Polyelectrolytes: Theory, Properties and Applications

38 Sara Llamas, Laura Fernández-Peña, Ana Mateos-Maroto et al.

The adsorbed layer presents a thickness defined as

1

D (l fN )B



(17)

The polyelectrolyte inside the region defined by the layer thickness (z <
D) feels an attraction energy of the order of kT. The value of σ allows defining
the structure of the polymer layer, when σ assumes values around
2 1 1 3/ 2
def a u f N
    the polymer chains lay flat onto the surface. The

increase of σ beyond σdef pushes the system to a condition in which the
electrostatic attraction polyelectrolyte – surface deforms the adsorbed layer.
Therefore, the layer thickness can be considered the consequence of an
intricate balance between the contribution associated with the confinement
entropy and the electrostatic attraction. This balance is the responsible of the
equilibrium thickness

2/3 1/3 1/3 1/3

D a lB f

  

(18)

It is also worth considering in the comprehensive description of the
adsorption of polyelectrolytes, the role of the anisotropic shape of the chains
on the adsorption that can induce an order transition in the adsorbed layer

when def a u ^2 14/13f13/15N7/5. However, this transition does not lead to

any change on the layer thickness. Further increases of the charge density,
2 2/3 1/ 2 1
L a u f N
   , leads to a crossover between dilute to semidilute

adsorbed layers. This transition does not modify the dependence of the
thickness on the charge density. Therefore, the adsorbed layers present a
quasi-2D layered structure. The increase of the charge density drives the
system to formation of isotropic 2D layers

e

2

D fa

 

(19)

When the formation of isotropic 2D layers occurs, it is possible to
consider that the energy of the chains, the electrostatic attraction to the surface,
and the confinement energy assume similar values. Further increases of the
charge density,     def ion, lead to a situation in which the density profile

of the adsorbed layers is determined by a complex balance between the