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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. 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

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  1. 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)

  2. Outline • Background • Collision modes of nanoclusters • Summary of previous results • Motivation • Our model • Simulation results • Summary and discussion

  3. 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.

  4. 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

  5. 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

  6. 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)

  7. 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

  8. 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)

  9. 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)

  10. 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

  11. Movie of typical rebound

  12. Histogram of restitution coefficient Restitution coefficient:

  13. 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)

  14. Calculation of Entropy The 1st law of thermodynamics …Work by the atom j on the atom i

  15. Time Evolution of Entropy

  16. Calculation of bond order parameters Steinhardt’s order parameter : number of neighboring atoms j i Time average

  17. 3D histogram FCC (perfect crystal) Super rebound (e>1) (after collision) 3D histogram of Q4 and Q6(Cl) Peak value

  18. Analysis of Bond Order Parameter Steinhart’s order parameter We investigate the distribution of

  19. 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.

  20. Structural difference between super and ordinary rebounds χ2value ：abundant in super clusters ：found in both clusters

  21. 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:

  22. 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

  23. 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

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