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The electrostatic persistence length calculated from Monte Carlo, variational and perturbation methods

Ullner, Magnus LU ; Jönsson, Bo LU ; Peterson, Carsten LU ; Sommelius, Ola LU and Söderberg, Bo LU (1997) In Journal of Chemical Physics 107(4). p.1279-1287
Abstract

Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-Hückel screening length, κ-1. As long as the salt content is low and κ-1 is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with κ-1. Decreasing the screening length, a controversial region is entered. We... (More)

Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-Hückel screening length, κ-1. As long as the salt content is low and κ-1 is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with κ-1. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as √ξp/κ, in agreement with experiment on flexible polyelectrolytes, where ξp is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the κ-1 dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic. A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length. For a sufficiently stiff chain, the persistence length varies quadratically with κ-1 in agreement with earlier theories.

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published
in
Journal of Chemical Physics
volume
107
issue
4
pages
9 pages
publisher
American Institute of Physics
external identifiers
  • scopus:0031185629
ISSN
0021-9606
language
English
LU publication?
yes
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d2e48467-dd19-4eab-9867-e864af682036
date added to LUP
2016-10-03 19:13:40
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2017-11-16 11:01:01
@article{d2e48467-dd19-4eab-9867-e864af682036,
  abstract     = {<p>Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-Hückel screening length, κ<sup>-1</sup>. As long as the salt content is low and κ<sup>-1</sup> is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with κ<sup>-1</sup>. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as √ξ<sub>p</sub>/κ, in agreement with experiment on flexible polyelectrolytes, where ξ<sub>p</sub> is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the κ<sup>-1</sup> dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic. A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length. For a sufficiently stiff chain, the persistence length varies quadratically with κ<sup>-1</sup> in agreement with earlier theories.</p>},
  author       = {Ullner, Magnus and Jönsson, Bo and Peterson, Carsten and Sommelius, Ola and Söderberg, Bo},
  issn         = {0021-9606},
  language     = {eng},
  month        = {07},
  number       = {4},
  pages        = {1279--1287},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {The electrostatic persistence length calculated from Monte Carlo, variational and perturbation methods},
  volume       = {107},
  year         = {1997},
}