The Dielectric Properties of Insulating Materials, III 

 Alternating and Direct Current Conductivity 



By E. J. MURPHY and S. O. MORGAN 



This paper deals with the variation of a-c conductivity with 

 frequency and with that of apparent d-c conductivity with charg- 

 ing time for dielectrics exhibiting anomalous dispersion (i.e., 

 having dielectric constants which decrease with increasing fre- 

 quency). The a-c conductivity of a dielectric exhibiting simple 

 anomalous dispersion approaches a constant limiting value 7oo as 

 the frequency increases. The discussion shows that y^ possesses 

 properties similar to those of the conductivity due to free ions, 

 although in most cases it depends upon the motions of polar mole- 

 cules or bound ions. It is also shown that the apparent conduc- 

 tivity for constant (d-c) potential approaches an initial value as 

 the charging time is diminished. This initial conductivity 70 is 

 demonstrated to be equal to the limiting value of the a-c conduc- 

 tivity attained at high frequencies (700), a relationship which 

 simplifies the description of the behavior of dielectrics exhibiting 

 simple anomalous dispersion. Dielectrics possessing the property 

 of anomalous dispersion then have two conductivities: one is due 

 to local motions of polar molecules or bound ions; the other is due 

 to the migration of free ions to the electrodes. 



Both 7o and 700 refer to methods of measurement. It is to be 

 noted that in many non-homogeneous dielectrics, especially those in 

 which one part is of much higher resistivity than the remainder, 

 both 7o and 700 may be a measure of a free ion conductivity. As 

 the equality of 70 and 7«, is independent of the nature of the 

 polarization responsible for them, experimental agreement between 

 a-c and d-c measurements cannot be used to distinguish whether 

 the dielectric loss in a material is due to polar molecules, to bound 

 ions, or to free ions present in a non-homogeneous dielectric. How- 

 ever, in homogeneous dielectrics 70 (or 700) is a conductivity due to 

 polar molecules or bound ions. 



Introduction 



' I ''HE preceding paper ^ dealt with the dielectric constant, showing 

 -■- mainly how it varies with the frequency of the applied alternating 

 voltage for those dielectrics which behave in the simplest manner, and 

 indicating the general character of the structural features responsible 

 for this behavior. The discussion is extended here to the conductivity, 

 1 Murphy and Morgan, B. S. T. J., 17, 640 (1938). 



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