Glass transitions, and cooperative length scales Chiara Cammarota - PowerPoint PPT Presentation

Glass transitions, and cooperative length scales Chiara Cammarota 26. 8. 2014 Cargèse

Questions on glass transition still to be answered � � Critical properties of the glass transition � � The glass transition does really exist? � � Does the static approach explain the mechanism for glass formation? � � Issues about the glass transition � � Relaxation time diverges exponentially at the transition � � Slow growth of the correlation length: the universal behavior is not within reach � � The low temperature phase is not known inaccessible critical region T g T K T d Time and length scales “ pleasure and pain” of the glass transition

A new glass transition

The ideal glass transition (the old one) � � � � An equilibrium configuration at temperature . T The RFOT theory: T.R. Kirkpatrick, D. Thirumalai, and P.G. Wolynes, Phys. Rev. A 40, 1045 (1989) N ( f ) = exp( l d s c ( f )) vs Ts c ( T ) l d Υ l θ ✓ Υ ◆ 1 / ( d − θ ) ∆ F I = Υ l θ l s = Potential energy Ts c Al ψ � � s /T T τ = τ 0 exp

Glass transition by random pinning C.C. and G.Biroli, PNAS 109 8850 (2012) We freeze a fraction of c particles randomly chosen in an equilibrium configuration at temperature . T l p Pin particles at fixed : ↑↑ τ p ↑↑ s c ↓ ↑ T c s

Glass transition by random pinning C.C. and G.Biroli, PNAS 109 8850 (2012) , : c T s P c ( T, c ) ' s c ( T ) � cY ( T ) c K ( T ) = s c ( T ) /Y ( T ) Υ P ( T, c ) ∼ Υ ( T ) Entropy vanishing transition induced by pinning! ✓ Υ P ◆ 1 / ( d − θ ) ◆ 1 / ( d − θ ) ✓ Υ l P s = = � l s The RFOT theory Ts P T ( s c � cY ) c reloaded: s ) ψ /T ⇥ ⇤ τ p ∼ exp A ( l p

Glass transition by random pinning An indirect study of the glass transition and of metastability in glass- formers. � S.Franz and G.Parisi, Phys. Rev. Lett. 79 , 2486 (1997) � An induced glass transition with favourable features: � For , the same glass phenomenology and critical properties as . � T > T K c < c K The configuration chosen to pin particles is always a typical equilibrium configuration. � Equilibrium can be observed in the glassy phase. � Study of the glass transition not left to doubtful extrapolations. � � The large amount of predictions: a stringent test for theories of glassiness (i.e. RFOT theory). inaccessible critical region T g T K T d , a second control parameter for the liquid-glass phase diagram c

The liquid-glass phase diagram T LIQUID T d V.Krakoviack, PRE 84, 050501(R) (2011) G.Szamel and E.Flenner EPL 101 66005 (2013) S.Nandi et al., arXiv:1401.3253 (2014) W.Kob and L.Berthier, PRE 85 011102 (2012) S.Gokhale et al., arXiv:1406.6478 (2014) T g F.Krzakala et al., Phys. Rev. X 2, 021005 (2012) F.Ricci-Tersenghi, and G.Semerjian, J.Stat.Mech. P09001 (2009) T K GLASS C.C. and G.Biroli, PNAS 109 8850 (2012) C.C. and G.Biroli, EPL 98 16011 (2012) C.C. and G.Biroli J.Chem.Phys. 138, 12A547 (2013) C.C., EPL 101 56001 (2013) C.C.and B.Seoane, arXiv:1403.7180 (2014)

