There are many problems accumulated in theory and practice of surface phenomena, solutions of which is bound to the knowledge of features of temperature dependence of the surface tension. Even in macroscopic systems the possibility of inversion of the temperature coefficient of surface tension (TCST) in liquid metals is theoretically allowed [1]. Very few information is available on the TCST along the melting curve of massive bodies, on the boundary solid-liquid as well as on boundaries solid-gas and liquid-gas. All the more complex situation takes place in nanosystems, where the data on temperature dependence of surface tension are needed to describe the influence of size on adhesion, wetting and spreading in such systems.
The attempt to obtain the analytical expression for the TCST has been performed in this research within the thermodynamics of surface phenomena [2] starting with the conditions of equilibrium in two- and three-phase systems in which one phase has the spherical form of nanosized radius. The known reference relations for various phase boundaries follow, as particular cases, when switching to macrodimensions. Our equation involves the Tolman parameter, the radius of surface of tension, the molar entropy and the molar volume. The special attention is paid to the cases when the radius and the pressure are constants. The possibilities for the inversion of TCST and for the non-linearity of temperature dependence of surface tension are under discussion.
The results of numerical calculations for the number of low melting liquid metals are given.
References
[1] CroxtonС. Liquid state physics – a statistical mechanical introduction, Cambridge, 1974, 400 p.
[2] Rusanov A.I. Phase equilibria and surface phenomena, Khimia, 1967, 388 p. [in Russian]