Melting of Argon Cluster: Dependence of Caloric Curves on MD Simulation Parameters

Mohamed Tabti, Adil Eddahbi, Said Ouaskit, Lahcen Elarroum

Laboratoire de la Physique de la Matière Condensée (LPMC), Mohammedia Faculté des Sciences Ben M’Sik, Université Hassan II, Casablanca, Morocco.

DOI: 10.4236/wjcmp.2012.23023                

Abstract

We report on molecular dynamics simulations performed using microcanonical ensemble to predict the melting of argon particles in nanometer size range 10 nm and to investigate the effect of the time step integration. We use the Lennard- Jones potential functions to describe the interatomic interactions, and the results are evaluated by using caloric curves of the melting phenomenon. Thermodynamic properties, including the total energy, Lindemann parameter, kinetic and potential distribution’s functions, are used to characterize the melting process. The data shows bimodal behavior only in a certain interval of integration time step Δt, while the internal energy increases monotonically with the temperature. For the other time step values, the back bending disappears. We claim that negative specific heat is related to a possible decrease of entropy in an isolated system; this can be interpreted as a result of the internal interactions, especially attractive process and specific relaxation time.

Keywords

Molecular Dynamics Calculations; Clusters; Entropy; Fluctuation; Internal Interaction; Self-Organization; Phase Transformations; Transition; Nanostructures; Melting; Argon

