The Critical Point

"Near the critical point," Moses Chan says, "is where things get interesting."

wires and insides of red machine
James Collins

Custom-built cryostat for cooling samples close to absolute zero.

He pops up from his chair and walks to a file cabinet, rummaging a moment before producing what looks like a small red-handled hammer, holds it up for inspection. The head is a stainless-steel cube, with a small round window. The chamber is half-filled with clear liquid.Chan, Evan Pugh professor of physics at Penn State and recently elected member of the National Academy of Sciences, motions me to follow, out of his office and down the hall to the faculty lounge. There's a kitchenette, and an electric hot pot on the counter. Chan removes the lid and plunges the instrument into the pot. The sealed chamber is now a pressure cooker.

"We'll heat this liquid, freon, beyond its critical point—that's 80 degrees C—then watch what happens," he says. He hurries to the adjacent conference room to flip on an overhead projector, then dashes back to the pot.

It's hot enough. Using paper towels to protect his fingers, he plucks the instrument out by the handle, shakes it twice, hustles back to the conference room, and lays it on the projector.

Enlarged on the wall screen the round window is completely transparent. Gone is the meniscus, the curved line that marked the level of liquid. "Above the critical point, the distinction between liquid and vapor simply disappears," Chan says. "There's only a single, undifferentiated fluid. "Now watch what happens as it cools."

In a few seconds, the little porthole turns a milky yellow; in another it fades to black. A few more seconds and the darkness resolves, and what re-emerges is two distinct phases: liquid and vapor.

Back in his office, Chan explains. As the chamber is heated, the liquid expands, becoming less dense. The vapor pressure increases, and the gas grows denser. In an ordinary tea kettle, the liquid would eventually come to a boil, with heat escaping the liquid in bubbles rising to the surface and leaving the kettle as steam. Here, though, in a sealed environment, there's nowhere for the steam to go.

Instead, near the critical point, the densities of the two phases are fluctuating wildly. If the molecules in a liquid are a tethered cluster of tennis balls, those in a gas are cut loose and bouncing off the walls. During fluctuation in density, the distance between molecules in each phase is yo-yoing back and forth: moving closer, then farther apart.

When the temperature gets above 80 degrees, the dueling densities simply merge. The two phases become indistinguishable. As the chamber cools back down, however, the fluctuations return. At the critical point their scale reaches a length of 4000 angstroms—which just happens to match the wavelength of visible light. The reason why everything goes black, Chan concludes, is that the fluctuations of the freon cancel out the light waves trying to pass through it. The light is scattered, deflected -"like the beam of your headlights when you're driving in a fog." Critical opalescence, the phenomenon is called. Another degree cooler and it passes.

Every substance has a critical point. Not only that, but critical points, with their unusual properties, are not limited to the liquid-to-vapor shift. The same rules describe other sorts of transitions as well. A magnet, for instance, has a critical point. Heated to a certain temperature, it abruptly loses its magnetism. Just before it does, there's a period of fluctuation. For Chan, who has spent 30 years studying the nature of critical transitions, what's fascinating is that shaky in-between time, when molecules share a different sort of communication.

man with glasses looks over large machine
James Collins

Moses Chan and a super-cooling apparatus. "Finding something a little different from the prediction is what we experimenters like the most," says Chan.

One of the properties that governs molecules in a bulk material, he explains, is what physicists call symmetry, which to hear Chan explain it, is something like peer pressure. "It's like a teenager who buys a baseball cap," he says. "Before he sees how his neighbors wear their hats, he is equally likely to wear it with the brim forward or back. But when he sees that all the others wear it backwards, there is peer pressure—a lowering of potential energy—and he conforms."

Similarly, if you think of a magnet as a lot of tiny arrows all in a row (as the German-American physicist Ernst Ising did back in 1925) at low temperature, Chan says, "they like to line up, all pointing in the same direction. Even if one arrow gets the urge to flip, the peer pressure is too great. It will soon flip back to conformity." This is the magnetized state.

