3 Weak Adsorption: Exactly Solvable Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 Planar Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Weak Adsorption: WKB Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1 WKB Approximation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Planar Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Cylindrical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.5 Conformational Properties of Adsorbed Polyelectrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Weak Adsorption: Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Comparing Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 27
5.2 Comparison Between Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6 Strong Adsorption: Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.1 Adsorption at a Cylindrical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Adsorption at a Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7 Limitations and Further Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1 Introduction
Adsorption of charged macromolecules, and polyelectrolytes in particular, onto
charged surfaces is of paramount importance in a wide range of technological
applications [1, 2], such as surface coating [3], colloid stabilization [4], and paper
making [5–7] and for a variety of biological systems [8–12]. Because of their charges,
most charged polymers are water-soluble, which makes them interesting candidates
for water-based, environmentally friendly technology. This aspect is even more
important for a number of biological systems. Here, examples include wrapping of
double-stranded DNA in nucleosomes [13–20], adsorption of single-stranded RNA
onto the interior of viral capsides [21–29], and polyelectrolyte multilayered vesicles
[30, 31]. Correspondingly, polyelectrolyte adsorption has received substantial attention for many decades. There are several valuable books and review articles on
the subject [8, 9, 32–34]. However, electrostatically driven polymer adsorption
shows a broad range of facets, not all of which have been addressed adequately in
the literature.
A fundamental step in polyelectrolyte adsorption is the transition from a free
state in solution to a bound polymer on an interface. Figure 1 illustrates such a
transition for the adsorption of a polyelectrolyte onto spherical colloidal particles
[35]. In the unbound state, the polymer chain explores the entropic degrees of
freedom, whereas in the bound state the attractive polymer–surface electrostatic
interactions dominate [8, 33, 36–39]. These two antagonistic trends dictate the
properties of adsorption. Theoretical studies of the adsorption behavior of polyelectrolytes onto planar and curved surfaces suggest a phase-transition-like behavior,
i.e., a bound polymer state appears at certain critical conditions, which depend
upon, e.g., the temperature, the charge density and curvature of the surface, the
polyelectrolyte linear charge density and its mechanical persistence [40–44]. An
important aspect of this review is to discuss recent advances on this issue.
2
R.G. Winkler and A.G. Cherstvy
3.1 Planar Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Weak Adsorption: WKB Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1 WKB Approximation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Planar Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Cylindrical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.5 Conformational Properties of Adsorbed Polyelectrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Weak Adsorption: Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Comparing Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 27
5.2 Comparison Between Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6 Strong Adsorption: Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.1 Adsorption at a Cylindrical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Adsorption at a Spherical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7 Limitations and Further Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1 Introduction
Adsorption of charged macromolecules, and polyelectrolytes in particular, onto
charged surfaces is of paramount importance in a wide range of technological
applications [1, 2], such as surface coating [3], colloid stabilization [4], and paper
making [5–7] and for a variety of biological systems [8–12]. Because of their charges,
most charged polymers are water-soluble, which makes them interesting candidates
for water-based, environmentally friendly technology. This aspect is even more
important for a number of biological systems. Here, examples include wrapping of
double-stranded DNA in nucleosomes [13–20], adsorption of single-stranded RNA
onto the interior of viral capsides [21–29], and polyelectrolyte multilayered vesicles
[30, 31]. Correspondingly, polyelectrolyte adsorption has received substantial attention for many decades. There are several valuable books and review articles on
the subject [8, 9, 32–34]. However, electrostatically driven polymer adsorption
shows a broad range of facets, not all of which have been addressed adequately in
the literature.
A fundamental step in polyelectrolyte adsorption is the transition from a free
state in solution to a bound polymer on an interface. Figure 1 illustrates such a
transition for the adsorption of a polyelectrolyte onto spherical colloidal particles
[35]. In the unbound state, the polymer chain explores the entropic degrees of
freedom, whereas in the bound state the attractive polymer–surface electrostatic
interactions dominate [8, 33, 36–39]. These two antagonistic trends dictate the
properties of adsorption. Theoretical studies of the adsorption behavior of polyelectrolytes onto planar and curved surfaces suggest a phase-transition-like behavior,
i.e., a bound polymer state appears at certain critical conditions, which depend
upon, e.g., the temperature, the charge density and curvature of the surface, the
polyelectrolyte linear charge density and its mechanical persistence [40–44]. An
important aspect of this review is to discuss recent advances on this issue.
2
R.G. Winkler and A.G. Cherstvy