Periodic boundary conditions: Difference between revisions
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A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques | computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus. | A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques | computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus. | ||
In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions |phase transition]] problems may arise. | In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions |phase transition]], where long-range fluctuations play an important role, problems may arise. | ||
*[[Cubic periodic boundary conditions | Cubic]] | *[[Cubic periodic boundary conditions | Cubic]] | ||
*[[Orthorhombic periodic boundary conditions | Orthorhombic]] | *[[Orthorhombic periodic boundary conditions | Orthorhombic]] | ||
Revision as of 15:35, 11 February 2010
A liquid, in the thermodynamic limit, would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones computer simulation. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as periodic boundary conditions. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods [1], where one can imagine the action takes place on the surface of a torus. In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a phase transition, where long-range fluctuations play an important role, problems may arise.
References
Related reading
- M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics 15 pp. 299-305 (1976)
- Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics 74 pp. 1864- (1981)
External resources
- Periodic boundary conditions in various geometries sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).