DOI: 10.1063/1.458153. A density functional theory of polymer phase transitions and interfaces

A density functional theory of polymer phase transitions and interfaces

10.1063/1.458153

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We employ density functional methods to derive the free energy and grand potential functionals appropriate to homopolymers and blends. The grand potential functionals are minimized by the single-monomer densities of the blends or homopolymers, and the nonideal portions of the free energies possess functional Taylor expansions whose coefficients are related to monomer–monomer direct correlation functions. In the limit that the polymerization indices become unity, the formalism reduces to that of atomic systems. By absorbing parts of the ideal free energy functionals into the nonideal contribution to the free energies, we demonstrate the formal equivalence of the theory of polymers to that of nonuniform atomic systems. The polymer formalism also reproduces the stability analyses of polymer phase transitions deduced by regarding dense polymeric liquids as atomic fluids. Nevertheless, for homogeneous polymeric fluids, the ideal free energy functionals become the well-known Flory–Huggins expressions for the entropy of mixing different homopolymers and the entropy of dissolving homopolymers in solvent. This suggests that numerical calculations, based on the correct ideal free energy functionals, will prove superior to calculations for polymers that derive from theories of atomic systems. We discuss extensions to block copolymers and mention numerous applications to polymer phase transitions and interfacial phenomena.

Bibliography

McMullen, W. E., & Freed, K. F. (1990). A density functional theory of polymer phase transitions and interfaces. The Journal of Chemical Physics, 92(2), 1413â1426.

Authors 2

William E. McMullen (first)
Karl F. Freed (additional)

