Negative normal restitution coefficient for the oblique impact of nanoclusters
Hisao Hayakawa and Kuniyasu Saitoh

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, JapanIntroduction
Restitution coefficient e, which represents the lost of energy at the impact, has been introduced so far for macroscopic bodies.
However, the increasing interest to nano-particles raises an important question to what extent the macroscopic concepts areapplicable and do they acquire new features in the nano-world. We have studied the oblique impact of nanoclusters numerically,and demonstrated the macroscopic collision model of adhesive dissipative particles well reproduces the observed behaviors of e.

Molecular Dynamics simulation
To demonstrate the oblique impact of nanoclusters, the molecular dynamics(MD) simulation is adopted. The H-passivated Si nanocluster, which iscoated by hydrogen atoms to reduce the surface reactivity, is mimicked by
the Tersoff potential.

H Si

Oblique impact of H-passivated Si nanoclusters

Due to the adhesive force
between the colliding twonanoclusters, the duration
time cannot be neglected. As
a result, a reorientation ofthe contact plane is occurred.
(Left) Dependence of theangular displacement

cos a  n(0)  n(tc )on the incident angle .
Restitution coefficients for nanoclusters
Theoretical model for the oblique impact
The impact theory for viscoelastic adhesive particles is adopted to the normal force
acting between two nanoclusters. It contains the Hertzian force, JKR force, and thedissipative force.
Because of the reorientation of the contact plane, the inertial force should beconsidered, and the conversation of the angular momentum leads the equation ofmotion

Dependence of the normal restitution coefficientof nanoclusters. Here, e is defined by the usual
manner as, where g is the relative velocity of colliding nanoclusters
Because of the reorientation of the contact plane,e becomes negative if the angular displacement ais large. We introduce the modified definition of e, which is always positive.

(The solid and broken lines in the figures are calculated from the solution of theabove equation of motion.)
Simplified model - modified Lennard-Jones (LJ) nanoclusters
To demonstrate the oblique impact ofnanoclusters by a simple model, weadopt modified LJ potential for theinteraction between the atoms in thenanoclusters (where C=0.2).
126      C  rr (r )  4 

The results of the normal restitution
coefficients are also well reproducedby the macroscopic theory, and negative
restitution coefficient is also observed.

Discussion and Conclusion
There are some discrepancies in the time development of x (about 1.0~1.4 times smaller than the MD simulation results). However, we findthe characteristics of the inelastic collision of nanoclusters are well explained by the macroscopic theory. We also conclude the anomalous
behavior of the restitution coefficient, i.e. negative e, can be observed in the oblique impacts of adhesive macroscopic particles.
Reference
Kuniyasu Saitoh, Anna Borova, Hisao Hayakawa, and Nikolai V. Brilliantov“Negative normal restitution coefficient for nanocluster collisions”, accepted to Phys. Rev. Lett. ( 2010 )arXiv:1005.5429 ( 2010 )