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

As a sequel to results obtained on the low-temperature behavior of liquids, a similar study is presented for solids. A molecule in a solid interacts with the other molecules of the crystal so that it is subjected to a specific multimolecular potential, kT 0 . At temperature T < T 0 , the molecules are localized, and at T > T 0 , they can participate in processes like self-diffusion and evaporation. As a consequence, the van't Hoff equation is disobeyed at a low temperature and properties like vapor pressure, diffusion rate, or reactivity are zero below the specific temperature, T 0 , which here can be interpreted as a temperature of thermal stability of the solid. To account for this view, the van't Hoff equation, represented by the green curve in the figure, is extended with a suitable pre-exponential factor, leading to the red curve. Three examples, taken from the literature, are analyzed to demonstrate its applicability. These examples are: the thermal dissociation of calcium carbonate, the sublimation equilibrium pressure of naphthalene, and that of ice. For some other solids, equilibria and dynamic properties, X ( T ), are examined by means of extrapolations in the X ( T ) versus T domain, showing the presence of an arrest temperature, which coincides, within experimental accuracy, with the T 0 value obtained from the corresponding vapor pressure. As with liquids, kT 0 is found to be proportional to the molecular pair potential.