Advanced

Planar screening by charge polydisperse counterions

Trulsson, M. LU ; Trizac, E. and Šamaj, L. (2018) In Journal of Physics Condensed Matter 30(3).
Abstract

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q). We work out analytically the one-plate and two-plate cases, at the level of non-linear PoissonBoltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full PoissonBoltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous... (More)

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q). We work out analytically the one-plate and two-plate cases, at the level of non-linear PoissonBoltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full PoissonBoltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions n(q), for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous n(q) behaviour are already featured by discrete mixtures with a relatively small number of constituents.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
electrostatic, Monte Carlo, Poisson-Boltzmann, two-plate interaction
in
Journal of Physics Condensed Matter
volume
30
issue
3
publisher
IOP Publishing
external identifiers
  • scopus:85040327021
ISSN
0953-8984
DOI
language
English
LU publication?
yes
id
b3a211a1-dd38-47dc-b0e3-0e64fc653fb9
date added to LUP
2018-01-22 10:28:44
date last changed
2018-05-29 10:24:31
@article{b3a211a1-dd38-47dc-b0e3-0e64fc653fb9,
  abstract     = {<p>We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), n(q). We work out analytically the one-plate and two-plate cases, at the level of non-linear PoissonBoltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full PoissonBoltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions n(q), for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous n(q) behaviour are already featured by discrete mixtures with a relatively small number of constituents.</p>},
  articleno    = {035001},
  author       = {Trulsson, M. and Trizac, E. and Šamaj, L.},
  issn         = {0953-8984},
  keyword      = {electrostatic,Monte Carlo,Poisson-Boltzmann,two-plate interaction},
  language     = {eng},
  month        = {01},
  number       = {3},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics Condensed Matter},
  title        = {Planar screening by charge polydisperse counterions},
  url          = {http://dx.doi.org/},
  volume       = {30},
  year         = {2018},
}