References 80 Referenced 76

{'key': '2024021009232416500_r1'}
10.1021/j150415a018 / J. Phys. Chem. (1942)
{'key': '2024021009232416500_r2a', 'first-page': '1', 'volume': '41', 'year': '1942', 'journal-title': 'Ann. N.Y. Acad. Sci.'} / Ann. N.Y. Acad. Sci. (1942)
10.1021/ja01259a068 / J. Am. Chem. Soc. (1942)
{'key': '2024021009232416500_r3'}
{'key': '2024021009232416500_r4'}
{'key': '2024021009232416500_r4a'}
10.1021/ja01071a023 / J. Am. Chem. Soc. (1964)
{'key': '2024021009232416500_r6', 'first-page': '343', 'volume': '2', 'year': '1969', 'journal-title': 'Macromolecules'} / Macromolecules (1969)
10.1021/j100562a008 / J. Phys. Chem. (1976)
10.1103/PhysRevLett.51.896 / Phys. Rev. Lett. (1983)
10.1021/ma00153a020 / Macromolecules (1985)
{'key': '2024021009232416500_r8b', 'first-page': '137', 'volume': '194', 'year': '1986', 'journal-title': 'Physica B (Amsterdam)'} / Physica B (Amsterdam) (1986)
10.1021/ma60078a047 / Macromolecules (1980)
10.1063/1.455116 / J. Chem. Phys. (1988)
10.1021/ma00164a008 / Macromolecules (1986)
10.1021/ma00168a040 / Macromolecules (1987)
10.1021/ma00181a043 / Macromolecules (1988)
10.1063/1.439809 / J. Chem. Phys. (1980)
10.1063/1.442226 / J. Chem. Phys. (1981)
10.1063/1.445747 / J. Chem. Phys. (1983)
10.1103/PhysRevB.19.2775 / Phys. Rev. B (1979)
10.1063/1.441326 / J. Chem. Phys. (1981)
10.1063/1.451510 / J. Chem. Phys. (1986)
10.1063/1.452848 / J. Chem. Phys. (1987)
10.1063/1.451925 / J. Chem. Phys. (1987)
10.1063/1.454288 / J. Chem. Phys. (1988)
10.1103/PhysRevA.35.3095 / Phys. Rev. A (1987)
10.1103/PhysRevLett.59.2184 / Phys. Rev. Lett. (1987)
10.1103/PhysRevLett.60.325 / Phys. Rev. Lett. (1988)
10.1103/PhysRevLett.59.1228 / Phys. Rev. Lett. (1987)
10.1063/1.454121 / J. Chem. Phys. (1988)
10.1063/1.434543 / J. Chem. Phys. (1977)
10.1080/00018737900101365 / Adv. Phys. (1979)
10.1103/PhysRevA.38.1527 / Phys. Rev. A (1988)
10.1103/PhysRevA.38.6384 / Phys. Rev. A (1988)
{'key': '2024021009232416500_r26', 'first-page': '1480', 'volume': '32', 'year': '1985', 'journal-title': 'Phys. Rev. B'} / Phys. Rev. B (1985)
10.1103/PhysRevLett.54.1059 / Phys. Rev. Lett. (1985)
10.1103/PhysRevLett.58.230 / Phys. Rev. Lett. (1987)
{'key': '2024021009232416500_r28a', 'first-page': '445', 'volume': '61', 'year': '1987', 'journal-title': 'Mol. Phys.'} / Mol. Phys. (1987)
10.1063/1.456600 / J. Chem. Phys. (1989)
{'key': '2024021009232416500_r29a'}
{'key': '2024021009232416500_r29b'}
10.1063/1.453566 / J. Chem. Phys. (1987)
{'key': '2024021009232416500_r30a', 'first-page': '5890', 'volume': '89', 'year': '1989', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1989)
10.1103/PhysRevLett.41.702 / Phys. Rev. Lett. (1978)
{'key': '2024021009232416500_r32'}
{'key': '2024021009232416500_r33', 'first-page': '3592', 'volume': '56', 'year': '1971', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1971)
10.1063/1.430632 / J. Chem. Phys. (1975)
10.1021/ma00233a014 / Macromolecules (1982)
10.1063/1.1744102 / J. Chem. Phys. (1958)
10.1063/1.455879 / J. Chem. Phys. (1989)
10.1063/1.454005 / J. Chem. Phys. (1988)
10.1063/1.451830 / J. Chem. Phys. (1986)
10.1063/1.451974 / J. Chem. Phys. (1987)
10.1063/1.453638 / J. Chem. Phys. (1987)
{'key': '2024021009232416500_r37d', 'first-page': '7036', 'volume': '84', 'year': '1986'} (1986)
10.1063/1.453320 / J. Chem. Phys. (1987)
10.1063/1.451010 / J. Chem. Phys. (1986)
10.1063/1.457479 / J. Chem. Phys. (1989)
{'key': '2024021009232416500_r38b'}
{'key': '2024021009232416500_r38c'}
10.1103/PhysRev.136.B864 / Phys. Rev. B (1964)
{'key': '2024021009232416500_r39a', 'first-page': '1441', 'volume': '137', 'year': '1965', 'journal-title': 'Phys. Rev. A'} / Phys. Rev. A (1965)
10.1080/00268978400101071 / Mol. Phys. (1984)
10.1103/PhysRevA.31.2672 / Phys. Rev. A (1985)
10.1103/PhysRevA.32.2909 / Phys. Rev. A (1985)
10.1080/00268978500101621 / Mol. Phys. (1985)
10.1080/00268978500102731 / Mol. Phys. (1985)
10.1080/00268978600100581 / Mol. Phys. (1986)
{'key': '2024021009232416500_r42', 'first-page': '7789', 'volume': '88', 'year': '1988', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1988)
{'key': '2024021009232416500_r42a'}
{'key': '2024021009232416500_r43'}
{'key': '2024021009232416500_r43a'}
10.1063/1.445310 / J. Chem. Phys. (1983)
10.1021/j100343a006 / J. Phys. Chem. (1989)
10.1103/PhysRevLett.60.809 / Phys. Rev. Lett. (1988)
10.1063/1.454377 / J. Chem. Phys. (1988)
{'key': '2024021009232416500_r46b', 'first-page': '3342', 'volume': '89', 'year': '1989', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1989)
10.1063/1.457159 / J. Chem. Phys. (1989)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:21 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 6:08 a.m.)
Indexed	4 months, 4 weeks ago (March 27, 2025, 4:16 a.m.)
Issued	35 years, 7 months ago (Jan. 15, 1990)
Published	35 years, 7 months ago (Jan. 15, 1990)
Published Print	35 years, 7 months ago (Jan. 15, 1990)

