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.

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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.

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The two-gradient version of the Scheutjens−Fleer self-consistent-field (SF-SCF) approach is employed for the analysis of the average conformations of side chains and corresponding contribution to the bending rigidity, or equivalently the induced persistence length, of molecular bottle brushes both under good and theta solvent conditions. This study is targeted to unravel conformational properties of poly(l-lysine)-graft-poly(ethylene glycol) copolymers in dilute aqueous solutions, where variation of temperature changes the solvent strength for poly(ethylene glycol) in a wide range. We focus on molecular brushes with moderate and high grafting density and large degree of polymerization of grafted chains. In this limit the predictions of an analytical mean-field theory for the dependences of the structural properties of the bottle brush on the architectural parameters are well confirmed. Both the induced persistence length and the ratio between the induced persistence length and the cross-sectional thickness of the bottle brush increase with increasing grafting density and/or increasing degree of polymerization of the grafted chains. However, in the range of moderate chain lengths and grafting densities this ratio remains small, which explains why the effects of the induced bending rigidity on the apparent persistence length have not been observed in earlier numerical experiments. We argue that only molecular bottle brushes with densely grafted long chains possess the potential for lyotropic ordering, both in solutions and at interfaces, due to the expected high effective segment asymmetry.

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The structure of a brush made of arm-grafted polymer stars is investigated using the Scheutjens–Fleer self-consistent field method. By using the “probe macromolecule” approach, conditional distributions of end- and branching points were obtained, which allowed for a detailed analysis of intramolecular correlations in the brush. Results strongly support a previously suggested “two population” picture of the star structure: stars in the brush are divided into two populations (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended toward the solvent. The stars in the “stretched” population have no arms that fold back toward the grafting surface and their free arms form a new sub-brush with effective grafting density determined solely by the total surface loading: molecular mass of polymer grafted onto unit area. With increasing grafting density or/and number of star arms the fraction of stars in the “stretched” population grows. The degree of backfolding of arms is estimated, the total fraction of backfolded arms is invariably small and decreases with increasing grafting density; only stars of the weakly extended population contribute to backfolding. The free ends within a given star are correlated: the ends of different arms are located approximately at the same distance from the grafting plane. Comparison of conditional ends distributions at fixed position of the branching points at different grafting densities reveals a conformational universality of grafted stars belonging to the weakly stretched population: the shape of the ends distribution does not depend on the grafting density but is determined solely by the position of the branching point. We also present analytical arguments showing that this effect is due to universal parabolic self-consistent potential acting on monomer units in the star brush, this potential is independent of the grafting density and the number of star arms.