Translational and rotational diffusion of model nanocolloidal dispersions by molecular dynamics simulations

Abstract

Molecular dynamics, MD simulations have been applied to model nanocolloids in solution at infinite dilution. Simulations were carried out with atomistically rough clusters of atoms with variable dimensions compared to the solvent molecule, using the Weeks–Chandler–Andersen (WCA) interaction between solute and solvent. Nanocolloidal particles containing between 20 and 256 atoms held together with strong Lennard-Jones interactions and with up to eight times the diameter of the solvent molecule were modelled. At liquid-like densities the translational and rotational self-diffusion coefficients for the nanocolloids of all sizes were statistically independent of the ratio of solute to solvent particle densities. The clusters induced a ‘layering’ of solvent molecules around them. The translational and rotational diffusion coefficients decreased with increasing cluster size and solvent density. The simulations reveal that there is a clear separation of timescales between angular velocity and orientation relaxation, consistent with the classical small-step diffusion picture encapsulated in Hubbard's relationship which is obeyed well by the simulation data. Application of the Stokes–Einstein (translation) and Stokes–Einstein–Debye (rotation) equations to these data indicate that the translational degrees of freedom experience a local viscosity in excess of the bulk value, whereas rotational relaxation generally experiences a smaller viscosity than the bulk, dependent on cluster size and solvent density and reasonably in accord with the Gierer–Wirtz model. Both of these observations are consistent with the observed layering of the solvent molecules around the cluster, whose effects appear to be significant for clusters on the nanoscale.