The liquid-glass phase diagram T Mean Field (statics and dynamics) results in Spin Glasses � Renormalization Group arguments � Hypernetted Chain computations � � � 1-Thermodynamics � and � 2- Dynamics LIQUID T d V.Krakoviack, PRE 84, 050501(R) (2011) G.Szamel and E.Flenner EPL 101 66005 (2013) S.Nandi et al., arXiv:1401.3253 (2014) W.Kob and L.Berthier, PRE 85 011102 (2012) S.Gokhale et al., arXiv:1406.6478 (2014) T g F.Krzakala et al., Phys. Rev. X 2, 021005 (2012) F.Ricci-Tersenghi, and G.Semerjian, J.Stat.Mech. P09001 (2009) T K GLASS c C.C. and G.Biroli, PNAS 109 8850 (2012) C.C. and G.Biroli, EPL 98 16011 (2012) C.C. and G.Biroli J.Chem.Phys. 138, 12A547 (2013) C.C., EPL 101 56001 (2013) C.C.and B.Seoane, arXiv:1403.7180 (2014)

The liquid-glass phase diagram T Mean Field (statics and dynamics) results in Spin Glasses � Renormalization Group arguments � 0.75 Hypernetted Chain computations � � (c h ,T h ) � 1-Thermodynamics � 0.7 and � 2- Dynamics LIQUID T d V.Krakoviack, PRE 84, 050501(R) (2011) G.Szamel and E.Flenner EPL 101 66005 (2013) 0.65 S.Nandi et al., arXiv:1401.3253 (2014) W.Kob and L.Berthier, PRE 85 011102 (2012) S.Gokhale et al., arXiv:1406.6478 (2014) T g T K (c) F.Krzakala et al., Phys. Rev. X 2, 021005 (2012) 0.6 F.Ricci-Tersenghi, and G.Semerjian, J.Stat.Mech. P09001 (2009) T K GLASS c C.C. and G.Biroli, PNAS 109 8850 (2012) C.C. and G.Biroli, EPL 98 16011 (2012) 0.55 C.C. and G.Biroli J.Chem.Phys. 138, 12A547 (2013) C.C., EPL 101 56001 (2013) C.C.and B.Seoane, arXiv:1403.7180 (2014) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

The liquid-glass phase diagram T Mean Field (statics and dynamics) results in Spin Glasses � Renormalization Group arguments � 0.75 Hypernetted Chain computations � � (c h ,T h ) � 1-Thermodynamics � 0.7 and � 2- Dynamics LIQUID T d V.Krakoviack, PRE 84, 050501(R) (2011) G.Szamel and E.Flenner EPL 101 66005 (2013) 0.65 T S.Nandi et al., arXiv:1401.3253 (2014) O F R nucleation W.Kob and L.Berthier, PRE 85 011102 (2012) S.Gokhale et al., arXiv:1406.6478 (2014) T g T K (c) F.Krzakala et al., Phys. Rev. X 2, 021005 (2012) 0.6 F.Ricci-Tersenghi, and G.Semerjian, J.Stat.Mech. P09001 (2009) T K GLASS c C.C. and G.Biroli, PNAS 109 8850 (2012) C.C. and G.Biroli, EPL 98 16011 (2012) 0.55 C.C. and G.Biroli J.Chem.Phys. 138, 12A547 (2013) C.C., EPL 101 56001 (2013) C.C.and B.Seoane, arXiv:1403.7180 (2014) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

The liquid-glass phase diagram T Mean Field (statics and dynamics) results in Spin Glasses � Renormalization Group arguments � 0.75 Hypernetted Chain computations � � (c h ,T h ) � RFIM critical behaviour & 1-Thermodynamics � S.Franz et al., arXiv:1105.5230 (2011) 0.7 and � MCT exp relaxation 2- Dynamics LIQUID T d V.Krakoviack, PRE 84, 050501(R) (2011) G.Szamel and E.Flenner EPL 101 66005 (2013) 0.65 T S.Nandi et al., arXiv:1401.3253 (2014) O F R nucleation W.Kob and L.Berthier, PRE 85 011102 (2012) S.Gokhale et al., arXiv:1406.6478 (2014) T g T K (c) F.Krzakala et al., Phys. Rev. X 2, 021005 (2012) 0.6 F.Ricci-Tersenghi, and G.Semerjian, J.Stat.Mech. P09001 (2009) T K GLASS c C.C. and G.Biroli, PNAS 109 8850 (2012) C.C. and G.Biroli, EPL 98 16011 (2012) 0.55 C.C. and G.Biroli J.Chem.Phys. 138, 12A547 (2013) C.C., EPL 101 56001 (2013) C.C.and B.Seoane, arXiv:1403.7180 (2014) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Cooperative length scales

