Forces between functionalized silica nanoparticles in solution

To prevent the flocculation and phase separation of nanoparticles in solution, nanoparticles are often functionalized with short chain surfactants. Here we present fully atomistic molecular dynamics simulations which characterize how these functional coatings affect the interactions between nanoparticles and with the surrounding solvent. For 5-nm-diameter silica nanoparticles coated with poly(ethylene oxide) (PEO) oligomers in water, we determined the hydrodynamic drag on two approaching nanoparticles moving through solvent and on a single nanoparticle as it approaches a planar surface. In most circumstances, macroscale fluid theory accurately predicts the drag on these nanoscale particles. Good agreement is seen with Brenner’s analytical solutions for wall separations larger than the soft nanoparticle radius. For two approaching coated nanoparticles, the solvent-mediated (velocity independent) and lubrication (velocity-dependent) forces are purely repulsive and do not exhibit force oscillations that are typical of uncoated rigid spheres.

Figure 1

(Color online) Cross sections of silica nanoparticles coated with PEO oligomers in water. Frames show a $7\times 15{\text{nm}}^2$ view of the larger $26\times 26\times 46{\text{nm}}^3$ system. The nanoparticles are shown at center separations of 11.5 nm (top), 8.0 nm (middle), and 6.0 nm (bottom). Elements C, O, H, and Si are blue, red, white and yellow, respectively.

Figure 2

(Color online) Force on nanoparticles approaching a plane surface of immobile water at 25 m/s as a function of center separation. The smallest system, with $L_{\perp }=13\text{nm}$ (black), shows a finite system-size effect. The larger systems, with $L_{\perp }=26\text{nm}$ (red or middle gray) and $L_{\perp }=39\text{nm}$ (blue or dark gray), converge to the Brenner prediction (green or light gray) for separations greater than 4.4 nm. The open circles are equilibrated forces in which the particles are held fixed at a given separation. $R_{\text{max}}$ (dashed) and $R_h$ (dotted) are defined in the text. Inset shows the time-averaged coating density versus radial distance.

Figure 3

(Color online) Force on approaching nanoparticles with relative velocities of 5 m/s (two middle light blue and dark blue lines) and 50 m/s (two upper light green and dark green lines) as a function of center separation. The lighter colors are data from runs in the $NVE$ ensemble and the darker colors were run in the thermostated $NVT$ ensemble. Data for equilibrated configurations are shown in black. Inset shows the equilibrated data as a log-linear plot. Circles and squares are for $L_{\perp }$ of 13 nm and 26 nm, respectively.