A theoretician working on glass

1. My principle aim in the original Hedrick lectures, as well as in this enlarged version was to show that (a) extremely simple observations are often the starting point of rich and fruitful theories and (b) many seemingly unrelated developments are in reality variations on the same simple theme.

2. A theoretician working on glass Courtesy Roald Hoffmann

3. The Theory of Glasses • Experimental phenomenology of glass • Energy landscapes & random first order transitions • T.R. Kirkpatrick, D. Thirumalai, R. Hall, Y. Singh, J.P. Stoessel, and P.G. Wolynes • The mosaic picture of random first order transitions • X.Y. Xia, V. Lubchenko, J. Stevenson, J. Schmalian • Quantum theory of glasses • V. Lubchenko

4. Dynamics and thermodynamics near the glass transition Super Arrhenius temperature dependence of rates “strong” 14 orders of magnitude SiO2 glycerol OTP “fragile” Ediger, Angell & Nagel, JPC 1996 Vogel-Fulcher Law

5. The glass transition and the “Kauzmann Paradox” Slower cooling leads to sharper change The 3rd law (?) T0Kauz = T0VF (±10°K)!!! ΔCP Sliquid -Scrystal 1/Tg Latent heat/Tm Ediger, Angell & Nagel, JPC 1996 Residual entropy diminishes with slower cooling ΔCP is larger for “fragile” liquids 1/Tm 1/T0 1/T

6. Aging: dynamics continues, but slower, in the glassy state V. Lubchenko & PGW, JCP (2004) Slow quench Alegria et al. Macromolecules, 1998 Fast quench Narayanaswamy, Tool, Moynihan “Non-linearity parameter” 0<x<1

7. Glasses have more low energy excitations than crystals Stephens, PRB, 1973 Raychaudhuri and Pohl, PRB 1982 CV/T Intercept CV =aT+AdebyeT3 Entropy of these excitations is still small Extrapolated to 300°K, this is ≈10-2kB

8. The “Standard Model” of Quantised amorphous solids W. Phillips, P.W. Anderson, Halprin, Varma Two-level tunneling states tunneling Strain int’n Continuum phonons ~Assume a distribution of ε, Δ Surprisingly small variation of (reflected in CV)

10. The Architecture of Aperiodic Crystals Model handbuilt by J.D. Bernal

21. RFOT theory predicts dynamic fragility from thermodynamics Dm=590/(m-16) Bohmer, Ngai, & Angell, JCP, (1993)

22. RFOT theory predicts fragility parameter, m m from RFOT m from experiment

23. RFOT predicts the non-exponentiality parameter from fragility and thermodynamics Mosaic picture ξ ξ=4.5a

24. RFOT predictions of CRR size agree with experiment Berthier et al. inequality Berthier et al. Science (2005) 310, 1797 Data from: Bohmer et al. J. Chem. Phys. (1993) 99, 4201

25. Shapes of CRR’s • Surface interaction energy wants compact shape • Shape entropy wants fractal shape Small surface area Large surface area Gebremichael et al. J. Chem. Phys 120, 4415

26. Percolation clusters and strings • The surface of percolation clusters and strings scales with volume: b=αN. Percolation: Strings:

27. Shape transition signals crossover temperature Mode Coupling Transition Log( Viscosity , P) String Transition Sc(Tg)/Sc Same as Hagedorn transition in string theory!

29. Non-equilibrium aging effect is predicted from fragility within RFOT theory

30. After long-aging the mosaic is more heterogeneous “Ultra-slow” relaxations

31. Local libraries lead to tunneling resonances Lubchenko & PGW N* ΔE=0

32. Density of Resonances ε<<Tg

35. Direct spectroscopic evidence of complex structure of 2LS

39. THE DEEPEST AND MOST INTERESTING UNSOLVED problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade The solution of the problem of spin glass in the late 1970s had broad implications in unexpected fields like neural networks, computer algorithms, evolution, and computational complexity. The solution of the more important and puzzling glass problem may also have a substantial intellectual spin-off. Whether it will help make better glass is questionable. P. W. Anderson Joseph Henry Laboratories of Physics Princeton University Science, 1995