Elastocapillarity and Rolling Dynamics of Solid Nanoparticles

We use molecular dynamics simulations of rolling dynamics of solid nanoparticles with size R_p in contact with soft elastic substrates to elucidate effect of capillary, elastic and friction forces on rolling motion. Our simulations have shown that a nanoparticle can be in stationary, steady rolling, and accelerating states depending on the nanoparticle-substrate work of adhesion, W, the magnitude of the net applied force, F, and the substrate shear modulus G. In the stationary state, the restoring torque produced in the contact area balances the torque due to the external force. The crossover rolling force F_r is proportional to WR_p. In the steady rolling state, F>F_r, the nanoparticle maintains a constant rolling velocity which is a manifestation of the balance between the rolling friction force and the applied force. The observed scaling relationships between the applied force and nanoparticle velocity reflect a viscoelastic nature of the substrate deformation dynamics. A nanoparticle begins to accelerate when the energy supplied to the nanoparticle exceeds the energy dissipated in the contact area due to viscoelastic substrate deformation. Using these simulation results, we have constructed a diagram of states in terms of dimensionless parameters F/WR_p and W/GR_p.