CHARGED POLYMERIC BRUSHES - STRUCTURE AND SCALING RELATIONS

We present numerical results from a self-consistent (mean)-field (SCF) model for the structure and scaling behavior of charged brushes and compare these with predictions of an analytical SCF model on the same system. The parameters we consider in this study are the chain length N, the average surface area sigma per anchored chain, the average distance m between neighboring charges on the chains, and the salt concentration phi(s). At high anchoring densities, three different regimes of brush behavior maybe distinguished. In the salt-free case, the behavior of the brush is dominated either by electrostatic interactions at high charge densities (osmotic brush) or by nonelectrostatic excluded-volume interactions at low charge densities (quasi-neutral brush). Upon adding salt in the solution, a third regime can be found (salted brush). The behavior in this regime, although resulting from electrostatic interactions, is very similar to that in a neutral brush and can effectively be described using an electrostatic excluded-volume parameter upsilon(el) approximately phi(s)-1 m-2. We find excellent agreement regarding structure as well as scaling relations between the two theories in these three (high anchoring density) regimes. At extremely low anchoring densities, agreement between the two theories is less good. This is due to the breakdown at low densities of the mean-field approximation presently used in the numerical model. In between, at intermediate anchoring density the analytical theory predicts a very peculiar regime, where the thickness H scales as H approximately N3 sigma-1 m-2. This so-called ''Pincus brush'', named after the author who originally described it, is not recovered with the numerical theory. For the wide range of parameters used, we find the Pincus regime is too small to be detected. This is probably true for any reasonable set of parameters.