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

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Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)

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) = Cδ2, 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 = n2C0 where n is the number of condensed but mobile counterions of valence z, and C0 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.

Keywords

Polarizability Electrical fluctuations Ionic dielectric relaxation Cylindrical polyelectrolytes 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Federal University of GoiásGoiâniaBrazil

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