Adv Polym Sci (2014) 255: 1–56
DOI: 10.1007/12_2012_183
# Springer-Verlag Berlin Heidelberg 2013
Published online: 15 March 2013
Strong and Weak Polyelectrolyte Adsorption
onto Oppositely Charged Curved Surfaces
Roland G. Winkler and Andrey G. Cherstvy
Abstract Polyelectrolytes are macromolecules composed of charged monomers and
exhibit unique properties due to the interplay of their flexibility and electrostatic
interactions. In solution, they are attracted to oppositely charged surfaces and interfaces
and exhibit a transition to an adsorbed state when certain conditions are met concerning
the charge densities of the polymer and surface and the properties of the solution. In
this review, we discuss two limiting cases for adsorption of flexible polyelectrolytes on
curved surfaces: weak and strong adsorption. In the first case, adsorption is strongly
influenced by the entropic degrees of freedom of a flexible polyelectrolyte. By contrast,
in the strong adsorption limit, electrostatic interactions dominate, which leads to
particular adsorption patterns, specifically on spherical surfaces. We discuss the
corresponding theoretical approaches, applying a mean-field description for the polymer and the polymer–surface interaction. For weak adsorption, we discuss the critical
adsorption behavior by exactly solvable models for planar and spherical geometries
and a generic approximation scheme, which is additionally applied to cylindrical
surfaces. For strong adsorption, we investigate various polyelectrolyte patterns on
cylinders and spheres and evaluate their stability. The results are discussed in the
light of experimental results, mostly of DNA adsorption experiments.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Weak Adsorption: Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Equation for the Green Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Density Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
R.G. Winkler (*)
Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation,
Forschungszentrum Ju ¨lich, 52425 Ju ¨lich, Germany
e-mail: r.winkler@fzjuelich.de
A.G. Cherstvy (*)
Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
e-mail: a.cherstvy@gmail.com
DOI: 10.1007/12_2012_183
# Springer-Verlag Berlin Heidelberg 2013
Published online: 15 March 2013
Strong and Weak Polyelectrolyte Adsorption
onto Oppositely Charged Curved Surfaces
Roland G. Winkler and Andrey G. Cherstvy
Abstract Polyelectrolytes are macromolecules composed of charged monomers and
exhibit unique properties due to the interplay of their flexibility and electrostatic
interactions. In solution, they are attracted to oppositely charged surfaces and interfaces
and exhibit a transition to an adsorbed state when certain conditions are met concerning
the charge densities of the polymer and surface and the properties of the solution. In
this review, we discuss two limiting cases for adsorption of flexible polyelectrolytes on
curved surfaces: weak and strong adsorption. In the first case, adsorption is strongly
influenced by the entropic degrees of freedom of a flexible polyelectrolyte. By contrast,
in the strong adsorption limit, electrostatic interactions dominate, which leads to
particular adsorption patterns, specifically on spherical surfaces. We discuss the
corresponding theoretical approaches, applying a mean-field description for the polymer and the polymer–surface interaction. For weak adsorption, we discuss the critical
adsorption behavior by exactly solvable models for planar and spherical geometries
and a generic approximation scheme, which is additionally applied to cylindrical
surfaces. For strong adsorption, we investigate various polyelectrolyte patterns on
cylinders and spheres and evaluate their stability. The results are discussed in the
light of experimental results, mostly of DNA adsorption experiments.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Weak Adsorption: Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Equation for the Green Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Density Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
R.G. Winkler (*)
Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation,
Forschungszentrum Ju ¨lich, 52425 Ju ¨lich, Germany
e-mail: r.winkler@fzjuelich.de
A.G. Cherstvy (*)
Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
e-mail: a.cherstvy@gmail.com