"It requires energy to break the mold," Chan continues. In this case, kinetic energy, or heat. Apply enough of it, and "molecules will defect." Above the critical point, those arrows are constantly flipping, back and forth. This too, however, represents a kind of unanimity: that of the non-magnetized state.

Near the critical point, however, the propensity to line up matches the propensity to flip, and neither dominates. The system doesn't know whether it wants to be magnetic or non-magnetic." Now push it just a little further, to the cool side. "One arrow may flip for good, and it has an influence on its neighbor. The next one wants to follow suit, and the next, and the next."

"Symmetry-breaking," Chan says, "is the making of a choice, forsaking an alternative. And the amazing thing is these molecules act in coordination. At the right temperature, all you need is someone to incite a riot and the disturbance can propagate out to a very long distance.

"According to the cosmologists," Chan says, "the Big Bang is a symmetry-breaking event. When the universe is very hot, there is no difference between energy and matter. At the Big Bang, there is a transition. A choice is made—to break down and settle into this universe we happen to be in."

Condensed-matter physicists, working with huge numbers of particles, have to rely on tatistical models to describe phase-transition processes. Such models must be tremendously simplified. Ising's was one-dimensional: a string of magnets in a row. Lars Onsager, the Norwegian-American chemist who would later win a Nobel prize, tackled the more difficult and more interesting problem of magnets arrayed on a two-dimensional lattice. "It's more interesting," Chan says, "because this system exhibits a phase transition at the critical point." Onsager's 1944 result, extended in 1952 by another eventual Nobel laureate, the Chinese-American physicist C. N. Yang, is one of the most famous papers in statistical mechanics.

So complex are the mathematics involved that no one has yet completely solved the magnet problem in three dimensions. But in 1984, 32 years after the two-dimensional Ising model was proposed, it was confirmed experimentally by Chan and his student Hyung-kook Kim at Penn State.

After earning his Ph.D. at Cornell in 1974, Chan, an experimentalist, had set out to explore the effect of dimensionality—with symmetry a basic property of bulk materials—on liquid-to-vapor phase changes. He wanted to see how a transition taking place on a flat surface, the heating of a thin film of liquid, say, compared to the same transition in a depth of liquid. Did the two models differ in fundamental ways?

Experimenting in two-dimensional matter, Chan says, is like peering down at tiny skaters on an ice rink. "A single skater is like a gas molecule, free to move anywhere across the ice, but unable to rise above it. If I put more skaters on the rink, eventually there will be collisions." That would be the vapor phase. "A liquid in two dimensions is a cluster of molecules—a bunch of skaters tired of colliding who have decided to join hands.

We did experiments on graphite, not ice," he says. He and Kim introduced methane vapor into a small metal cell containing a graphite sample. As the cell cooled, the methane settled onto the graphite surface in liquid and vapor patches. Then the experimenters slowly varied the temperature in the cell and mapped out the densities of the two phases. What we measured was precisely what Onsager and Yang predicted," Chan says.

Since that time, Chan and his students have created experimental systems that have confirmed—or refuted—a number of theoretical predictions. ("Finding something a little different from the prediction is what we experimenters like the most," he confesses.) In most of these studies, the material of choice has been liquid helium, which, Chan says, in addition to demonstrating the properties common to all fluids, also offers the unique advantage that "at very low temperatures it very clearly manifests its quantum-mechanical nature."

Helium, he explains, is the only substance that will not solidify even if cooled to absolute zero. At very low temperatures -below 2.17 degrees K—it becomes a superfluid: a liquid with no viscosity, that is, no resistance to flow. Chan picks up a cup of coffee that has been sitting neglected at his elbow, removes the lid. "If this were a superfluid," he explains, "and if I were to take a spoon and stir it, the coffee would go on rotating forever." Pause. "Well, not exactly," he amends. "The rotation will slowly decay. But the time of decay is longer than the age of the universe."

