for the considered surface geometry. Specifically, we consider planar, cylindrical,
and spherical surfaces. This review is motivated by the adsorption of biological
molecules onto, typically, cylinders and spheres. Our studies are geared towards a
better understanding of the physico-chemical properties of nucleosome core
particles of eucaryotic genomic DNA and an understanding of the complexation
of flexible nucleic acid genomes with oppositely charged highly basic interiors of
capsid shells, which are typical of many spherical and filamentous viruses. Naturally, the applicability of the ideas is much broader and applications in various
fields will be discussed.
In general, we will not discuss adsorption onto planar surfaces and structure
formation on such surfaces as they occur in polyelectrolyte multilayer formation [2,
140–143]. Such systems are addressed in a review by Lindholm and Cohen Stuart in
this series [144].
2 Weak Adsorption: Theoretical Model
The weakly charged polyelectrolyte chain is described by a continuous space curve
with the linear charge density r ¼ e/l 0 , where e is the elementary charge and l 0 the
intercharge separation. The intramolecular Coulomb and intersegmental excludedvolume interactions are not taken into account explicitly, but are instead
incorporated into the Kuhn segment of the length l. Expressions for its dependence
on the Debye screening length l D ¼ 1/k are provided in the literature [56,
145–149]. We assume that intramolecular charge–charge interactions perturb
the polymer statistics only slightly. Hence, we consider a polymer chain under
Y-solvent conditions. Under bad or good solvent conditions, the scaling properties
for critical adsorption might be altered [9]. Taking counterions and salt ions
into account using the Debye–Hu ¨ckel potential, this corresponds to the limit
where the Debye–Hu ¨ckel potential between two Kuhn segments with the charge
q ¼ rl separated by l obeys q
2 e
Àkl
=El ( k B T . For k ¼ 0, this means l B =l ( 1,
where l B ¼ e
2
=ðEk B TÞ is the Bjerrum length, E the dielectric permittivity, T the
temperature, and k B Boltzmann’s constant. The oppositely charged surface has a
homogeneous charge density s and is impenetrable to solvent molecules and
polyelectrolyte chains. The solvent is treated as a continuous medium of constant
dielectric permittivity with E ¼ 80. The counterions and salt ions are taken into
account on the level of the linearized Poisson–Boltzmann equation [59]. Its solution
yields the polyelectrolyte–surface interaction potential, i.e., the Debye–Hu ¨ckel
potential for the particular geometry. The latter is derived assuming a constant
surface charge density, without accounting for possible charge regulation effects or
for coupling of the surface potential to the density profile of a polyelectrolyte in the
proximity of the interface (see Sects. 6.1.1 and 6.2.1). Because the polyelectrolyte
and the surface are weakly charged, no release of counterions upon adsorption will
occur. Other approximations employed include the same value of the dielectric
6
R.G. Winkler and A.G. Cherstvy
and spherical surfaces. This review is motivated by the adsorption of biological
molecules onto, typically, cylinders and spheres. Our studies are geared towards a
better understanding of the physico-chemical properties of nucleosome core
particles of eucaryotic genomic DNA and an understanding of the complexation
of flexible nucleic acid genomes with oppositely charged highly basic interiors of
capsid shells, which are typical of many spherical and filamentous viruses. Naturally, the applicability of the ideas is much broader and applications in various
fields will be discussed.
In general, we will not discuss adsorption onto planar surfaces and structure
formation on such surfaces as they occur in polyelectrolyte multilayer formation [2,
140–143]. Such systems are addressed in a review by Lindholm and Cohen Stuart in
this series [144].
2 Weak Adsorption: Theoretical Model
The weakly charged polyelectrolyte chain is described by a continuous space curve
with the linear charge density r ¼ e/l 0 , where e is the elementary charge and l 0 the
intercharge separation. The intramolecular Coulomb and intersegmental excludedvolume interactions are not taken into account explicitly, but are instead
incorporated into the Kuhn segment of the length l. Expressions for its dependence
on the Debye screening length l D ¼ 1/k are provided in the literature [56,
145–149]. We assume that intramolecular charge–charge interactions perturb
the polymer statistics only slightly. Hence, we consider a polymer chain under
Y-solvent conditions. Under bad or good solvent conditions, the scaling properties
for critical adsorption might be altered [9]. Taking counterions and salt ions
into account using the Debye–Hu ¨ckel potential, this corresponds to the limit
where the Debye–Hu ¨ckel potential between two Kuhn segments with the charge
q ¼ rl separated by l obeys q
2 e
Àkl
=El ( k B T . For k ¼ 0, this means l B =l ( 1,
where l B ¼ e
2
=ðEk B TÞ is the Bjerrum length, E the dielectric permittivity, T the
temperature, and k B Boltzmann’s constant. The oppositely charged surface has a
homogeneous charge density s and is impenetrable to solvent molecules and
polyelectrolyte chains. The solvent is treated as a continuous medium of constant
dielectric permittivity with E ¼ 80. The counterions and salt ions are taken into
account on the level of the linearized Poisson–Boltzmann equation [59]. Its solution
yields the polyelectrolyte–surface interaction potential, i.e., the Debye–Hu ¨ckel
potential for the particular geometry. The latter is derived assuming a constant
surface charge density, without accounting for possible charge regulation effects or
for coupling of the surface potential to the density profile of a polyelectrolyte in the
proximity of the interface (see Sects. 6.1.1 and 6.2.1). Because the polyelectrolyte
and the surface are weakly charged, no release of counterions upon adsorption will
occur. Other approximations employed include the same value of the dielectric
6
R.G. Winkler and A.G. Cherstvy