Polyelectrolytes: Theory, Properties and Applications

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

where

0 0 0

(^1) abm (^1) am (^1) bm
m am bm
0m 0m 0m
; ;
S S S
S S S
S S S
     
  

. (18)

The subscript m means that the concerned quantities are calculated at the
peak position qm. For x = 1/2, Eq. 18 becomes

-1 -1 1/ 2m (^1) Tm 1/ 2m
am bm m
mm
2
;
P P P
S S S
N P N P
    
   

. (19)

Figure 7. Symmetric partially charged DCPs : effects of f and salt on the critical
parameter for microphase separation. c vs f for different values of salt. Here we
used x = 1/2,  = 0.3, N = 100, as = 0, bs = 0.5, ab = 0.15.

Figure 7 shows the variations of the critical parameter c versus f for
different values of salt. As the ionic strength increases, electrostatic
interactions are screened out and c decreases substantially tending to its
neutral limit seen at the intercept with the y-axis for f = 0. There is a factor
exceeding thirty between c (f = 0) and c (f = 0.3) at salt = 0. It is worth
noting that both counter ions due to the monomer ionization and added salt
contribute to the screening but the latter dominates if salt exceeds f/2 which,
for f = 0.1 and  = 0.2, is 0.01. Even for a low degree of ionization, the impact
of charges on the critical parameter is high and the ionic enhanced stability is
significant. In the absence of salt, it was found in [28] that c increases linearly

0.0 0.1 0.2 0.3

0.1

0.2

0.3

0.4

0.5

Benmouna et al. Figure 7

salt = 0

0.2

0.1



c

f

0.05

0.02