quadratically with the polymer charge density. To compensate for this repulsion
and to still trigger adsorption, higher critical adsorption parameters and surface
charge densities are necessary, as we have shown recently [50]. Notably, for the
planar interface in the limit of low salt ka ( 1, the scaling of s c ðkÞ is also modified
from the canonical cubical to a weaker quadratic dependence on k. A contrary
example of polyelectrolyte adsorption onto high-dielectric interfaces has been
presented [233].
Reversibility of Adsorption—The employed model of weak adsorption implies
reversible and equilibrium adsorption under all studied conditions. This assumption
can be violated, particularly at low salt concentrations, when stronger and virtually
irreversible adsorption of polyelectrolytes is expected to take place. There has to be
a critical solution salinity below which the assumption of “weak” adsorption is no
longer valid. The chains are likely to be adsorbed irreversibly (on experimentally
relevant time-scales) by strong polyelectrolyte–surface attraction. Likewise, above
some critical salinity and for well-shielded surface potentials, the kinetics of
adsorption might be extremely slow on experimentally relevant timescales. The
physical reason is that the polymer chains diffusing in solution are only rarely
captured by a Debye-length-thin layer of attractive potential near the adsorbing
boundary. In this review, we thus avoid many interesting issues regarding the
kinetics of polyelectrolyte adsorption as a function of solution salinity and chain
length, focusing instead on equilibrium properties and critical adsorption
characteristics.
Criterion for Adsorption—A related issue is an experimentally relevant criterion
for polyelectrolyte adsorption. The scaling relations presented above for critical
adsorption are determined by the condition of a zero eigenvalue l 0 . This is certainly
inaccessible in experiments. Often, the criterion for adsorption is chosen such that
the chain is near the surface most of the time, say >90%. Such a requirement will
give rise to higher critical surface charge densities and to potentially different
scaling relations.
Possible Nonmonotonic Effect of Salt—Our simple model neglects inter- and
intrachain electrostatic interactions. The latter can be incorporated into the final
result via an effective salt-dependent persistence length, whereas the former
requires more elaborate adsorption models to be implemented. It has been found
experimentally for adsorption of some polyelectrolytes [234] that the addition of
salt has two major effects. The first effect, the standard screening of chain-surface
attraction at higher salt, is captured in our model. The second effect is connected to
the changes in polyelectrolyte stiffness. Namely, in the low-salt limit if the amount
of salt is increased, the chain persistence length is reduced and the interchain
electrostatic repulsions in the adsorbed layer are diminished. Both effects,
neglected in our model, can facilitate polyelectrolyte adsorption at low-to-intermediate salt concentrations. This is in contrast to the progressively weaker adsorption
at higher salt predicted by our model and caused by pure screening of polymer
surface attraction [66]. More results are presented in a recent publication [235]. A
nonuniform dependence of the amount of adsorbed polyelectrolyte on salt concentration, or screening-enhanced adsorption, which has been observed for a number of
Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved. . .
49
and to still trigger adsorption, higher critical adsorption parameters and surface
charge densities are necessary, as we have shown recently [50]. Notably, for the
planar interface in the limit of low salt ka ( 1, the scaling of s c ðkÞ is also modified
from the canonical cubical to a weaker quadratic dependence on k. A contrary
example of polyelectrolyte adsorption onto high-dielectric interfaces has been
presented [233].
Reversibility of Adsorption—The employed model of weak adsorption implies
reversible and equilibrium adsorption under all studied conditions. This assumption
can be violated, particularly at low salt concentrations, when stronger and virtually
irreversible adsorption of polyelectrolytes is expected to take place. There has to be
a critical solution salinity below which the assumption of “weak” adsorption is no
longer valid. The chains are likely to be adsorbed irreversibly (on experimentally
relevant time-scales) by strong polyelectrolyte–surface attraction. Likewise, above
some critical salinity and for well-shielded surface potentials, the kinetics of
adsorption might be extremely slow on experimentally relevant timescales. The
physical reason is that the polymer chains diffusing in solution are only rarely
captured by a Debye-length-thin layer of attractive potential near the adsorbing
boundary. In this review, we thus avoid many interesting issues regarding the
kinetics of polyelectrolyte adsorption as a function of solution salinity and chain
length, focusing instead on equilibrium properties and critical adsorption
characteristics.
Criterion for Adsorption—A related issue is an experimentally relevant criterion
for polyelectrolyte adsorption. The scaling relations presented above for critical
adsorption are determined by the condition of a zero eigenvalue l 0 . This is certainly
inaccessible in experiments. Often, the criterion for adsorption is chosen such that
the chain is near the surface most of the time, say >90%. Such a requirement will
give rise to higher critical surface charge densities and to potentially different
scaling relations.
Possible Nonmonotonic Effect of Salt—Our simple model neglects inter- and
intrachain electrostatic interactions. The latter can be incorporated into the final
result via an effective salt-dependent persistence length, whereas the former
requires more elaborate adsorption models to be implemented. It has been found
experimentally for adsorption of some polyelectrolytes [234] that the addition of
salt has two major effects. The first effect, the standard screening of chain-surface
attraction at higher salt, is captured in our model. The second effect is connected to
the changes in polyelectrolyte stiffness. Namely, in the low-salt limit if the amount
of salt is increased, the chain persistence length is reduced and the interchain
electrostatic repulsions in the adsorbed layer are diminished. Both effects,
neglected in our model, can facilitate polyelectrolyte adsorption at low-to-intermediate salt concentrations. This is in contrast to the progressively weaker adsorption
at higher salt predicted by our model and caused by pure screening of polymer
surface attraction [66]. More results are presented in a recent publication [235]. A
nonuniform dependence of the amount of adsorbed polyelectrolyte on salt concentration, or screening-enhanced adsorption, which has been observed for a number of
Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved. . .
49