Influence of the dividing surface notion on the formulation of Tolman's law

TL;DR

This paper generalizes Tolman's law to incorporate various notions of the dividing surface, accounting for size-dependent interfacial properties in small droplets and bubbles, thus refining the understanding of surface tension curvature effects.

Contribution

It introduces a generalized formulation of Tolman's law based on a generalized Gibbs adsorption equation for different dividing surface definitions.

Findings

Generalized Tolman's law applicable to any dividing surface notion.

Derived size-dependent corrections to surface tension for small droplets and bubbles.

Provides a theoretical framework for more accurate modeling of nanoscale interfacial phenomena.

Abstract

The influence of the surface curvature on the surface tension of small droplets at equilibrium with a surrounding vapour, or small bubbles at equilibrium with a surrounding liquid, can be expanded as {\gamma}(R) = {\gamma}(planar) - .../R + O(1/R^2). According to Tolman's law, the first-order coefficient in this expansion is obtained from the planar limit of the Tolman length, i.e., the deviation between the equimolar radius and the Laplace radius. Here, Tolman's law is generalized such that it can be applied to any notion of the dividing surface, beside the Laplace radius, on the basis of a generalization of the Gibbs adsorption equation which consistently takes the size dependence of interfacial properties into account.