Ionic contribution to the complex dielectric constant of a polymer under dc bias

A diffusion equation for the distribution of ionic impurities in a polymer under a dc field has been solved analytically for the conditions that neither injection nor absorption of impurity ions takes place at either electrode and that the ions do not interact. By using the solution of the diffusion equation, an ionic contribution to the complex dielectric constant is calculated. The most important results are as follows. (1) At high temperatures and low frequencies, the dielectric loss factor of the polymer decreases exponentially with the time elapsed after the application of the dc bias. (2) The dielectric constant is not greatly affected by the bias. (3) The ionic contribution to the loss factor in the absence of the dc bias is represented as ?_i^″ = 4πνDq²/ωkT, where ν is the density of mobile ions, D the diffusion coefficient, q the charge of an ion, ω the angular frequency, k the Boltzmann constant, and T the absolute temperature. (4) A method is presented for distinguishing between the apparent activation energy for diffusion and that for generation of mobile ions.