DOI: 10.1063/1.436531. Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice

Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice

10.1063/1.436531

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The number of configurations of nonoverlapping rods on a square lattice is computed for various packing fractions and orientations of the rods. From the number of configurations, the entropies of the configurations are computed and compared with the results of approximate formulas of DiMarzio that are much used in statistical–mechanical theories of liquid crystals. For rods of three lattice sites, our calculations and Dimarzio’s formulas agree to within 0.5% for packing fractions less than 0.5. Some calculations for rods of ten lattice sites also showed good agreement.

Bibliography

McCrackin, F. L. (1978). Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice. The Journal of Chemical Physics, 69(12), 5419â5423.

Authors 1

Frank L. McCrackin (first)

References 18 Referenced 21

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10.1111/j.1749-6632.1942.tb47940.x / Ann. N. Y. Acad. Sci. (1942)
{'key': '2024020917332737300_r2', 'first-page': '1049', 'volume': '57', 'year': '1960', 'journal-title': 'Chem. Rev.'} / Chem. Rev. (1960)
10.1063/1.1676783 / J. Chem. Phys. (1971)
10.1063/1.431958 / J. Chem. Phys. (1976)
{'key': '2024020917332737300_r2c', 'first-page': '295', 'volume': '7', 'year': '1969', 'journal-title': 'Mol. Cryst. Liq. Cryst.'} / Mol. Cryst. Liq. Cryst. (1969)
10.1080/15421407108083541 / Mol. Cryst. Liq. Cryst. (1971)
10.1063/1.1734989 / J. Appl. Phys. (1959)
10.1021/ma60056a035 / Macromolecules (1977)
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10.1080/15421407608084310 / Mol. Cryst. Liq. Cryst. (1976)
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10.1063/1.434920 / J. Chem. Phys. (1977)
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{'key': '2024020917332737300_r5e', 'first-page': '1094', 'volume': '68', 'year': '1978', 'journal-title': 'Chem. Phys.'} / Chem. Phys. (1978)
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Dates

Type	When
Created	22 years, 6 months ago (Feb. 27, 2003, 4:26 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 2:24 p.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 6:06 p.m.)
Issued	46 years, 8 months ago (Dec. 15, 1978)
Published	46 years, 8 months ago (Dec. 15, 1978)
Published Print	46 years, 8 months ago (Dec. 15, 1978)

Funders 0

None

BibTeX

@article{McCrackin_1978, title={Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice}, volume={69}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.436531}, DOI={10.1063/1.436531}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={McCrackin, Frank L.}, year={1978}, month=dec, pages={5419–5423} }

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