The idea that rigidity and orderliness go together is a triumph of modern theoretical physics. But how these two properties interrelate when a liquid is cooled and becomes solid-like -- a phenomenon called the glass transition -- has been less clear. Now, University of Illinois chemical physics professor Peter Wolynes and graduate student Xiaoyu Xia have found a way to explain the odd behavior of glassy materials.
"A periodic array of atoms in a crystal behaves differently than a fluid," said Wolynes, who holds the James R. Eiszner Chair in chemistry at the UI. "For example, you can't move just one atom in an array without displacing the entire structure. The rigidity of glass, an amorphous solid, is more mysterious. Without any apparent order, this chaotic jumble of atoms behaves as if rigidly frozen."
Glassy phenomena typically occur on long time scales. "How rapidly the time scale increases as the material is cooled is what determines the 'fragility,' " Wolynes said. "The fragility differentiates rapid glass-formers -- like polymers -- from slow ones -- such as ordinary window glass. Quantitatively relating fragility to other glass-forming characteristics has been an elusive goal, however."
Ten years ago, Wolynes developed a theory called the Random First Order Transition Theory of Glasses that qualitatively described the glass-transition phenomenon. The resulting mathematical expression was based upon microscopic theories of freezing.
Unlike ordinary freezing -- which typically involves only a few orderly patterns -- it appeared there were many patterns into which a liquid could freeze and still be called disordered, Wolynes said. The number of possible freezing patterns seemed to be correlated with the material's rigidity.
"In the intervening years, we realized we could take our theory and quantitatively explain the one number that was needed to distinguish one glassy substance from another -- the fundamental flow characteristic called fragility," Wolynes said. "We could then correlate a material's fragility with thermodynamic measurements of its heat capacity."
While the heat capacity of a liquid is rather high, at the glass transition it falls to a value more typical of the crystalline state. The heat capacity is especially interesting because it is related to the amount of disorder, or entropy, in a substance: A liquid with a large heat capacity loses entropy much more rapidly as it cools. By measuring the heat capacity of a substance, and then plugging it into their equation, the researchers can predict the speed at which the molecular motion changes with temperature.
"The fact that all glassy materials can now be expressed in a universal form gives us much greater confidence that we truly understand the glass-transition phenomenon," Wolynes said. "This knowledge will be useful in many other fields of study, including protein folding." Wolynes and Xia described their theory in the March 28 issue of the Proceedings of the National Academy of Sciences.