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Molecular dynamics studies of two hard-disk particles in a rectangular box I. Thermodynamic properties and position autocorrelation functions

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Abstract

Molecular dynamics simulations have been carried out for the simple few-body systems of two hard-disk particles confined within a 2-dimensional rectangular box. Wall pressures, the collision frequencies, density profiles, two-particle probability distributions, and position autocorrelation functions were computed to examine the thermodynamic, structural and time-dependent properties of such systems. Excellent agreement was found between simulation results and theoretical predictions recently proposed by Munakata and Hu. Detailed dynamic effects are also discussed to describe configurational particle trajectories including fast/slow relaxation processes observed in the position autocorrelation functions.

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References

  • Alder, B. J. and Wainwright, T. E., “Studies in Molecular Dynamics. I. General Method,”J. Chem. Phys.,31, 459 (1959).

    Article  CAS  Google Scholar 

  • Alder, B. J., Hoover W.G. and Wainwright, T. E., “Cooperative Motion of Hard Disks Leading to Melting,”Phys. Rev. Lett.,11, 241 (1963).

    Article  Google Scholar 

  • Allen, M. P. and Tildesley, D. J., “Computer Simulation of Liquids,” Clarendon Press, Oxford (1987).

    Google Scholar 

  • Allen, M. P. and Tildesley, D. J. (eds.), “Computer Simulation in Chemical Physics,” Kluwer Academic Publishers (1993).

  • Awazu, A., “Liquid-Solid Phase Transition of a System with Two Particles in a Rectangular Box,”Phys. Rev. E,63, 032102 (2001).

    Article  CAS  Google Scholar 

  • Dellago, Ch. and Posch, H.A., “Lyapunov Instability, Local Curvature, and the Fluid-Solid Phase Transition in Two-Dimensional Particle Systems,”Physica A,230, 364 (1996).

    Article  CAS  Google Scholar 

  • Kegel, W. K., Reiss, H. and Lekkerkerker, H. N.W., “Freezing Transition in Very Small Systems of Hard Spheres,”Phys. Rev. Lett.,83, 5298 (1999).

    Article  CAS  Google Scholar 

  • Kim, S.-C. and Suh, S.-H., “Adsorption of Multi-Component Hard Sphere Fluids in Micropores,”Mol. Phys.,99, 81 (2001).

    Article  CAS  Google Scholar 

  • Lee, H.-T. and Rhee, H.-K., “Steam Tolerance of Fe/ZSM-5 Catalyst for the Selective Catalytic Reduction of NOx,”Korean J. Chem. Eng.,19, 574 (2002).

    Article  CAS  Google Scholar 

  • MacElroy, J. M.D. and Suh, S.-H., “Computer Simulation of Moderately Dense Hard-Sphere Fluids and Mixtures in Microcapillaries,”Mol. Phys.,60, 475 (1987).

    Article  CAS  Google Scholar 

  • MacElroy, J. M. D. and Suh, S.-H., “Equilibrium and Nonequilibrium Molecular Dynamics Studies of Diffusion in Model One Dimensional Micropores,”Microporous and Mesoporous Mat.,48, 195 (2001).

    Article  CAS  Google Scholar 

  • MacElroy, J. M.D., Pozhar, L. A. and Suh, S.-H., “Self-Diffusion in a Fluid Confined within a Model Nanopore Structure,”Colloids and Surf. A,187, 493 (2001).

    Article  Google Scholar 

  • Munakata, T. and Hu, G., “Statistical Mechanics of Two Hard Disks in a Rectangular Box,”Phys. Rev. E,65, 066104 (2002).

    Article  Google Scholar 

  • Murthy, C. S. and Singer, K., “Description of the Molecular Trajectories in Simple Liquids,”J. Phys. Chem.,91, 21 (1987).

    Article  CAS  Google Scholar 

  • Nemeth, Z. T. and Lowen, H., “Freezing in Finite Systems: Hard Discs in Circular Cavities,”J. Phys.: Condens. Matter,10, 6189 (1998).

    Article  CAS  Google Scholar 

  • Oh, H.-S., Kang, K.-K., Kim, M.-H. and Rhee, H.-K., “Synthesis of MFIType Zeolites Under Atmospheric Pressure,”Korean J. Chem. Eng.,18, 113 (2001).

    Article  CAS  Google Scholar 

  • Park, S.-H., Lee, J.-H. and Rhee, H.-K., “Disproportionation of 1,2,4-Trimethylbenzene over Zeolite NU-87,”Korean J. Chem. Eng.,17, 198 (2000).

    Article  CAS  Google Scholar 

  • Roco, M.C., Williams, R. S. and Alivisatos, P. (eds.), “Nanotechnology Research Directions,” Kluwer Academic Publishers (2000); also on website http://itri.loyola.edu/nano/IWGN.Research.Directions/

  • Suh, S.-H. and MacElroy, J.M. D., “Molecular Dynamics Simulation of Hindered Diffusion in Microcapillaries,”Mol. Phys.,58, 445 (1986).

    Article  CAS  Google Scholar 

  • Suh, S.-H., Heo, N.-H. and Nicholson, D., “Knudsen Diffusion in the Sequentially Linked Spherical Pores,”J. Chem. Eng. Japan,31, 644 (1998).

    Article  CAS  Google Scholar 

  • Suh, Y.-W. and Rhee, H.-K., “Synthesis of Stable Mesostructured Zirconia: Tween Surfactant and Controlled Template Removal,”Korean J. Chem. Eng.,20, 65 (2003).

    Article  CAS  Google Scholar 

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Correspondence to Soong-Hyuck Suh.

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Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University

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Suh, SH., Lee, JW., Moon, H. et al. Molecular dynamics studies of two hard-disk particles in a rectangular box I. Thermodynamic properties and position autocorrelation functions. Korean J. Chem. Eng. 21, 504–510 (2004). https://doi.org/10.1007/BF02705441

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  • DOI: https://doi.org/10.1007/BF02705441

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