Curvature dependence of the surface tension of liquid and vapor nuclei

The surface tension and the Tolman length have been presented as series in terms of the interface curvature $c.\mathrm{}$ The expansion has been limited by a linear term on $c$ for the Tolman length and a square one for the surface tension. In the framework of the van der Waals capillarity theory the expansion coefficients have been expressed in terms of the planar interface characteristics. The coefficients asymptotic behavior has been derived in the vicinity of the liquid-vapor critical point. For the van der Waals fluid, the results of expansions have been compared with the data of direct numerical calculations. A wide curvature interval of the suitability of derived formulas has been stated. This fact allows the use of them in the homogeneous nucleation theory to calculate the critical nucleus formation work.