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	F. Gulminelli and P. Chomaz, “Critical Behavior in the Coexistence Region of Finite Systems,” Physical Review Letters, Vol. 82, No. 7, 1999, pp. 1402-1405. doi:10.1103/PhysRevLett.82.1402
[2]	M. D’Agostino, et al., “Nuclear Liquid-Gas Phase Transition: Experimental Signals,” Nuclear Physics A, Vol. 749, 2005, pp. 55c-64c. doi:10.1016/j.nuclphysa.2004.12.008
[3]	P. Chomaz and F. Gulminelli, “The Challenges of Finite-System Statistical Mechanics,” The European Physical Journal A, Vol. 30, No. 1, 2006, pp. 317-331. doi:10.1140/epja/i2006-10126-5
[4]	D. H. E. Gross, “Microcanonical Thermodynamics: Phase Transitions in ‘Small’ Systems,” World Scientific, Singapore, 2001.
[5]	D. H. E. Gross, “Micro-Canonical Statistical Mechanics of Some Non-Extensive Systems,” Chaos, Solitons & Fractals, Vol. 13, No. 3, 2002, pp. 417-430. doi:10.1016/S0960-0779(01)00023-6
[6]	M. Schmidt, et al., “Experimental Determination of the Melting Point and Heat Capacity for a Free Cluster of 139 Sodium Atoms,” Physical Review Letters, Vol. 79, No. 1, 1997, pp. 99-103. doi:10.1103/PhysRevLett.79.99
[7]	T. Bachels, et al., “Melting of Isolated Tin Nanoparticles,” Physical Review Letters, Vol. 85, No. 6, 2000, pp. 1250-1253. doi:10.1103/PhysRevLett.85.1250
[8]	R. Kofman, et al., “Melting of Isolated Tin Nanoparticles,” Physical Review Letters, Vol. 86, No. 7, 2001, pp. 1388-1392. doi:10.1103/PhysRevLett.86.1388
[9]	M. Schmidt, et al., “Negative Heat Capacity for a Cluster of 147 Sodium Atoms,” Physical Review Letters, Vol. 86, No. 7, 2001, pp. 1191-1194. doi:10.1103/PhysRevLett.86.1191
[10]	M. Schmidt, et al., “Caloric Curve across the Liquid- to-Gas Change for Sodium Clusters,” Physical Review Letters, Vol. 87, 2001, Article ID: 203402. doi:10.1103/PhysRevLett.87.203402
[11]	M. Schmidt and H. Haberland, “Agrégats Comme Pré- curseurs des Nano-Objets Clusters as Precursors of Nano-Objects,” Comptes Rendus Physique, Vol. 3, 2002, pp. 327-340. doi:10.1016/S1631-0705(02)01326-9
[12]	F. Gobet, et al., “Cluster Multifragmentation and Percolation Transition. A Quantitative Comparison for Two Systems of the Same Size,” Physical Review A, Vol. 63, No. 3, 2001, Article ID: 033203. doi:10.1103/PhysRevA.63.033202
[13]	F. Gobet, et al., “Probing the Liquid-To-Gas Phase Transition in a Cluster via a Caloric Curve,” Physical Review Letters, Vol. 87, No. 20, 2001, Article ID: 203401. doi:10.1103/PhysRevLett.87.203401
[14]	F. Gobet, et al., “Direct Experimental Evidence for a Negative Heat Capacity in the Liquid-to-Gas Phase Transition in Hydrogen Cluster Ions: Backbending of the Caloric Curve,” Physical Review Letters, Vol. 89, No. 18, 2002, Article ID: 183403. doi:10.1103/PhysRevLett.89.183403
[15]	B. Farizon, et al., “Direct Observation of Multi-Ionization and Multifragmentation in High Velocity Cluster-Atom Collision,” Chemical Physics Letters, Vol. 252, 1996, pp. 147-152. doi:10.1016/S0009-2614(96)00125-X
[16]	M. Farizon, B. Farizon, S. Ouaskit and T. D. Mark, “Fragment Size Distributions and Caloric Curve in Colli- sion Induced Cluster Fragmentation,” American Institute of Physics, Vol. 970, 2008, pp. 165-174.
[17]	F. Mandl, “Statistical Physics,” 2nd Edition, Wiley, New York, 1991.
[18]	F. Mandl, “Statistical Physics,” 2nd Edition, Wiley, New York, 1991.
[19]	C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, Vol. 52, No. 1-2, 1988, pp. 479-487. doi:10.1007/BF01016429
[20]	G. R. Vakili-Nezhaad and G. A. Mansoori, “An Application of Non-Extensive Statistical Mechanics to Nanosystems,” Journal of Computational and Theoretical Nano- science, Vol. 1, No. 2, 2004, pp. 227-229.
[21]	M. Pirooz, et al., “Nonextensivity and Nonintensivity in Nanosystems: A Molecular Dynamics Simulation,” Jour- nal of Computational and Theoretical Nanoscience, Vol. 2, No. 1, 2005, pp. 138-147.
[22]	Y.-F. Chang, “Entropy, Fluctuation Magnified and Internal Interactions,” Entropy, Vol. 7, No. 3, 2005, pp. 190- 198. doi:10.3390/e7030190
[23]	Y.-F. Chang, “Possible Decrease Ofentropy Due to Internal Interactions in Isolated Systems,” Apeiron, Vol. 4, No. 4, 1997, pp. 97-99.
[24]	L. D. Landau and E. M. Lifshitz, “Statistical Physics,” Pergamon Press, Oxford, 1980.
[25]	H. Schafer, et al., “Absolute Entropies from Molecular Dynamics. Simulation Trajectories,” Journal of Chemical Physics, Vol. 113, No. 18, 2000, pp. 7809-7817. doi:10.1063/1.1309534
[26]	B. I. Lev and A. Y. Zhugaevych, “Statistical Description of Model Systems of Interacting Particles and Phase Transitions Accompanied by Cluster Formation,” Physical Review, Vol. 57, No. 6, 1998, pp. 6460-6469.
[27]	L. Verlet, “Computer Experiments on Classical Fluids,” Physical Review, Vol. 159, 1967, p. 98. doi:10.1103/PhysRev.159.98
[28]	K. Esf Arjani and G. A. Mansoori, “Theoretical and Computatioanl Nanoscience and Nanotechnology (Forth- coming),” 2005.
[29]	Y. J. Lee, J. Y. Maeng, E.-K. Lee, B. Kim, S. Kim and K.-K. Han, “Melting Behaviours of Icosahedral Metal Clusters Studied by Monte Carlo Simulations,” Journal of Computational Chemistry, Vol. 21, No. 5, 2000, pp. 380- 387. doi:10.1002/(SICI)1096-987X(20000415)21:5<380::AID-JCC4>3.3.CO;2-3
[30]	P. Labastie and R. L. Whetten, “Statistical Thermody-namics of the Cluster SolidLiquid Transition,” Physical Review Letters, Vol. 65, 1990, pp. 1567-1570. doi:10.1103/PhysRevLett.65.1567
[31]	J. F. Lutsko, et al., “Molecular-Dynamics Study of Lat- tice-Defect-Nucleated Melting in Metals Using an Embedded-Atom-Method Potential,” Physical Review B, Vol. 40, No. 5, 1989, p. 2841. doi:10.1103/PhysRevB.40.2841
[32]	R. S. Berry, et al., “Entropy and Phase Coexistence in Clusters: Metals vs. Nonmetals,” Entropy, Vol. 12, No. 5, 2010, pp. 1303-1324. doi:10.3390/e12051303
[33]	A. Proykova, et al., “Dynamical Coexistence of Phases in Molecular Clusters,” The Journal of Physical Chemistry C, Vol. 115, No. 18, 2001, pp. 8583-8591. doi:10.1063/1.1406976