Tag Archives: Pierfrancesco Urbani

The glassy side of fractals

An April 24, 2014 news item on Nanowerk highlights a breakthrough in glass (wordplay intended),

Colorful church windows, beads on a necklace and many of our favorite plastics share something in common — they all belong to a state of matter known as glasses. School children learn the difference between liquids and gases, but centuries of scholarship have failed to produce consensus about how to categorize glass.

Now, combining theory and numerical simulations, researchers have resolved an enduring question in the theory of glasses by showing that their energy landscapes are far rougher than previously believed.

An April 23, 2014 Duke University news release by Erin Weeks (also on EurekAlert), which originated the news item, provides a diagram (am I the only one who thinks these resemble cow udders?) and more infotmation,

Glasses form when their molecules get jammed into fractal "wells," as shown on the right, rather than smooth or slightly rough wells (left). Photo credit: Patrick Charbonneau. Courtesy: Duke University

Glasses form when their molecules get jammed into fractal “wells,” as shown on the right, rather than smooth or slightly rough wells (left). Photo credit: Patrick Charbonneau. Courtesy: Duke University

“There have been beautiful mathematical models, but with sometimes tenuous connection to real, structural glasses. Now we have a model that’s much closer to real glasses,” said Patrick Charbonneau, one of the co-authors and assistant professor of chemistry and physics at Duke University.

One thing that sets glasses apart from other phase transitions is a lack of order among their constituent molecules. Their cooled particles become increasingly sluggish until, caged in by their neighbors, the molecules cease to move — but in no predictable arrangement. One way for researchers to visualize this is with an energy landscape, a map of all the possible configurations of the molecules in a system.

Charbonneau [Patrick Charbonneau, one of the co-authors and assistant professor of chemistry and physics at Duke University] said a simple energy landscape of glasses can be imagined as a series of ponds or wells. When the water is high (the temperature is warmer), the particles within float around as they please, crossing from pond to pond without problem. But as you begin to lower the water level (by lowering the temperature or increasing the density), the particles become trapped in one of the small ponds. Eventually, as the pond empties, the molecules become jammed into disordered and rigid configurations.

“Jamming is what happens when you take sand and squeeze it,” Charbonneau said. “First it’s easy to squeeze, and then after a while it gets very hard, and eventually it becomes impossible.”

Like the patterns of a lakebed revealed by drought, researchers have long wondered exactly what “shape” lies at the bottom of glass energy landscapes, where molecules jam. Previous theories have predicted the bottom of the basins might be smooth or a bit rough.

“At the bottom of these lakes or wells, what you find is variation in which particles have a force contact or bond,” Charbonneau said. “So even though you start from a single configuration, as you go to the bottom or compress them, you get different realizations of which pairs of particles are actually in contact.”

Charbonneau and his co-authors based in Paris and Rome showed, using computer simulations and numeric computations, that the glass molecules jam based on a fractal regime of wells within wells.

The new description makes sense of several behaviors seen in glasses, like the property known as avalanching, which describes a random rearrangement of molecules that leads to crystallization.

Understanding the structure of glasses is more than an intellectual exercise — materials scientists stand to advance from the knowledge, which could lead to better control of the aging of glasses.

Here’s a link to and a citation for the paper,

Fractal free energy landscapes in structural glasses by Patrick Charbonneau, Jorge Kurchan,     Giorgio Parisi, Pierfrancesco Urbani & Francesco Zamponi. Nature Communications 5, Article number: 3725 doi:10.1038/ncomms4725 Published 24 April 2014

This paper is behind a paywall but there is a free preview available through ReadCube Access.