Nonequilibrium transitions in glassy flows II. Peter Schall University of Amsterdam

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1 Nonequilibrium transitions in glassy flows II Peter Schall University of Amsterdam

2 Flow of glasses 1st Lecture Glass Phenomenology Basic concepts: Free volume, Dynamic correlations

3 Apply Shear Glass?

4 Soft Glasses Visco-elastic properties colloidal glass Microscopic structure / dynamics foam Atoms DNA Polymers gel Granular a m

5 Average Flow and Fluctuations Non-affine displacements 1. Subtract linear profile Δ 2. Compare with neighbors Δ Δ

6 Non-affine displacements z y x shear d(t- t) d(t) Affine transformation Γ d aff (t) = d(t- t) + Γ d(t- t) neighbors D 2 min = (d aff (t) d(t)) 2 Falk and Langer, PRE Affine non-affine

7 Non-affine displacements Subtract linear profile Affine fit Subtract coarse grained Lost nearest neighbors Chikkadi, Schall, Phys Rev E (212)

8 Spatial Correlations Δ = : difference vector : spatial average A : any non-affine measure Α(r) Α(r+ )

9 Power-law Correlations z x 3 D 2 min Correlation -1 y 1 6 z / d 15 r 1.5 C D 2min (r) Z(µm) α x / d X(µm) V. Chikkadi, G.Wegdam, B. Niehuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212 r/σ System Size Power-law scaling up to system size

10 Power-law Correlations z x 3 D 2 min Correlation -1 y 1 6 z / d 15 r 1.5 C D 2min (r) Z(µm) α x / d Origin X(µm) System? r/σ V. Chikkadi, G.Wegdam, B. Niehuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212 Power-law scaling up to system size Size

11 Power-law Correlations z y z / µm x Shear strain x / µm ε xz Induce Local Quadrupole ε ~ 1/r 3 x V. Chikkadi, G.Wegdam, B. Nienhuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212

Power-law Correlations z y z / µm x 6 4 2 Shear strain 2 4 6 8 1 x / µm ε xz Elasticity.2.1 -

12 Power-law Correlations z y z / µm x Shear strain x / µm ε xz Elasticity Induce Local Strain Quadrupole Field ε ~ 1/r 3 x V. Chikkadi, G.Wegdam, B. Nienhuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212 Elastic continuum

13 Elastic Correlations Displacements Elastic continuum (Hutchinson 26) Strain Field

Homogeneous flow z x Shear strain ε xz Quadrupolar Strain Correlation Symmetry: Signature of Elasticity 3 15.2.1 y 6 z / d.2 z / µm 4 2-15 -3.

14 Homogeneous flow z x Shear strain ε xz Quadrupolar Strain Correlation Symmetry: Signature of Elasticity y 6 z / d.2 z / µm x / d V. Chikkadi, G.Wegdam, B. Nienhuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212 Elastic interactions x / µm Self organization of STZ

15 Yielding Approaching yielding. γ c γ γ c A. Ghosh, V. Chikkadi, S. Zapperi, P. Schall, in preparation (216)

16 Yielding Fractal clusters Cluster evolution Percolation? Log(Gyration radius) Fraction in largest cluster Log(cluster size) Cluster size Strain γ A. Ghosh, V. Chikkadi, Fraction S. Zapperi, of activep. particles Schall, in preparation (216)

17 towards faster flow γ. Diffusion rate t D -1 Driven Flow 1 Fluid.49 Supercooled Fluid Viscous Flow.58 Glass.64 φ Critical Scaling

18 1. Transition to Driven flows Homogeneous Inhomogeneous 6 4 z / µm 4 2 z / µm x / µm 1 x / µm 1 V. Chikkadi et al. Phys. Rev. Lett. (211) γ τ

z/µm z/µm z/µm 6 4 2 6 6 4 2 Shear banding transition z / d 3 15-15 -3 3 15 4 Nature

19 z/µm z/µm z/µm Shear banding transition z / d Nature of this transition? 2-15 z / d z / d γτ x/µm x/d

20 Shear bandingno transition quadrupolar symmetry liquid like Z Fundamental Solid Liquid transition -1 1 Z(µm) 2 Origin? X(µm) -1 V. Chikkadi, G.Wegdam, B. Niehuis, P.S., PRL 211 V. Chikkadi, P.S., PRE 212 Quadrupolar -1 1 X symmetry Z 1 solid like

