### Abstract

The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood's many-body single-occupancy model. The single-occupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. As we should expect, the excellent agreement found here with all relevant previous work shows very clearly that configurational properties, such as the equation of state, do not require the maximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squares and hard cubes the free-volume theory provides a good description of the high-density solid-phase pressure. Hard parallel squares appear to exhibit a second-order melting transition at a density of 0.79 relative to close-packing. Hard parallel cubes have a more complicated equation of state, with several relatively-gentle curvature changes, but nothing so abrupt as to indicate a first-order melting transition. Because the number-dependence for the cubes is relatively large the exact nature of the cube transition remains unknown.

Original language | English |
---|---|

Pages (from-to) | 715-732 |

Number of pages | 18 |

Journal | Journal of Statistical Physics |

Volume | 136 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2009 |

### Keywords

- molecular dynamics
- computational methods
- melting transition
- virial-coefficients
- canonical ensemble
- spheres
- entropy
- gases
- equation
- system
- state
- phase

### Cite this

*Journal of Statistical Physics*,

*136*(4), 715-732. https://doi.org/10.1007/s10955-009-9795-0

**Single-speed molecular dynamics of hard parallel squares and cubes.** / Hoover, W. G.; Hoover, Carol G.; Bannerman, Marcus N.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 136, no. 4, pp. 715-732. https://doi.org/10.1007/s10955-009-9795-0

}

TY - JOUR

T1 - Single-speed molecular dynamics of hard parallel squares and cubes

AU - Hoover, W. G.

AU - Hoover, Carol G.

AU - Bannerman, Marcus N.

PY - 2009/8

Y1 - 2009/8

N2 - The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood's many-body single-occupancy model. The single-occupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. As we should expect, the excellent agreement found here with all relevant previous work shows very clearly that configurational properties, such as the equation of state, do not require the maximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squares and hard cubes the free-volume theory provides a good description of the high-density solid-phase pressure. Hard parallel squares appear to exhibit a second-order melting transition at a density of 0.79 relative to close-packing. Hard parallel cubes have a more complicated equation of state, with several relatively-gentle curvature changes, but nothing so abrupt as to indicate a first-order melting transition. Because the number-dependence for the cubes is relatively large the exact nature of the cube transition remains unknown.

AB - The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood's many-body single-occupancy model. The single-occupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. As we should expect, the excellent agreement found here with all relevant previous work shows very clearly that configurational properties, such as the equation of state, do not require the maximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squares and hard cubes the free-volume theory provides a good description of the high-density solid-phase pressure. Hard parallel squares appear to exhibit a second-order melting transition at a density of 0.79 relative to close-packing. Hard parallel cubes have a more complicated equation of state, with several relatively-gentle curvature changes, but nothing so abrupt as to indicate a first-order melting transition. Because the number-dependence for the cubes is relatively large the exact nature of the cube transition remains unknown.

KW - molecular dynamics

KW - computational methods

KW - melting transition

KW - virial-coefficients

KW - canonical ensemble

KW - spheres

KW - entropy

KW - gases

KW - equation

KW - system

KW - state

KW - phase

U2 - 10.1007/s10955-009-9795-0

DO - 10.1007/s10955-009-9795-0

M3 - Article

VL - 136

SP - 715

EP - 732

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 4

ER -