Kunimasa Miyazaki (CECAM meeting 06/28/2013) Hidden Amorphous Orders near the Jamming and Glass Transitions.

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Kunimasa Miyazaki (CECAM meeting 06/28/2013) Hidden Amorphous Orders near the Jamming and Glass Transitions

What is the Jamming Transition? H. Tanaka’s homepage The volume fraction (density) of the hard balls poured into a jar randomly is always about ! ! or INTRODUCTION NOT

Jamming Transition and Dynamic Transition Mean Field “Theory” of the Glass transition (RFOT) High T Low T coordinate potential energy total energy For hard spheres, we use or instead of coordinate total volume volume or Low High

coordinate total volume Visualize the “Energy” Landscape This is nothing but the Jamming transition Jamming Transition and Dynamic Transition

(Average values) -1 of the bottoms coordinate volume or total volume Low High The average will be lowered as density increases Brummer, Reichman (2005) Zamponi, Parisi (2009) Mari, Krzakala, Kurchan (2009)

d=2 Ozawa, Kuroiwa, Ikeda, and KM, PRL (2012) Initial density dependence of jamming transition points See also Chaudhuri, Berthier, Sastry, PRL 104 (2010) Pica Ciammarra, Canigrio, Candia, Soft Matter 6 (2010) 2957 d=3 Binary Hard Spheres with size ratio 1.4 and composition ratio 0.5:0.5 Jamming Transition and Dynamic Transition

S. Torquato et al., PRL (2000) Structural Properties of Jammed States Crystalline Order What is jammed packing denser than 0.648? Is this just a less random (or more ordered) packing? HCP=0.74 φ J =0.64…

Structural Properties of Jammed States Orientational Order Parameters See also Schreck, O’Hern, Silbert, PRE 84 (2011) d=3 d=2 Ozawa, Kuroiwa, Ikeda, and KM, PRL (2012)

Schreck et al. PRE (2011) Orientational Order Parameters Structural Properties of Jammed States Our jammed packing

Orientational Order Parameters Structural Properties of Jammed States Correlation btwn local free volume and local crystalline order

Order hidden in Disorder (or Mosaic)? Ozawa, Kuroiwa, Ikeda, and KM, PRL (2012) Structural Properties of Jammed States

Finite Size Scaling According to the wisdom of RFOT, a single length due to dynamic transition governs the scaling before dynamic transition points but below the transition point, both a dynamic length and activation processes would influence (in opposite ways) the scaling and thus no simple finite scaling would be observed. Structural Properties of Jammed States

Finite Size Scaling d=3 d=2 Ozawa, Kuroiwa, Ikeda, and KM, PRL (2012) Structural Properties of Jammed States

CONCLUSIONS Dynamic (MCT) transition point marks the qualitative change of the free energy landscape (inherent structures) More puzzles than answers… What is the configurational properties beyond dynamic (MCT) transition point? Do the “orders” have anything to do with, for example, MOSAICs and MRCOs ? Why does MCT work so well quantitatively? Is it just fortuitous? etc…