(34b) Molecular Dynamic Study of Hydrodyanmic Drag and Diffusion for Nanoparticles at Liquid Vapour Interface

Particle tracking experiments on the mean square displacement of micron-sized, spherical, Brownian colloids diffusing at an air/water interface indicate that the colloidâ??s translational drag coefficient is greater, by a factor of two or more, than the value obtained by a continuum (Stokes flow) calculation on a flat surface. To rationalize this difference, additional dissipative forces arising from the pinning of the contact line at the colloid surface as it moves have been suggested. A further complication is the fact that measurements in which a non-Brownian deterministic force (e.g. a magnetic or capillary attraction force) acts on the particle, and the drag is calculated from the resulting velocity, are in agreement with the Stokes simulations.

To provide insight, we undertake molecular dynamic simulations of a colloid diffusing along a solvent interface based on generic Lennard-Jones interactions. The colloid is a section of a rigid atomic lattice to create a rough surface and allow contact line pinning. The solvent is a tetramer chain molecule which has a relatively sharp vapor/liquid interface. By varying the interaction strength between the solvent and colloid atoms, different equilibrium immersion depths are achieved corresponding to conditions between complete wetting (strong interaction) and non-wetting (weak interaction). We calculate the drag coefficient of a colloid calculated from its mean square displacement due to Brownian diffusion, and for a colloid dragged along the interface at constant velocity. We find that the MD calculated drag coefficients for each method are within 10 percent of each other. The drag coefficients monotonically increase with increasing depth of immersion. While in qualitative agreement with Stokes flow simulations of the drag, the MDcalculated coefficients are, for each immersion depth, smaller than the continuum calculations. We attribute the discrepancy to the fact that the interfacial thickness is not negligibly smaller than the size of the colloid, as would be the case in the continuum calculation. Measurements of the orientation of the colloid as it moves along the surface under Brownian or applied forces indicate that it rotates and sometimes becomes pinned. However, the fact that the drag coefficients by each method of MD simulation agree with each other establishes that despite pinning, no additional forces are exerted on the colloid during Brownian motion.