Interaction between two polyelectrolyte brushes

We report molecular dynamics simulations on completely charged polyelectrolyte brushes grafted to two parallel surfaces. The pressure Π is evaluated as a function of separation D between the two grafting planes. For decreasing separation, Π shows several regimes distinguished by their scaling with D which reflects the different physical nature of the various regimes. At weak compression the pressure obeys the 1/D power law predicted by scaling theory of an ideal gas of counterions in the osmotic brush regime. In addition we find that the brushes shrink as they approach each other trying to avoid interpenetration. At higher compressions where excluded volume interactions become important, we obtain scaling exponents between -2 at small grafting density ρa and -3 at large ρa. This behavior indicates a transition from a brush under good solvent condition to the melt regime with increasing grafting density.