DOI: 10.1063/1.468456. Virial coefficients and close-packing of hard spheres and disks

Virial coefficients and close-packing of hard spheres and disks

10.1063/1.468456

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Using recently calculated 8th virial coefficients for hard spheres and disks, singularities in the virial expansion are reinvestigated. Using a Padé analysis, it is concluded that the singularities are associated with crystalline close-packing and not random close-packing nor with the fluid→solid phase transition. Accurate equations of state are developed for hard sphere and disk fluids. Estimates of 9th and higher virial coefficients are also given.

Bibliography

Sanchez, I. C. (1994). Virial coefficients and close-packing of hard spheres and disks. The Journal of Chemical Physics, 101(8), 7003â7006.

Authors 1

Isaac C. Sanchez (first)

References 23 Referenced 66

10.1088/0305-4470/26/19/014 / J. Phys. A (1993)
10.1063/1.1725286 / J. Chem. Phys. (1964)
10.1063/1.1840521 / J. Chem. Phys. (1967)
{'key': '2023071014153943400_r3', 'first-page': '607', 'volume': '85A', 'year': '1976', 'journal-title': 'Physica'} / Physica (1976)
{'key': '2023071014153943400_r3a', 'first-page': '584', 'volume': '87A', 'year': '1977'} (1977)
10.1007/BF01011091 / J. Stat. Phys. (1982)
10.1007/BF01008253 / J. Stat. Phys. (1982)
{'key': '2023071014153943400_r5', 'first-page': '943', 'volume': '26', 'year': '1992', 'journal-title': 'J. Phys. A'} / J. Phys. A (1992)
10.1016/0021-9797(76)90114-4 / J. Colloid Interface Sci. (1976)
{'key': '2023071014153943400_r7'}
10.1080/00018739300101464 / Adv. Phys. (1993)
{'key': '2023071014153943400_r9'}
10.1088/0022-3727/2/6/311 / Brit. Appl. Phys. (J. Phys. D) (1969)
10.1098/rspa.1970.0189 / Proc. R. Soc. London, Ser. A (1970)
10.1039/f29767201667 / J. Chem. Soc. Faraday Trans. 2 (1976)
10.1103/PhysRevA.27.1053 / Phys. Rev. A (1983)
10.1103/PhysRevA.32.2347 / Phys. Rev. A (1985)
10.1063/1.467028 / J. Chem. Phys. (1994)
10.1002/9780470142684.ch5 / Adv. Chem Phys. (1981)
10.1063/1.1672048 / J. Chem. Phys. (1969)
{'key': '2023071014153943400_r18'}
10.1088/0022-3719/12/17/005 / J. Phys. C (1979)
10.1063/1.1670653 / J. Chem. Phys. (1968)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:13 a.m.)
Deposited	1 year, 8 months ago (Jan. 3, 2024, 7:34 p.m.)
Indexed	2 months ago (July 4, 2025, 9:24 a.m.)
Issued	30 years, 10 months ago (Oct. 15, 1994)
Published	30 years, 10 months ago (Oct. 15, 1994)
Published Print	30 years, 10 months ago (Oct. 15, 1994)

