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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.

Off-lattice molecular dynamics simulations are carried out to study fully charged polyelectrolyte brushes with salt, and a comparison with an off-lattice self-consistent field (SCF) theory including finite stretching and volume effects [Biesheuvel et al. Macromolecules 2008, 41, 6254] is presented. The SCF approach is able to reproduce the brush heights at different grafting densities, salt concentrations, and chain lengths on a semiquantitative level. At high grafting densities, the density profiles obtained with both techniques exhibit a particularly close agreement, while at low densities systematic deviations between their shapes are observed. The approximation of local electroneutrality, which the SCF approach is based on, is studied, and its implications are discussed. In this context, the strengths and limitations of the SCF model are analyzed in detail.

Off-lattice MD-simulations of polyelectrolyte brushes in good solvent are compared with various different mean-field theories. We demonstrate the importance of excluded volume effects under the present solvent conditions, which had intentionally been left out in some of the classical mean-field approaches of Pincus or Zhuina et al. We evaluate the accuracy of the Debye-approximation in the simulations and of a recently introduced self-consistent-field theory by Biesheuvel et al. Finally, we discuss the significance of finite extensibility of the chains that is of particular importance for charged systems.

The static and dynamic properties of a system of end-grafted flexible ring polymer chains grafted to a flat substrate and exposed to a good solvent are studied by using a molecular dynamics method. The monomers are described by a coarse-grained bead-spring model. Varying the grafting density ρ and the degree of polymerization or chain length N, we obtain the density profiles of monomers, study the structural properties of the chain (radius of gyration, bond orientational parameters, etc.), and also present the dynamic characteristics such as chain energy and bond force. Compared with a linear polymer brush, the ring polymer brush exhibits different static and dynamic properties for moderate or short chain length, while it behaves like linear polymer brush in the regime of long chain length.