To precisely determine the onset of superfluidity in adsorbed helium films, Chan's students used a torsional pendulum fixed to a porous bob. The pendulum is rotated back and forth at a specific frequency. When helium is adsorbed on the surface of the bob, the mass of the bob increases, measurably lowering the frequency of rotation. When cooled below 2.17 degrees, however, the helium turns to superfluid, at which point "it is completely decoupled from the twisting motion, as if it is not there," Chan says. The pendulum rotates without resistance.

"This property doesn't show up in other fluids—they freeze solid first," Chan says. "So we use this system—the superfluid transition in helium—to try to understand aspects of critical phenomena not available in other systems."

In the idealized world of physical "systems," until recently, Chan has written, "disorder and impurities were often viewed as unavoidable nuisances that masked . . . true behavior." Particularly the behavior of critical-phase transitions. "The old way of thinking was if you put any kind of junk into a pure system, the critical transition would be ruined.

scientist studies machine dropping from ceiling with a woman and man at his side
James Collins

Making final adjustments to measure fluctuations near the liquid-vapor critical point of nitrogen. Chan is joined by graduate student Sarah Weber, left, and visiting professor Klaus Knorr.

But the real world is never pure," he says. A recent thrust in his lab, therefore, has been to see just what does happen when impurities are introduced. One major obstacle has been finding a way to introduce impurities in precisely controlled amounts.

Chan opens a desk drawer, and pulls out a pinky-sized vial. Unscrewing the lid, he removes what looks like a skinny translucent cork or a glue stick, and motions me to hold out my palm. "Be careful with it," he says. "It's glass." Strands of silica, actually, woven into a mesh of microscopic fineness. An aerogel. It's featherlight, and no wonder. "This particular one is only eight times the density of air."

First made by chemist Steven Kistler of Stanford in the 1930s, silica aerogels are formed by a sol-gel process: particles of silica dust are suspended in a solvent which then sets as a gel. Subsequent drying leaves only the porous glass frame, or "host," a perfect sample of controlled disorder. Injected with liquid helium, Chan explains, "the aerogel itself becomes the impurity." To get the precise amount of impurity you want, you simply adjust the amount of the starting chemical that forms the silica network.

When helium-filled aerogels are cooled to the superfluid critical point, Chan has found, a phase transition still takes place. This level of disorder, at least, doesn't change that physical fact. What's surprising, Chan says, is that the helium's properties at transition—the patterns of fluctuation near the critical point—are completely changed. "The presence of disorder seems to alter how the material approaches the critical point," he says. "It seems to follow a completely different path." This change, he says, seems related to the structure of the aerogel—the way the silica strands are connected. "There are very few of them, and so they have to be connected at a long length scale. The speculation is that the fluctuation in density of the helium is at the same length scale."

The National Science Foundation recently established a Materials Research Science and Engineering Center at Penn State to exploit just this type of behavior. The Center for Collective Phenomena in Restricted Geometries, one of 29 MRSECs across the country, will bring together 13 Penn State researchers from the departments of physics, electrical engineering, chemistry, and materials science to explore the science and the possible uses of aerogel-type hosts. Possible technologies include nanometer-sized superconducting wires and tunable light-controlled crystals, which might someday become optical switches speeding signal-processing along the Internet.

For Chan, the director of the new center, this kind of technologically relevant, interdisciplinary work is a new experience. "But I have learned a lot already," he says. "And I have enjoyed the interaction.

"You might have got the impression that I like to work on very esoteric things—and I do. But I have found that doing interesting things and doing useful things don't have to be exclusive."

Moses H.W. Chan, Ph.D., is Evan Pugh professor of physics in the Eberly College of Science, 104 Davey Laboratory, University Park, PA 16802; 814-863-2622; chan@phys.psu.edu. Hyung-kook Kim, Ph.D., is professor and head of the department of physics at Pusan National University in Korea.

Related links

Moses Chan's homepage

Physicists find strong evidence of a new, supersolid phase of matter(News release, 9/3/04)

Last Updated May 01, 2001