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Variational approach to the structure and thermodynamics of linear polyelectrolytes with Coulomb and screened Coulomb interactions

Jönsson, Bo LU ; Peterson, Carsten and Söderberg, Bo (1995) In Journal of Physical Chemistry 99(4). p.1251-1266
Abstract

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between all monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N3 rather than N4, as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed.... (More)

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between all monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N3 rather than N4, as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high- and low-temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities. The accuracy of the approximations introduced is tested against Monte Carlo simulations for problem sizes ranging from N = 20 to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a byproduct a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes-2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-T approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds. © 1995 American Chemical Society.

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published
in
Journal of Physical Chemistry
volume
99
issue
4
pages
16 pages
publisher
The American Chemical Society
external identifiers
  • Scopus:0001100381
ISSN
0022-3654
language
English
LU publication?
no
id
e8f1e7b6-e2ec-4df8-be4d-db6e8a5be297
date added to LUP
2016-10-03 19:20:52
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2016-11-01 14:42:27
@misc{e8f1e7b6-e2ec-4df8-be4d-db6e8a5be297,
  abstract     = {<p>A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between all monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N<sup>3</sup> rather than N<sup>4</sup>, as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high- and low-temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities. The accuracy of the approximations introduced is tested against Monte Carlo simulations for problem sizes ranging from N = 20 to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a byproduct a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes-2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-T approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds. © 1995 American Chemical Society.</p>},
  author       = {Jönsson, Bo and Peterson, Carsten and Söderberg, Bo},
  issn         = {0022-3654},
  language     = {eng},
  number       = {4},
  pages        = {1251--1266},
  publisher    = {ARRAY(0x8214a88)},
  series       = {Journal of Physical Chemistry},
  title        = {Variational approach to the structure and thermodynamics of linear polyelectrolytes with Coulomb and screened Coulomb interactions},
  volume       = {99},
  year         = {1995},
}