Polyelectrolyte brush bilayer at thermal equilibrium: A density functional theory approach

By means of the density functional theory framework, the long-standing problem of a Polyelectrolyte brush bilayer at thermal equilibrium is studied. The density profiles of top and bottom brushes plus the counterions are calculated analytically. Additionally, the electrostatic potential is obtained as a function of the system parameters. Based on the results, it turns out that by varying the Bjerrum length, the distribution of the particles drastically is changed. The counterions are condensed on the monomers and the Manning condensation takes place. Interestingly, at high Bjerrum lengths two sharp electrostatic potential peaks loom in the vicinity of the brush covered surfaces. Additionally, it is revealed that there is a critical Bjerrum length in which the equation of state of the system is changed. The critical Bjerrum length is calculated analytically and it scales as N^{−3}.