520 BELL SYSTEM TECHNICAL JOURNAL 



lous dispersion ; this will be called the polarization conductivity '^ and 

 designated by 7poi in this paper. 



The magnitude of the polarization conductivity of a material is 

 proportional to the number of polarizable units of structure such as 

 polar molecules or bound ions per unit volume which contribute to 

 anomalous dispersion. It also depends upon the mobility which these 

 polarizable units have in the local translational or rotational motions 

 in which they engage in consequence of thermal agitation. It finally 

 depends upon the permanent dipole moment of the polar molecules or 

 upon the charges upon the bound ions. 



The concentration of ions able to contribute to conduction in di- 

 electrics is generally low because in many cases the free ion conductivity 

 depends mainly upon a small percentage of impurity in the material. 

 On the other hand, the concentration of polarizable units which are 

 able to contribute to the polarization conductivity may be much larger 

 and in fact even equal to the total number of molecules per unit volume. 

 Consequently, the polarization conductivity Tpoi may often be more 

 reproducible in measurements upon different specimens of the same 

 dielectric than is the free ion conductivity.^ It may well be that in 

 many materials diffusion coefficients, thermal conductivity, mechanical 

 dissipation and other similar properties which might be expected on 

 theoretical grounds to be related to electrical conductivity will bear a 

 simpler or more easily demonstrated relationship to polarization 

 conductivity than to free ion conductivity. 



An example of the advantage of using the infinite-frequency conduc- 

 tivity instead of the d-c conductivity appears in measurements of the 

 conductivity of ice. In Fig. 5 the infinite-frequency conductivity (or 

 polarization conductivity) of ice is plotted against the reciprocal of 

 the absolute temperature, using unpublished data of the writers. The 

 data for 700 are reproducible and the curve shows a relation similar to 

 that usually observed for the d-c conductivity of solids. Direct- 

 current measurements on the same specimens on the other hand 

 yielded very erratic results. It may be seen from Fig. 5 that the 

 polarization conductivity is much higher than the d-c conductivity. 



^ We suggest for this conductivity the name polarization conductivity because it 

 is a property of polarizable units of structure. In cases where the polarization is due 

 to the change of orientation of polar molecules, we might instead refer to it as an 

 orientational conductivity or a polar molecule conductivity, contrasting it thereby with 

 the translational aspect of ordinary conduction by free ions. As ions which are 

 loosely bound to some stationary or moving unit of the dielectric structure are often 

 capable of producing anomalous dispersion, at least two types of polarization con- 

 ductivity are possible; these may be described as the orientational conductivity and 

 the bound ion conductivity. 



'' Joffe has obtained evidence that the initial conductivity, which we show here 

 to be in some cases a polarization conductivity, is often superior in reproducibility to 

 the final conductivity. (Cf. Reference 15.) 



