Polyelectrolytes: Theory, Properties and Applications

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

(z yps)

sp

3

1e

2



  

(21)

Combining the equations 20 and 21 is possible to arrive

(z yps)

p sp p salt

3

z z 1 e 0.67 sinh(y / 2)

2

    



 (22)

The total adsorption can be obtained from the sum of a contribution
associated with the charge compensation (θcc = -zs/zp with zs is the charge of
the surface) and the specific contribution θsp. Therefore, the use of this model
provides information related to the total adsorption as a function of the charge
density of the surface and the salt concentration.
The Random Sequential Adsorption (RSA) model has been also used for
describing the irreversible adsorption of polyelectrolytes and other materials
(colloids or proteins) onto solid surfaces [54, 78]. This model considers that
the polyelectrolyte presents a disk-like shape and their adsorption onto the
solid surfaces occurs following a random pattern. This model assumes that the
adsorption can only occur onto the free positions of the surface, being the
overlapping between disks completely forbidden. Considering these issues, the
maximum coverage (θ) is given by the so-called jammimg threshold jam [78]

jam 0.55 (23)

jam is always smaller than the maximum coverage that can be expected for

traditional hexanol packing (θ ≈ 0.91). The RSA model provide a relationship
between the adsorbed density and the coverage defined as follows

   Rd (24)

with Rd being the disk radius that can be assumed to be similar to thegyration
radius of the polyelectrolyte chains. The bare expressions for the RSA model
can be easily modified to introduce the electrostatic contribution to the
adsorption [79]. The repulsion between the polymers chains is expected to
increase the area occupied by a single polyelectrolyte chain. Thus, it is