Polyelectrolyte Brushes: Debye Approximation and Mean-Field Theory

Oft-lattice computer simulations of polyelectrolyte brushes are carried out using the Debye approximation with explicit counterions but implicit salt. The results are compared with explicit salt ion simulations and self-consistent field theory. We demonstrate that the data generated with these different techniques are in excellent agreement, thereby confirming the validity of the Debye approximation in the context of polyelectrolyte brushes. The efficiency of the Debye approximation is verified through benchmark computations. Further on, we develop an improved Flory-type mean-field model, based on the original argument by Pincus, but taking into account both the excluded volume and finite extensibility of chains. On the basis of this model, we demonstrate how the interplay of counterion pressure and excluded volume repulsion explains the observed effect of salt on the swelling of the brush under good solvent conditions. The brush height as a function of grafting density is investigated, and it is argued that the resulting power law scaling of -1/3 is incapable of distinguishing between excluded volume and electrostatic effects.