### Abstract

Surface tension and the length δ (distance between the Gibbs surface of tension R_{s} and the equimolar surface R_{e}) of simple liquid droplet (Lennard-Jones and Yukawa) are computed over a wide range of droplet sizes up to about 4×10^{6} molecules. The study is based on the Gibbs theory of capillarity combined with the density-functional approach to gas-liquid nucleation. Since this method provides behavior of the surface tension fully consistent with the tension of the planner surface, the constant in Tolman's equation δ_{∞} can be determined unequivocally from the asymptotic behavior of σ_{s}. Comparison of the tension given by Tolman's equation against the result of exact thermodynamic relations reveals that Tolman's equation is valid only when the droplet holds more than 10^{6} molecules for the simple fluid systems near their triple points, in contrast to the conventional wisdom that Tolman's equation may be applicable down to droplets holding a few hundreds of molecules.

Original language | English (US) |
---|---|

Pages (from-to) | 4063-4070 |

Number of pages | 8 |

Journal | Journal of Chemical Physics |

Volume | 109 |

Issue number | 10 |

DOIs | |

State | Published - Dec 1 1998 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*109*(10), 4063-4070. https://doi.org/10.1063/1.477006

**Validity of Tolman's equation : How large should a droplet be?** / Koga, Kenichiro; Zeng, X. C.; Shchekin, A. K.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 109, no. 10, pp. 4063-4070. https://doi.org/10.1063/1.477006

}

TY - JOUR

T1 - Validity of Tolman's equation

T2 - How large should a droplet be?

AU - Koga, Kenichiro

AU - Zeng, X. C.

AU - Shchekin, A. K.

PY - 1998/12/1

Y1 - 1998/12/1

N2 - Surface tension and the length δ (distance between the Gibbs surface of tension Rs and the equimolar surface Re) of simple liquid droplet (Lennard-Jones and Yukawa) are computed over a wide range of droplet sizes up to about 4×106 molecules. The study is based on the Gibbs theory of capillarity combined with the density-functional approach to gas-liquid nucleation. Since this method provides behavior of the surface tension fully consistent with the tension of the planner surface, the constant in Tolman's equation δ∞ can be determined unequivocally from the asymptotic behavior of σs. Comparison of the tension given by Tolman's equation against the result of exact thermodynamic relations reveals that Tolman's equation is valid only when the droplet holds more than 106 molecules for the simple fluid systems near their triple points, in contrast to the conventional wisdom that Tolman's equation may be applicable down to droplets holding a few hundreds of molecules.

AB - Surface tension and the length δ (distance between the Gibbs surface of tension Rs and the equimolar surface Re) of simple liquid droplet (Lennard-Jones and Yukawa) are computed over a wide range of droplet sizes up to about 4×106 molecules. The study is based on the Gibbs theory of capillarity combined with the density-functional approach to gas-liquid nucleation. Since this method provides behavior of the surface tension fully consistent with the tension of the planner surface, the constant in Tolman's equation δ∞ can be determined unequivocally from the asymptotic behavior of σs. Comparison of the tension given by Tolman's equation against the result of exact thermodynamic relations reveals that Tolman's equation is valid only when the droplet holds more than 106 molecules for the simple fluid systems near their triple points, in contrast to the conventional wisdom that Tolman's equation may be applicable down to droplets holding a few hundreds of molecules.

UR - http://www.scopus.com/inward/record.url?scp=0001646504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001646504&partnerID=8YFLogxK

U2 - 10.1063/1.477006

DO - 10.1063/1.477006

M3 - Article

AN - SCOPUS:0001646504

VL - 109

SP - 4063

EP - 4070

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

ER -