radius the pressure difference across the interface increases the chemical potential of the nanoparticle form compared to that of the same material in bulk form i e at a flat interface as described by eqn 2 s np u2245 s bulk u2062 exp u2061 2 u2062 u03b3 np l u2062 v m np rtr eqn u2062 2 where s np and s bulk are the solubilities of the nanoparticle and bulk form respectively of the relevant material v m np is the molar volume of the nanoparticle material r is the universal gas constant and t is temperature the regions between neighboring nanoparticles in a coating i e pores can behave as capillaries a liquid condensed in such a pore as illustrated in fig5 a has a curved liquid vapor interface across which there is a pressure difference this pressure difference is described by eqn 3 u03b4 u2062 u2062 p u03b3 condensate u2061 1 x 1 r c eqn u2062 3 where u03b3 condensate is the surface tension of the condensate vapor interface r c is the capillary radius and x is the internal diameter of the hourglass shaped capillary condensate between nanoparticles see fig5 a the same pressure effect which increases the solubility of nanoparticles in solid liquid equilibrium decreases the vapor pressure and therefore volatility of capillary condensates in a liquid vapor equilibrium eqn 4 rt u2062 u2062 ln u2061 p.