Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition

We conduct molecular dynamics simulations of the collision of atomic clusters with a weakly attractive surface. We focus on an intermediate regime, between soft landing and fragmentation, where the cluster undergoes deformation on impact but remains largely intact and will either adhere to the surface (and possibly slide) or be reflected. We find that the outcome of the collision is determined by the Weber number We, i.e., the ratio of the kinetic energy to the adhesion energy, with a transition between adhesion and reflection occurring as We passes through unity. We also identify two distinct collision regimes: in one regime, the collision is largely elastic and deformation of the cluster is relatively small, but in the second regime, the deformation is large and the adhesion energy starts to depend on the kinetic energy. If the transition between these two regimes occurs at a similar kinetic energy to that of the transition between reflection and adhesion, then we find that the probability of adhesion for a cluster can be bimodal. In addition, we investigate the effects of the angle of incidence on adhesion and reflection. Finally, we compare our findings both with recent experimental results and with macroscopic theories of particle collisions.

Figure 1

Snapshots showing a selection of 147-atom clusters after equilibration on surfaces with various $C$ values. The solid clusters (top row) were equilibrated at $T^{*}=0.27$.

Figure 2

The initial configuration for the collisions studied at $v_0^{*}=0.4$, 1.6, and 2.6 (top). The lighter surface atoms follow Newtonian dynamics, and the darker surface atoms follow Langevin dynamics. Snapshots of the 147-atom cluster colliding with the substrate with $C=0.35$ with initial velocities $v_0^{*}=0.4$, 1.6, and 2.6, respectively, at time $t^{*}=9$ (bottom).

Figure 3

The $z$ component of velocity of the center of mass $v_z^{*}$ of the 147-atom icosahedron plotted versus time for initial velocities $v_0^{*}=0.4$, 1.6, and 2.6. The coefficient of restitution $e$ is defined here as the ratio of the maximum velocity after the collision $v_f^{*}$ to the maximum velocity before the collision $v_i^{*}$.

Figure 4

The evolution of the $z$ component of the radius of gyration $R_z$ of the 147-atom cluster colliding with the substrate with $C=0.35$ for initial velocities $v_0^{*}=0.4$, 1.6, and 2.6.

Figure 5

The evolution of (a) the cluster-surface potential energy $E^{\mathit{cs}}$, (b) the cluster potential energy $E^c$, and (c) the thermal kinetic energy $E_{\mathit{\text{thermal}}}^k$ of the 147-atom cluster (equilibrated initially at $T^{*}=0.13$) colliding with the substrate with $C=0.35$ for initial velocities $v_0^{*}=0.4$, 1.6, and 2.6.

Figure 6

The probability of adhesion versus the initial velocity $v_0^{*}$ averaged over 100 trials with random orientations with $C=0.35$ for the three different cluster sizes incident on the flat surface.

Figure 7

The maximum deformation of the cluster at the moment of peak reflected velocity (the pull-off) $v_f^{*}$ versus impact velocity $v_0^{*}$ for different size clusters.

Figure 8

For $C=0.35$ (a) the adhesion energy per atom $E_f^a$ at pull-off as a function of impact velocity, (b) $E_f^a$ as a function of $\Delta R_f^g∕R^g$, and (c) $E_f^a{N}^{1∕2}$ as a function of impact velocity for the three different cluster sizes. From (c), we observe that the total adhesion energy $(N\times E_f^a)$ scales as $N^{1∕2}$ in the small deformation regime.

Figure 9

The coefficient of restitution $e$ for the three different cluster sizes on the flat surface as a function of initial velocity at $C=0.35$ for normal incidence.

Figure 10

The ratio of the reflected kinetic energy $E_f^K$ to $E_f^a$ or Weber number We at the point of peak reflected velocity for the different size clusters with $C=0.35$.

Figure 11

The adhesion probability versus initial velocity $\left(v_0^{*}\right)$ of the 147-atom icosahedral cluster on the flat substrate for different $C$ values.

Figure 12

The probability of adhesion versus the normal component of the initial velocity $v_{0z}^{*}$ averaged over 50 trials with $C=0.35$ for non-normal incidence of the 147-atom icosahedron on the substrate. The lines shown are to guide the eye.

Figure 13

The final velocity component parallel to the substrate of clusters that are captured by the substrate as a function of the initial velocity component parallel to the substrate $v_{0y}^{*}$ for $C=0.35$ (a) and $C=0.55$ (b). The clusters slide easily for $C=0.35$ as indicated by the linear dependence of the final velocity on the initial velocity component, but for $C=0.55$, there is a threshold incident angle to the surface before sliding takes place.