Stability behavior of anionic spherical polyelectrolyte brushes in the presence of La(III) counterions

In this paper we discuss the stability behavior of spherical polyelectrolyte brushes (SPB) in the presence of trivalent lanthanum counterions. Stability behavior is measured through the rate of coagulation of the SPB as a function of the lanthanum concentration using simultaneous static and dynamic light scattering. As the counterion concentration increases, we observe coagulation of the SPB which in turn leads to a dramatic decrease in the stability of our particles. Since the rate of coagulation is dependent upon the balance between the repulsive interactions and the thermal energy of the diffusing particles (reaction-limited colloidal aggregation; RLCA), we then can relate the measured particle stability to the value of the repulsive potential in the RLCA regime. These "microsurface potential measurements" (MSPM) allow us to measure repulsive energies down to the order of kB T. From the repulsive energy of the particles we can then determine precise information about the net surface potential Ψ0 of the SPB as a function of the lanthanum counterion concentration. Moreover, we demonstrate that a simple mean-field model predicts the stability of the SPB in the presence of lanthanum counterions with high accuracy.