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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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
Bockris, J.O’M., Reddy, A.K.N.: Modern Electrochemistry, vol. V1, p. 251. Plenum Press, New York (1977)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (1985)
Schellman, J.A., Stigter, D.: Electrical double layer, zeta potential, and electrophoretic charge of double-stranded DNA. Biopolymers 16, 1415 (1977)
Stigter, D.: Electrophoresis of highly charged colloidal cylinders in univalent salt-solutions. J. Colloid Interface Sci. 53 (2), 296 (1975)
Stigter, D.: Evaluation of the counterion condensation theory of polyelectrolytes. Biophys. J. 69, 380 (1995)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-33840-8_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33839-2
Online ISBN: 978-3-319-33840-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)