Theory and Simulation of Capillary Forces on a Nanoparticle at a Liquid-Vapor Interface

The Young-Laplace equation of a liquid-vapor interface serves as the basis of the continuum theory of capillarity. We use molecular dynamics simulations to investigate a nanoparticle straddling a liquid-vapor interface and explore if the Young-Laplace equation can be used to describe capillary action at nanoscale. In equilibrium, the interface is flat and intersects with the nanoparticle surface. When the nanoparticle is out of equilibrium location but still straddles the interface, a capillary rise or fall will occur, inducing a restoring force that drives the nanoparticle back to its equilibrium location. Our simulation results fit well to the continuum theory of capillarity. The force on the nanoparticle is approximately linear with displacement from its equilibrium location and the associated spring constant depends logarithmically on the lateral span of the interface. Our results clarify the physical foundation of a method of modeling soft matter solutions in which the interface is replaced by a potential well for particles straddling the interface or solutes dispersed in the liquid phase. With this method, the solvent is eliminated and larger systems can be modeled.