These are intellectually wonderful times for science.

1. The Physics of Window Glass –and other everyday scientific mysteries that are deeper than you might thinkUBC, Vancouver, March 19, 2008J.S. LangerUniversity of California, Santa Barbara

2. These are intellectually wonderful times for science. • Instruments allow us to see individual atoms and the outer edges of the universe. • Computers solve complex mathematical problems and simulate systems composed of millions of molecules. • And now we can explore some old topics in new ways: The mysterious glass transition. Snowflakes and pattern formation.

3. The Mysterious Glass Transition Science Magazine, Vol. 309, 83 (2005) 125’th Anniversary Issue: 125 outstanding problems in all of science

4. Ancient Egyptian glass jar from the New Kingdom (Louvre)

5. Roman glass vessel, circa 50 AD – 150 AD

6. Sainte Chapelle, Paris

8. A familiar, non-glassy, phase transition: Water freezes to become ice. cool Ice crystals form at a thermodynamic freezing temperature. The energy of the crystal is lower than that of the liquid. The crystal is in a state of thermodynamic equilibrium.

9. Copper-Nickle alloy – micrograph showing dendritic (snowflake-like) crystals

10. The glass transition from liquid-like to solid-like states is very different from crystal growth. Glass Blowing

11. The Glass TransitionDramatic change in viscosity, no crystallization • It spreads instantly. Place a drop of hot molten glass on a table.

12. A slightly cooler drop takes minutes to spread.

13. A yet cooler drop takes years or centuries. • And an even cooler drop may keep its shape for times longer than the age of the universe. It seems to be infinitely viscous. A glass is not in a state of thermodynamic equilibrium.

14. Why is it important to understand this phenomenon? • Most everyday materials, including biological materials, are noncrystalline. Or else, like sand, they are highly disordered arrangements of tiny crystals. • Most everyday materials are not in mechanical and/or thermal equilibrium. We need to understand how they function, deform and break.

15. T. Haxton and A. Liu: MD simulation of 2D glass. The temperature is nonzero but is below the glass transition; the shear rate is constant but very small on the molecular time scale.

16. Initial state

17. New state

18. Elements of a Theory • As temperature decreases, thermal noise becomes weaker. • Molecular rearrangements require thermally excited motions of increasingly large numbers of molecules – perhaps chains of small displacements. • The probability that these motions will happen becomes very small (→ zero ?) as the temperature decreases. This is a theoretical work in progress.

19. At low temperatures, glasses become brittle.

20. Brittle fracture patterns look like snowflakes, or butterfly wings, or ...??

21. Snowflakes and Pattern Formation K. Libbrecht: Snowflake

23. Johannes Kepler (1571-1630, most famous for his laws of planetary motion) may have been the first person who thought that natural pattern formation could be understood scientifically.

27. Succinonitrile dendrite – much less complicated than water for scientific purposes.

28. Succinonitrile

29. Scanning electron micrograph of a Nickel-based alloy

30. Instability: The key to pattern formation liquid Diffusion of heat or molecules is fastest at surface irregularities (the lightning-rod effect). Therefore irregularities sharpen and grow. crystalline solid What triggers this instability? Why do irregularities occur?

31. Albert Einstein, ca. 1905

32. Molecular Chaos Molecular chaos was understood first by Einstein in 1905 (the same year in which he wrote his papers on special relativity and the photelectric effect). He studied the irregular “Brownian” motion of very small dust particles in water. He used statistical methods to deduce from this motion the number of molecules in a cubic centimeter of water. His answer was approximately 1023 = 100,000,000,000,000,000,000,000.

33. As a result, dendritic patterns are extremely sensitive to changes in growth conditions such as temperature. Because snowflakes form in a turbulent atmosphere, where growth conditions are always changing, no two are exactly alike. Molecular Chaos and Snowflakes We now understand that complex dendritic patterns are triggered by molecular chaos. The growing dendrite selectively amplifies – by a huge amount – the microscopic molecular fluctuations at its tip.

35. SN dendrites at six different temperatures. The position of the first sidebranches can be predicted accurately by the thermal fluctuation theory.

36. The new frontiers in the science of pattern formation (“morphogenesis”) are in biology. What tricks does Nature use to form biological patterns? In what ways are these patterns similar to fracture and snowflakes? Or are they entirely different?

40. Conch shell

42. Two concluding remarks • The glass transition, and pattern formation in physics and biology, are examples of complex, dynamic, “nonequilibrium” phenomena that we are only just beginning to understand. • The big challenge will be to develop a broadly applicable science of complexity that is both quantitative and predictive.