critical surface charge densities and weaker ka scaling in the low-salt limit. This
consistent geometry-mediated decline in the scaling exponent for cylindrical and
spherical surfaces is fully consistent with experimental data on polyelectrolyte complexation [129]. The data provide clear evidence that the planar Wiegel-like solution
[40] does not reproduce the critical scaling behavior detected for instance in a series of
experiments of the Dubin group. We hope that this fact, as well as the novel description
of the underlying physics, will find a proper appreciation among experimentalists.
The issue of critical polyelectrolyte adsorption is intimately coupled to the
polymer-mediated bridging attraction between oppositely charged macro-ions
immersed in a polymer solution. Moreover, electrostatically driven self-assembly
of single-stranded RNA molecules on the interior of positively charged capsids, as
it occurs in many spherical and rod-like single-stranded viruses, offers another field
for potential applications of our theoretical results. The WKB method developed
above has recently been implemented to weak polyelectrolyte adsorption under
confined conditions [49] and to adsorption onto low-dielectric interfaces [50]. The
power of the WKB approach can even be extended to more complicated adsorption
situations, such as patchy surfaces, specific charged patterns on concave and convex
interfaces, Janus particles, etc., and other (nearly arbitrary) potentials of polyelectrolyte–surface interactions. This might open an avenue to approach more realistic
situations of polyelectrolyte adsorption and to quantitatively reproduce experimental results in the future.
In the limit of strong adsorption, we analyzed the energetics of highly stable
complexes of thin polyelectrolyte worm-like chains with cylindrical and spherical
particles of opposite charge. An important conclusion here is that overcharging of
complexes is penalized by the electrostatic Born self-energy term, rendering nearly
neutral and undercharged complexed most abundant, in agreement with outcomes
from a number of complexation experiments [192]. For a cylindrical surface, the
applications of our results include a description of the phase transitions in DNA
duplexes, wrapping of single-stranded DNAs onto carbon nanotubes, DNA
wrapping on cylindrical dendrimer molecules, etc. For a spherical colloid, the
wrapping of polyelectrolytes mimics in particular DNA complexation with the
histone core proteins in nucleosomes. Moreover, the theoretical description of
helical charge patterns of adsorbed polyelectrolytes on a cylinder and solenoidal
wrapping of polyelectrolytes on a sphere offer a framework for addressing
DNA–DNA and nucleosome–nucleosome electrostatic interactions [25].
The various concepts applied above are extremely useful and provide valuable
insight into polyelectrolyte adsorption. Comparison with experimental results
confirms a variety of predicted dependencies and provides a deeper understanding
of the underlying physical phenomena. On the other hand, there are still a number of
effects that cannot be accounted for by the current theoretical description. Here,
further extensions and refinements of the models are necessary.
Acknowledgements We thank J.-F. Berret, P. Dubin, G. Manning, M. Muthukumar,
H. Schiessel, S. Stoll, and M. Ullner for many insightful discussions and correspondence. Special
thanks go to S. Stoll for providing us the snapshots presented in Figs. 1 and 2. The work was
supported by the German Research Foundation, DFG grant CH 707/5-1 to AGC.
Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved. . .
51
consistent geometry-mediated decline in the scaling exponent for cylindrical and
spherical surfaces is fully consistent with experimental data on polyelectrolyte complexation [129]. The data provide clear evidence that the planar Wiegel-like solution
[40] does not reproduce the critical scaling behavior detected for instance in a series of
experiments of the Dubin group. We hope that this fact, as well as the novel description
of the underlying physics, will find a proper appreciation among experimentalists.
The issue of critical polyelectrolyte adsorption is intimately coupled to the
polymer-mediated bridging attraction between oppositely charged macro-ions
immersed in a polymer solution. Moreover, electrostatically driven self-assembly
of single-stranded RNA molecules on the interior of positively charged capsids, as
it occurs in many spherical and rod-like single-stranded viruses, offers another field
for potential applications of our theoretical results. The WKB method developed
above has recently been implemented to weak polyelectrolyte adsorption under
confined conditions [49] and to adsorption onto low-dielectric interfaces [50]. The
power of the WKB approach can even be extended to more complicated adsorption
situations, such as patchy surfaces, specific charged patterns on concave and convex
interfaces, Janus particles, etc., and other (nearly arbitrary) potentials of polyelectrolyte–surface interactions. This might open an avenue to approach more realistic
situations of polyelectrolyte adsorption and to quantitatively reproduce experimental results in the future.
In the limit of strong adsorption, we analyzed the energetics of highly stable
complexes of thin polyelectrolyte worm-like chains with cylindrical and spherical
particles of opposite charge. An important conclusion here is that overcharging of
complexes is penalized by the electrostatic Born self-energy term, rendering nearly
neutral and undercharged complexed most abundant, in agreement with outcomes
from a number of complexation experiments [192]. For a cylindrical surface, the
applications of our results include a description of the phase transitions in DNA
duplexes, wrapping of single-stranded DNAs onto carbon nanotubes, DNA
wrapping on cylindrical dendrimer molecules, etc. For a spherical colloid, the
wrapping of polyelectrolytes mimics in particular DNA complexation with the
histone core proteins in nucleosomes. Moreover, the theoretical description of
helical charge patterns of adsorbed polyelectrolytes on a cylinder and solenoidal
wrapping of polyelectrolytes on a sphere offer a framework for addressing
DNA–DNA and nucleosome–nucleosome electrostatic interactions [25].
The various concepts applied above are extremely useful and provide valuable
insight into polyelectrolyte adsorption. Comparison with experimental results
confirms a variety of predicted dependencies and provides a deeper understanding
of the underlying physical phenomena. On the other hand, there are still a number of
effects that cannot be accounted for by the current theoretical description. Here,
further extensions and refinements of the models are necessary.
Acknowledgements We thank J.-F. Berret, P. Dubin, G. Manning, M. Muthukumar,
H. Schiessel, S. Stoll, and M. Ullner for many insightful discussions and correspondence. Special
thanks go to S. Stoll for providing us the snapshots presented in Figs. 1 and 2. The work was
supported by the German Research Foundation, DFG grant CH 707/5-1 to AGC.
Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved. . .
51