the salt concentration of the electrolyte solution. The adsorption onto a spherical
surface has been studied by a self-consistent variational approach by Haronska et al.
[57]. We recently presented exact analytical results for critical adsorption onto a
sphere by replacing the Debye–Hu ¨ckel potential with the Hulthe ´n potential [58–60].
We have proposed a unified approach for polyelectrolyte adsorption onto planar,
cylindrical and spherical surfaces [48] by applying the Wentzel–Kramers–Brillouin
(WKB) approximation of quantum mechanics [61–64]. In addition, Linse and Shubin
[65, 66] used lattice models to study polyelectrolyte adsorption at planar oppositely
charged surfaces, thereby extending previous approaches [67, 68]. A scaling theory
has been developed by Borisov et al. [69] and Dobrynin et al. [70] (see also [8, 9] and
references therein), which predicts strong conformational changes of the adsorbed
polyelectrolytes when the surface charged density is varied.
More specific models have been used to study the limit of strong polyelectrolyte
adsorption. Here, in contrast to the weak adsorption case, the adsorption energy
per persistence length of the adsorbing polyelectrolyte chain is large compared with
the energy of thermal fluctuations, and the structure of the adsorbed polyelectrolyte
is determined by the surface attraction and intramolecular repulsion rather than
chain entropy. This leads to the formation of well-defined patterns of polyelectrolytes on the interfaces. In the case of attractive spheres, tennis-ball patterns [71,
72], rosettes [73, 74], or solenoids [59, 71, 75, 76] have been predicted (see Fig. 2
for examples). For cylinders, helical structures [77–79] or strip patterns have been
suggested [77, 80–82]. The investigated systems also diversify according to the
polyelectrolyte flexibility. In some of the above references and others [83–90],
flexible chains are considered, whereas the influence of polymer persistence has
been addressed in Refs. [71, 73, 74, 76–79, 91–94].
Computer simulations of polyelectrolyte adsorption – in particular Monte Carlo
studies – confirmed a number of theoretical predictions (see [96–101] for recent
advances). In a series of articles, Wallin and Linse [102–104] investigated the
influence of chain flexibility, linear charge density, and sphere radius on the complexation of polyelectrolytes with micelles. Akinchina and Linse [105] found
transitions between tennis-ball-like, solenoid, and rosette-like structures by varying
the polyelectrolyte persistence length only. Taking into account the intramolecular
charge–charge interactions by a Debye–Hu ¨ckel potential, Stoll and colleagues
[35, 95, 106] and Kong and Muthukumar [107] undertook similar studies on the
adsorption of polyelectrolytes onto oppositely charged spheres. Figure 2 illustrates
various conformations of a semiflexible polyelectrolyte. Such studies are of particular
interest because the results can directly be compared to theoretical predictions, which
are often also based on Debye–Hu ¨ckel potentials. Messina and coworkers [108–110]
demonstrated that in the case of strong electrostatic coupling it is even possible to
adsorb a polyelectrolyte with charges of the same sign as a sphere. In addition, the
adsorption of polyelectrolytes onto oppositely charged planar surfaces has been
studied by Yamakov et al. [111], Ellis et al. [112], and Messina [113, 114], who
also considered the influence of image charges on the adsorption characteristics. We
would also like to mention simulation studies addressing counterion condensation
onto polyelectrolyte chains [115–120]. This corresponds to strong adsorption of
(several) small spherical particles.
4
R.G. Winkler and A.G. Cherstvy
surface has been studied by a self-consistent variational approach by Haronska et al.
[57]. We recently presented exact analytical results for critical adsorption onto a
sphere by replacing the Debye–Hu ¨ckel potential with the Hulthe ´n potential [58–60].
We have proposed a unified approach for polyelectrolyte adsorption onto planar,
cylindrical and spherical surfaces [48] by applying the Wentzel–Kramers–Brillouin
(WKB) approximation of quantum mechanics [61–64]. In addition, Linse and Shubin
[65, 66] used lattice models to study polyelectrolyte adsorption at planar oppositely
charged surfaces, thereby extending previous approaches [67, 68]. A scaling theory
has been developed by Borisov et al. [69] and Dobrynin et al. [70] (see also [8, 9] and
references therein), which predicts strong conformational changes of the adsorbed
polyelectrolytes when the surface charged density is varied.
More specific models have been used to study the limit of strong polyelectrolyte
adsorption. Here, in contrast to the weak adsorption case, the adsorption energy
per persistence length of the adsorbing polyelectrolyte chain is large compared with
the energy of thermal fluctuations, and the structure of the adsorbed polyelectrolyte
is determined by the surface attraction and intramolecular repulsion rather than
chain entropy. This leads to the formation of well-defined patterns of polyelectrolytes on the interfaces. In the case of attractive spheres, tennis-ball patterns [71,
72], rosettes [73, 74], or solenoids [59, 71, 75, 76] have been predicted (see Fig. 2
for examples). For cylinders, helical structures [77–79] or strip patterns have been
suggested [77, 80–82]. The investigated systems also diversify according to the
polyelectrolyte flexibility. In some of the above references and others [83–90],
flexible chains are considered, whereas the influence of polymer persistence has
been addressed in Refs. [71, 73, 74, 76–79, 91–94].
Computer simulations of polyelectrolyte adsorption – in particular Monte Carlo
studies – confirmed a number of theoretical predictions (see [96–101] for recent
advances). In a series of articles, Wallin and Linse [102–104] investigated the
influence of chain flexibility, linear charge density, and sphere radius on the complexation of polyelectrolytes with micelles. Akinchina and Linse [105] found
transitions between tennis-ball-like, solenoid, and rosette-like structures by varying
the polyelectrolyte persistence length only. Taking into account the intramolecular
charge–charge interactions by a Debye–Hu ¨ckel potential, Stoll and colleagues
[35, 95, 106] and Kong and Muthukumar [107] undertook similar studies on the
adsorption of polyelectrolytes onto oppositely charged spheres. Figure 2 illustrates
various conformations of a semiflexible polyelectrolyte. Such studies are of particular
interest because the results can directly be compared to theoretical predictions, which
are often also based on Debye–Hu ¨ckel potentials. Messina and coworkers [108–110]
demonstrated that in the case of strong electrostatic coupling it is even possible to
adsorb a polyelectrolyte with charges of the same sign as a sphere. In addition, the
adsorption of polyelectrolytes onto oppositely charged planar surfaces has been
studied by Yamakov et al. [111], Ellis et al. [112], and Messina [113, 114], who
also considered the influence of image charges on the adsorption characteristics. We
would also like to mention simulation studies addressing counterion condensation
onto polyelectrolyte chains [115–120]. This corresponds to strong adsorption of
(several) small spherical particles.
4
R.G. Winkler and A.G. Cherstvy