Arrest as a General Property of the Supercooled Liquid State

Abstract

Owing to the universal presence of intermolecular interactions, it has to be expected that at some well-defined lower temperature a liquid loses its dynamic properties like fluidity and self-diffusion. As a sequel to two earlier papers on the discovery of such an arrest temperature T0 for supercooled water at 243 K, where also the coexisting vapor pressure was found to become zero, in this paper a further study is undertaken of the behavior of a selection of other liquids. At first, two simple equations of state (van der Waals and virial) are shown in principle to predict a zero vapor pressure at a finite temperature. The interaction parameters B (second virial coefficient) and μJT (Joule-Thomson coefficient) of the vapor are found to become virtually infinite at a temperature T0,B, with a value equal or close to the T0 derived from the liquid properties. Just as earlier found for water, the latter is obtained by extrapolation of several available dynamic and equilibrium data, which should produce an intersection with the temperature axis at the same T0 value. With the exception of molten salts and liquid pure metals, this condition appears to be fulfilled quite accurately. Thus, the temperature of arrest is a general phenomenon for supercooled liquids. As an illustration, it is shown how the PVT diagram of carbon dioxide can be extended into the supercooled temperature region. It is argued that T0 is the temperature below which the Boltzmann energy, kT, is lower than the minimal energy needed for a molecule to break the interactions with its surrounding molecules. We propose to name this minimal energy, kT0, the multimolecular potential of the liquid object. The relationship of the liquid multimolecular potential with the pair potential, ε, of the molecular species is established for various examples and appears to be a proportionality with ε ≈ 2kT0.

Deviation from van’t Hoff Behavior of Solids at Low Temperature

“…5 Also, it shows that the multimolecular potential, defined as kT 0 , 6 of ice is 0.66 times its value for water. This agrees with the more open structure of ice, with its larger intermolecular distances, as follows from its low density.…”

“…In our earlier paper concerning the behavior of liquids, 6 we discussed extensively the possibility of a linear relationship between the arrest temperature and the parameter ε/ k , which is an essential quantity in, for example, the Lennard-Jones or the Stockmayer formulation of the pair potential between simple spherical or quasispherical molecules. Indeed, for a considerably broad selection of such molecules, this linearity could be established.…”

“…In ref (6), we proposed to define the multimolecular potential, kT 0 , as the Boltzmann energy, below which the mutual interactions of the molecules keep them locally stuck. The stronger the interaction, the higher the temperature at which, for instance, evaporation or (self)diffusion starts.…”

“…6 Remarkably, T 0 was found to be proportional to the energy parameter ε/ k of the molecular pair potential of the solvent. 6 …”

“…5 The phenomenon was also shown to exist for a variety of other liquids, wherein, similarly, many properties converge to zero at the same finite temperature, T 0 , a specific property of the liquid, always found to occur in its supercooled region. 6 …”