Dielectric constant, averaged charge separation

Statistically, II is the average deviation of Mr) on the molecular surface we view it as being indicative of the local polarity, or charge separation, that is present even in molecules having zero dipole moments (Brinck, Murray, and Politzer 1992a), e.g., BF3 and p-dini-trobenzene. We have shown that II correlates in a general fashion with several empirical polarity scales and with the dielectric constant (Brinck, Murray, and Politzer 1992a Murray et al. 1994). 

In the above —e is the electronic charge, a the average ionic separation, N Avo-gadro s number, s the dielectric constant, and R the gas constant. Generally, C2VS is small relative to unity one then deals with the extreme limiting law ... 

Implications. These results have an important implication concerning the use of Fourier analysis of DC transients in polymeric materials to extract the frequency-dependence of the dielectric response (12)- In order for the principle of superposition to apply the electric field inside the material being measured must be time- and space-invariant. This critical condition may not be met in polymers which contain mobile ionic impurities or injected electrons. Experimentally, we can fix only the average of the electric field. Moreover, our calculations demonstrate that the bulk field is not constant in either time or space. Thus, the technique of extracting the dielectric response from the Fourier components of the transient response is fundamentally flawed because the contribution due to the formation of ionic and electronic space-charge to the apparent frequency-dependent dielectric response can not generally be separated from the dipole contribution. 

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