## Computation of the Hydrodynamic Radius of Charged Nanoparticles from Nonequilibrium Molecular Dynamics

We have used nonequilibrium molecular dynamics to simulate the flow of water molecules around a charged nanoparticle described at the atomic scale. These nonequilibrium simulations allowed us to compute the friction coefficient of the nanoparticle and then to deduce its hydrodynamic radius. We have compared two different strategies to thermostat the simulation box, since the low symmetry of the flow field renders the control of temperature non trivial. We show that both lead to an adequate control of the temperature of the system. To deduce the hydrodynamic radius of the nanoparticle we have employed a partial thermostat, which exploits the cylindrical symmetry of the flow field. Thereby, only a part of the simulation box far from the nanoparticle is thermostated. We have taken into account the finite concentration of the nanoparticle when calculating the friction force acting on it. We have focused on the case of polyoxometalate ions, which are inorganic charged nanoparticles. It appears that, for a given structure of the nanoparticle at the atomic level, the hydrodynamic radius significantly increases with the nanoparticles charge, a phenomenon that had not been quantified so far using molecular dynamics. The presence of an added salt only slightly modifies the hydrodynamic radius.