Water-dispersed lamellar phases of symmetric poly(styrene)-block-poly(acrylic acid) diblock copolymers: model systems for flat dense polyelectrolyte brushes.

We investigate the static properties of a water-dispersed lamellar ( L) phase formed in the melt state with a nearly symmetric poly(styrene)-block-poly(acrylic acid) (PS- b-PAA) diblock copolymer. The PAA brush is considered as a model flat polyelectrolyte ( PE) brush of controlled surface density. Thanks to small-angle X-ray scattering, its behavior in water is studied as a function of (i) its ionization, through the pH of the dispersions which is increased by an addition of a known amount of a base, i.e. sodium hydroxyde NaOH, and (ii) in the presence of a monovalent salt, i.e. sodium chloride NaCl, of concentration C(S). At low pH, we find that the brush effectively behaves as a neutral brush. At high pH, the brush is in the so-called "osmotic regime", in which all sodium counterions are trapped within the brush volume and stretch the chains via an osmotic effect. The properties of such a brush in the presence of a monovalent salt, confirm this result, showing a C(S)(-1/3) dependence in the brush height L(O), in agreement with mean-field predictions. The L(O)- C(S) profiles at different ionizations give access to the actual brush internal charge fraction f. The results are found to be in very good quantitative agreement with experimental measures found in the literature, and can be completely and quantitatively described by Oosawa's approach to counterion condensation in a semi-dilute to concentrated solution of charged, rod-like chains.