Self-diffusion coefficients and shear viscosity of model nanocolloidal dispersions by molecular dynamics simulation

Abstract

The self-diffusion coefficients $D$ of both species in model nanocolloidal dispersions have been computed using molecular dynamics (MD) simulation, in which three-dimensional model spherical colloidal particles were in a molecularly discrete solvent. The effects of the relative density, size, and concentration of the two species were explored. Simulations were carried out at infinite dilution (a single colloidal particle) and at finite packing fractions (many colloidal particles) in the simulation cell using single interaction centers between the model colloidal particles and solvent molecules. The calculations used the Weeks-Chandler-Andersen (WCA) or Lennard-Jones (LJ), interaction potentials between all species. Nanocolloid particles with diameters up to \ensuremath{\sim}6 times the solvent molecule were modeled. At liquidlike densities the self-diffusion coefficients of the colloidal particles, ${D}_{c},$ for all sizes and packing fractions, statistically exhibited no mass dependence but a significant colloid particle size dependence. This can be interpreted in a systematic manner using a Mori series expansion. The first Mori coefficient (which is inversely proportional to particle mass) dominates the value of the self-diffusion coefficient for both species, and which also leads to a formal cancellation of the mass dependence at the order of the first Mori coefficient ${K}_{B1}$ (the self-diffusion coefficient is therefore determined by a ``static'' property to this order). The values of ${D}_{c}$ at each packing fraction are found to be approximately inversely proportional to the colloidal particle diameter, quantitatively following the same trend as the Stokes-Einstein equation, even for the small colloidal particle sizes and finite colloidal particle concentrations studied here. Another consequence of the dominance of the first Mori coefficient is that the normalized velocity autocorrelation function of the colloidal particle at a short time can be represented well at all state points and packing fractions by the analytic form $\ensuremath{\simeq}\mathrm{cos}({\ensuremath{\Omega}}_{0}t),$ where ${\ensuremath{\Omega}}_{0}=\sqrt{{K}_{B1}},$ which is the so-called Einstein frequency. LJ and WCA systems with otherwise the same system parameters manifest the same oscillation frequency, but the LJ oscillation amplitudes are larger and the values of ${D}_{c}$ are smaller. The self-diffusion coefficients and shear viscosities obey a volume fraction dependence similar to that found for much larger colloidal particles.