We have developed an analytical self-consistent-field (SCF) theory describing conformations of weakly charged polyelectrolyte chains tethered to the solid−liquid interface and immersed in a solution of low molecular weight salt. Depending on the density of grafting of the polyelectrolytes to the interface and on the salt concentration we distinguish three main asymptotic regimes of behavior of the grafted layer. These regimes are characterized by (i) unscreened Coulomb repulsion between polyions, (ii) screening of the interchain interactions predominantly by counterions, or (iii) screening ensured by co-ions and counterions of the salt, respectively. We have demonstrated that all the structural and thermodynamic properties of the brush are determined by two dimensionless parameters, i.e., the bare Gouy−Chapman length normalized by the characteristic brush thickness and the bulk Debye screening length, respectively. The theory describes contraction of the brush as a whole and its internal structural rearrangements with increasing salt concentration. In particular, we consider variation of the polymer density profile and distributions of the end segments and small ions with increasing salt concentration. The maximum sensitivity of the brush to the addition of salt is predicted in the intermediate range of grafting density while dense and sparse brushes are less affected by added salt.
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.
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.
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