1. T. Odagaki Department of Physics, Kyushu University T. Yoshidome, A. Koyama, A. Yoshimori and J. Matsui Japan-France Seminar, Paris September 30, 2005

2. Glass transition singularities Dynamic transition Thermodynamic transition Phenomenological understanding Free energy landscape

3. Phenomenological understanding : Heat capacity T. Tao &T.O(PRE 2002),T.O et al (JCP 2002),T. Tao et al (JCP2005) Energy of basin a Probability of being in basin a at t ： Quenched ： Annealed a

4. ☆ Annealed to quenched transition ☆ Cooling rate dependence Annealed-to-quenched transition and cooling rate dependence 20 basins:Einstein oscillators slow fast T. Tao, T. O and A. Yoshimori: JCP 122, 044505 (2005)

5. 1. Free Energy Landscape, CRR and SRR 2. Density Functional Theory and FEL 3. Principal Component Analysis and FEL 4 ． Unifying Concept for Glass Transition Outline

6. Landau theory for phase transitions State realized in the presence of a suitable constraint

7. Free energy landscape picture State realized in the presence of a suitable constraint Configurational space

8. Definition of the free energy landscape Many basins appear below some temperature Support fast and slow relaxations Quasi-thermodynamic transition Potential energy landscape does not have these properties.

9. Basic Concept for the FEL Free energy landscape Configurational Partition Function for a constrained system Choice for the gate function ① Within topologically identical Voronoi polyhedra: mathematically well-defined, but hard to calculate ② Gaussian fields: practical

10. Simultaneously and cooperatively rearranging regions SRR: Difference between two adjacent basins CRR: Atoms involved in the transition state

11. Density functional theory Glass formation Y. Singh et al PRL(1985), C. Kaur & S. P.Das PRL(2001) as a function of Free energy landscape

12. : Direct correlation function Percus-Yevick approximation Ramakrishnan-Yussouff free energy functional

13. Forced relaxation in FCC

14. basin1basin2 No of atoms in the core ： 32 Ｓｔｒｉｎｇ ｍｏｔｉ ｏｎ and CRR

15. No of atoms in the core ： 18 basin 1 basin 2 Ｓｔｒｉｎｇ ｍｏｔｉ ｏｎ and CRR

16. basin1 basin2 No of atoms in the core ： 10 Ｓｔｒｉｎｇ ｍｏｔｉｏｎ and CRR

17. Density dependence of the size of CRR # of atoms in the core below which no relaxation occurs

18. Principal component analysis for molecular simulations Representative point in configurational space.

19. Mode projection onto 3D-real space FastSlow Total dynamics Slow dynamics Fast dynamics 600 K

20. FEL in Principal component analysis FEL : ---The observed rate of y l in a simulation. Probability distribution for y l

21. Dynamics on FEL y l / λ l 1/2 400 K (>T g ) 200 K (<T g ) 2D contour maps of FEL’s. y l+1 / λ l+1 1/2 y l / λ l 1/2

22. Waiting time distribution for slow relaxation Prob. of activation free energy Waiting time distribution :Size of CRR by Adam and Gibbs SRR CRR

23. Unifying concept Characteristic Temperature Equation

24. V B Kokshenev & P D Borges, JCP 122, 114510 (2005)

25. Unified understanding by the FEL -Crystallization T Liquid Crystal

26. T Super cooled Liquid slow relaxation fast relaxation Glass Ideal Glass Trapped in a basin Liquid Unified understanding by the FEL -Vitrification

27. Conclusion Phenomenological understanding Construction of free energy landscape ○ Dynamics in the FEL Separation of slow dynamics ○Dynamics: Gaussian to non-Gaussian transition ○Thermodynamics: Annealed to quenched transition ○ Density functional theory ○ Clear definition of CRR and SRR ○ Principal component analysis