Dielectric disperison of linear polyelectrolytes

A three-dimensional (gaussian) model is formulated that permits evaluation of the one-dimensional fourier cosine transform of the counterion-counterion coulombic interaction energy ?_k. It is shown that ?_kis much larger for small k than was assumed by Oosawa; consequently, the magnitude of his dielectric increment, and also his relaxation time, must be drastically revised to smaller values. Evidently, the self-field of the fluctuation is large enough to seriously depress the amplitude of the spontaneous fluctuations, and to force Ohmic conduction of the ions at a rate far in excess of the rate of translational diffusion. Finally, it is noted that in highly conducting bulk solvents, where both positive and negative counterfoils coexist in the ion-atmosphere, one might expect to observe a low-frequency component of the dielectric relaxation arising from unequal rates of diffusion of the positive and negative species, in analogy with the situation for spherical colloidal particles. In such a circumstance, the basic counterfoil fluctuation mechanism proposed by Oosawa would acquire a new validity.