12 F. Benmouna, R. Kaci and M. Benmouna
3.2. Mismatch of the Block Copolymer–Solvent Interactions
The thermodynamic symmetry between blocks A and B is broken when
the solvent exhibits a preferential affinity for one of the DCP parts, say block
A. The consequences of this mismatch are evaluated by considering the plots
of Saa(q) vs qR^22 g inferred from the neutral limit of Eq. 5 and x = 1/2
2
1
as bs ab
11
aa as 1
bs1
1 2 1(^112)
1
Sq
S S q
Sq
, (14)
where S(q) and S’(q) are defined as
1 1/ 2 1 T (^1)
2
;
P q P q
S q S q S q
N P q N P q
. (15)
The symmetry breaking concomitant to the indicated preferential affinity
preserves the qualitative features of the interplay between micro and macro
phase separation, but leads to more elaborate formulae involving three -
parameters. The fact that ab governs the micro structured phase with a
characteristic length qm^1 while as and bs control the macrophase behavior at
q = 0 remains valid. Unlike the previous case, however decoupling of
composition (micro) and concentration (macro) fluctuations observed in the
symmetric case (ps = as = bs) ceases and mismatch of solvent interactions
with A and B monomers introduces substantial changes to the conditions of
phase separation. Figure 4 shows the variations of qRmg^22 (panel a) and Saa(qm)
(panel b) against ab fixing as and changing bs. Panel c of this figure gives
some examples of how the scattering envelop Saa(q) versus qR^22 g changes with
ab and how the peak diverges when approaching the conditions of micro
phase separation. The peak position qm changes slightly with ab in a way
dependent on the value of bs. For low bs, qm decreases smoothly with ab and
the corresponding intensity Saa(qm) diverges at a relatively low ab. For high
bs, qm increases and the conditions of microphase separation are reached at a
much high value of ab. It is interesting to note that when bs increases, a
stronger inter block incompatibility is required for the microphase separation
to take place.