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Rebounds with a restitution coefficient larger than unity in nanocluster collisions. Hiroto Kuninaka Faculty of Education, Mie Univ. Collaborator: Hisao Hayakawa (YITP, Kyoto Univ.). Physics of Granular Flows (2013/JUN/27). Outline. Background Collision modes of nanoclusters

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rebounds with a restitution coefficient larger than unity in nanocluster collisions

Rebounds with a restitution coefficient larger than unity in nanocluster collisions

HirotoKuninaka

Faculty of Education, Mie Univ.

Collaborator: Hisao Hayakawa (YITP, Kyoto Univ.)

Physics of Granular Flows (2013/JUN/27)

outline
Outline
  • Background
    • Collision modes of nanoclusters
    • Summary of previous results
  • Motivation
  • Our model
  • Simulation results
  • Summary and discussion
background
Background
  • Nanoscale collisions are subject to thermal fluctuation and cohesive interaction.
  • Collisional properties of nanoscale objects are different from those of macroscopic objects

M. Kalweit and D. Drikakis:

Phys. Rev. B 74, 235415 (2006)

Impact

parameter

  • Binary collision of Lennard-Jones clusters
  • Collision modes are classified into two
  • main modes: coalescence and stretching
  • separationwhich depends on impact
  • speed and impact parameter.
some collision modes in cohesive collisions
Some collision modes in cohesive collisions

M. Kalweit and D. Drikakis:

Phys. Rev. B 74, 235415 (2006)

Coalescence

Stretching separation

u=5.38

x=0.36

u=1.58

X=0.0

rebound mode of nanoclusters
Rebound mode of nanoclusters
  • Nano-scale object can exhibit elastic rebound
  • modeunder special condition
  • Surface-coated clusters are known to show
  • elastic rebounds.

M. Suri and T. Dumitricaˇ, Phys. Rev. B 78, 081405R (2008)

H-passivated Si cluster and substrate

slide6

Our model

HK and H. Hayakawa:

Phys. Rev. E. 79, 031309 (2009)

  • Each cluster has 682 “atoms”.
  • “Atoms” are bound together
  • by modified Lennard-Jones potential U(rij).

z

cohesive parameter

( atoms in each cluster)

: material parameter

( surface atom of Cu)

: distance between “atoms” in one cluster

( surface atom of Cl)

summary of our previous results
Summary of our previous results

HK and H. Hayakawa:

Phys. Rev. E. 79, 031309 (2009)

T=0.02 (1.2[K])

N. V. Brilliantov et al. (2008)

Stick (ii) multitime collision (iii) e<1: ordinary rebound

(iv) e>1: super rebound

motivation
Motivation
  • What is the difference between the ordinary rebound mode and the super rebound mode?
  • We investigate the thermodynamic and structural properties of the clusters.
  • We introduce an order parameter to characterize the crystalline structure of the system.

HK and H. Hayakawa: Phys. Rev. E. 86, 051302 (2012)

simulation setup

Model

Simulation Setup
  • Each cluster has 236 “atoms”.
  • “Atoms” are bound together
  • by modified Lennard-Jones potential U(rij).

9 layers(30.6Å)

cohesive parameter

( i, j : atoms in each cluster)

( i : surface atom of Cu)

( j : surface atom of Cl)

simulation setup1
Simulation Setup
  • Initial configuration:
  • FCC with the lowest
  • volume fraction:
  • Initial equilibration to desired temperature by velocity scaling method
  • We give translational
  • speed by accelerating the clusters. (g=0.02ε/(σm))

T=0.4ε0

Kinetic temperature

0

2000

Simulation step

histogram of restitution coefficient
Histogram of restitution coefficient

Restitution coefficient:

kinetic temperature
Kinetic temperature

kinetic temperature:

T=0.04ε0(4.8 [K]), V=0.2 (ε0/M)1/2(15.7 [m/s])

Cp

Ct

Cp

Ct

Super rebound (e=1.01)

Ordinary rebound (e=0.62)

slide14

Calculation of Entropy

The 1st law of thermodynamics

…Work by the atom j

on the atom i

slide16

Calculation of bond order parameters

Steinhardt’s order parameter

: number of neighboring

atoms

j

i

Time average

3d histogram
3D histogram

FCC (perfect crystal)

Super rebound (e>1)

(after collision)

3D histogram of

Q4 and Q6(Cl)

Peak value

analysis of bond order parameter
Analysis of Bond Order Parameter

Steinhart’s order parameter

We investigate

the distribution of

quantifying the discrepancy
Quantifying the discrepancy

Chi-square

number of atoms

at j-th bin (ordinary)

number of atoms

at j-th bin (super)

The discrepancy is

largest at m=4.

2 value

Structural difference between super and

ordinary rebounds

χ2value

:abundant in super clusters

:found in both clusters

potential energy of local structure
Potential Energy of Local Structure

Atoms with the order

  • Positioned on corners of the cluster
  • We define a local structure with the atoms and the nearest atoms to calculate its potential energy

Nearest particles:

potential energy of a local structure
Potential energy of a local structure

Change in averaged potential energy of local structures

Structure abundant in “super clusters”

Structure abundant in “ordinary clusters”

acceleration

collision

acceleration

collision

Potential energy /ε

Simulation step

Simulation step

  • Potential energy after equillibration、at the onset of collision、and at the end of colliison
conclusion
Conclusion
  • We investigated the thermodynamic and structural properties of nanoclusters.
  • The difference can be found in the distribution of

between super clusters and ordinary clusters.

  • The potential energy of the characteristic local structure in super cluster has high potential energy after equilibration.
    • Slight decrease of the potential energy can be found
    • Such a decrease may cause super rebounds