Equilibrium conformations of star-branched polyelectrolytes in dilute solutions are studied on the basis of a numerical self-consistent-field (SCF) approach and analytical theories. It is shown that, even in a dilute salt-free solution, the intramolecular Coulombic repulsion in many-armed stars is strongly screened by counterions which are localized preferentially in the intrastar space. As a result, the dependence of the star size on the number of branches levels off for many-armed stars. Addition of salt results in additional screening and in contraction of the stars. The scaling prediction R ∼ c s -1/5 for the star size as a function of the salt concentration c s is well confirmed by SCF calculations. A decrease in the star size can also be induced by an increase in the concentration of the polyelectrolyte in the solution. We have observed significant contraction of the stars with increasing concentration below the overlap threshold, i.e. in dilute solutions. The latter effect is more pronounced for stars with a small number of branches. The screening of the intramolecular Coulombic repulsion due to added salt is compared with that occurring upon increasing the concentration of the polyelectrolyte.

Both an asymptotic analytical analysis for chain length N → ∞ and exact numerical calculations for finite chain lengths were applied to the structural properties of polyelectrolyte brushes under poor solvent conditions in a self-consistent field framework. We extend previous work on polyelectrolyte brushes and find evidence for a structural phase transition caused by internal phase separation in the polyelectrolyte brush upon a decrease of the solvent quality. In the limit of long chains, when a local electroneutrality approximation is exact, we find that the transition in the brush is continuous and tends to be second order. In the numerical calculations which employ the full Poisson−Boltzmann equation, a parameter window is found in which the structural phase transition is first-order. This is proven by the existence of a hysteresis loop in various properties of the brush, such as the degree of dissociation, the average height, the electrostatic potential profile, and the overall and end segment−density profiles. Apart from this difference as to the order of the transition, we find extremely good correspondence between the numerical calculations and the analytical asymptotic analysis for long polymer chains. The structure of the internally phase-separated layer is characterized by a condensed phase near the surface, a dilute swollen layer extending far into solution, and a thin interface between the two regions.

Using the numerical model of Scheutjens and Fleer we investigated, on a self-consistent field level, the equilibrium structure of the neurofilament brush formed by the projection domains of NF-H, NF-M, and NF-L proteins. Although the actual amino-acid sequences in the projection domains are coarse-grained, the different (realistic) solubilities of amino-acid residues and the specific distribution of its intrinsic charges inside the arms of the NF proteins are taken explicitly into account. We collect strong evidence that the electrostatic interactions are a dominant force that controls the NF brush structure. There exists a remarkable spatial separation of the H, M, and L tails. In a dephosphorylated NF we found confined and flowerlike conformations for the H and M projection domains, respectively. We demonstrate that the ionization of KSP repeats in NF proteins triggers a conformational transition in the H tail that leads to the expulsion of its terminal (KEP) domain to the periphery of the NF brush. We argue that the phosphorylation of the NF proteins in axons can both increase the interfilament distance and stabilize cross bridges between neurofilaments.

A self-consistent-field model is developed which enables the calculation of the interaction potential between two polymer-coated mesoscopic particles. We use a cylindrical coordinate system, in which the polymer density profile can vary in both the radial and axial direction. Data are presented for the free energy of interaction for two particles with end-attached polymer chains in a good (athermal) solvent. The repulsion is considerably weaker than predicted by converting the pair potential between flat plates to that between spheres, using Derjaguin's approximation. This is explained by the greater freedom of the polymer chains to move laterally out of the widening gap between the particles as compared to polymer chains between flat surfaces.

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