522 BELL SYSTEM TECHNICAL JOURNAL 



This list shows that there are at least three main types of infinite- 

 frequency conductivity. The first of these is the type which depends 

 upon the change of the orientation of polar molecules according to the 

 Debye theory. This type of polarization conductivity is of more 

 theoretical interest than any of the others and perhaps also of more 

 practical importance; as already mentioned, it may be described as an 

 orientational conductivity to emphasize that no translational mobility 

 is necessary for it to occur. 



TABLE I 



Expressions for the Constant Value 7«j Approached by the A-C 

 Conductivity as the Frequency Increases 



Type of Polarization 



1. The Orientational Polarization due to Polar Mole- 



2. A Distortional Polarization having a Relaxation- 



Time given by r = r// Too = ;j^ • ( ^^3 — ) 



3. Polarizations due to Spatial Variations of Conduc- 

 tivity and Dielectric Constant 



(o) A two-layer dielectric, layers 1 and 2 having re- 

 spectively static dielectric constants 61 and ti and 



free-ion conductivities 71 and 72 Too = 7 ; rv;; j r 



(ei + f^%r\y\ + T2) 

 (i) Special case of (3fl) where ti is much larger 



than T2 Too = { i ) 



(c) Special case of (3&) where ti = 62 Too = Ti/4 



{d) Special case of (3a) consisting of a high resistance 



transition layer at the dielectric/electrode 



interface, where ti is the conductivity of the 



dielectric Too = Ti 



(e) Conducting spheres dispersed in an insulating 



medium of the same dielectric constant Too = />7i 



Note: The infinite-frequency conductivity Too is given here in e.s.u. (See equation 

 20.) In Table I of the preceding paper {B. S. T. J., 17, 640 (1938)) the values of 

 (eo — «oo) and t are given for the polarizations listed above; the expressions given 

 there for t should be divided by 47r in the case of Items ia, c, d and e, as should also 

 the expressions for eo — 600 in the case of Item 2. The quantities which appear in 

 the above Table are defined in an appendix to the preceding paper. ti and T2 are 

 expressed in e.s.u. in this table. 



The remaining members of the list of Table I originate in the 



properties of ions rather than those of molecules. These ions must be 



more or less bound in order to have an infinite-frequency conductivity 



differing from the zero-frequency conductivity.^ The nature and 



* It will be recalled that the terms infinite-frequency and zero-frequency are not 

 used here in their general meaning but merely as a convenient way to indicate opposite 

 directions of extrapolation of dispersion curves. They refer respectively to the high- 

 frequency extremity of a dispersion curve where 7' becomes practically independent 

 of frequency and to the low-frequency extremity where the dielectric constant 

 becomes practically independent of frequency. 



71 



