Size Dependence of the Surface Tension of Nanoparticles
The linear relationship between surface tension γs and radius $$~{{R}_{{\text{s}}}}$$ of small particles (nanoparticles) was derived in the 1960s by Rusanov as $${{{\gamma }}_{{\text{s}}}} = K{{R}_{{\text{s}}}},$$ where K is the coefficient of proportionality. In this work, a more generalized dependence is obtained in the context of Gibbs’ theory of thermodynamics for curved interfaces on the same size scales for a randomly selected interface, including an equimolecular surface with radius $${{R}_{{\text{e}}}}{\text{.}}$$ It is shown that when $${{R}_{0}} \geqslant R \geqslant {\delta }$$ (where $${\delta } = {{R}_{{\text{e}}}} - {{R}_{{\text{s}}}},$$$${{R}_{0}}$$ is a characteristic radius limiting the range of the Rusanov equation’s applicability), linear dependence $${\gamma } = KR$$ should be valid for all $$R \in \left[ {{{R}_{{\text{s}}}},{{R}_{{\text{e}}}}} \right].$$ Parameter $$K~$$ is estimated for metal nanodroplets and solid metal nanoparticles as well.