The mysterious glass transition

© 2007 American Institute of Physics, S-0031-9228-0702-210-7 Often, when we physicists ask the right questions, we realize that even the most commonplace parts of our world remain deeply puzzling. In its 125th anniversary issue, Science magazine asked many such questions.1 My eye was caught by, “What is the nature of the glassy state? Where and why does liquid end and glass begin? ” I chuckled, partly because I knew the editors had made a perceptive choice, but also because I had just wandered inadvertently into that field of research and was beginning to appreciate its depth and subtlety. I also was learning that glass physics is a highly contentious subject—a sure sign that there is still a lot to learn about it. My curiosity-driven excursion through glass physics started more than a decade ago with fracture and earthquake dynamics. I decided to look at amorphous solids because I thought their liquidlike structure would make them easier to understand than crystals; I would have no dislocations or grain boundaries to worry about. Then I moved from fracture to plasticity because I wanted to understand how molecules rearrange themselves near advancing crack tips; so I found myself in the mysterious world of glass dynamics. A molten glass doesn’t suddenly solidify when cooled; it gradually becomes more and more viscous. If we put a drop of sufficiently hot molten glass on a flat surface, it quickly spreads like a liquid. A drop ten degrees or so cooler does the same thing but may take minutes or hours. If we cool it more, it will retain its shape for years or centuries, or perhaps for longer than the age of the universe. We ought to understand what is happening here—but we don’t. We don’t know what kind of transformation occurs when a liquid becomes a glass or even whether that familiar change of state is actually a thermodynamic phase transition like condensation or solidification, or something completely different. Consider a supercooled, glassforming liquid that somehow has escaped crystallization, and assume that this liquid consists of molecules interacting only via short-ranged forces. Those forces must be such that longrange crystalline order is frustrated; that is, the energetically preferred local arrangements of the molecules don’t fit neatly together to fill all space in a periodic array. As a result, the molecular structure of the system resembles a liquid even at low enough temperatures that the material behaves like a solid. Now forget about complicated phenomena such as fracture. Instead, think about simple linear viscosity, in other words, the ratio of shear stress to shear flow in the limit of vanishingly small driving force. Irreversible motion of this kind, as opposed to reversible elastic deformation, requires molecules to change positions relative to one another. At low temperatures T, the rearrangements must be thermally activated. The energy barrier that they must overcome to move around each other, say ΔE, is larger than kBT, where kB is Boltzmann’s constant; thus the predicted viscosity has what is called an Arrhenius form, which means it is proportional to exp (ΔE/kBT) with a temperature-independent ΔE. At yet lower temperatures, say T less than some TA, an Arrhenius fit to the viscosity requires that ΔE grows with decreasing T and appears to become infinite at some nonzero temperature T0. Below T0, the material seems to be completely frozen, so much so that it is in a state of “broken ergodicity,” which means it violates Josiah Willard Gibbs’s assumption that such systems explore statistically significant fractions of their possible states on experimental time scales. Indeed, apart from the thermal jiggling of molecules in their local environments, the glassy molecular configurations seem to be stuck forever near just one of those configurational states. How can that happen? And what is happening at higher temperatures between T0 and TA? Apparently, as T falls below TA, increasingly large cooperative motions requiring increasing activation energies ΔE are needed to achieve local rearrangements. What are those motions? What features of the molecular dynamics are responsible for such behavior?