36 Sara Llamas, Laura Fernández-Peña, Ana Mateos-Maroto et al.
Borukhov et al. [59] proposed that a correct description of the polyelectrolyte
adsorption onto solid surfaces requires considering different length scales.
These lengths are the Edward correlation length, the Debye-Hückel screening
one, and an additional one associated with the electrostatic and/or short-range
interactions. The theoretical predictions of the model proposed by Borukhov et
al. [59] showed good agreement with both experimental results and mean-field
calculations [67-70]. The aforementioned length scales are strongly dependent
on the specific nature of the polyelectrolyte considered and the ionic strength.
The model by Borukhov et al. [59] predicts that both thickness D and surface
concentration Γ scales with p-1/2, being p the charge density of the polymer for
highly charged polymer under low ionic strength conditions. On the side, an
increase of the ionic strength leads to new scaling laws for D and Γ
1/ 2D cb
p
(10)
1/ 2
bp
c
(11)
with cb being the salt concentration. Equation (11) describes the surface
concentration for weak polyelectrolytes, being for the case of highly charged
one defines as
1/ 2cb
p (12)
Dobrynin and Rubinstein [71-73] developed another theory that provides a
framework overcoming the limitations associated with the mean-field
approaches. This latter does not capture correctly the real structure of the
polyelectrolyte layers which in most cases presents a structure of a highly
correlated Wigner liquid [74-76]. Therefore, a complete description of the
adsorption requires considering the role of the electrostatic correlations on the
process [76]. The theory developed by Dobrynin and Rubinsteins [71-73]
considers polymer chains with a monomer number defined by N, and only a
fraction f of these monomers corresponds to charged monomers. The
monomer size is defined by a. The interaction between the charges along the
chains can be described by an unscreened Coulomb potential. In absence of