Polyelectrolytes: Theory, Properties and Applications

Adsorption of Polyelectrolytes onto Charged Surfaces 41

necessary to define an effective disk radius, Reffd , to account for the effects

associated with the repulsions. This allows describing the coverage as,

2

d

jam eff

d

R

R



   

 (25)

The effective radius is related to the effective interaction between
neighbor chains that must be considered similar to the thermal energy. Thus, it
is possible to estimate the effective disk radius by

u 2R effd kT

(26)

where u(r) defines the interaction potential between two chains with a distance
between their centers defined by r. The simplest way to describe the
interaction between charged spheres in solution is the use of a screened
Coulombic potential [79]



2 Rd^2 r

B eff

d

ee

u r kTl Z

1 R r

 

 



(27)

with Zeff defined as the effective charge. When highly charged objects are
considered the value of Zeff can be considered a constant assuming a value
defined as [80]

eff d d 

B

R

Z 4 R 6

l

  

(28)

The RSA model provides a good qualitative explanation for several
phenomena associated with the polyelectrolyte adsorption, among them the
increase of the adsorbed mass with the decrease of the polyelectrolyte charge

density. This can be considered the consequence of the decrease of the Reffd as

the effective charge of the polymer increases with the consequent increase of
the adsorbed mass [79, 80]. The RSA model including the electrostatic
contributions provides similar results than the Wigner regime of the model