  In this paper we perform molecular dynamics simulations of a spherical
polyelectrolyte brush and counterions in a salt-free medium. The dielectric
discontinuity on the grafted nanoparticle surface is taken into account by the
method of image charges. Properties of the polyelectrolyte brush are obtained
for different parameters, including valency of the counterions, radius of the
nanoparticle, and the brush total charge. The monovalent counterions density
profiles are obtained and compared with a simple mean-field theoretical
approach. The theory allows us to obtain osmotic properties of the system.
