Abstract
In Chap. 2 we developed a method to determine the natural electrical thermal fluctuations and their spectral distribution across two points in the neighbourhood of a spherical electrically charged particles immersed in an ionic solution. The essence of the method is to consider the charged sphere with its surrounding ionic atmosphere as a capacitor and a resistor in parallel.
In this chapter we apply this method to estimate the electrical fluctuations (field and potential) around rod-like rigid polyelectrolyte bearing a uniform surface charge distribution dispersed in an aqueous salt solution of pointlike ions. We performed computer simulations to solve the Poisson–Boltzmann (P-B) equation and also developed formulas to calculate the fluctuations in the case of a low potential, Debye–Hückel approximation (linearized P-B equation). We apply the formalism to a DNA solution which is a well-known model for a biopolymer. They are shown plots of the potential and electric field fluctuations as a function of the Debye–Hückel length, κ −1, and distance, d, from the polyelectrolyte surface for several molecular sizes.
Part of this chapter was reprinted with permission from [José A. Fornés, Phys. Rev. E 57,2, 2104, (1998)] Copyright (1998) by the American Physical Society.
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Notes
- 1.
The origin of this equation is the Poisson equation: \(\bigtriangleup \psi = -\frac{\rho }{\epsilon \epsilon _{ 0}}\) with \(\rho = ze_{0}(n_{+} - n_{-}) = nze_{0}(\exp (-\frac{ze_{0}\psi } {kT} ) -\exp (\frac{ze_{0}\psi } {kT} )) = -2nze_{0}\sinh (\frac{ze_{0}\psi } {kT} )\), with n + and n − being the average concentration of the ions.
- 2.
This condition comes to approximate \(\sinh (ze_{0}\psi (r)/kT) \approx ze_{0}\psi (r)/kT\) in the Poisson–Boltzmann equation.
References
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Fornés, J.A. (2017). Electrical Fluctuations Around a Charged Colloidal Cylinder in an Electrolyte. In: Electrical Fluctuations in Polyelectrolytes . SpringerBriefs in Molecular Science. Springer, Cham. https://doi.org/10.1007/978-3-319-33840-8_3
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DOI: https://doi.org/10.1007/978-3-319-33840-8_3
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