Polyelectrolytes: Theory, Properties and Applications

Structural Properties and Phase Behavior ... 23

2 (2 1)

ag b a

N  N N6/v v , (23)

which exhibits a stronger dependency on Na compared to Nb.

5.2. Weakly Charged Micelles

The scaling behavior for charged micelles depends on the degree of
ionization. For weakly charged micelles, small ions are distributed freely
outside the corona (see Figure 12a while for strongly charged micelles, counter
ions accumulate inside the stretched corona creating an osmotic regime as
shown in Figure 12b.
In the micelle formation, the balance between the surface energy of the
collapsed B-core and the energy of the stretched A-corona plays a crucial role.
If the core contribution to the free energy dominates, the cmc is essentially
determined by the parameters of the neutral system while for a dominant
contribution coming from the stretched corona, the cmc depends on the
number of charges Nch as

4/3 1/3

ln cmc NNch a

   . (24)

Figure 12. Schematic representation of a) weakly charged micelles where counterions
are free outside the corona, b) strongly charged micelles where counter ions are
confined inside the corona (osmotic regime).