We use a self-consistent mean-field (SCF) theory to determine the behavior of grafted polyacids.In these systems, the charge on a brush segment depends on its local environment and on the pH of the solution. The scaling dependence of the brush height on salt concentration is significantly different from that for a brush with constant charge density. In the latter case, the thickness is a continuously decreasing function of " whereas for a brush of weak polyacids the thickness passes through a maximum. The numerical SCF results show qualitative agreement with predictions obtained from a simple scaling model based upon a block profile with a uniform degree of dissociation.

We present numerical results from a self-consistent (meanbfield (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 per anchored chain, the average distance m between neighboring charges on the chains, and the salt concentration +#. At high anchoring densities, three different regimes of brush behavior may be 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 (quasineutral 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 vel -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 -N3 r1 m2. 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.

We use numerical self-consistent field (SCF) calculations to determine the interfacial behavior of AB diblocks in a blend of immiscible homopolymers, A and B. In particular, we compare the compatibilizing effect of relatively short and long AB copolymers. In the calculations, we explicitly take into account the formation of micellar or multilamellar phases. The results show that the interfacial tension can be reduced to zero only if the blocks in the diblock are longer than the corresponding homopolymer. Our two-dimensional SCF calculations reveal that short diblocks form multilamellar structures in the blend, whereas a microemulsion is formed when relatively long copolymers are added to the A/B mixture. These observations are compared with experiments on blends of polystyrene (PS), polymethyl methacrylate (PMMA), and PS-PMMA symmetric diblock copolymers. By measuring the contact angle of PS droplets on the PMMA layer, we can obtain a direct estimate for the interfacial tension at the PS/PMMA interface. The experiments also reveal that negligible interfacial tensions and emulsionlike structures are only obtained with relatively long diblocks.

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