whereas Odijk [164] and Skolnick and Fixman [165] suggest the rod limit l
el
p $ r
2
k
À2 . The dependence of the persistence length on k has been reexamined theoretically in detail [147]. The salt-dependent renormalization of the persistence length
can modify the predicted k dependence of s c at high salt concentrations, thus
providing slopes closer to those observed experimentally of about 1–1.8.
We do not attempt here a quantitative comparison with the experimental data
because our model of a single sphere complexed by a flexible polyelectrolyte is
too simple for this purposes and it neglects some important structural features of
colloids and polyelectrolytes. Instead, the complexation of semiflexible polyelectrolytes with a sphere needs to be considered, which is a challenging problem that
so far has remained untouched.
Complex formation of polyelectrolytes with some globular proteins (e.g., serum
albumin, lysozyme), which possess nonhomogeneous charge distributions, has also
been studied in experiments [124, 132, 137, 173]. Some additional interesting
effects were detected. For instance, it was shown that polyelectrolyte–protein
binding can occur on the wrong side of the isoelectric point. Moreover, the
negatively charged polyelectrolytes were shown to bind to net negatively charged
proteins due to polyelectrolyte electrostatic attraction to positive charge patches on
the protein surface [124]. In some cases, the strength of polyelectrolyte–protein
binding was shown to reach a maximum or a plateau at 10–30 mM of simple salt in
solution. It was suggested that the corresponding Debye screening lengths are on
the order of the protein size or of the typical separation of negatively and positively
charged domains on the protein surface. Then, at such values of k the electrostatic
attraction of polyelectrolytes to positively charged protein domains is substantial,
whereas the repulsion from negatively charged regions is already screened [131,
173] (short-range attraction and long-range repulsion paradigm).
Further theoretical studies are required to include this charge patchiness in the
model of electrostatic complexation of polyelectrolytes with oppositely charged
objects, with the ultimate model example being the adsorption of polyelectrolytes
onto Janus-like net-neutral particles with oppositely charged hemispheres [174].
Moreover, in order to clarify the appearance of polyelectrolyte-induced bridging
attraction between two spherical particles [175–177], the influence of the length of
a polymer and its charge density on the properties of the (onset of) aggregation
process and the structure of the resulting coacervates can be studied in experiments.
6 Strong Adsorption: Theoretical Model
In the limit of strong adsorption, the polyelectrolyte adsorption energy is large
compared to the thermal fluctuations of the polymer chain. Hence, the structural
properties of adsorbed chains are essentially governed by maximization of
polyelectrolyte–surface electrostatic interactions and minimization of polyelectrolyte–polyelectrolyte repulsion [59]. Therefore, we consider a polyelectrolyte chain
30
R.G. Winkler and A.G. Cherstvy
el
p $ r
2
k
À2 . The dependence of the persistence length on k has been reexamined theoretically in detail [147]. The salt-dependent renormalization of the persistence length
can modify the predicted k dependence of s c at high salt concentrations, thus
providing slopes closer to those observed experimentally of about 1–1.8.
We do not attempt here a quantitative comparison with the experimental data
because our model of a single sphere complexed by a flexible polyelectrolyte is
too simple for this purposes and it neglects some important structural features of
colloids and polyelectrolytes. Instead, the complexation of semiflexible polyelectrolytes with a sphere needs to be considered, which is a challenging problem that
so far has remained untouched.
Complex formation of polyelectrolytes with some globular proteins (e.g., serum
albumin, lysozyme), which possess nonhomogeneous charge distributions, has also
been studied in experiments [124, 132, 137, 173]. Some additional interesting
effects were detected. For instance, it was shown that polyelectrolyte–protein
binding can occur on the wrong side of the isoelectric point. Moreover, the
negatively charged polyelectrolytes were shown to bind to net negatively charged
proteins due to polyelectrolyte electrostatic attraction to positive charge patches on
the protein surface [124]. In some cases, the strength of polyelectrolyte–protein
binding was shown to reach a maximum or a plateau at 10–30 mM of simple salt in
solution. It was suggested that the corresponding Debye screening lengths are on
the order of the protein size or of the typical separation of negatively and positively
charged domains on the protein surface. Then, at such values of k the electrostatic
attraction of polyelectrolytes to positively charged protein domains is substantial,
whereas the repulsion from negatively charged regions is already screened [131,
173] (short-range attraction and long-range repulsion paradigm).
Further theoretical studies are required to include this charge patchiness in the
model of electrostatic complexation of polyelectrolytes with oppositely charged
objects, with the ultimate model example being the adsorption of polyelectrolytes
onto Janus-like net-neutral particles with oppositely charged hemispheres [174].
Moreover, in order to clarify the appearance of polyelectrolyte-induced bridging
attraction between two spherical particles [175–177], the influence of the length of
a polymer and its charge density on the properties of the (onset of) aggregation
process and the structure of the resulting coacervates can be studied in experiments.
6 Strong Adsorption: Theoretical Model
In the limit of strong adsorption, the polyelectrolyte adsorption energy is large
compared to the thermal fluctuations of the polymer chain. Hence, the structural
properties of adsorbed chains are essentially governed by maximization of
polyelectrolyte–surface electrostatic interactions and minimization of polyelectrolyte–polyelectrolyte repulsion [59]. Therefore, we consider a polyelectrolyte chain
30
R.G. Winkler and A.G. Cherstvy