Size dependence of linear tension at a curved two-dimensional phase boundary

In the framework of thermodynamics of surface and interphase boundaries, an equation is obtained for the dependence of linear tension on the radius of the tension line at the boundary of two-dimensional phases located on a flat surface and separated by a curved line. According to the obtained relationship, calculations have been carried out and the required dependence has been constructed in dimensionless coordinates ($\tau \text{/}{\tau }_{\infty }$, $r\text{/}{\delta }_{\tau }$), which is of a universal nature and does not depend on the specific nature of two-dimensional phases. The obtained curve is also of a universal nature according to the type of two-dimensional interface (liquid–vapor, solid–vapor, solid–liquid, solid–solid). In this work, a comparison is made with the solution of a similar problem of finding the dimensional dependence of surface tension on the nanoparticle size σ(r) for the cases of positive and negative curvature considered by the authors earlier.