This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Powered by TCPDF (www.tcpdf.org) This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Batys, Piotr; Luukkonen, Sohvi; Sammalkorpi, Maria Ability of Poisson-Boltzmann Equation to Capture Molecular Dynamics Predicted Ion Distribution around Polyelectrolytes Published in: Physical Chemistry Chemical Physics DOI: 10.1039/C7CP02547E Published: 01/09/2017 Document Version Peer reviewed version Please cite the original version: Batys, P., Luukkonen, S., & Sammalkorpi, M. (2017). Ability of Poisson-Boltzmann Equation to Capture Molecular Dynamics Predicted Ion Distribution around Polyelectrolytes. Physical Chemistry Chemical Physics, 19, 24583-24593. https://doi.org/10.1039/C7CP02547E
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This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.
Powered by TCPDF (www.tcpdf.org)
This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user.
Batys, Piotr; Luukkonen, Sohvi; Sammalkorpi, MariaAbility of Poisson-Boltzmann Equation to Capture Molecular Dynamics Predicted IonDistribution around Polyelectrolytes
Published in:Physical Chemistry Chemical Physics
DOI:10.1039/C7CP02547E
Published: 01/09/2017
Document VersionPeer reviewed version
Please cite the original version:Batys, P., Luukkonen, S., & Sammalkorpi, M. (2017). Ability of Poisson-Boltzmann Equation to CaptureMolecular Dynamics Predicted Ion Distribution around Polyelectrolytes. Physical Chemistry Chemical Physics,19, 24583-24593. https://doi.org/10.1039/C7CP02547E
Ability of Poisson-Boltzmann Equation to Capture Molecular Dynamics Predicted Ion Distribution around Polyelectrolytes
Piotr Batys,a,b,* Sohvi Luukkonena and Maria Sammalkorpia
Here, we examine polyelectrolyte (PE) and ion chemistry specificity in ion condensation via all-atom molecular dynamics
(MD) simulations and assess the ability of the Poisson-Boltzmann (PB) equation to describe the ion distribution predicted by
the MD simulations. The PB model enables extracting parameters characterizing the ion condensation. We find that the
modified PB equation which contains the effective PE radius and the energy of the ion-specific interaction as empirical fitting
parameters describes ion distribution accurately at large distances but close to the PE, especially when strongly localized
charge or specific ion binding sites are present, the mean field description of PB fails. However, the PB model captures the
MD predicted ion condensation in terms of Manning radius and fraction of condensed counterions for all the examined PEs
and ion species. We show that the condensed ion layer thickness in our MD simulations collapses on a single master curve
for all the examined simple, monovalent ions (Na+, Br+, Cs+, Cl-, and Br-) and PEs when plotted against the Manning parameter
(and consequently the PE line charge density). The significance of this finding is that, contrary to the Manning radius
extracted from the mean field PB model, the condensed layer thickness in the all atom detail MD modelling does not depend
on the PE chemistry or counterion type. Furthermore, the fraction of condensed counterions in the MD simulations exceeds
the PB theory prediction. The findings contribute toward understanding and modelling ion distribution around PEs and other
charged macromolecules in aqueous solutions, such as DNA, functionalized nanotubes, and viruses.
Introduction
Polyelectrolytes (PEs) are polymers that contain ionic or
ionisable repeating electrolyte groups. In aqueous solution, the
electrolyte groups dissociate to solvated counterions and a
charged polymer. Depending on the PE and the counterion
species, as well as, solution characteristics including excess salt,
the solvated ions can condense onto the polyions. The degree
and extent of this ion condensation, and its influence on PE-PE
interactions, is at key role in dictating PE materials
characteristics, for example for using them in industrial
solubilisation and flocculation,1-3 separation,4-6 drug delivery,7-
10 tunable and responsive coatings,8,11-13 adhesives,14
sensors,6,15-17 and tissue engineering.18,19 Besides technological
interest, many important biopolymers, such as DNA, RNA and
proteins, are PEs and experience ion condensation.
Excess salt contributes to the ion atmosphere around the PEs.
Therefore, it is not surprising that the responses of hydrated PE
assemblies, namely complexes and multilayers, are sensitive to
the addition of salt. The presence of ions can lead to responses
such as shrinking, swelling, loosening, or even dissociation at
high enough concentration.20-26 Furthermore, the counterion
type has been linked to the solubility,27 kinetics,28 stability,29
and composition of PE complexes,30-33 as well as their thermal
response.23
Most commonly, ion condensation in PE systems is described by
Manning’s theory, a mean field Poisson-Boltzmann (PB)
description that models the polyion as an idealized, infinitely
long line charge and the counterions within Debye-Huckel
approximation.34,35 Sharp has elaborated the Manning picture
by investigating the effect of excess salt in the system through
the nonlinear Poisson−Boltzmann equation.36 For monovalent
ions and low charge densities, the PB approach is consistent
with simple numerical models37,38 and is able to predict various
PE solution proprieties including electrophoretic migration,
surface adsorption or osmotic pressure in a concentration range
from 0.0003 to 0.15 M.38-40 Notably, the Manning mean field
picture breaks down in the presence of additional divalent salt,
or strongly interacting systems.37,41-43 Specifically, several
studies in which the PE is defined as a rigid rod or a line charge
with varying charge density,37,44 or a flexible chain of beads,45
have pointed out the importance of charge correlations in ion
condensation around PEs in strongly interacting systems.
Mean-field models do not take into account the molecular level
structure and inhomogeneity in the PE charge distribution. Ion
type specific effects can be incorporated partially to the PB
description via modifications, see e.g. Refs.46,47. All these effects
in PE-ion systems, however, can be captured by particle level
descriptions, such as Monte Carlo, or molecular dynamics (MD).
Both, primitive numerical models in which the PEs are described
as a rigid rod or a line charge with varying charge density37,42,48-
a. Department of Chemistry and Materials Science, School of Chemical Engineering, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.
b. Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, PL-30239 Krakow, Poland.
† E-mail: [email protected]; [email protected]; Tel: +358-50-371-7434. Electronic Supplementary Information (ESI) available: Additional details and data about the system size and force-field comparison. See DOI: 10.1039/x0xx00000x
Table 2. The calculated Poisson-Boltzmann parameters. The table presents the radius of the PB cell R, the Manning parameter ξ, the fraction of condensed ions as predicted by the
PB theory 𝑥𝑐𝑚𝑖𝑛 (the lower limit of the fraction of condensed ions), the effective radius of the PE r0 (PB fitting parameter), the ion-specific interaction V0 (fitting parameter), the
Manning radius rM, the fraction of condensed ions xc, and the radius of the condensed layer rcl. The values in the parentheses correspond to the error estimate of the fitting procedure.
System R [nm] ξ 𝒙𝒄𝒎𝒊𝒏 Ion r0 [nm] V0 [kBT] rM [nm] xc rcl [nm]
(Finland) are gratefully acknowledged. The authors thank Dr.
Hanne Antila for useful discussions and providing source code
segments that aided in the work.
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