4 F. Benmouna, R. Kaci and M. Benmouna
charged DCPs in solution is presented. In section 3, symmetric diblocks are
considered to examine first the conditions of decoupling of concentration and
composition fluctuations and the interplay between macro and microphase
transitions. Then, the mismatch of monomer/solvent interactions and
preferential miscibility towards block A are examined in details. The effects of
long range electrostatic interactions for partially charged symmetric DCPs are
examined in terms of the degree of ionization and ionic strength. Further
polyelectrolyte effects are considered in section 4 for non symmetric diblocks.
In section 5, we present a brief account for the micelle formation focusing on
the critical micelle concentration (cmc) and the aggregation number. Scaling
arguments from the literature are invoked to distinguish between star like and
crew cut configurations, weakly and strongly charged DCPs. Section 6
presents some discussions and concluding remarks.
2. THE RANDOM PHASE APPROXIMATION FOR DISPERSED
PARTIALLY CHARGED DIBLOCK COPOLYMERS IN
SOLUTION
As mentioned above, studies of partially charged DCPs in solution are
rather scarce especially for dispersed chains despite their interesting structural
properties and phase behavior due to the competition between hydrophobic
and hydrophilic interactions and the long range polyelectrolyte effects. Here,
we present a theoretical formalism based on the RPA focusing on the
structural properties and the phase behavior prior to the conditions of
aggregation and micelle formation. The starting point is the generalized RPA
equation in matrix form
S^11 qS 0 q v αqf (1)where S(q) and S 0 (q) represent the structure matrices with and without
interactions, respectively; q is the amplitude of the scattering wave vector; v
and (q)f are the interaction matrices for excluded volume and long range
Coulomb interactions, respectively. The neutral limit of Eq. 1 has been derived
by Benoit et al. [22, 23] using a diagrammatic method by summing series of
terms corresponding to chain of single contacts. It can be considered as a
generalization of the celebrated Zimm’s [24, 25] formula expressed in matrix
form for an arbitrary multi component mixture. It gives the theoretical basis