Variable-structure cell theory of liquids and glasses

A new kind of cell theory -- one which formally accounts for the possibility of amorphous phases -- is presented. The equilibrium partition function is transformed exactly by first classifying all particle configurations according to multidimensional potential-energy minima and then assigning to each minimum a system-spanning set of cells such that, for configurations near enough the minimum, each cell contains one particle. The theory is then extended to general amorphous systems, and approximate descriptions of supercooled liquids and glass transitions are given.

A simple model calculation of the equilibrium and quenched properties of two-dimensional systems, based on this general theory, is then presented. The particular model chosen is essentially a Bernal liquid, so that the distribution of molecular coordination numbers plays a central role. The basic model of Bernal is simplified, however, in that the Bernal polygons available to the system are restricted to a few basic types and is further modified to allow for small-amplitude vibrations of the molecules about their lattice sites. Quenching is then effected by freezing the coordination-number distribution (which is determined by a single ordering parameter, in the present, simplified treatment) at its "glass-transition" value. The equilibrium and quenched thermodynamic functions are calculated analytically, and substantial qualitative agreement with well known characteristics of real liquids and glasses is obtained. Finally, a simple kinetic analysis of the model is presented, and it is found that, for large enough potential-energy barriers to structural rearrangement, the model exhibits an operationally defined glass transition.