Focus: A Tale of Two Liquids

Published October 6, 2003  |  Phys. Rev. Focus 12, 11 (2003)  |  DOI: 10.1103/PhysRevFocus.12.11

Physics of the Liquid-Liquid Critical Point

Francesco Sciortino, Emilia La Nave, and Piero Tartaglia

Published October 6, 2003
Figure 1
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Split personality. Theory and computer simulations support the notion that water and similar substances have two distinct liquid phases under extreme conditions.

There’s water and then there’s water–or so goes a theory that attempts to explain the many odd properties of the ubiquitous liquid of life. For more than a decade, some theorists have argued that water has two distinct liquid forms or “phases.” A new analysis in the 3 October PRL bolsters that idea and predicts that any liquid that expands as it cools must have two distinct phases.

Water may be the most common and familiar of liquids, but it is nonetheless a physical oddity. Most substances steadily contract as they cool, but water first contracts, and then expands, so that its density reaches a maximum near 4 degrees Celsius. For decades, researchers have puzzled over this and many other quirks. The anomalies show through most clearly in water quickly chilled below zero Celsius so that it temporarily remains liquid at below-freezing temperatures–a process known as “supercooling.”

In 1992, computer simulations suggested that supercooled water might come in two distinct phases, a high density phase in which the molecules pack together more tightly, and a low density phase in which they snuggle together more loosely. At high pressure and very low temperatures, supercooled water should pass abruptly from the low density phase to the high density phase, just as steam suddenly condenses into water. The transition would be extremely difficult to observe, as experimenters would have to prevent the supercooled water from freezing for a very long time. Nonetheless, theorists realized that the mere existence of a temperature and pressure at which such transitions become possible–a so-called critical point–would exert a subtle influence that could neatly explain all of water’s weirdness.

Now a theoretical analysis predicts which liquids ought to have two phases. Any liquid that eventually expands as it cools must have a liquid-liquid critical point, report Francesco Sciortino, Emilia La Nave, and Piero Tartaglia of the University of Rome, “La Sapienza.” They studied how the energy of a liquid depends on the precise way the molecules in it jumble together.

Molecules in a liquid can fit themselves into many different disorderly arrangements. The molecules push and pull each other, so each arrangement has a slightly different energy. To represent every possible configuration of the molecules, theorists can construct a “potential energy landscape,” an abstract moonscape in which the peaks represent the high energy configurations that the liquid avoids and the valleys represent the low energy configurations that it prefers. The Rome researchers studied the statistical properties of the landscape for liquids, such as the range of valley depths, and used these properties to link density variations to the existence of two phases. They found that liquids with a maximum density above their freezing points have potential energy landscapes that inevitably produce two liquid phases. To bolster their insight, they then used a computer simulation to show that the potential energy landscape of water behaves as their theory said it must.

The new work lends credence to the idea that liquid water has two forms, says physicist H. Eugene Stanley of Boston University, because the researchers took a new approach, yet reached the same conclusion as other studies. “It’s truly outstanding,” he says. “They’ve found the conditions under which you have this liquid-liquid critical point.”

–Adrian Cho

Adrian Cho is a freelance science writer in Grosse Pointe Woods, Michigan.


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