DOI: 10.1063/1.1679222. Molecular theory of the translational Stokes-Einstein relation

Molecular theory of the translational Stokes-Einstein relation

10.1063/1.1679222

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A molecular-statistical derivation is presented for the Stokes-Einstein expression for the translational diffusion constant for a Brownian (large) particle. The friction constant is expressed in terms of a correlation function of the forces on the particle, and this correlation function is related to the correlation function of pressure fluctuations in a volume equal to that of the particle. Whereas the forces are those on the particle surface, the pressure fluctuations are a property of the liquid solvent. The amplitude of the pressure fluctuations can be obtained from fluctuation theory and the time dependence can be obtained from hydrodynamics, which in turn can be derived from molecular-statistical considerations. Although the exact numerical factors cannot be obtained, the linear dependence of the friction constant on the radius of the Brownian particle is derived. Finally, a discussion of the diffusion constant for small diffusing particles is presented.

Bibliography

Kivelson, D., Jensen, S. J. K., & Ahn, M.-K. (1973). Molecular theory of the translational Stokes-Einstein relation. The Journal of Chemical Physics, 58(2), 428â433.

Authors 3

Daniel Kivelson (first)
S.J. Knak Jensen (additional)
Myong-Ku Ahn (additional)

References 42 Referenced 17

{'key': '2024020909583808900_r1'}
10.1063/1.1724117 / J. Chem. Phys. (1946)
{'key': '2024020909583808900_r2a', 'first-page': '2381', 'volume': '13', 'year': '1963', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1963)
10.1063/1.1725558 / J. Chem. Phys. (1964)
10.1063/1.1678688 / J. Chem. Phys. (1972)
10.1143/PTP.33.423 / Prog. Theor. Phys. (1965)
{'key': '2024020909583808900_r6'}
10.1111/j.1749-6632.1945.tb36170.x / Ann. N.Y. Acad. Sci. (1945)
10.1063/1.1743136 / J. Chem. Phys. (1956)
{'key': '2024020909583808900_r9', 'first-page': '143', 'volume': '68B', 'year': '1964', 'journal-title': 'Natl. Bur. Std.'} / Natl. Bur. Std. (1964)
10.1016/0031-8914(70)90005-4 / Physica (Utr.) (1970)
{'key': '2024020909583808900_r11'}
{'key': '2024020909583808900_r12'}
{'key': '2024020909583808900_r13'}
{'key': '2024020909583808900_r14'}
10.1063/1.1696718 / J. Chem. Phys. (1965)
{'key': '2024020909583808900_r16'}
{'key': '2024020909583808900_r17'}
10.1016/0031-8914(64)90056-4 / Physica (Utr.) (1964)
{'key': '2024020909583808900_r18'}
10.1080/00319107108083815 / Phys. Chem. Liq. (1971)
10.1016/0031-8914(65)90112-6 / Physica (Utr.) (1965)
10.1021/j100863a035 / J. Phys. Chem. (1967)
{'key': '2024020909583808900_r21a', 'first-page': '235', 'volume': '7', 'year': '1963', 'journal-title': 'Mol. Phys.'} / Mol. Phys. (1963)
10.1021/j150404a002 / J. Phys. Chem. (1940)
{'key': '2024020909583808900_r22'}
{'key': '2024020909583808900_r23'}
10.1103/PhysRevA.2.2005 / Phys. Rev. A (1970)
10.1103/PhysRevA.3.1394 / Phys. Rev. A (1971)
10.1088/0370-1328/86/5/306 / Proc. Phys. Soc. Lond. (1965)
10.1063/1.1727719 / J. Chem. Phys. (1966)
10.1103/PhysRev.157.153 / Phys. Rev. (1967)
10.1103/PhysRev.170.151 / Phys. Rev. (1968)
10.1103/PhysRevA.1.18 / Phys. Rev. A (1970)
10.1063/1.1673845 / J. Chem. Phys. (1970)
{'key': '2024020909583808900_r28', 'first-page': '405', 'volume': '136', 'year': '1964', 'journal-title': 'Phys. Rev. A'} / Phys. Rev. A (1964)
10.1063/1.1727978 / J. Chem. Phys. (1966)
{'key': '2024020909583808900_r29'}
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{'key': '2024020909583808900_r31'}
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Dates

Type	When
Created	21 years, 6 months ago (Feb. 4, 2004, 5:30 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 5:59 a.m.)
Indexed	1 year, 6 months ago (Feb. 9, 2024, 10:18 a.m.)
Issued	52 years, 7 months ago (Jan. 15, 1973)
Published	52 years, 7 months ago (Jan. 15, 1973)
Published Print	52 years, 7 months ago (Jan. 15, 1973)

Funders 0

None

BibTeX

@article{Kivelson_1973, title={Molecular theory of the translational Stokes-Einstein relation}, volume={58}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1679222}, DOI={10.1063/1.1679222}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Kivelson, Daniel and Jensen, S.J. Knak and Ahn, Myong-Ku}, year={1973}, month=jan, pages={428–433} }

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