Passive circular Brownian motion of asymmetric particles weakly bound to a planar surface

We use a simple model of particle shape to investigate how particle asymmetry affects particle-surface interaction, orientation, and stochastic dynamics over a planar surface. With this geometric model, we construct potential energy curves as a function of particle orientation relative to the surface, and identify the potential energy minimum for particles of various shapes ranging from symmetric (sphere) to asymmetric (oval-shaped). The calculated difference between particle centroid position and potential energy minimum location is used to define an offset, which is useful for comparison with experimental particle trajectories. For asymmetric particles the potential energy minimum location is decoupled from the center of the particle long-axis. Based on these observations, we construct a Brownian motion model of a rigid rotor with one end fixed to the planar surface. In the case of asymmetric particles, the resulting stochastic trajectories exhibit passive circular Brownian motion, thus providing one possible microscopic mechanism for the stochastic dynamics of fluorescence upconversion nanoparticles near a surface previously reported by us.