A new class of conductive composite materials, solvent-free ionically grafted nanoparticles, were modeled by coarse-grained molecular dynamics methods. The grafted oligomeric counterions were observed to migrate between different cores, contributing to the unique properties of the materials. We investigated the dynamics by analyzing the dependence on temperature and structural parameters of the transport properties (self-diffusion coefficients, viscosities and conductivities) and counterion migration kinetics. Temperature dependence of all properties follows the Arrhenius equation, but chain length and grafting density have distinct effects on different properties. In particular, structural effects on the diffusion coefficients are described by the Rouse model and the theory of nanoparticles diffusing in polymer solutions, viscosities are strongly influenced by clustering of cores, and conductivities are dominated by the motions of oligomeric counterions. We analyzed the migration kinetics of oligomeric counterions in a manner analogous to unimer exchange between micellar aggregates. The counterion migrations follow the “double-core” mechanism and are kinetically controlled by neighboring-core collisions.