Equilibrium conformations of annealed star-branched polyelectrolytes (polyacids) are calculated with a numerical self-consistent-field (SCF) model. From the calculations we obtain also the size and charge of annealed polyelectrolyte stars as a function of the number of arms, pH, and the ionic strength. The results are compared with predictions from analytical theory. Upon varying the number of branches or the ionic strength of the solution, the star size changes nonmonotonically, which is in agreement with the analytical predictions. The salt concentration at this maximum is directly related to the charge density of the star. The internal structural properties of the star corona (the polymer density, the ionization profiles, and the distribution of the end points) are analyzed. The shape of the density profiles indicates increasing local stretching of the branches as a function of the distance from the star center. Furthermore, a bimodal end-point distribution is found and interpreted in analogy to that predicted earlier by analytical SCF theory for planar polyelectrolyte brushes. Results of recent experiments with annealed star-shaped micelles are discussed on the basis of our numerical model calculations.

The theory developed by Scheutjens and Fleer to describe polymer adsorption and depletion is used to calculate the density profile of nonadsorbing polymers near a surface. The theory predicts damped oscillations in the segment density profile with a wavelength of about the coil size. As a consequence, the interaction energy between two surfaces immersed in a solution of nonadsorbing polymers is an oscillatory function of the separation distance, too. The decay length of the oscillations is proportional to the coil size and independent of the polymer concentration. The oscillations are associated with a liquid-like layering of polymer coils near the surface. An increase in concentration or chain length causes a decrease in the amplitude of the oscillations, because the stronger interpenetration of the coils suppresses inhomogeneities. In dilute solutions no oscillations are observed, because the decay length of the oscillations is smaller than the depletion correlation length, in analogy with the Fisher-Widom criterion in simple fluids. For polymer solutions it is found that the Fisher-Widom condition coincides with the overlap concentration. Our results show that the blob size is not the only relevant length scale above the overlap concentration. The size of the individual coils plays a role, too.