Polyelectrolyte Brushes: Debye Approximation and Mean-Field Theory

Abstract

Off-lattice computer simulations of polyelectrolyte brushes are carried out using the Debye approximation with explicit counterionsbutimplicitsalt.Theresultsarecomparedwithexplicitsalt ion simulations and self-consistent field theory. We demonstrate that the data generated with these different techniques are in excellent agreement,therebyconfirmingthevalidityoftheDebyeapproximation in the context of polyelectrolyte brushes. The efficiency of the Debye approximation is verified through benchmark computations. Further on,wedevelopanimprovedFlory-typemean-fieldmodel,basedonthe 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 excludedvolumerepulsionexplainstheobservedeffectofsaltontheswellingofthebrushundergoodsolventconditions.Thebrush 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.