M. Scott Shell, a fourth-year graduate student working with Professors Debenedetti and Panagiotopoulos, has obtained a significant theoretical result on the properties of saddles in multidimensional potential energy surfaces (energy landscapes). The research, published January 23 in Physical Review Letters , has important implications for the theory of the glass transition.
It is a well-known fact that by cooling a liquid fast enough, crystallization can be avoided, and the liquid is eventually transformed into a glass. Glasses, like crystals, are solid, and in both classes of materials atomic motions are restricted to small vibrational displacements. However, glasses are microscopically disordered, and this makes them attractive for numerous technologies.
Thermodynamics dictates that the equilibrium state of a substance is completely specified by its temperature and pressure. Glasses, however, are also influenced by the details of the process by which they are formed. The specific ways in which glasses evolve in time are fundamental players in these materials. The need to treat explicitly these kinetic aspects of the glassy state greatly complicates theoretical analysis. One of the more promising theoretical frameworks is the so-called “energy landscape” approach. This substance-specific landscape is given by the energies of interaction among a glass’ molecules. The characteristics of an energy landscape, such as its ruggedness and topology, are crucial to the resulting properties of the glass. Much previous research has focused on characterizing local minima in the energy landscape of a wide range of substances.
Shell, Debenedetti and Panagiotopoulos showed that saddles in energy landscapes obey certain rules. They established relationships between the depth of minima, the height of saddles, and their shapes. The resulting theory sets the stage for a rigorous connection between kinetics and thermodynamics in glasses.
 M.S. Shell, P.G. Debenedetti, and A.Z. Panagiotopoulos, “Saddles in the Energy Landscape: Extensivity and Thermodynamic Formalism”, Phys. Rev. Lett., 92, 035506 (2004).