Surface potential of spherical polyelectrolyte brushes in the presence of trivalent counterions

We consider the ζ-potential and the effective charge of spherical polyelectrolyte brushes (SPBs) in aqueous solution in the presence of trivalent europium ions. The SPB consists of a polystyrene core of ca. 250 nm diameter onto which long chains of the strong polyelectrolyte poly(styrene sulfonate) are grafted (contour length: 82 nm). At low concentration of EuCl₃ the chains are stretched to nearly full length. If the concentration of the trivalent ions is raised, the surface layer of the polyelectrolyte chains collapses. The ζ-potential of the SPB is calculated from the electrophoretic mobilities measured at different concentrations of EuCl₃. At the collapse, ζ decreases by the partial neutralization of the charges by the trivalent ions. The experimental ζ-potential thus obtained agrees with the theoretical surface potential Ψ_theo calculated for the effective shear plane by a variational free energy model of the SPB.