions lead to super-Arrhenius? Purpose of this study: Fragility vs. Dynamic Heterogeneities P. G. Debenedetti and F. H. Stillinger, Nature 410, 259-267 (2001) Binary soft spheres (Yamamoto-Onuki) Log(Viscosity in poise) T g / T indivisual? collective? homogeneous? heterogeneous?

Is the model detail really trivial? (a) Kob-Andersen LJ model (KALJ) (d) Coslovich-Pastore network model (NTW) Ni 80 P 20 SiO 2 (b) Wahnström LJ model (WAHN) ☐ ! WAHN (K=0.64) (c) Hiwatari-Hansen softsphere model (SS) △ SS (K=0.42) ◯ KALJ (K=0.27) ▽ NTW (K=0.09)

4-point correlations for Dynamic Heterogeneities(2000 ～ ) Glotzer, Berthier, Bilori, Chandler, Sastry, Szamel, ... Kim-Saito, JCP(2013) mobile Schematic illustration of DH (Ediger) ξ Low T χ ( q ) 4 t mobile High T t=0 ξ fluctuations in “local dynamics” δ F(k, t) F ( k, t ) = S ( k ) × exp[( − t/ τ α ) β ] F r ( k, t ) = F ( k, t ) + δ F r ( k, t ) correlations of fluctuations in 2-point → 4-point χ ( q ) 4 ( k, t ) = h δ F q ( k, t ) δ F − q ( k, t ) i We need 4-point correlations to determine length time scales of DH!!

3-time extension of 4-point correlations Kim-Saito, PRE(2009), JCP(2010), JCP(2013) mobile Mizuno-Yamamoto, PRE(2011) time interval: t ξ t mobile t=0 0 scan time: τ Variance of F(k, t) → 4-point (1-time interval) χ 4 ( t ) � � δ F ( k, t ) 2 � F ( k, t ) = S ( k ) × exp[( − t/ τ α ) β ] ∼ exp[ − τ / τ hetero ]? τ hetero vs τ α ? We need 3-time correlations to determine time scales of DH!!

Lifetime of Dynamic Heterogeneity remains controversial... ✓ τ hetero . τ α ‣ Perera-Harrowell (binary soft discs) ‣ Flenner-Szamel (Kob-Andersen LJ) ‣ Doliwa-Heuer (hard discs) ‣ Weeks (colloidal glasses) ✓ at low T τ hetero � τ α ‣ Yamamoto-Onuki, Mizuno-Yamamoto (binary soft spheres) ‣ Leonard-Berthier (fragile KCM model) ‣ Ediger, Richert, ... (NMR, hole-burning, photo-bleach) ‣ Orrit, Kaufman, ... (single molecule experiments) To resolve all controversy, we comprehensively examine multi-time correlation functions!!

Why use multi-time correlations?: On the analogy of 2D-NMR and 2D-IR spectroscopies 3-time extension of χ 4 (t) F 4 ( k, t 3 , t 2 , t 1 ) = h ρ k ( τ 3 ) ρ − k ( τ 2 ) ρ k ( τ 1 ) ρ − k (0) i mobile ∆ F ( k, t 3 , t 2 , t 1 ) = F 4 ( k, t 3 , t 2 , t 1 ) − F ( k, t 1 ) F ( k, t 3 ) t 1 t 2 t 3 time τ 2 0 τ 1 τ 3 Key strategies: ① Analyze couplings of t 1 - t 3 motions mobile if homogeneous dynamics, Δ F → 0 ② Change the waiting time t 2 quantify relaxation time of DH τ hetero

[WAHN fragile glasses] Change the waiting time t 2 : How dose Dynamical Heterogeneity decay with time? t 1 t 2 t 3 DH still survives for time scale longer than τ α !! τ hetero > τ α τ 2 0 τ 1 τ 3 T=0.58 (low T )

[NTW strong glasses] Change the waiting time t 2 : How dose Dynamical Heterogeneity decay with time? t 1 t 2 t 3 DH decays much faster than τ α even at low T !! τ hetero < τ α τ 2 0 τ 1 τ 3 T=0.32 (low T )

Result: Average lifetime τ hetero Z Z “Volume” of heterogeneous dynamics: ∆ hetero ( t 2 ) = ∆ F ( k, t 3 , t 2 , t 1 ) dt 1 dt 3 ☐ ! WAHN (K=0.64) △ SS (K=0.42) ◯ KALJ (K=0.27) Low T ▽ NTW (K=0.09) Low T fragility Low T Low T ∆ hetero ( t 2 ) ∆ hetero (0) ∼ exp[ − ( t 2 / τ hetero ) β ]

Discussion: Is DH related to Locally Preferred Structures? Coslovich-Pastore, JCP(2007) Kim-Saito, JCP(2013) ☐ ! WAHN (K=0.64) KALJ WAHN(icosahedron) △ SS (K=0.42) ◯ KALJ (K=0.27) ▽ NTW (K=0.09) fragility τ α !● ! KALJ ☐ ! WAHN fragility !● ! KALJ τ LS / τ α ◯ ! WAHN Are long-lived icosahedral LPSs related to τ hetero ? T g / T

�� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � �� � � � � � � � � � � � � � � � � Discussion: Is DH related to Locally Preferred Structures? Leocmach-Tanaka, Nat. Commun.(2012) Kim-Saito, JCP(2013) b ☐ ! WAHN (K=0.64) △ SS (K=0.42) ◯ KALJ (K=0.27) ▽ NTW (K=0.09) fragility Icosahedra Crystal-like - - d b der 1.4 1.2 � r 2 ( w 6 , t dh )/ �� r 2 ( t dh ) � bulk 1 0.8 0.6 (4) (4) 0.4 0.2 Icosahedron w * w dod 6 6 0 Are long-lived icosahedral − 5 − 4 − 3 − 2 − 1 0 10 2 · w 6 LPSs related to τ hetero ? d PMMA polydisperse colloids

Summary: Dynamic Heterogeneities and Fragility P. G. Debenedetti and F. H. Stillinger, ☐ ! WAHN (K=0.64) Nature 410, 259-267 (2001) △ SS (K=0.42) ◯ KALJ (K=0.27) ▽ NTW (K=0.09) Log(Viscosity in poise) fragility T g / T K. Kim and S. Saito, J. Chem. Phys. 138, 12A506 (2013)