Polyelectrolytes: Theory, Properties and Applications

Adsorption of Polyelectrolytes onto Charged Surfaces 37

inert salt, the polyelectrolyte presents a rod-like conformation formed by N/ge
electrostatic blob, with ge being the number of monomer in a blob

1/ 3 2 / 3

L elN / geau f N (13)

where u = lB/a. The electrostatic energy of the polyelectrolyte chains for the
surface Wpe can be assumed to be one time kT for each electrostatic blob in the
chain, being k the Boltzman constant

2 4 / 3

WpekTu f N (14)

It is important to consider that the adsorption requires the replacement of
the counterions onto the charged surface by the monomers. The counterion
layer presents a thickness defined by λ which can be considered larger than
the average distance between polyions RlB1/3 2/3 in the limit of surface

charge density lower than WC l f NB  ^233. These conditions allow applying

the classical Poisson-Boltzmann approach. In addition to the attractive
component, the role of the average repulsion between neighbors, Wrep, must be
also considered

22 2/3

rep B

WC

W kTl f N kT

R





(15)

The increase of the charge density until the limit σ > σWC leads to a
situation in which the distance between the polyions becomes longer that the
average distance polyion-surface. Therefore, the repulsive component
becomes larger than kT. This situation induces the appearance of ordering of
the polyelectrolyte chains onto the surface leading to the formation of a highly
correlated Wigner liquid [74]. This allows defining the energy of a polyion by

the electroneutrality condition R^2 fN. Therefore, the polyelectrolyte chains
at a distance z of the surface are attracted in such a way that can be considered
analogous to that expected for the attraction of a charged disk with a radius R
and a charge defined by fN,

 

1/ 2

W (z)att kT WC 1 zR

   

 (16)