The magnitude and location of the surface tension of curved interfaces

A thermodynamic definition is given for the spatial distribution of the force in a curved interface that manifests itself macroscopically as the ‘‘surface tension.’’ A general thermodynamic characterization of a curved interface requires a complete knowledge of this force distribution. While a thermodynamic description in terms of a ‘‘surface tension’’ acting on a ‘‘surface of tension’’ is always incomplete, we identify circumstances under which this description is useful and we show how, in these circumstances, the ‘‘surface tension’’ and the location of the ‘‘surface of tension’’ can be derived from the force distribution. Using external field methods, we derive molecular level expressions for the force distribution in planar, cylindrical, and spherical liquid–vapor interfaces in terms of the intermolecular pair potential and the one- and two-particle distribution functions.