508 BELL SYSTEM TECHNICAL JOURNAL 



layer of dielectric whose resistance may be high enough that the inter- 

 face does not become completely charged during the time allowed for 

 charging. For the alternating current case this implies a decrease of 

 capacity with increasing frequency, which is equivalent to the anoma- 

 lous dispersion which has been described for the case of dipole polariza- 

 tions. It should be particularly emphasized that the term anomalous 

 dispersion describes a type of variation of dielectric constant with 

 frequency which can be produced by a number of different physical 

 mechanisms. 



The two-layer dielectric is of less interest than a generalization of 

 this type of polarization which includes heterogeneous systems com- 

 posed of particles of one dielectric dispersed in another. This type 

 of heterogeneous dielectric is of considerable importance since such 

 systems represent the actual structure of many practical dielectrics. 

 Such a generalization of the two-layer dielectric has been made by 

 K. W. Wagner ^ who developed the theory for the case of spheres of 

 relatively high conductivity dispersed in a continuous medium of low 

 conductivity. The conditions for the existence of an interfacial 

 polarization are, as in the two-layer case, that 6172 + ^271, where the 

 symbols have the significance just given. This type of polarization, 

 which is variously referred to as an interfacial polarization, an ionic 

 polarization and a Maxwell -Wagner polarization, shows anomalous 

 dispersion like other absorptive polarizations. When the particle 

 size is small as compared with the electrode separation it may be 

 treated as a uniformly distributed polarization. 



The magnitude and time of relaxation of interfacial polarizations 

 are determined by the differences in e and 7 of the two components. 

 There is a widely prevalent opinion that this type of polarization 

 always has such long relaxation-times as to be observed only at very 

 low frequencies. While this is true for mixtures of very low-con- 

 ductivity components, the general equations show that for the case 

 where one component has a high conductivity — for example equal to 

 that of a salt solution — the dispersion may occur in the radio frequency 

 range. 



Several special types of interfacial polarization have been proposed 

 to explain the dielectric properties of various non-homogeneous di- 

 electrics where something regarding the nature of the inhomogeneity 

 is known. The dielectric constant of cellulose, for example, receives 

 a contribution from an interfacial polarization due to the water and 

 dissolved salt which it contains. Experimental evidence indicates 

 that an aqueous solution of various salts is distributed through the 



9 K. W. Wagner, Arch. f. Elektrotechn., 2, pp. 374 and 383. 



