1. How Mysterious is the Mysterious Glass Transition? Itamar Procaccia The Weizmann Institute of Science Weizmann Institute: Einat Aharonov, Eran Bouchbinder, Valery Ilyin, Edan Lerner, Ting-Shek Lo, Natalya Makedonska, Ido Regev and Nurith Schupper. Emory University: George Hentschel Leiden, August 25 2008

2. Glass phenomenology The three common conceptes: jamming, Vogel-Fulcher, Kauzmann

3. A very popular model: a 50-50 binary mixture of particles interacting via soft repulsion potential With ratio of `diameters’ 1.4 Simulations: both Monte Carlo and Molecular Dynamics with 4096 particles enclosed in an area L x L with periodic boundary conditions. We ran simulations at a chosen temperature, fixed volume and fixed N. The units of mass, length, time and temperature are Previous work (lots): Deng, Argon and Yip, P. Harrowell et al, etc: for T>0.5 the system is a “fluid”; for T smaller - dynamical relaxation slows down considerably.

5. The conclusion was that “defects” do not show any ‘singular’ behaviour, so they were discarded as a diagnostic tool.

6. The liquid like defects disappear at the glass transition!

7. For temperature > 0.8 For 0.3 < T < 0.8 Associated with the disappearance of liquid like defects there is an increase of typical scale

9. Rigorous Results (J.P. Eckmann and I.P., arXiv:0802.3404) The system is ergodic at all temperatures

10. Consequences: there is no Vogel-Fulcher temperature! There is no Kauzman tempearture! There is no jamming! (the three no’s of Khartoum)

11. Statistical Mechanics We define the energy of a cell of type i Similarly we can measure the areas of cells of type i

12. Denote the number of boxes available for largest cells Then the number of boxes available for the second largest cells is The number of possible configurations W is then Denote

14. A low temperature phase Note that here the hexagons have disappeared entirely!

17. First result :

20. Specific heat anomalies

21. The anomalies are due to micro-melting (micro-freezing of crystalline clusters) We have an equation of state !!!

23. Summary The ‘glass transition’ is not an abrupt transition, rather a very smeared out phenomenon in which relaxation times increase at the T decreases. There is no singularity on the way, no jamming, no Vogel-Fulcher, no Kauzman We showed how to relate the statistical mechanics and structural information in a quantitative way to the slowing down and to the relaxation functions. We could also explain in some detail the anomalies of the specific heat Remaining task: How to use the increased understanding to write a proper theory of the mechanical properties of amorphous solid materials. (work in progress). Since nothing gets singular, statistical mechanics is useful

24. E. Aharonov, E. Bouchbinder, V. Ilyin, N. Makedonska, I. Procaccia and N. Schupper, Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity, Europhys. Lett. 77, 56002 (2007). Also: cond-mat/0608305. Valery Ilyin, Edan Lerner, Ting-Shek Lo, Itamar Procaccia, Statistical Mechanics of the Glass Transition in One-Component Liquids with Anisotropic Potential, Phys. Rev. Lett.,99, 135702 (2007). Also: arXiv:0705.1043v1 Valery Ilyin, Nataliya Makedonska, Itamar Procaccia, Nurith Schupper, Mechanical Properties of Glass Forming Systems, Phys. Rev. E 76, 052401 (2007). Also: arXiv:0705.1834v1 H. G. E. Hentschel, V. Ilyin, N. Makedonska, I. Procaccia and N. Schupper, Statistical mechanics of the glass transition as revealed by a Voronoi tesselation, Phys. Rev. E 75, 050404 (2007) Also: cond-mat/0608443. H.G.E.Hentschel and Itamar Procaccia, Theory of Relaxation Dynamics in Glass-Forming Hydrogen-Bonded Liquids, Phys.Rev. E.77,031507 (2008). Also: arXiv:0709.4404 Some references:

25. Valery Ilyin, Itamar Procaccia, Ido Regev, Nurith Schupper, Ageing and Relaxation in Glass Forming Systems, Phys. Rev. E 77, 061509 (2008) Also: arXiv:0803.2602 Jean-Pierre Eckmann and Itamar Procaccia, Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities, Phys. Rev. E, 78, 011503 (2008)., Also: arXiv:0802.4346 Edan Lerner and Itamar Procaccia, Quantitative Theory of a Relaxation Function in a Glass-Forming System, Phys. Rev. Lett., submitted. Movie: Avi(9M), Mpeg ( 4M). Also: arXiv:0804.1205 Edan Lerner, Itamar Procaccia and Ido Regev, Quantitative Theory of a Time- Correlation Function in a One-Component Glass-Forming Liquid with Anisotropic Potential, PRE., submitted. Also: arXiv:0806.3685 H. G. E. Hentschel, Valery Ilyin and Itamar Procaccia, Non-Universality of the Specific Heat in Glass Forming Systems, Phys. Rev. Lett., submitted. Also:arXiv:0808.2736 H. G. E. Hentschel, Valery Ilyin, Itamar Procaccia and Nurith Schupper, Theory of Specific Heat in Glass Forming Systems. Phys. Rev. E, submitted. Also::arXiv:0808.2138

26. Strains, stresses etc. We are interested in the shear modulus Dynamics of the stress

27. Zwanzig-Mountain (1965)