Dielectric Relaxation Around a Charged Colloidal Cylinder in an Electrolyte

Abstract

The polarizability and the corresponding dielectric relaxation of the Debye–Hückel (DH) atmosphere surrounding a charged rod-like polyelectrolyte immersed in an ionic solution of a symmetrical electrolyte is determined following the method developed in the former chapter.

Several formulas are given to estimate the DH atmosphere parameters, namely: the polarizability at zero frequency, α(0), the relaxation time, τ, the cloud capacitance, C,the average displacement of the ionic cloud, δ, the square root dipole moment quadratic fluctuation, $<p^{2}> ^{1/2}$, and the thermal fluctuating field, $<E^{2}> ^{1/2}.$ The Poisson–Boltzmann equation is solved numerically in order to apply the theory to a highly charged polyelectrolyte as DNA in solution, although also are given formulas valid for the DH approximation. It is predicted a dispersion in the polarizability and correspondingly in the dielectric constant of these solutions in the microwave region. For instance, considering the DNA length of 1000 Å, with its reduced linear charge density ξ ₀ = 4. 25, and ionization factor γ = 0. 5, immersed in a NaCl solution (40 mM) we predict a polarizability of the DH atmosphere at zero frequency $\alpha (0) = 1 \times 10^{-33}\ \mathrm{Fm}^{2}$ ( ≃ 6. 1 × 10⁶ times greater than the mean value of the polarizability of water) and the corresponding fluctuating dipole moment $p = 2.1 \times 10^{-27}$ cm ( ≃ 600 times greater than the permanent dipole moment of water molecule). The relaxation time and the average displacement of the ionic cloud is τ = 1. 6 ns and δ = 14 Å, respectively. This displacement is produced by the thermal fluctuating field, which, in this case, at room temperature is $<E^{2}> ^{1/2} = 2 \times 10^{6}$ V/m.

Reprinted from [José A. Fornés, J. Colloid Interface Sci. 222, 97, (2000)] Copyright (2000), with permission from Elsevier.