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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alder, B. J. and Wainwright, T. E., “Studies in Molecular Dynamics. I. General Method,”J. Chem. Phys.,31, 459 (1959).
Alder, B. J., Hoover W.G. and Wainwright, T. E., “Cooperative Motion of Hard Disks Leading to Melting,”Phys. Rev. Lett.,11, 241 (1963).
Allen, M. P. and Tildesley, D. J., “Computer Simulation of Liquids,” Clarendon Press, Oxford (1987).
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).
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).
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).
Kim, S.-C. and Suh, S.-H., “Adsorption of Multi-Component Hard Sphere Fluids in Micropores,”Mol. Phys.,99, 81 (2001).
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).
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).
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).
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).
Munakata, T. and Hu, G., “Statistical Mechanics of Two Hard Disks in a Rectangular Box,”Phys. Rev. E,65, 066104 (2002).
Murthy, C. S. and Singer, K., “Description of the Molecular Trajectories in Simple Liquids,”J. Phys. Chem.,91, 21 (1987).
Nemeth, Z. T. and Lowen, H., “Freezing in Finite Systems: Hard Discs in Circular Cavities,”J. Phys.: Condens. Matter,10, 6189 (1998).
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).
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).
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).
Suh, S.-H., Heo, N.-H. and Nicholson, D., “Knudsen Diffusion in the Sequentially Linked Spherical Pores,”J. Chem. Eng. Japan,31, 644 (1998).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02705441