Reexamination of Tolman's law and the Gibbs adsorption equation for curved interfaces

TL;DR

This paper clarifies the relationship between different definitions of surface tension for curved interfaces, reaffirming the validity of Tolman's law and the Gibbs adsorption equation through free-energy minimization.

Contribution

It corrects a previous claim by demonstrating that the two surface tension definitions are equivalent for the Laplace radius, reinforcing foundational thermodynamic principles.

Findings

Confirmed the equivalence of surface tension definitions $\gamma$ and $ar\gamma$ for curved interfaces.

Reaffirmed the validity of Tolman's law and Gibbs adsorption equation.

Clarified misconceptions in prior derivations of surface tension for curved surfaces.

Abstract

In manuscript arXiv:1703.08719 [cond-mat.soft], it was claimed that the well-known deduction of Tolman's law is not rigorous, since Tolman's argument implies that two different definitions of the surface tension, called $\gamma$ and $\bar\gamma$ in the manuscript, coincide. This claim is retracted as it can be shown by free-energy minimization that $\gamma = \bar\gamma$ indeed holds for the Laplace radius. Joachim Gro\ss, Philipp Rehner, Carlos Vega, \O{}ivind Wilhelmsen, and the anonymous reviewers of The Journal of Chemical Physics contributed to finding the mistake in the manuscript.