The Polarizability of Rod-Like Polyelectrolytes: An Electric Circuit View

Abstract

In this chapter we use the fluctuation-dissipation theorem (FDT) to estimate the polarizability or dielectric constant as a function of the frequency for low electric field of a polyelectrolyte immersed in an ionic solution; the idea is to consider each charged group within the polyelectrolyte framework and its neighbourhood as a resistor and a capacitor in series. We obtained for the longitudinal polarizability α _∥(0) = C δ ², where C is the total polyelectrolyte-ionic capacitance and δ the average displacement of the ‘bound’ ions under the influence of the thermal fluctuating field. Any of the theories which predict α _∥(0), δ, and the relaxation time τ, can be used to estimate R and C, on the other hand, R, C and δ can be obtained independently by modeling the system. Using Mandel’s results we obtain for the total polyelectrolyte-ionic longitudinal capacitance C = n ² C ₀ where n is the number of condensed but mobile counterions of valence z, and C ₀ is the elementary capacitance, $C_{0} = (ze_{0})^{2}/kT$. We obtain results that are consistent with the experimental data of Takashima for the dielectric dispersion of DNA solutions.

Part of this chapter was reprinted with permission from [José A. Fornés, Phys. Rev. E 57,2, 2110, (1998)] Copyright (1998) by the American Physical Society.