Negative Normal Restitution Coefficient Found in Simulation of Nanocluster Collisions

The oblique impacts of nanoclusters are studied theoretically and by means of molecular dynamics. In simulations we explore two models—Lennard-Jones clusters and particles with covalently bonded atoms. In contrast with the case of macroscopic bodies, the standard definition of the normal restitution coefficient yields for this coefficient negative values for oblique collisions of nanoclusters. We explain this effect and propose a proper definition of the restitution coefficient which is always positive. We develop a theory of an oblique impact based on a continuum model of particles. A surprisingly good agreement between the macroscopic theory and simulations leads to the conclusion that macroscopic concepts of elasticity, bulk viscosity, and surface tension remain valid for nanoparticles of a few hundred atoms.

Figure 1

Initial (left) and final stage (right) of the nanocluster collision. The initial relative velocity is ${\mathbf{v}}_{12}(0)=\mathbf{V}$ and the incident angle is $\gamma$. The unit normal $\mathbf{n}$ specifies the orientation of the contact plane. For large $\gamma$ a noticeable reorientation of this plane is observed. Here the collision of H-passivated Si nanospheres (model B) is shown.

Figure 2

Dependence on the incident angle $\gamma$ of the normal restitution coefficients $e$, and $\tilde{e}$ according to the standard definitions (4) and modified definition (5). Open circles and squares are, respectively, the MD results for $e$ and $\tilde{e}$, while dashed and solid lines correspond to theoretical predictions. The upper panel refers to model A and the lower panel to model B. Note that the coefficient $e$ is always positive.

Figure 3

Dependence of the angular displacement $\alpha =\mathrm{arcos}[\mathbf{n}(0)·\mathbf{n}(t_c)]$ of the unit normal $\mathbf{n}$, Eq. (2), on the incident angle $\gamma$. Open squares and circles are the MD results for the model A and B, respectively. Solid and broken lines are the corresponding theoretical predictions, $\alpha ={\int }_0^{t_c}\Omega (t)dt$ (see text for detail).