Polyelectrolyte brush at thermal equilibrium: A density functional theory approach

The long standing problem of Polyelectrolyte brushes at thermal equilibrium is approached here by using density functional theory (DFT) framework. The results confirm that by increasing the Bjerrum length of the medium, the counterions get absorbed by the brush monomers and they condensate on the monomers, the effect that is known as Manning condensation. Additionally, it turns out that by increasing the Bjerrum Length, the monomers get depleted from the surface, however, the counterions get ac- cumulated around the surface. These two effects could have potential technological applications in biotechnology etc and they show that how Polyelectrolyte brushes re- spond to the variation of the Bjerrum length as a key parameter in the charged systems. Additionally, the equation of state of the Polyelectrolyte brush is calculated for the first time and it turns out that the pressure inside a Polyelectrolyte brush scales as N^{−4} and l_B^{-2}. This finding paves the way for tackling more complex systems.