DOI: 10.1063/1.2402167. Finite-size effects in simulations of nucleation

Finite-size effects in simulations of nucleation

10.1063/1.2402167

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We investigate the importance of finite-size effects in simulations of nucleation processes. Most molecular dynamics simulations of first order phase transitions, such as vapor-liquid nucleation, are performed in the canonical NVT ensemble where, owing to the fixed total number of molecules N, the growth of the new phase causes the depletion of the metastable phase. This effect may lead to significant errors in the simulation and even to the impossibility of observing nucleation in a small finite system. We present a theory to estimate the system size beyond which these finite-size effects are expected to be negligible. This optimization saves valuable calculation time and can extend the range of supersaturations and rates attainable by simulations by several orders of magnitude. Our results are applicable to diverse situations, such as crystallization, capillary condensation, or the melting of nanoclusters.

Bibliography

Wedekind, J., Reguera, D., & Strey, R. (2006). Finite-size effects in simulations of nucleation. The Journal of Chemical Physics, 125(21).

Authors 3

Jan Wedekind (first)
David Reguera (additional)
Reinhard Strey (additional)

References 42 Referenced 127

10.1088/0953-8984/4/38/001 / J. Phys.: Condens. Matter (1992)
{'volume-title': 'Nucleation: Basic Theory With Applications', 'year': '2000', 'key': '2023070402350531900_c2'} / Nucleation: Basic Theory With Applications (2000)
{'volume-title': 'Computer Simulation of Liquids', 'year': '1989', 'key': '2023070402350531900_c3'} / Computer Simulation of Liquids (1989)
{'edition': '2nd ed.', 'volume-title': 'Understanding Molecular Simulation', 'year': '2002', 'key': '2023070402350531900_c4'} / Understanding Molecular Simulation (2002)
10.1038/35099513 / Nature (London) (2001)
10.1063/1.477658 / J. Chem. Phys. (1998)
10.1063/1.1417536 / J. Chem. Phys. (2001)
10.1063/1.465981 / J. Chem. Phys. (1993)
10.1063/1.1524192 / J. Chem. Phys. (2003)
10.1063/1.462557 / J. Chem. Phys. (1992)
10.1103/PhysRevB.34.1841 / Phys. Rev. B (1986)
10.1063/1.2218845 / J. Chem. Phys. (2006)
10.1103/PhysRevLett.96.225701 / Phys. Rev. Lett. (2006)
10.1103/PhysRevLett.96.245701 / Phys. Rev. Lett. (2006)
{'volume-title': 'Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation', 'year': '1974', 'key': '2023070402350531900_c15'} / Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation (1974)
{'key': '2023070402350531900_c16', 'first-page': '227', 'volume': '119', 'year': '1926', 'journal-title': 'Z. Phys. Chem'} / Z. Phys. Chem (1926)
{'key': '2023070402350531900_c17', 'first-page': '719', 'volume': '24', 'year': '1935', 'journal-title': 'Ann. Phys.'} / Ann. Phys. (1935)
{'volume-title': 'Kinetic Theory of Liquids', 'year': '1946', 'key': '2023070402350531900_c18'} / Kinetic Theory of Liquids (1946)
{'key': '2023070402350531900_c19', 'first-page': '1', 'volume': '18', 'year': '1943', 'journal-title': 'Acta Physicochim. URSS'} / Acta Physicochim. URSS (1943)
10.1146/annurev.physchem.46.1.489 / Annu. Rev. Phys. Chem. (1995)
10.1063/1.450396 / J. Chem. Phys. (1986)
10.1021/j100083a003 / J. Phys. Chem. (1994)
10.1063/1.471145 / J. Chem. Phys. (1996)
10.1063/1.1322082 / J. Chem. Phys. (2000)
10.1021/jp0115805 / J. Phys. Chem. B (2001)
10.1063/1.1809115 / J. Chem. Phys. (2004)
10.1103/PhysRevLett.76.2754 / Phys. Rev. Lett. (1996)
10.1063/1.477509 / J. Chem. Phys. (1998)
10.1063/1.1412608 / J. Chem. Phys. (2001)
10.1063/1.1621855 / J. Chem. Phys. (2003)
10.1080/0892702031000152091 / Mol. Simul. (2004)
10.1063/1.1896345 / J. Chem. Phys. (2005)
S. Wonczak, Ph.D. thesis, Universität zu Köln, 2001.
{'volume-title': 'J. Chem. Phys.', 'key': '2023070402350531900_c34'} / J. Chem. Phys.
{'volume-title': 'J. Chem. Phys.', 'key': '2023070402350531900_c35'} / J. Chem. Phys.
10.1021/jp002107e / J. Phys. Chem. A (2000)
10.1103/PhysRevE.64.011602 / Phys. Rev. E (2001)
10.1103/RevModPhys.77.371 / Rev. Mod. Phys. (2005)
{'year': '1969', 'key': '2023070402350531900_c39'} (1969)
10.1063/1.555829 / J. Phys. Chem. Ref. Data (1989)
{'key': '2023070402350531900_c41', 'first-page': '1', 'volume': '118a', 'year': '1911', 'journal-title': 'Commun. Phys. Lab. Univ. Leiden'} / Commun. Phys. Lab. Univ. Leiden (1911)
10.1039/tf9666201097 / Trans. Faraday Soc. (1966)