A first correlation length-scale from random pinning C.C. and B.Seoane, arXiv: 1403.7180 (2014) Amorphous order reconstructed by at � HNC computations in an least pinned particles . � Hard Sphere system First principle computation of a cooperative length scale ξ c ( φ ) = 1 /c 1 /d with c K ∼ s c ( φ ) such that s P c ( c K , φ ) = 0 K S.Karmakar, and I.Procaccia, arXiv:1105.4053 (2011) L.Berthier, and W.Kob PRE 85 011102 (2012) B.Charbonneau et al., Phys. Rev. Lett. 108, 035701 (2012)

A first correlation length-scale from random pinning C.C. and B.Seoane, arXiv: 1403.7180 (2014) Amorphous order reconstructed by at � HNC computations in an least pinned particles . � Hard Sphere system First principle computation of a cooperative length scale ξ c ( φ ) = 1 /c 1 /d with c K ∼ s c ( φ ) such that s P c ( c K , φ ) = 0 K S.Karmakar, and I.Procaccia, arXiv:1105.4053 (2011) L.Berthier, and W.Kob PRE 85 011102 (2012) B.Charbonneau et al., Phys. Rev. Lett. 108, 035701 (2012) 2.8 2.6 2.4 2.2 2 ξ c ∼ 1 /s 1 / 3 1.8 ξ ( φ ) c 1.6 1.4 Quite a slowly divergent � 1.2 length-scale! � 1 Irrelevant in the 0.8 experimentally/numerically 0.6 0.595 0.6 0.605 0.61 0.615 0.62 0.625 0.63 accessible region φ , 1 /T 1 /T K

More than one correlation length scale! C.C. and B.Seoane, arXiv: 1403.7180 (2014) S.Franz, and A.Montanari, J.Phys.A 40 F251 (2007) G.Biroli, J.-P.Bouchaud, A.Cavagna et al., Nat.Phys. 4 771 (2008) G.M.Hocky, T.E.Markland, D.R.Reichman, PRL 108 225506 (2012) L.Berthier, and W.Kob PRE 85 011102 (2012) When does the boundary select the cavity configuration? ξ P S ∼ Y ( φ ) /S c ( φ )

More than one correlation length scale! C.C. and B.Seoane, arXiv: 1403.7180 (2014) S.Franz, and A.Montanari, J.Phys.A 40 F251 (2007) G.Biroli, J.-P.Bouchaud, A.Cavagna et al., Nat.Phys. 4 771 (2008) G.M.Hocky, T.E.Markland, D.R.Reichman, PRL 108 225506 (2012) L.Berthier, and W.Kob PRE 85 011102 (2012) When does the boundary select the cavity configuration? 20 l P S ( φ ) ξ ( φ ) 10 ξ P S 15 ξ c ξ P S ( φ ) l P S ( φ ) 10 1 ξ P S ∼ Y ( φ ) /S c ( φ ) 0.001 0.01 φ K − φ 5 A faster divergence! � � 0 A way to test the � 0.618 0.62 0.622 0.624 0.626 0.628 0.63 RFOT theory φ , 1 /T 1 /T K

More than two correlation length scales… P.Scheidler, W.Kob, K.Binder, and G.Parisi, Phil.Mag.B 82 283 (2002) W.Kob, S. Roldán-Vargas, and L.Berthier, Nat.Phys. 8, 164-167 (2012) G.Gradenigo et al., J. Chem. Phys. 138, 12A509 (2013) How far the wall selects the left-side configuration? � � The high/low- interface behaves like an � q elastic manifold in a random field environment! G.Biroli and C.C., to appear An effect of the self induced disorder encoded in the wall configurations q ( z ) z