DOI: 10.1063/1.446209. Theory of critical micelle concentration for solutions of block copolymers

Theory of critical micelle concentration for solutions of block copolymers

10.1063/1.446209

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A simple microscopic model for micellar formation in mixtures of block copolymers and homopolymers is presented. The size, number of chains, and energy of formation of micelle are calculated. The fraction of copolymer chains aggregating into micelles is computed as a function of the overall copolymer content. A critical micelle concentration behavior is found for low copolymer contents even for weak incompatibilities of species. The similarity with an aborted phase transition is underlined.

Bibliography

Leibler, L., Orland, H., & Wheeler, J. C. (1983). Theory of critical micelle concentration for solutions of block copolymers. The Journal of Chemical Physics, 79(7), 3550â3557.

Authors 3

Ludwik Leibler (first)
Henri Orland (additional)
John C. Wheeler (additional)

References 38 Referenced 357

{'key': '2024020923593605000_r1', 'first-page': '58', 'volume': '101', 'year': '1961', 'journal-title': 'Makromol. Chem.'} / Makromol. Chem. (1961)
10.1002/pol.1969.160070801 / J. Polym. Sci. Part A (1969)
10.1021/ma60013a018 / Macromolecules (1970)
10.1002/pen.760170823 / Polym. Eng. Sci. (1977)
{'key': '2024020923593605000_r3a', 'first-page': '313', 'volume': '12', 'year': '1979', 'journal-title': 'Macromolecules'} / Macromolecules (1979)
10.1021/ma00230a033 / Macromolecules (1982)
10.1016/0032-3861(79)90016-8 / Polymer (1979)
10.1021/ma60077a037 / Macromolecules (1980)
{'key': '2024020923593605000_r5a'}
10.1002/marc.1982.030030608 / Makromol. Chem. Rapid Commun. (1982)
{'key': '2024020923593605000_r7'}
10.1007/BF01539016 / Colloid Polym. Sci. (1979)
10.1016/0032-3861(79)90147-2 / Polymer (1979)
10.1002/polc.5070340106 / J. Polym. Sci. Part C (1971)
10.1002/marc.1980.030011213 / Makromol. Chem. Rapid Commun. (1980)
10.1002/polc.5070260106 / J. Polym. Sci. C (1969)
{'key': '2024020923593605000_r11a', 'first-page': '400', 'volume': '11', 'year': '1970', 'journal-title': 'Am. Chem. Soc. Polym. Preprints'} / Am. Chem. Soc. Polym. Preprints (1970)
{'key': '2024020923593605000_r11b', 'first-page': '340', 'volume': '18', 'year': '1977'} (1977)
{'key': '2024020923593605000_r12'}
10.1021/ma50006a010 / Macromolecules (1981)
10.1002/marc.1981.030020409 / Makromol. Chem. Rapid Commun. (1981)
{'key': '2024020923593605000_r14a', 'volume': '15', 'year': '1982', 'journal-title': 'Macromolecules'} / Macromolecules (1982)
10.1021/ma00230a054 / Macromolecules (1982)
{'key': '2024020923593605000_r16'}
{'key': '2024020923593605000_r17', 'first-page': '2622', 'volume': '62', 'year': '1975', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1975)
10.1016/0021-9797(77)90282-X / J. Colloid Interface Sci. (1977)
10.1021/j100459a008 / J. Phys. Chem. (1980)
10.1063/1.441320 / J. Chem. Phys. (1981)
{'key': '2024020923593605000_r19'}
{'key': '2024020923593605000_r20'}
{'key': '2024020923593605000_r21'}
{'key': '2024020923593605000_r22'}
{'key': '2024020923593605000_r23'}
10.1002/pol.1971.110091006 / J. Polym. Sci. Part B (1971)
10.1063/1.430632 / J. Chem. Phys. (1975)
{'key': '2024020923593605000_r25'}
10.1021/j100617a012 / J. Phys. Chem. (1974)
{'key': '2024020923593605000_r27', 'first-page': '1085', 'volume': '51', 'year': '1979', 'journal-title': 'Pure Appl. Chem.'} / Pure Appl. Chem. (1979)

Dates

Type	When
Created	22 years, 5 months ago (Feb. 28, 2003, 12:03 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 8:25 p.m.)
Indexed	3 weeks, 1 day ago (Aug. 2, 2025, 1:28 a.m.)
Issued	41 years, 10 months ago (Oct. 1, 1983)
Published	41 years, 10 months ago (Oct. 1, 1983)
Published Print	41 years, 10 months ago (Oct. 1, 1983)

Funders 0

None

BibTeX

@article{Leibler_1983, title={Theory of critical micelle concentration for solutions of block copolymers}, volume={79}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.446209}, DOI={10.1063/1.446209}, number={7}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Leibler, Ludwik and Orland, Henri and Wheeler, John C.}, year={1983}, month=oct, pages={3550–3557} }

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