Dielectric properties of polyelectrolytes. IV. Calculation of dielectric dispersion by a stochastic model

Abstract

The theory of the dielectric dispersion of a rodlike polyelectrolyte derived by Oosawa on the basis of thermal fluctuation of the counterion concentration is rewritten by a discrete charged site model and stochastic behavior of the counterions. The values of dielectric increment, conductivity increment and relaxation time are derived as functions of the charge density, number of sites, length of the polyion and transition rates of counterions between two adjacent sites. The expressions are given for two cases; the number of bound ions to a single site is 0 or 1, and in the other case the number is not limited, the latter case containing Oosawa's result. The effect of counterion‐counterion interaction on each Fourier mode of the fluctuation is evaluated in some cases. It is large for the fluctuation of longer wavelength, which broadens the dispersion pattern.