Polyelectrolytes: Theory, Properties and Applications

Structural Properties and Phase Behavior ... 17

with the number of charges which is roughly the case here for f > 0.1 and
salt = 0 otherwise c shows, as expected, an f^2 dependence somewhat more
pronounced as salt increases.

4 .2. Non Symmetric Diblock Copolymers

With a composition x different from 1/2, the size symmetry of A and B
blocks is broken and the expression of Saa(q) gets a little more complicated
adding to the variety of interactions (i.e; ab, as, bs and charge parameters).
The combined effects of f and x are illustrated in Figure 8 where panels a and b

give qRmg^22 and Saa(qm) against x when f varies from 0 to 0.25 while panel c

shows Saa(q) vs qR^22 g for selected values of x. For small x (i.e; x  0.1), the

peak is rather broad and its intensity weak which means that near x = 0.1,
polyelectrolyte effects are rather weak and qm does not change much with f. As
x goes up, the peak becomes sharper and progressively gains in intensity as f
decreases. Interestingly, polyelectrolyte effects are strongest at x = 1/2 for the
height Saa(qm) but for the peak position, the difference between f = 0 and 0.25
is highest at x = 0.75. Also, note that Saa(qm) vs x exhibits a peaked structure
with enhanced broadening and shift downward as f increases (panel b). An
increase in the ionic strength generates as expected a strong screening of long
range electrostatic repulsion and trends towards the neutral DCP system.

In panels a and b of Figure 9, we give qR^22 mg and Saa(qm) against x when

salt goes from 0 to 0.25 while in panel c we show Saa(q) vs qR^22 g for selected

values of x. Adding a small amount of salt (salt = 0.1) induces a strong
screening of electrostatic interactions at all values of x. Part a shows that for
qm, the neutral limit is practically recovered at salt = 0.1. The shape of the
Saa(qm) vs x is peaked and near x  0.1, Saa(qm) is insensitive to salt while for
x  0.7, Saa(qm) increases slightly with salt. At a low fraction of charged
monomers, the peak is rather broad, its intensity low which means that near
x = 0.1, polyelectrolyte effects remain weak and qm does not change much
with salt. For 0.1 x 0.5, polyelectrolyte effects are more pronounced with
larger differences going from salt = 0 to salt = 0.25. The variation of the

critical parameter for microphase separation c with x can be inferred from

Eqs. 17 and 18.