Dependence of the condensate chemical potential on droplet size in thermodynamics of heterogeneous nucleation within the gradient DFT

• Joint consideration of polar and nonpolar fluids.
• Density profiles for stable and critical droplets.
• Computation of the condensate chemical potential for water and argon.
• Analysis of capillary, electrostatic and molecular contributions.

A scheme of computation of the condensate chemical potential per molecule as a function of the droplet equimolecular radius for stable and critical droplets on uncharged or charged spherical particle of molecular size at heterogeneous nucleation has been considered. The scheme is based of the gradient density functional theory (DFT) with the van der Waals (vdW) and Carnahan–Starling (СS) models for the hard-sphere contribution to intermolecular interaction in liquid and vapor phases and interfaces. The particle serving as a condensation center in the case of heterogeneous nucleation has been characterized by an attractive short-range molecular potential and the long-range electric Coulomb potential. The dielectric permittivities of the droplet–vapor systems have been taken as known functions of the local condensate density and temperature for polar and nonpolar fluids. Detailed numerical calculations of the density profiles in critical and stable equilibrium droplets at water or argon nucleation in presence of the capillary, electrostatic and molecular forces have been performed. Dependence of the condensate chemical potential in the droplet on the droplet equimolecular radius has been analyzed in the case of homogeneous and heterogeneous nucleation and compared for water and argon within the vdW and СS models for the hard-sphere part of the equation of state.