Blurring of island size distribution function in theory of nucleation

Numerical solutions of the kinetic equation of the theory of nucleation at a constant pumping of monomers are obtained in the case of two-dimensional islands growing in a ballistic or diffusion regime on a solid surface. The island size distributions obtained in various approximations are compared. It is shown that, even in the absence of Ostwald’s ripening, an increase in the critical size leads to a radical increase in the variance, which is not taken into account in the overwhelming majority of analytical models. The blurring of the distribution as a result of an increase in the critical nucleus size almost does not influence the temporal asymptotics of the mean nucleus size. The effect of blurring is much more pronounced in the ballistic growth regime. The obtained results suggest that it is necessary to improve analytical models for determining the shape of the distribution in the growth stage for various condensing systems.