✍ Scribed by José A. Fornés
No coin nor oath required. For personal study only.
The polarizability and corresponding dielectric relaxation of the Debye-H ückel (DH) atmosphere surrounding a charged rod-like polyelectrolyte immersed in an ionic solution of a symmetrical electrolyte is determined following the method developed by J. A. Fornés [Phys. Rev. E 57, 2110 (1998)]. 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 to apply the theory to a highly charged polyelectrolyte such as DNA in solution, although formulas valid for the DH approximation are also given. A dispersion in the polarizability and correspondingly in the dielectric constant of these solutions in the microwave region is predicted. For instance, considering a 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 α(0) of 1 × 10 -33 Fm 2 ( 6.1 × 10 6 ) times greater than the mean value of the polarizability of water) and the corresponding fluctuating dipole moment p of 2.1 × 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 are 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 × 10 6 V/m.
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