Theory of cluster size distribution

Though Kelvin equation and Becker-Doring theory have long found acceptance in the area of nucleation theory, there is a need to investigate. This basically can be divided into two parts: one is classical mechanical part to find the main shape of cluster size distribution and the other is quantum mechanical part to determine those local barriers caused by "magic" numbers.;In the classical mechanical part, some thermodynamic properties, such as the size-dependent latent heat, the size-and-shape-dependent surface tension, the mixing entropy, and the work done by carrier gases, are modified in advance. A modified Kelvin equation is derived and used in the further derivation of cluster size distribution. In the quantum mechanical part, the Clemenger-Nilsson model is utilized to simulate those peaks with "magic" numbers shown in the molecular beam mass spectra, and the result from the Clemenger-Nilsson model is modified with the aid of the uncertainty relation of energy and time so as to show peaks with "magic" numbers as well as the correlation between peaks with "magic" numbers.