Adsorption of Polyelectrolytes onto Charged Surfaces 352
2
el1
(7)
where el is the blob size, and Δσ is the overcompensation parameter defined
by
f (8)
with Γ being the surface coating of monomers. The increase of the charge
density of the surface renders important the excluded volume interactions, thus
leading to an increase of the thickness of the adsorbed layer δev with the charge
density of the surface
2ev el 2
(9)
The above described conditions allow also predicting the appearance of a
weak overcompensation of the surface charge. The increase of the ionic
strength push the system to a condition in which the electrostatic interactions
present a short-range character, becoming preminent the excluded volume one.
The adsorption of polyelectrolyte onto charged surfaces is strongly dependent
on the short-range interactions as was pointed out by Joanny [63]. The mean-
field approaches applied to describe the polymer adsorption give information
of the adsorption profiles under different conditions and surface nature [64].
Shafir and Andelman [18] pointed out using the mean-field theory that the
overcompensation increases with the ionic strength, reaching maximum values
around 20-40% over the charge of the bare surface.
One of the most important issues associated with the mean-field theory on
the description of the polymer adsorption is their limitation to the description
of weakly charged polyelectrolytes. However, it does not account correctly for
strongly charged systems in which both short and long-range interactions are
involved. This can be solved successfully applying the functional density
theory, which accounts for the bond potentials, long-range electrostatic
interactions, the excluded-volume effects, and intramolecular correlations
associated with the chain connectivity [65, 66].
An alternative to the mean-field theory for explaining the adsorption of
polyelectrolyte onto solid surfaces are the descriptions based on scaling laws,