21 Structural transition? Pair correlation function. Shear band Static band g(r) r

22 First order transition diffusion time scale 1-1 x 2 / µm t t(γ 2 /γ 1 ) γ = t γ i Discontinuity in diffusion time scale! V. Chikkadi, et al. Phys. Rev. Lett. (214) P. Schall, Harvard University

23 First order transition? P(ζ) Order Parameter ζ ζ 1 ζ 2 ζ What is the right order parameter? ζ : Time evolution

First order transition? (<K>/N)/ µm 2 s 12 1 8 6 4 2. γ / s.

1 1-4 5 1 15 ζ = <K> t obs /s / t obs f(ζ) δ r i V.

24 First order transition? (<K>/N)/ µm 2 s γ / s * * ζ = <K> t obs /s / t obs f(ζ) δ r i V. Chikkadi, et al. Phys. Rev. Lett. (214) ζ /< ζ > Dynamic Order Parameter (Garrahan, Chandler 29) N K = i=1 t obs t= δr i 2 ζ /< ζ > ζ /< ζ > ζ /< ζ > extensive in Space AND Time First order transition in 4D space-time ζ 1 ζ 2

25 Mechanical Spectroscopy strain stress Oscillatory Rheology time Linear Response:. stress = G γ sin(ωt) + G γ cos(ωt) storage modulus loss modulus

26 Origin of yielding? Mechanical Spectroscopy log G log G Failure strain Linear Response:. stress = G γ sin(ωt) + G γ cos(ωt) storage modulus loss modulus

27 Simultaneous X-ray + Rheology Rheology Struct. Fact. S(q) G G D. Denisov, T. Dang, B. Struth, P.S., Sci. Rep. (213)

28 Simultaneous X-ray + Rheology Yielding: Oscillatory Shear 1 5 Rheology Structure G and G, Pa Strain γ γ Solid and liquid-like structure factor Denisov et al. Sci. Rep. (215)

Simultaneous X-ray + Rheology Yielding: Oscillatory Shear 1 5 Rheology γ Structure G and G, Pa 1 4 1 3 1-1 γ 1

29 Simultaneous X-ray + Rheology Yielding: Oscillatory Shear 1 5 Rheology γ Structure G and G, Pa γ Strain γ γ 1 Sharp transition! Denisov et al. Sci. Rep. (215) π/2 π 3π/2 2π angle C(α) -1 1

30 Simultaneous X-ray + Rheology Yielding: Oscillatory Shear Rheology + Struct. Order parameter Correlation of C( β=π) Sharp drop of Order parameter Strain γ Shear-induced First-order transition Denisov et al. Sci. Rep. (215) G and G

31 towards lower density γ. Diffusion rate t D -1 Driven Flow Fluid 2.49 Supercooled Fluid Viscous Flow.58 Glass.64 φ

32 Foam Simulations unjammed jammed φ ~.74 φ ~ 1 V. Cikkadi, E. Woldhuis, M. van Hecke, P. Schall (EPL 215)

33 2. Transition to low density unjammed jammed V. Cikkadi, E. Woldhuis, M. van Hecke, P. Schall (EPL 215)

34 2. Transition to low density Pair correlation of active spots V. Cikkadi, E. Woldhuis, M. van Hecke, P. Schall (EPL 215)

35 Conclusions Slow flow of glasses long-range correlated, critical state Material failure (yielding, banding) Nonequilibrium transitions (1st and 2nd order) Evidence of Universality Dynamic or thermodynamic transitions?

36 Thanks to... Vijay Chikkadi (PhD, now Post doc) Dmitry Denisov (Post Doc) Soft Matter Group Amsterdam

Flow of Glasses. Peter Schall University of Amsterdam

Flow of Glasses. Peter Schall University of Amsterdam Flow of Glasses Peter Schall University of Amsterdam Liquid or Solid? Liquid or Solid? Example: Pitch Solid! 1 day 1 year Menkind 10-2 10 0 10 2 10 4 10 6 10 8 10 10 10 12 10 14 sec Time scale Liquid!