DOI: 10.1063/1.434125. Monte Carlo study of a phase-separating liquid mixture by umbrella sampling

Monte Carlo study of a phase-separating liquid mixture by umbrella sampling

10.1063/1.434125

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Recently developed nonphysical sampling methods—umbrella sampling—have been used to obtain the free energy and other properties of a binary liquid mixture exhibiting phase separation with an upper critical solution point. The system is a mixture of two identical Lennard-Jones liquids in which the interactions between the components are characterized by a range parameter σ12 obeying the Lorentz rule, but an energy parameter ε12= (1−α) (ε11ε22)1/2 violating the Berthelot rule. The sampling methods enable one to cover wide ranges of temperature and composition with few Monte Carlo experiments, successfully sampling the metastable regions and obtaining the coexistence curve. The case α=0.25 is studied in detail, and compared with some theoretical predictions. An estimate is made of the minimum value of α required for phase separation at low pressures.

Bibliography

Torrie, G. M., & Valleau, J. P. (1977). Monte Carlo study of a phase-separating liquid mixture by umbrella sampling. The Journal of Chemical Physics, 66(4), 1402â1408.

Authors 2

G. M. Torrie (first)
J. P. Valleau (additional)

References 21 Referenced 181

10.1146/annurev.pc.25.100174.002333 / Ann. Rev. Phys. Chem. (1974)
{'key': '2024020914585463900_r2'}
10.1016/0009-2614(74)80109-0 / Chem. Phys. Lett. (1974)
{'key': '2024020914585463900_r4'}
{'key': '2024020914585463900_r5'}
{'key': '2024020914585463900_r6'}
10.1063/1.433290 / J. Chem. Phys. (1976)
10.1103/PhysRev.182.307 / Phys. Rev. (1969)
10.1063/1.1673541 / J. Chem. Phys. (1970)
10.1016/0031-8914(74)90231-6 / Physica (1974)
{'key': '2024020914585463900_r11', 'first-page': '539', 'volume': '1', 'year': '1968', 'journal-title': 'J. Phys. A. Ser. 2'} / J. Phys. A. Ser. 2 (1968)
10.1063/1.1701689 / J. Chem. Phys. (1967)
10.1080/00268977300100761 / Mol. Phys. (1973)
10.1063/1.1674820 / J. Chem. Phys. (1971)
10.1080/00268977300102531 / Mol. Phys. (1973)
10.1080/00268977000101261 / Mol. Phys. (1970)
10.1080/00268977200101511 / Mol. Phys. (1972)
10.1080/00268977200100031 / Mol. Phys. (1972)
10.1080/00268977200101521 / Mol. Phys. (1972)
10.1063/1.1674033 / J. Chem. Phys. (1970)
10.1103/PhysRevA.5.939 / Phys. Rev. A (1972)

Dates

Type	When
Created	22 years, 6 months ago (Feb. 27, 2003, 5:23 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 10:50 a.m.)
Indexed	2 months, 1 week ago (June 24, 2025, 11:13 a.m.)
Issued	48 years, 6 months ago (Feb. 15, 1977)
Published	48 years, 6 months ago (Feb. 15, 1977)
Published Print	48 years, 6 months ago (Feb. 15, 1977)

