Application of liquid dynamics theory to the glass transition

In monatomic liquid dynamics theory, the system moves among a large number of intersecting nearly harmonic valleys in the many-particle potential energy surface. The same potential surface underlies the motion of atoms in the supercooled liquid. As temperature is decreased below the melting temperature, the motion among the potential valleys will begin to freeze out, and the system will pass out of equilibrium. It is therefore necessary to develop a nonequilibrium theory, based on the Hamiltonian motion. The motion is separated into two distinct parts, and idealized as follows: (a) the vibrational motion within a single valley is assumed to be purely harmonic, and remaining in equilibrium; and (b) the transit motion, which carries the system from one valley to another, is assumed to be instantaneous, and energy and momentum conserving. This idealized system is capable of exhibiting a glass transition behavior. An elementary model, incorporating the idealized motion, is the independent atom model, originally developed to treat self diffusion in monatomic liquids. For supercooled liquids, in the independent atom model, the vanishing of self diffusion at a finite temperature implies the same property for the transit probability. The vanishing of the transit probability at a finite temperature supports the view that transits are not merely thermally activated, but are controlled by phase-space correlations. For supercooled liquid sodium, the transit probability has Vogel-Tamann-Fulcher temperature dependence. The independent atom model is shown to be capable of exhibiting all the essential glass transition properties, including rate dependence of the glass transition temperature, and both exponential and nonexponential relaxation.