Role of surface forces in heterogeneous nucleation on wettable nuclei

Heterogeneous nucleation on mesoscopic wettable particles: A hybrid thermodynamic/density-functional theory

“…2 In this section we formulate generalized version of these equations for the description of heterogeneous nucleation on mesoscopic wettable particles.…”

“…At the fixed temperature, the vapor density 1 is determined solely by , and so is the density of the bulk liquid 2 . For the open system, the grand thermodynamic potential is given by…”

“…⌬ hs (¯) is the excess free-energy density, and it can be calculated accurately via the Carnahan-Starling 22 formula ⌬ hs ( )ϭk B T (4 Ϫ3 )/(1Ϫ ) 2 , where k B is the Boltzmann constant, T is the temperature, and ϭ d 3 /6 ͑d is the hard-sphere diameter and is the density͒. In Eq.…”

“…The former is for relatively thick liquid films, while the latter is for the thin structural films. 2 In the case of nonpolar LJ fluid, the power-law approximation to ⌸(h) is given by…”

“…10,11 We will present a hybrid approach by combining the DFT with a classical nucleation theory. 2,4 The latter 2,4 yields general relations among thermodynamical and kinetic properties of the system, while the DFT provides important properties of the liquid droplet, such as the dependence of the chemical potential of the liquid droplet on the droplet size. Outcomes of the hybrid theory include the threshold value of the chemical potential ͑or the threshold value of the supersaturation͒ for barrierless nucleation, the height of the activation barrier to nucleation, the half-width of the barrier, as well as the position of the minimum and maximum on the curve of free energy of droplet formation versus the droplet size.…”