Funders 0

None

BibTeX

@article{Sanchez_1994, title={Virial coefficients and close-packing of hard spheres and disks}, volume={101}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.468456}, DOI={10.1063/1.468456}, number={8}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Sanchez, Isaac C.}, year={1994}, month=oct, pages={7003–7006} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        4
      ]
    ],
    "date-time": "2025-07-04T13:24:27Z",
    "timestamp": 1751635467337
  },
  "reference-count": 23,
  "publisher": "AIP Publishing",
  "issue": "8",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1994,
        10,
        15
      ]
    ]
  },
  "abstract": "<jats:p>Using recently calculated 8th virial coefficients for hard spheres and disks, singularities in the virial expansion are reinvestigated. Using a Pad\u00e9 analysis, it is concluded that the singularities are associated with crystalline close-packing and not random close-packing nor with the fluid\u2192solid phase transition. Accurate equations of state are developed for hard sphere and disk fluids. Estimates of 9th and higher virial coefficients are also given. \u2009</jats:p>",
  "DOI": "10.1063/1.468456",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:13:04Z",
    "timestamp": 1027685584000
  },
  "page": "7003-7006",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 66,
  "title": "Virial coefficients and close-packing of hard spheres and disks",
  "prefix": "10.1063",
  "volume": "101",
  "author": [
    {
      "given": "Isaac C.",
      "family": "Sanchez",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Chemical Engineering Department, University of Texas, Austin, Texas 78712"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2023071014153943400_r1",
      "doi-asserted-by": "crossref",
      "first-page": "4805",
      "DOI": "10.1088/0305-4470/26/19/014",
      "volume": "26",
      "year": "1993",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2023071014153943400_r2",
      "doi-asserted-by": "crossref",
      "first-page": "939",
      "DOI": "10.1063/1.1725286",
      "volume": "40",
      "year": "1964",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071014153943400_r2a",
      "doi-asserted-by": "crossref",
      "first-page": "4181",
      "DOI": "10.1063/1.1840521",
      "volume": "46",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071014153943400_r3",
      "first-page": "607",
      "volume": "85A",
      "year": "1976",
      "journal-title": "Physica"
    },
    {
      "key": "2023071014153943400_r3a",
      "first-page": "584",
      "volume": "87A",
      "year": "1977"
    },
    {
      "key": "2023071014153943400_r4",
      "doi-asserted-by": "crossref",
      "first-page": "533",
      "DOI": "10.1007/BF01011091",
      "volume": "27",
      "year": "1982",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2023071014153943400_r4a",
      "doi-asserted-by": "crossref",
      "first-page": "129",
      "DOI": "10.1007/BF01008253",
      "volume": "29",
      "year": "1982",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2023071014153943400_r5",
      "first-page": "943",
      "volume": "26",
      "year": "1992",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2023071014153943400_r6",
      "doi-asserted-by": "crossref",
      "first-page": "483",
      "DOI": "10.1016/0021-9797(76)90114-4",
      "volume": "56",
      "year": "1976",
      "journal-title": "J. Colloid Interface Sci."
    },
    {
      "key": "2023071014153943400_r7"
    },
    {
      "key": "2023071014153943400_r8",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1080/00018739300101464",
      "volume": "42",
      "year": "1993",
      "journal-title": "Adv. Phys."
    },
    {
      "key": "2023071014153943400_r9"
    },
    {
      "key": "2023071014153943400_r10",
      "doi-asserted-by": "crossref",
      "first-page": "863",
      "DOI": "10.1088/0022-3727/2/6/311",
      "volume": "2",
      "year": "1969",
      "journal-title": "Brit. Appl. Phys. (J. Phys. D)"
    },
    {
      "key": "2023071014153943400_r11",
      "doi-asserted-by": "crossref",
      "first-page": "479",
      "DOI": "10.1098/rspa.1970.0189",
      "volume": "319",
      "year": "1970",
      "journal-title": "Proc. R. Soc. London, Ser. A"
    },
    {
      "key": "2023071014153943400_r12",
      "doi-asserted-by": "crossref",
      "first-page": "1667",
      "DOI": "10.1039/f29767201667",
      "volume": "72",
      "year": "1976",
      "journal-title": "J. Chem. Soc. Faraday Trans. 2"
    },
    {
      "key": "2023071014153943400_r13",
      "doi-asserted-by": "crossref",
      "first-page": "1053",
      "DOI": "10.1103/PhysRevA.27.1053",
      "volume": "27",
      "year": "1983",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2023071014153943400_r14",
      "doi-asserted-by": "crossref",
      "first-page": "2347",
      "DOI": "10.1103/PhysRevA.32.2347",
      "volume": "32",
      "year": "1985",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2023071014153943400_r15",
      "doi-asserted-by": "crossref",
      "first-page": "6684",
      "DOI": "10.1063/1.467028",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071014153943400_r16",
      "doi-asserted-by": "crossref",
      "first-page": "397",
      "DOI": "10.1002/9780470142684.ch5",
      "volume": "48",
      "year": "1981",
      "journal-title": "Adv. Chem Phys."
    },
    {
      "key": "2023071014153943400_r17",
      "doi-asserted-by": "crossref",
      "first-page": "635",
      "DOI": "10.1063/1.1672048",
      "volume": "51",
      "year": "1969",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071014153943400_r18"
    },
    {
      "key": "2023071014153943400_r19",
      "doi-asserted-by": "crossref",
      "first-page": "L659",
      "DOI": "10.1088/0022-3719/12/17/005",
      "volume": "12",
      "year": "1979",
      "journal-title": "J. Phys. C"
    },
    {
      "key": "2023071014153943400_r20",
      "doi-asserted-by": "crossref",
      "first-page": "3688",
      "DOI": "10.1063/1.1670653",
      "volume": "49",
      "year": "1968",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/101/8/7003/13604837/7003_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/101/8/7003/13604837/7003_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        1,
        4
      ]
    ],
    "date-time": "2024-01-04T00:34:22Z",
    "timestamp": 1704328462000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/101/8/7003/482414/Virial-coefficients-and-close-packing-of-hard"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1994,
        10,
        15
      ]
    ]
  },
  "references-count": 23,
  "journal-issue": {
    "issue": "8",
    "published-print": {
      "date-parts": [
        [
          1994,
          10,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.468456",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1994,
        10,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1994,
        10,
        15
      ]
    ]
  }
}