Nucleation theory beyond the deterministic limit. I. The nucleation stage

This work addresses theory of nucleation and condensation based on the continuous Fokker-Plank type kinetic equation for the distribution of supercritical embryos over sizes beyond the deterministic limit, i.e., keeping the second derivative with respect to size. The first part of the work treats the nucleation stage. It is shown that the size spectrum should be generally obtained by the convolution of the initial distribution with the Gaussian-like Green function with spreading dispersion. It is then demonstrated that the fluctuation-induced effects can be safely neglected at the nucleation stage, where the spectrum broadening due to the nonlinear boundary condition is much larger than the fluctuational one. The crossover between the known triangular and double exponential distributions under different conditions of material influx into the system is demonstrated. Some examples of size distributions at the nucleation stage in different regimes of material influx are also presented.