Funders 0

None

BibTeX

@article{McMullen_1990, title={A density functional theory of polymer phase transitions and interfaces}, volume={92}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.458153}, DOI={10.1063/1.458153}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={McMullen, William E. and Freed, Karl F.}, year={1990}, month=jan, pages={1413–1426} }

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      "year": "1964",
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    },
    {
      "key": "2024021009232416500_r6",
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      "volume": "2",
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      "first-page": "2352",
      "DOI": "10.1021/j100562a008",
      "volume": "80",
      "year": "1976",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2024021009232416500_r8",
      "doi-asserted-by": "crossref",
      "first-page": "896",
      "DOI": "10.1103/PhysRevLett.51.896",
      "volume": "51",
      "year": "1983",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r8a",
      "doi-asserted-by": "crossref",
      "first-page": "2179",
      "DOI": "10.1021/ma00153a020",
      "volume": "18",
      "year": "1985",
      "journal-title": "Macromolecules"
    },
    {
      "key": "2024021009232416500_r8b",
      "first-page": "137",
      "volume": "194",
      "year": "1986",
      "journal-title": "Physica B (Amsterdam)"
    },
    {
      "key": "2024021009232416500_r9",
      "doi-asserted-by": "crossref",
      "first-page": "1602",
      "DOI": "10.1021/ma60078a047",
      "volume": "13",
      "year": "1980",
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    {
      "key": "2024021009232416500_r10",
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      "first-page": "1704",
      "DOI": "10.1063/1.455116",
      "volume": "89",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r11",
      "doi-asserted-by": "crossref",
      "first-page": "2501",
      "DOI": "10.1021/ma00164a008",
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      "journal-title": "Macromolecules"
    },
    {
      "key": "2024021009232416500_r11a",
      "doi-asserted-by": "crossref",
      "first-page": "440",
      "DOI": "10.1021/ma00168a040",
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      "journal-title": "Macromolecules"
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    {
      "key": "2024021009232416500_r12",
      "doi-asserted-by": "crossref",
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    {
      "key": "2024021009232416500_r13",
      "doi-asserted-by": "crossref",
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      "DOI": "10.1063/1.439809",
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    {
      "key": "2024021009232416500_r14",
      "doi-asserted-by": "crossref",
      "first-page": "1996",
      "DOI": "10.1063/1.442226",
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      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r15",
      "doi-asserted-by": "crossref",
      "first-page": "6387",
      "DOI": "10.1063/1.445747",
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      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r16",
      "doi-asserted-by": "crossref",
      "first-page": "2775",
      "DOI": "10.1103/PhysRevB.19.2775",
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      "year": "1979",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021009232416500_r17",
      "doi-asserted-by": "crossref",
      "first-page": "2559",
      "DOI": "10.1063/1.441326",
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      "year": "1981",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r18",
      "doi-asserted-by": "crossref",
      "first-page": "5971",
      "DOI": "10.1063/1.451510",
      "volume": "85",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r18a",
      "doi-asserted-by": "crossref",
      "first-page": "4853",
      "DOI": "10.1063/1.452848",
      "volume": "87",
      "year": "1987",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r19",
      "doi-asserted-by": "crossref",
      "first-page": "4146",
      "DOI": "10.1063/1.451925",
      "volume": "86",
      "year": "1987",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r19a",
      "doi-asserted-by": "crossref",
      "first-page": "7757",
      "DOI": "10.1063/1.454288",
      "volume": "88",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r20",
