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REBOUNDS WITH A RESTITUTION COEFFICIENT LARGER THAN UNITY IN NANOCLUSTER COLLISIONS Hiroto Kuninaka Faculty of Education, Mie Univ. Physics of Granular Flows (2013/JUN/27) Collaborator: Hisao Hayakawa (YITP, Kyoto Univ.)

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

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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) Binary collision of Lennard-Jones clusters Collision modes are classified into two main modes: coalescence and stretching separation which depends on impact speed and impact parameter. Impact parameter

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Some collision modes in cohesive collisions M. Kalweit and D. Drikakis: Phys. Rev. B 74, 235415 (2006) Coalescence u=1.58 X=0.0 u=5.38 x=0.36 Stretching separation

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M. Suri and T. Dumitricaˇ, Phys. Rev. B 78, 081405R (2008) Rebound mode of nanoclusters Nano-scale object can exhibit elastic rebound mode under special condition Surface-coated clusters are known to show elastic rebounds. H-passivated Si cluster and substrate

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Each cluster has 682 “atoms”. “Atoms” are bound together by modified Lennard-Jones potential U(r ij ). : distance between “atoms” in one cluster z cohesive parameter : material parameter ( atoms in each cluster) ( surface atom of C u ) ( surface atom of C l ) HK and H. Hayakawa: Phys. Rev. E. 79, 031309 (2009) Our model

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T=0.02 (1.2[K]) N. V. Brilliantov et al. (2008) (i)Stick (ii) multitime collision (iii) e<1: ordinary rebound (iv) e>1: super rebound HK and H. Hayakawa: Phys. Rev. E. 79, 031309 (2009) Summary of our previous results

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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)

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Simulation Setup Model 9 layers(30.6 Å ) Each cluster has 236 “atoms”. “Atoms” are bound together by modified Lennard-Jones potential U(r ij ). cohesive parameter ( i, j : atoms in each cluster) ( i : surface atom of C u ) ( j : surface atom of C l )

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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)) Kinetic temperature T=0.4ε 0 Simulation step 2000 0

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Movie of typical rebound

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Histogram of restitution coefficient Restitution coefficient:

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Kinetic temperature T=0.04ε 0 (4.8 [K]), V=0.2 (ε 0 /M) 1/2 (15.7 [m/s]) kinetic temperature: Ordinary rebound (e=0.62) Super rebound (e=1.01) CpCtCpCt CpCtCpCt

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

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Time Evolution of Entropy

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

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3D histogram Super rebound (e>1) (after collision) FCC (perfect crystal) Peak value Before collisionAfter collision Ordinary0.14400.1228 Super0.11520.1699 3D histogram of Q4 and Q6(C l )

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

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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.

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χ2 value Structural difference between super and ordinary rebounds ： abundant in super clusters ： found in both clusters

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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:

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Change in averaged potential energy of local structures accelerationcollision Simulation step acceleration collision Potential energy after equillibration 、 at the onset of collision 、 and at the end of colliison Structure abundant in “ordinary clusters” Potential energy /ε Structure abundant in “super clusters” Potential energy of a local structure

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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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