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To help better interpret experimental measurement of nanoparticle size, it is important to understand how their diffusion depends on the physical and chemical features of surface ligands. In this study, explicit solvent molecular dynamics simulations are used to probe the effect of ligand charge and flexibility on the diffusion of small gold nanoparticles. The results suggest that despite a high bare charge (+18 e), cationic nanoparticles studied here have reduced diffusion constants compared to a hydrophobic gold nanoparticle by merely a modest amount. Increasing the ligand length by 10 CH2 units also has a limited impact on the diffusion constant. For the three particles studied here, the difference between estimated hydrodynamic radius and radius of gyration is on the order of one solvent layer (3–5 Å), confirming that the significant discrepancies found in the size of similar nanoparticles by recent transmission electron microscopy and dynamic light scattering measurements were due to aggregation under solution conditions. The limited impact of electrostatic friction on the diffusion of highly charged nanoparticles is found to be due to the strong anticorrelation between electrostatic and van der Waals forces between nanoparticle and environment, supporting the generality of recent observation for proteins by Matyushov and co-workers. Including the first shell of solvent molecules as part of the diffusing particle has a minor impact on the total force autocorrelation function but reduces the disparity in relaxation time between the total force and its electrostatic and van der Waals components.
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