Variational approach to the structure and thermodynamics of linear polyelectrolytes with Coulomb and screened Coulomb interactions
(1995) In Journal of Physical Chemistry 99(4). p.12511266 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 monomerpairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fastconvergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N^{3} rather than N^{4}, 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 monomerpairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fastconvergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N^{3} rather than N^{4}, 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 lowtemperature 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 sizes2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on lowT approximations to endend and monomermonomer separations. It is argued that the former increases faster than linearly with the number of bonds.
(Less)
 author
 Jönsson, Bo ^{LU} ; Peterson, Carsten ^{LU} and Söderberg, Bo ^{LU}
 organization
 publishing date
 1995
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Physical Chemistry
 volume
 99
 issue
 4
 pages
 16 pages
 publisher
 The American Chemical Society
 external identifiers

 scopus:0001100381
 ISSN
 00223654
 DOI
 10.1021/j100004a027
 language
 English
 LU publication?
 yes
 id
 e8f1e7b6e2ec4df8be4ddb6e8a5be297
 date added to LUP
 20161003 19:20:52
 date last changed
 20180529 10:27:40
@article{e8f1e7b6e2ec4df8be4ddb6e8a5be297, 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 monomerpairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fastconvergent 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 lowtemperature 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 sizes2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on lowT approximations to endend and monomermonomer separations. It is argued that the former increases faster than linearly with the number of bonds.</p>}, author = {Jönsson, Bo and Peterson, Carsten and Söderberg, Bo}, issn = {00223654}, language = {eng}, number = {4}, pages = {12511266}, publisher = {The American Chemical Society}, series = {Journal of Physical Chemistry}, title = {Variational approach to the structure and thermodynamics of linear polyelectrolytes with Coulomb and screened Coulomb interactions}, url = {http://dx.doi.org/10.1021/j100004a027}, volume = {99}, year = {1995}, }