      "doi-asserted-by": "crossref",
      "first-page": "3095",
      "DOI": "10.1103/PhysRevA.35.3095",
      "volume": "35",
      "year": "1987",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021009232416500_r21",
      "doi-asserted-by": "crossref",
      "first-page": "2184",
      "DOI": "10.1103/PhysRevLett.59.2184",
      "volume": "59",
      "year": "1987",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r21a",
      "doi-asserted-by": "crossref",
      "first-page": "325",
      "DOI": "10.1103/PhysRevLett.60.325",
      "volume": "60",
      "year": "1988",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r22",
      "doi-asserted-by": "crossref",
      "first-page": "1228",
      "DOI": "10.1103/PhysRevLett.59.1228",
      "volume": "59",
      "year": "1987",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r22a",
      "doi-asserted-by": "crossref",
      "first-page": "1967",
      "DOI": "10.1063/1.454121",
      "volume": "88",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r23",
      "doi-asserted-by": "crossref",
      "first-page": "74",
      "DOI": "10.1063/1.434543",
      "volume": "67",
      "year": "1977",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r24",
      "doi-asserted-by": "crossref",
      "first-page": "143",
      "DOI": "10.1080/00018737900101365",
      "volume": "28",
      "year": "1979",
      "journal-title": "Adv. Phys."
    },
    {
      "key": "2024021009232416500_r25",
      "doi-asserted-by": "crossref",
      "first-page": "1527",
      "DOI": "10.1103/PhysRevA.38.1527",
      "volume": "38",
      "year": "1988",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021009232416500_r25a",
      "doi-asserted-by": "crossref",
      "first-page": "6384",
      "DOI": "10.1103/PhysRevA.38.6384",
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      "year": "1988",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021009232416500_r26",
      "first-page": "1480",
      "volume": "32",
      "year": "1985",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021009232416500_r27",
      "doi-asserted-by": "crossref",
      "first-page": "1059",
      "DOI": "10.1103/PhysRevLett.54.1059",
      "volume": "54",
      "year": "1985",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r28",
      "doi-asserted-by": "crossref",
      "first-page": "230",
      "DOI": "10.1103/PhysRevLett.58.230",
      "volume": "58",
      "year": "1987",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r28a",
      "first-page": "445",
      "volume": "61",
      "year": "1987",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024021009232416500_r29",
      "doi-asserted-by": "crossref",
      "first-page": "4622",
      "DOI": "10.1063/1.456600",
      "volume": "90",
      "year": "1989",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r29a"
    },
    {
      "key": "2024021009232416500_r29b"
    },
    {
      "key": "2024021009232416500_r30",
      "doi-asserted-by": "crossref",
      "first-page": "697",
      "DOI": "10.1063/1.453566",
      "volume": "87",
      "year": "1987",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r30a",
      "first-page": "5890",
      "volume": "89",
      "year": "1989",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r31",
      "doi-asserted-by": "crossref",
      "first-page": "702",
      "DOI": "10.1103/PhysRevLett.41.702",
      "volume": "41",
      "year": "1978",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021009232416500_r32"
    },
    {
      "key": "2024021009232416500_r33",
      "first-page": "3592",
      "volume": "56",
      "year": "1971",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r33a",
      "doi-asserted-by": "crossref",
      "first-page": "1327",
      "DOI": "10.1063/1.430632",
      "volume": "62",
      "year": "1975",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021009232416500_r34",
      "doi-asserted-by": "crossref",
      "first-page": "1283",
      "DOI": "10.1021/ma00233a014",
      "volume": "15",
      "year": "1982",
      "journal-title": "Macromolecules"
    },
    {
      "key": "2024021009232416500_r35",
      "doi-asserted-by": "crossref",
      "first-page": "258",
      "DOI": "10.1063/1.1744102",
      "volume": "28",
      "year": "1958",
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    {
      "key": "2024021009232416500_r39a",
      "first-page": "1441",
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