Charged Polymer Brushes: Counterion Incorporation and Scaling Relations

Amphiphilic block copolymers consisting of a fluid hydrophobic and a polyelectrolyte part form monolayers at the air/water interface. With x-ray reflectivity it is shown that the hydrophobic block is a nm-thick melt, while the polyelectrolyte forms an osmotically swollen brush of constant thickness, independent of grafting density and with stochiometric counter ion incorporation. Only at high salt conditions (above 0.1 M), the brush shrinks and the thickness scales with the molecular area and the salt concentration (corrected for excluded volume interactions) with an exponent $-1/3\mathrm{}$.