Modified classical homogeneous nucleation theory and a new minimum in free energy change 2. Behavior of free energy change with a minimum calculated for various systems

In the previous study, modified classical homogeneous nucleation theory considering the free energy change in parent phase was developed, which revealed the presence of a minimum in nucleation curve (the curve of total free energy change versus nuclear radius) of binary solution. In the present study, using the modified theory, numerical calculations were performed for other various systems; liquid and solid solution systems with compound nuclei and mixed gas systems with liquid nuclei. The calculated results also proved the presence of a minimum in each nucleation curve of these various systems. The minimum in nucleation curves has been passed unnoticed by many researchers in various fields. Therefore, Kevin equation is misunderstood as it describes the maximum state. However, it should be the minimum state that Kelvin equation describes. The large difference between the critical radius size of water droplet calculated at the maximum point (17 Å at 200% humidity) and the observed micron order size of water droplet in cloud and fog can be explained through considering that the micron order droplet should be in the minimum state. The contradiction comes from the misunderstanding that a nucleation curve has only a maximum. Therefore, it is essential to review the various nucleation phenomena on the standpoint of the presence of a minimum. The influence of the change of initial content, initial pressure, interfacial tension, and number of nuclei in 1 mol system to the behavior of nucleation curve was discussed

Modified classical homogeneous nucleation theory and a new minimum in free energy change 1. A new minimum and Kelvin equation

The main concern of classical homogeneous nucleation theory has been a thermodynamic description of initial stage of nucleation from embryo to nucleus with a little larger size over the critical one, thus, the change of parent phase in the system has been assumed to be negligible because of the largeness in volume and mass comparing that of nuclei. As a result, the nucleation curve (free energy change versus nucleus size) passes through well-known single maximum point corresponding to the critical size of the nucleus. In the present study, thermodynamics of the classical homogeneous nucleation was re-visited and developed a modified equation for multi-component solution and gas system with multi-component nuclei by taking into account the change of the free energy of parent phase. Using this equation, the calculation of nucleation curve beyond the size of critical nucleus became possible. A calculation of A–B binary solution system revealed a new minimum point in the nucleation curve, in addition to the maximum point. This minimum point indicates the theoretical possibility to stabilize a large amount of nano-nuclei in equilibrium with the supersaturated parent phase. In addition, Kelvin equation was proved at the extremum on the nucleation curve. Many scientists have misunderstood that Kelvin equation corresponds to the maximum state because they have unnoticed the presence of the minimum and its stability. At the minimum state, the nuclei should be more stable than those at the maximum state. Thus, Kelvin equation should correspond to the minimum state rather than the maximum state