A theory of the rotations of molecules in solids and of the dielectric constant of solids and liquids

Abstract

It is well known that Rochelle salt, NaKC 4 H 4 O 6 . 4H 2 O, for a limited range of temperature may, for practical purposes, he said to have an infinite dielectric constant analogous to the infinite permeability of iron in its ferromagnetic state. Such states, it is now realized, occur in a number of phenomena and a common description is of value; we shall refer to them as co-operative states . The co-operative state in Rochelle salt is limited by an upper critical temperature T u (or Curie Point) such that for T > T u the susceptibility though large is finite and decreases rapidly as T increases. Unlike the corresponding magnetic substances there is also a lower critical temperature T l such that for T < T l the susceptibility is again finite and decreases as T decreases. It is agreed that these phenomena are to be explained by the orientation of polar molecules in the crystal—the polar molecules in these particular crystals being undoubtedly water molecules present as water of crystallization. The co-operative state and the upper critical temperature T u can be explained by an exact analogy of the Weiss-Langevin theory of ferromagnetism, and no difficulties are raised by the large size of the necessary molecular field. The interaction energy of electrical dipoles is so large that it supplies precisely the necessary term which it fails to do in the magnetic case. The explanation of this part of the phenomenon requires the polar water molecules to be orientating freely under the influence of the effective applied electric field. The lower critical temperature T l can and must then be explained, it is believed, by a failure of the free rotations at lower temperatures which can so cut down the efficiency of the response to the applied field that the material is no longer self- polarizing. Again the dielectric constant of ice or water is finite at all temperatures, and falls to low values even for low frequencies as the temperature is decreased below 150° K. This can only be understood, assuming that the H 2 O molecule in ice or water carries the same dipole as in steam, or even a comparable one. if its orientations are not free but severely restricted by the local Held of its neighbours, even at the highest temperatures for which the dielectric constant of water has been investigated. The water dipoles are so numerous and so strong that water and ice would be co-operative at all temperatures if the dipole carriers were even approximately free. Somewhat similar phenomena occur for other polar liquids such as some of the alcohols and nitrobenzene which arc believed to be explicable in the same way. Rochelle salt, and its variants in which ammonium replaces potassium, arc the only known substances with a co-operative state. While there is probably general agreement about these qualitative explanations, it seems that no quantitative discussion has yet been given, even of any simplified model, which really displays behaviour of the types observed. Such a discussion of a simple model will be given in this paper. The exact results for the simple model reproduce many of the features observed, but naturally the model is too much simplified to expect it to provide a faithful representation of every detail. It is, however, possible to sec the modifications necessary in the model to make it the better fit the facts, and to see. moreover, that these modifications arc physically reasonable. The need for such a quantitative theory was first brought clearly to my notice at a conference on the solid state held in Leningrad in 1932. As will appear, however, an essential feature of the theory is an application of the ideas of order and disorder in metallic alloys, where the ordered state is typically co-operative, recently put forward by Bragg and Williams.* As soon as their ideas are incorporated the theory “ goes."