Application of liquid dynamics theory the 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 ener gy surface, The same potential surface underlies the motion of atoms in the supercooled liquid. As temperature is decreased below the melting temperat ure, the motion among the potential valleys will begin to freeze out, and t he system will pass out of equilibrium. It is therefore necessary to develo p a nonequilibrium theory, based on the Hamiltonian motion. The motion is s eparated into two distinct parts, and idealized as follows: (a) the vibrati onal motion within a single valley is assumed to be purely harmonic, and re maining in equilibrium; and (b) the transit motion, which carries the syste m from one valley to another, is assumed to be, instantaneous, and energy a nd momentum conserving. This idealized system is capable of exhibiting a,gl ass transition behavior. An elementary model, incorporating the idealized m otion, is the independent atom model, originally developed to treat self di ffusion in monatomic liquids. For supercooled liquids, in the independent a tom 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 no t merely thermally activated, but are controlled by phase-space correlation s. For supercooled liquid sodium, the transit probability has Vogel-Tamann- Fulcher temperature dependence. The independent atom model is shown to be c apable of exhibiting all the essential glass transition properties, includi ng rate dependence of the glass transition temperature, and both exponentia l and nonexponential relaxation. [S1063-651X(99)01412-9].