Polyelectrolytes: Theory, Properties and Applications

24 F. Benmouna, R. Kaci and M. Benmouna

Minimization of the free energy with respect to the aggregation number
yields

ab

4

h

2 1/3

ag

Nc

NN

N







(25)

It is worthnoting that when Nag increases, counterions tend to be trapped
inside the corona tending to an osmotic regime characteristic of strongly
charged micelles. But at a certain stage, counterions inside the corona start to
oppose further micelle’s growth.

5.3. Strongly Charged Micelles

Figure 12b describes the case of strongly charged micelles where counter
ions are confined inside the stretched corona. The osmotic pressure of trapped
counter ions and the electrostatic repulsion between A-monomers determine
the micelle stability and the equilibrium aggregation number [28, 34, 35]

b

a

2

ag 3

N

N

N

. (26)

The aggregation number depends more on the size of charged blocks Na
than on that of the neutral blocks Nb.
In this section, we have briefly sketched the scaling behavior of micelles
limiting our discussions to mc and Nag and the relevant parameters Na, Nb and
Nch. For more details on these aspects, the reader is referred to the original
work cited for example in refs [28, 33 - 36 ].

DISCUSSIONS AND CONCLUSION

One the main points in this chapter is to show that the RPA provides
a reasonable framework for modeling the structural properties and
phase behavior of dispersed partially charged DCPs in solution. It gives a
clear consistent description of all the relevant parameters governing both