Dates

Type	When
Created	18 years, 8 months ago (Dec. 7, 2006, 7:54 p.m.)
Deposited	2 years, 1 month ago (July 3, 2023, 10:35 p.m.)
Indexed	1 month ago (July 30, 2025, 6:48 a.m.)
Issued	18 years, 8 months ago (Dec. 7, 2006)
Published	18 years, 8 months ago (Dec. 7, 2006)
Published Online	18 years, 8 months ago (Dec. 7, 2006)
Published Print	18 years, 8 months ago (Dec. 7, 2006)

Funders 0

None

BibTeX

@article{Wedekind_2006, title={Finite-size effects in simulations of nucleation}, volume={125}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2402167}, DOI={10.1063/1.2402167}, number={21}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Wedekind, Jan and Reguera, David and Strey, Reinhard}, year={2006}, month=dec }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        30
      ]
    ],
    "date-time": "2025-07-30T10:48:38Z",
    "timestamp": 1753872518419,
    "version": "3.41.2"
  },
  "reference-count": 42,
  "publisher": "AIP Publishing",
  "issue": "21",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2006,
        12,
        7
      ]
    ]
  },
  "abstract": "<jats:p>We investigate the importance of finite-size effects in simulations of nucleation processes. Most molecular dynamics simulations of first order phase transitions, such as vapor-liquid nucleation, are performed in the canonical NVT ensemble where, owing to the fixed total number of molecules N, the growth of the new phase causes the depletion of the metastable phase. This effect may lead to significant errors in the simulation and even to the impossibility of observing nucleation in a small finite system. We present a theory to estimate the system size beyond which these finite-size effects are expected to be negligible. This optimization saves valuable calculation time and can extend the range of supersaturations and rates attainable by simulations by several orders of magnitude. Our results are applicable to diverse situations, such as crystallization, capillary condensation, or the melting of nanoclusters.</jats:p>",
  "DOI": "10.1063/1.2402167",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        12,
        8
      ]
    ],
    "date-time": "2006-12-08T00:54:58Z",
    "timestamp": 1165539298000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 127,
  "title": "Finite-size effects in simulations of nucleation",
  "prefix": "10.1063",
  "volume": "125",
  "author": [
    {
      "given": "Jan",
      "family": "Wedekind",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Universit\u00e4t zu K\u00f6ln Institut f\u00fcr Physikalische Chemie, , Luxemburger Strasse 116, D-50939 K\u00f6ln, Germany"
        }
      ]
    },
    {
      "given": "David",
      "family": "Reguera",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Universitat de Barcelona Departament de F\u00edsica Fonamental, , Mart\u00ed i Franqu\u00e8s 1, 08028 Barcelona, Spain"
        }
      ]
    },
    {
      "given": "Reinhard",
      "family": "Strey",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Universit\u00e4t zu K\u00f6ln Institut f\u00fcr Physikalische Chemie, , Luxemburger Strasse 116, D-50939 K\u00f6ln, Germany"
        }
      ]
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2006,
        12,
        7
      ]
    ]
  },
  "reference": [
    {
      "key": "2023070402350531900_c1",
      "doi-asserted-by": "publisher",
      "first-page": "7627",
      "DOI": "10.1088/0953-8984/4/38/001",
      "volume": "4",
      "year": "1992",
      "journal-title": "J. Phys.: Condens. Matter"
    },
    {
      "volume-title": "Nucleation: Basic Theory With Applications",
      "year": "2000",
      "key": "2023070402350531900_c2"
    },
    {
      "volume-title": "Computer Simulation of Liquids",
      "year": "1989",
      "key": "2023070402350531900_c3"
    },
    {
      "edition": "2nd ed.",
      "volume-title": "Understanding Molecular Simulation",
      "year": "2002",
      "key": "2023070402350531900_c4"
    },
    {
      "key": "2023070402350531900_c5",
      "doi-asserted-by": "publisher",
      "first-page": "711",
