Considerations of the Isothermal−Isobaric Homogeneous Nucleation of a Vapor in the Presence of an Inert Carrier Gas

The nucleation process of a vapor in the presence of a carrier gas is investigated under isothermal−isobaric conditions. The constancy of the pressure in the system can in principle be maintained by a change of the volume of the system or the addition of the condensed amount of substance, respectively. The first possibility is used in several experiments and it is discussed in this contribution. The pressure of the carrier gas increases and the pressure of the condensing species decreases during the formation of nuclei, or droplets. The droplet formation causes a depletion of the mother phase. The initial amount of condensable species is distributed on droplets of identical size and having a determined concentration and a remaining vapor part in the frame of the model. A large number of such possibilities exist if the initial amount of condensable species is large. These states of the system are compared to the initial state of the system, the supersaturated vapor, by calculating the difference in the Gibbs free energy of nucleation. A free energy surface is obtained in the droplet size- droplet concentration space. This surface shows maxima and minima that may be determined by Kelvin-like equations. The true bottom of the valley of the surface must be calculated by the determination of gradient curves. This bottom line connects the relatively stable states of the system. The Kelvin-like curves and the bottom line of the surface exhibit a nucleation phase and Ostwald ripening. The true stable state of the system will be obtained by all these curves. It is the equilibrium between the bulk liquid and the saturation vapor pressure. The considerations are applied in a simple kinetic model for droplet growth. By this way it is possible to determine the rate constant for the droplet growth without further assumptions. Good agreement is observed to experimental results.