Configurational excitations in condensed matter, and the "Bond Lattice" model for the liquid-glass transition

The characteristics of glasslike transitions in supercooled liquids and plastic crystals are discussed and a nearest neighbor interaction scheme, termed the "bond lattice" model, is proposed to account for the thermodynamic aspects of the phenomenon. Although the excitations of the bond lattice have features in common with those of the Ising lattice, the bond lattice has a zeroth order (noncooperative) case in which the thermodynamic properties are meaningful and readily evaluated. The zeroth order expressions appear adequate to account for the configurational heat capacity of the covalent bonded liquid ZnCl₂, but are clearly incapable of explaining the transition behavior of most molecular and hydrogenbonded glasses. In these cases it is believed the configurational excitations have considerable cooperative character. While the complex cooperative problem is not properly treated in this paper, we show how an ad hoc introduction of temperature-dependent bond energies (a sort of Bragg-Williams approximation) modifies the bond lattice model properties in the direction demanded by experiment. A second order transition between supercooled liquid and glass is not required by the treatment. An expression for transport properties, based on a postulated exponential relationship between rearrangement probabilities and degree of configurational excitation, is evaluated. The VTF (Fulcher) equation, commonly used to describe transport properties of viscous liquids, results as a good approximation. The VTF T₀ parameter is determined mainly by the bond strength parameter of the model, while the B parameter can be related to the change of heat capacity at T_g. It is implied that glasses with little or no thermal manifestation of T_g will have large and almost Arrhenius temperature dependences, as seems characteristic of the strong network glasses, BeF₂, GeO₂, and perhaps SiO₂. The VTF transport parameters for the intermediate case of ZnCl₂ are well predicted using the same molecular excitation parameters which account for the configurational heat capacity.