      "DOI": "10.1038/35099513",
      "volume": "413",
      "year": "2001",
      "journal-title": "Nature (London)"
    },
    {
      "key": "2023070402350531900_c6",
      "doi-asserted-by": "publisher",
      "first-page": "9901",
      "DOI": "10.1063/1.477658",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c7",
      "doi-asserted-by": "publisher",
      "first-page": "10903",
      "DOI": "10.1063/1.1417536",
      "volume": "115",
      "year": "2001",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c8",
      "doi-asserted-by": "publisher",
      "first-page": "5374",
      "DOI": "10.1063/1.465981",
      "volume": "99",
      "year": "1993",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c9",
      "doi-asserted-by": "publisher",
      "first-page": "340",
      "DOI": "10.1063/1.1524192",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c10",
      "doi-asserted-by": "publisher",
      "first-page": "6989",
      "DOI": "10.1063/1.462557",
      "volume": "96",
      "year": "1992",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c11",
      "doi-asserted-by": "publisher",
      "first-page": "1841",
      "DOI": "10.1103/PhysRevB.34.1841",
      "volume": "34",
      "year": "1986",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070402350531900_c12",
      "doi-asserted-by": "publisher",
      "first-page": "034705",
      "DOI": "10.1063/1.2218845",
      "volume": "125",
      "year": "2006",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c13",
      "doi-asserted-by": "publisher",
      "first-page": "225701",
      "DOI": "10.1103/PhysRevLett.96.225701",
      "volume": "96",
      "year": "2006",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023070402350531900_c14",
      "doi-asserted-by": "publisher",
      "first-page": "245701",
      "DOI": "10.1103/PhysRevLett.96.245701",
      "volume": "96",
      "year": "2006",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "volume-title": "Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation",
      "year": "1974",
      "key": "2023070402350531900_c15"
    },
    {
      "key": "2023070402350531900_c16",
      "first-page": "227",
      "volume": "119",
      "year": "1926",
      "journal-title": "Z. Phys. Chem"
    },
    {
      "key": "2023070402350531900_c17",
      "first-page": "719",
      "volume": "24",
      "year": "1935",
      "journal-title": "Ann. Phys."
    },
    {
      "volume-title": "Kinetic Theory of Liquids",
      "year": "1946",
      "key": "2023070402350531900_c18"
    },
    {
      "key": "2023070402350531900_c19",
      "first-page": "1",
      "volume": "18",
      "year": "1943",
      "journal-title": "Acta Physicochim. URSS"
    },
    {
      "key": "2023070402350531900_c20",
      "doi-asserted-by": "publisher",
      "first-page": "489",
      "DOI": "10.1146/annurev.physchem.46.1.489",
      "volume": "46",
      "year": "1995",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2023070402350531900_c21",
      "doi-asserted-by": "publisher",
      "first-page": "2325",
      "DOI": "10.1063/1.450396",
      "volume": "84",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c22",
      "doi-asserted-by": "publisher",
      "first-page": "7748",
      "DOI": "10.1021/j100083a003",
      "volume": "98",
      "year": "1994",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023070402350531900_c23",
      "doi-asserted-by": "publisher",
      "first-page": "5181",
      "DOI": "10.1063/1.471145",
      "volume": "104",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c24",
      "doi-asserted-by": "publisher",
      "first-page": "9741",
      "DOI": "10.1063/1.1322082",
      "volume": "113",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c25",
      "doi-asserted-by": "publisher",
      "first-page": "11683",
      "DOI": "10.1021/jp0115805",
      "volume": "105",
      "year": "2001",
      "journal-title": "J. Phys. Chem. B"
    },
    {
      "key": "2023070402350531900_c26",
      "doi-asserted-by": "publisher",
