Validity of Tolman’s equation: How large should a droplet be?

Authors

Kenichiro Koga, University of Nebraska-LincolnFollow
Xiao Cheng Zeng, University of Nebraska-LincolnFollow
A.K. Shchekin, St. Petersburg State University

Date of this Version

9-8-1998

Comments

Published by American Institute of Physics. J. Chem. Physics VOLUME 109, NUMBER 10, 8 SEPTEMBER 1998. ©1998 American Institute of Physics. Permission to use. http://jcp.aip.org/.

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 4x10⁶ 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_x 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 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.