The Glass Transition

When most liquids cool, they wait until a particular temperature and then, all at once, crystallize — the atoms snap out of their wandering and lock into a repeating lattice, the liquid releases a gulp of heat, and what was fluid is suddenly an ordered solid with a sharp edge between the two states. Water does it at zero, and the change is total. But some liquids, cooled quickly enough, never find that moment. They just get thicker. They thicken and thicken until they are rigid enough to hold a shape and ring when struck, and the whole time their atoms stay exactly as jumbled as they were in the melt. That is glass: a solid with the strength and stillness of a solid and the disordered inner arrangement of a liquid, frozen mid-wander.

So glass is not really a state the way ice is a state. It is a liquid that ran out of time. As a glass-forming liquid cools, its viscosity climbs — not gently but catastrophically, by something like fifteen orders of magnitude over a fairly small drop in temperature — and the time it takes for an atom to shuffle past its neighbors grows along with it, from billionths of a second toward seconds, toward minutes, toward forever. At some point the rearranging becomes so slow that the atoms simply cannot find their way to the crystal before the cooling pins them where they are. Nothing snaps; no heat is released; there is no clean line. The liquid just thickens past the point of being able to flow, and we call the temperature where that happens the glass transition — though it is less a transition than a seizing-up, and because it is fundamentally a question of running out of time, it isn't even fixed: cool the liquid more slowly, give the atoms longer to keep rearranging, and the transition slides to a lower temperature. The glass remembers how fast it was made.

Here is the part that has kept physicists awake for most of a century, and the reason the glass transition is routinely called one of the deepest unsolved problems in the physics of solids. When a liquid crystallizes, you can see why it became rigid: the atoms lined up, the structure changed, order appeared. But when a liquid becomes a glass, almost nothing visible happens to its structure at all. Fire X-rays through a glass and through the liquid it came from and the patterns are nearly the same — both disordered, both formless, no new arrangement, no lattice, no order to point to. And yet between them the dynamics have slowed by a factor of a thousand trillion. Something brings the motion almost to a halt, and whatever it is leaves no fingerprint we have learned to read. The structure barely moves; the time to move through it explodes. Philip Anderson, who won a Nobel for understanding disordered solids, wrote in 1995 that "the deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition," and guessed it might be cracked within the decade. It was not. The candidate explanations — a hidden length scale growing through the liquid, a landscape of energy traps the system falls into — are still arguing with each other.

There is even a whiff of paradox underneath, found by Walter Kauzmann in 1948. If you take the supercooled liquid and extrapolate its entropy — its disorder — downward as it cools, the line keeps falling, and at a certain temperature it would drop below the entropy of the crystal. That should be impossible: a jumbled liquid cannot be more orderly than the neat lattice it refused to become. And yet the numbers march straight toward it. What saves the situation is exactly the glass transition, which intervenes first and freezes the liquid before the entropy can do the forbidden thing — almost as if the kinetic accident of glass-forming were covering for a thermodynamic one. Whether there is a real, deeper transition hiding just below, an "ideal glass" we can never quite cool slowly enough to reach, is one of the oldest open arguments in the field.

What is settled is the thing everyone gets wrong, so it is worth saying plainly: glass does not flow. The story that the windows of old cathedrals are thicker at the bottom because the glass has slowly sagged downward over the centuries is false, and pleasingly so. The panes are uneven because of how they were made — spun flat while molten by a glassblower, which leaves them thicker toward the middle — and the glaziers, sensibly, often set the heavy edge at the bottom. As for flow: glass at room temperature is so monstrously viscous that for a windowpane to visibly sag would take on the order of ten to the twenty-third years, which is to say longer than the present age of the universe by something like thirteen orders of magnitude. The medieval glass has not moved and will not. Glass is not a slow liquid. It is a solid that merely remembers being one.