Size Dependence of the Surface Tension of Nanoparticles

Abstract

The linear relationship between surface tension γ_s 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.