42 Sara Llamas, Laura Fernández-Peña, Ana Mateos-Maroto et al.
proposed by Dobrynin and Rubinstein [71-73]. However, this model is not
able to describe those phenomena occurring under conditions in which the
charge density is highly screened due to the important role of the non-
electrostatic interaction and the lacked irreversibility of the adsorption process
[54].
There are other models describing, at least partially, many issues
associated with the adsorption of polyelectrolytes onto solid surfaces. These
model are based in different assumptions [55, 56]. However, a comprehensive
description is difficult. In addition to the different theoretical models
developed, different simulation methodologies have provided important
insights in different issues of the polymer adsorption onto solid surface [81-
83]. Linse [84] using mean-field lattice calculations obtained a description of
the adsorption of weak polyelectrolytes onto charged surfaces with opposite
charge. Their results showed the appearance of different factor governing the
adsorption process including, independently of the adsorption conditions: the
size and concentration of the polymers, charge density of both polymer chains
and surfaces, and the non-electrostatic contributions to the adsorption.
Molecular dynamic simulations have been also used for describing the
adsorption of polyelectrolytes onto charged surfaces [85]. For this purpose, a
Lennard-Jones potential is used to describe the interactions occurring between
the different components involved in the system. The molecular dynamic
simulations have allowed predicting that the adsorbed amount increases with
the charge density for most of the systems. Additionally, the simulations
predict a monotonical dependence of the thickness on the surface charge
density and the important role of the hydrophilic/hydrophobic character of
both surfaces and polyelectrolyte on the control of the adsorption processes.
The surface coverage and the degree of overcharging occurring during the
adsorption have been found extraordinary dependent on the short range
interactions. This agrees with the results obtained by Wang et al. [86]
combining Monte Carlo and Density Functional Theory simulations.
The charge reversal upon the adsorption of polyelectrolyte onto solid
surfaces was also found by Narambuena et al. [87] Furthermore, they pointed
out the important role of the entropy gain associated with the counterions
release occurring during the adsorption on the control of the process. Coarse-
grained models have shown that the bulk conformation remains arrested in the
polyelectrolyte layer [88].
An additional way to model theoretically polyelectrolyte adsorption is by
use of the adsorption isotherms which can be easily generalized in the
following expression [89]: