Thermodynamic properties of stable and unstable vapor shells around lyophobic nanoparticles

Existence of stable and unstable spherical shell-like vapor interlayers (or concentric nanobubbles) near lyophobic surfaces has been proved and their thermodynamic properties have been studied within the square gradient density functional theory. The equilibrium density profiles around lyophobic nanoscopic particles (without and with electric charge) in a stretched argon-like liquid have been computed. The combination of the Carnahan–Starling and the mean-field models for fluid–fluid interaction and the total Lennard-Jones potential of interaction between the particle and fluid molecule have been used. The lyophobicity of the particle has been controlled by the energy parameter for attraction of molecules of the particle and the fluid molecules. This parameter has been taken considerably smaller than the energy parameter for fluid–fluid molecular attraction. As a result, two equilibrium radial density profiles corresponding to two concentric vapor shells around particle were found at a fixed value of the condensate chemical potential below its value for the flat equilibrium. It was shown that the smaller shell is related to the minimum of the work of the vapor shell formation and represents a stable nanobubble, while the larger shell corresponds to the maximum of this work and refers to the unstable critical nanobubble. The equimolecular radii of the stable and unstable concentric nanobubbles increase with the radius of the core particle. The curve of the dependence of the chemical potential of fluid molecules in the bubble with the lyophobic core particle on the bubble radius has a minimum, below which heterogeneous nucleation of bubbles becomes thermodynamically barrierless. The appearance of the electric charge on the particle shifts the minimum of the condensate chemical potential deeper and inhibits bubble nucleation. The dependence of the bubble surface tension on the radius of the equimolecular dividing surface and the charge of the particle has been found for bubble at heterogeneous nucleation and compared with that for bubble and droplet at homogeneous nucleation and droplet at heterogeneous nucleation on lyophilic particle.