We present a small angle neutron scattering (SANS) study of polystyrene-b-sodium (sulfamate/carboxylate) isoprene (PS-PSCI) nanoparticles in aqueous media. The SANS experiments are complemented by static and dynamic light scattering measurements. A detailed analysis of the scattering form factor obtained by SANS for the self-assembled block polyelectrolyte spherical nanoparticles implies a two-region power-law model for the radial volume fraction profiles. The theoretically predicted scaling of the osmotic brush regime phi(r) similar to r(-2) for the inner region and the osmotic annealing brush regime phi(r) similar to r(-8/3) for the outer region are in agreement with our experimental findings. A concentrated shell of PSCI polyelectrolyte chains collapsed on the polystyrene core is needed in the form factor analysis so that the aggregation number of the nanoparticles is self-consistent. The self-assembled nanoparticles are found to be kinetically frozen i.e. their aggregation number is not sensitive to the solution conditions and is defined by the preparation protocol. The size of the spherical nanoparticles tends to decrease upon the addition of salt and the drop of pH.