      "first-page": "12259",
      "DOI": "10.1063/1.1809115",
      "volume": "121",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c27",
      "doi-asserted-by": "publisher",
      "first-page": "2754",
      "DOI": "10.1103/PhysRevLett.76.2754",
      "volume": "76",
      "year": "1996",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023070402350531900_c28",
      "doi-asserted-by": "publisher",
      "first-page": "8451",
      "DOI": "10.1063/1.477509",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c29",
      "doi-asserted-by": "publisher",
      "first-page": "8913",
      "DOI": "10.1063/1.1412608",
      "volume": "115",
      "year": "2001",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c30",
      "doi-asserted-by": "publisher",
      "first-page": "10764",
      "DOI": "10.1063/1.1621855",
      "volume": "119",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c31",
      "doi-asserted-by": "publisher",
      "first-page": "179",
      "DOI": "10.1080/0892702031000152091",
      "volume": "30",
      "year": "2004",
      "journal-title": "Mol. Simul."
    },
    {
      "key": "2023070402350531900_c32",
      "doi-asserted-by": "publisher",
      "first-page": "184514",
      "DOI": "10.1063/1.1896345",
      "volume": "122",
      "year": "2005",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023070402350531900_c33",
      "unstructured": "S.\u2008Wonczak, Ph.D. thesis, Universit\u00e4t zu K\u00f6ln, 2001."
    },
    {
      "volume-title": "J. Chem. Phys.",
      "key": "2023070402350531900_c34"
    },
    {
      "volume-title": "J. Chem. Phys.",
      "key": "2023070402350531900_c35"
    },
    {
      "key": "2023070402350531900_c36",
      "doi-asserted-by": "publisher",
      "first-page": "9328",
      "DOI": "10.1021/jp002107e",
      "volume": "104",
      "year": "2000",
      "journal-title": "J. Phys. Chem. A"
    },
    {
      "key": "2023070402350531900_c37",
      "doi-asserted-by": "publisher",
      "first-page": "011602",
      "DOI": "10.1103/PhysRevE.64.011602",
      "volume": "64",
      "year": "2001",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2023070402350531900_c38",
      "doi-asserted-by": "publisher",
      "first-page": "371",
      "DOI": "10.1103/RevModPhys.77.371",
      "volume": "77",
      "year": "2005",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "year": "1969",
      "key": "2023070402350531900_c39"
    },
    {
      "key": "2023070402350531900_c40",
      "doi-asserted-by": "crossref",
      "first-page": "639",
      "DOI": "10.1063/1.555829",
      "volume": "18",
      "year": "1989",
      "journal-title": "J. Phys. Chem. Ref. Data"
    },
    {
      "key": "2023070402350531900_c41",
      "first-page": "1",
      "volume": "118a",
      "year": "1911",
      "journal-title": "Commun. Phys. Lab. Univ. Leiden"
    },
    {
      "key": "2023070402350531900_c42",
      "doi-asserted-by": "publisher",
      "first-page": "1097",
      "DOI": "10.1039/tf9666201097",
      "volume": "62",
      "year": "1966",
      "journal-title": "Trans. Faraday Soc."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2402167/14735942/214505_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2402167/14735942/214505_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        7,
        4
      ]
    ],
    "date-time": "2023-07-04T02:35:19Z",
    "timestamp": 1688438119000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/125/21/214505/349054/Finite-size-effects-in-simulations-of-nucleation"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2006,
        12,
        7
      ]
    ]
  },
  "references-count": 42,
  "journal-issue": {
    "issue": "21",
    "published-print": {
      "date-parts": [
        [
          2006,
          12,
          7
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.2402167",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2006,
        12,
        7
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2006,
        12,
        7
      ]
    ]
  },
  "article-number": "214505"
}