Funders 0

None

BibTeX

@article{Torrie_1977, title={Monte Carlo study of a phase-separating liquid mixture by umbrella sampling}, volume={66}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.434125}, DOI={10.1063/1.434125}, number={4}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Torrie, G. M. and Valleau, J. P.}, year={1977}, month=feb, pages={1402–1408} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        6,
        24
      ]
    ],
    "date-time": "2025-06-24T15:13:00Z",
    "timestamp": 1750777980367
  },
  "reference-count": 21,
  "publisher": "AIP Publishing",
  "issue": "4",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1977,
        2,
        15
      ]
    ]
  },
  "abstract": "<jats:p>Recently developed nonphysical sampling methods\u2014umbrella sampling\u2014have been used to obtain the free energy and other properties of a binary liquid mixture exhibiting phase separation with an upper critical solution point. The system is a mixture of two identical Lennard-Jones liquids in which the interactions between the components are characterized by a range parameter \u03c312 obeying the Lorentz rule, but an energy parameter \u03b512= (1\u2212\u03b1) (\u03b511\u03b522)1/2 violating the Berthelot rule. The sampling methods enable one to cover wide ranges of temperature and composition with few Monte Carlo experiments, successfully sampling the metastable regions and obtaining the coexistence curve. The case \u03b1=0.25 is studied in detail, and compared with some theoretical predictions. An estimate is made of the minimum value of \u03b1 required for phase separation at low pressures.</jats:p>",
  "DOI": "10.1063/1.434125",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        2,
        27
      ]
    ],
    "date-time": "2003-02-27T22:23:30Z",
    "timestamp": 1046384610000
  },
  "page": "1402-1408",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 181,
  "title": "Monte Carlo study of a phase-separating liquid mixture by umbrella sampling",
  "prefix": "10.1063",
  "volume": "66",
  "author": [
    {
      "given": "G. M.",
      "family": "Torrie",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Lash Miller Chemical Laboratories, University of Toronto, Toronto, Ontario, Canada"
        }
      ]
    },
    {
      "given": "J. P.",
      "family": "Valleau",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Lash Miller Chemical Laboratories, University of Toronto, Toronto, Ontario, Canada"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020914585463900_r1",
      "doi-asserted-by": "crossref",
      "first-page": "461",
      "DOI": "10.1146/annurev.pc.25.100174.002333",
      "volume": "25",
      "year": "1974",
      "journal-title": "Ann. Rev. Phys. Chem."
    },
    {
      "key": "2024020914585463900_r2"
    },
    {
      "key": "2024020914585463900_r3",
      "doi-asserted-by": "crossref",
      "first-page": "578",
      "DOI": "10.1016/0009-2614(74)80109-0",
      "volume": "28",
      "year": "1974",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020914585463900_r4"
    },
    {
      "key": "2024020914585463900_r5"
    },
    {
      "key": "2024020914585463900_r6"
    },
    {
      "key": "2024020914585463900_r7",
      "doi-asserted-by": "crossref",
      "first-page": "1937",
      "DOI": "10.1063/1.433290",
      "volume": "65",
      "year": "1976",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020914585463900_r8",
      "doi-asserted-by": "crossref",
      "first-page": "307",
      "DOI": "10.1103/PhysRev.182.307",
      "volume": "182",
      "year": "1969",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020914585463900_r9",
      "doi-asserted-by": "crossref",
      "first-page": "3665",
      "DOI": "10.1063/1.1673541",
      "volume": "52",
      "year": "1970",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020914585463900_r10",
      "doi-asserted-by": "crossref",
      "first-page": "143",
      "DOI": "10.1016/0031-8914(74)90231-6",
      "volume": "73",
      "year": "1974",
      "journal-title": "Physica"
    },
    {
      "key": "2024020914585463900_r11",
      "first-page": "539",
      "volume": "1",
      "year": "1968",
      "journal-title": "J. Phys. A. Ser. 2"
    },
    {
      "key": "2024020914585463900_r12",
      "doi-asserted-by": "crossref",
      "first-page": "4714",
      "DOI": "10.1063/1.1701689",
      "volume": "47",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020914585463900_r13",
      "doi-asserted-by": "crossref",
      "first-page": "883",
      "DOI": "10.1080/00268977300100761",
      "volume": "25",
      "year": "1973",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r14",
      "doi-asserted-by": "crossref",
      "first-page": "5237",
      "DOI": "10.1063/1.1674820",
      "volume": "54",
      "year": "1971",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020914585463900_r15",
      "doi-asserted-by": "crossref",
      "first-page": "1351",
      "DOI": "10.1080/00268977300102531",
      "volume": "26",
      "year": "1973",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r16",
      "doi-asserted-by": "crossref",
      "first-page": "279",
      "DOI": "10.1080/00268977000101261",
      "volume": "19",
      "year": "1970",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r17",
      "doi-asserted-by": "crossref",
      "first-page": "357",
      "DOI": "10.1080/00268977200101511",
      "volume": "24",
      "year": "1972",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r18",
      "doi-asserted-by": "crossref",
      "first-page": "41",
      "DOI": "10.1080/00268977200100031",
      "volume": "23",
      "year": "1972",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r19",
      "doi-asserted-by": "crossref",
      "first-page": "391",
      "DOI": "10.1080/00268977200101521",
      "volume": "24",
      "year": "1972",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020914585463900_r20",
      "doi-asserted-by": "crossref",
      "first-page": "600",
      "DOI": "10.1063/1.1674033",
      "volume": "53",
      "year": "1970",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020914585463900_r21",
      "doi-asserted-by": "crossref",
      "first-page": "939",
      "DOI": "10.1103/PhysRevA.5.939",
      "volume": "5",
      "year": "1972",
      "journal-title": "Phys. Rev. A"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/66/4/1402/18904534/1402_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/66/4/1402/18904534/1402_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T15:50:10Z",
    "timestamp": 1707493810000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/66/4/1402/216119/Monte-Carlo-study-of-a-phase-separating-liquid"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1977,
        2,
        15
      ]
    ]
  },
  "references-count": 21,
  "journal-issue": {
    "issue": "4",
    "published-print": {
      "date-parts": [
        [
          1977,
          2,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.434125",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1977,
        2,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1977,
        2,
        15
      ]
    ]
  }
}