On the mechanical stability conditions for nanoparticles in vacuum and under an external pressure

A condition of the mechanical stability of non-volatile nanoparticles in a chemically inert medium is derived from the non-negativity of the second variation of the Helmholtz free energy of the 'small object - gaseous medium' system. Two cases have been analyzed: (i) a non-volatile nanoparticle with the surface tension depending on its radius; (ii) a limiting case of bigger objects when the surface tension corresponds to its constant macroscopic value. It has been shown that the external pressure should increase stability of nanoparticles. However, the effect under consideration should be noticeable at high pressures only. (paper)